Phillips Curve Specification And the Decline in U. S. Output and ...
Phillips Curve Specification And the Decline in U. S. Output and ...
Phillips Curve Specification And the Decline in U. S. Output and ...
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<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong><br />
<strong>And</strong> <strong>the</strong> <strong>Decl<strong>in</strong>e</strong> <strong>in</strong> U. S. <strong>Output</strong> <strong>and</strong> Inflation Volatility *<br />
Robert J. Gordon<br />
Northwestern University <strong>and</strong> NBER<br />
First Draft to be Presented at Symposium on<br />
The <strong>Phillips</strong> <strong>Curve</strong> <strong>and</strong> <strong>the</strong> Natural Rate of Unemployment,<br />
Institut für Welwirtschaft<br />
Kiel, Germany<br />
June 3‐4, 2007<br />
____________________<br />
*I am grateful to Rob McMenam<strong>in</strong> for excellent research assistance on this paper <strong>and</strong> to<br />
Ian Dew‐Becker for his <strong>in</strong>sights <strong>and</strong> assistance on previous related papers.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong><br />
<strong>And</strong> <strong>the</strong> <strong>Decl<strong>in</strong>e</strong> <strong>in</strong> U. S. <strong>Output</strong> <strong>and</strong> Inflation Volatility<br />
ABSTRACT<br />
Journalists have recently characterized <strong>the</strong> Fed’s view that <strong>the</strong> slope of <strong>the</strong> United States<br />
<strong>Phillips</strong> <strong>Curve</strong> (PC) has become substantially flatter, by a factor of at least half, s<strong>in</strong>ce <strong>the</strong> mid‐<br />
1980s. The flatten<strong>in</strong>g of <strong>the</strong> <strong>Phillips</strong> curve is documented <strong>in</strong> a particular style of PC research<br />
based on <strong>the</strong> New Keynesian <strong>Phillips</strong> <strong>Curve</strong> (NKPC) literature, <strong>in</strong> which PC specifications<br />
<strong>in</strong>volve l<strong>in</strong>ks between <strong>the</strong> current <strong>in</strong>flation rate <strong>and</strong> short lags on <strong>in</strong>flation, <strong>and</strong> on <strong>the</strong> current<br />
unemployment rate. The first part of this paper uses a wide variety of statistical tests to show<br />
that <strong>the</strong> Fed’s PC equation, as based on research by Roberts (2006), is strongly rejected both by<br />
traditional <strong>and</strong> nontraditional tests when compared to <strong>the</strong> Gordon “triangle” model that was<br />
developed <strong>in</strong> <strong>the</strong> early 1980s. The Roberts version of <strong>the</strong> NKPC is entirely nested <strong>in</strong> <strong>the</strong> triangle<br />
model, allow<strong>in</strong>g each of its exclusion restrictions to be tested, <strong>and</strong> each is rejected at high levels<br />
of statistical significance.<br />
The rema<strong>in</strong>der of <strong>the</strong> paper asks why <strong>the</strong> volatility of <strong>in</strong>flation, of output changes <strong>and</strong> of<br />
<strong>the</strong> output gap has decl<strong>in</strong>ed substantially after 1984, a f<strong>in</strong>d<strong>in</strong>g on which U. S. macroeconomists<br />
share an unusual consensus. Our analysis based on a small macroeconometric model concludes<br />
that about 1/3 of <strong>the</strong> reduction <strong>in</strong> <strong>the</strong> volatility of real GDP can be traced to <strong>the</strong> role of supply<br />
shocks <strong>in</strong> <strong>the</strong> triangle <strong>in</strong>flation equation. More important are errors <strong>in</strong> <strong>the</strong> output gap or “IS”<br />
equation that quantifies <strong>the</strong> role of monetary policy <strong>in</strong> reduc<strong>in</strong>g output when <strong>in</strong>terest rates are<br />
high <strong>and</strong> stimulat<strong>in</strong>g output when <strong>in</strong>terest rates are low.<br />
To highlight <strong>the</strong> role of <strong>Phillips</strong> curve specifications <strong>in</strong> <strong>the</strong> analysis of reduced U.S.<br />
bus<strong>in</strong>ess cycle volatility, we show that <strong>the</strong> Roberts/NKPC type <strong>Phillips</strong> curve specification<br />
misses much of <strong>the</strong> role of supply shocks <strong>in</strong> contribut<strong>in</strong>g to reduced volatility <strong>in</strong> both <strong>in</strong>flation<br />
<strong>and</strong> output. F<strong>in</strong>ally, we f<strong>in</strong>d no role at all for monetary policy <strong>in</strong> reduc<strong>in</strong>g <strong>the</strong> volatility of<br />
<strong>in</strong>flation or output, unless monetary policy is more broadly def<strong>in</strong>ed to <strong>in</strong>clude <strong>the</strong> component of<br />
“IS stabilization” represented by <strong>the</strong> f<strong>in</strong>ancial deregulation of <strong>the</strong> late 1970s that reduced <strong>the</strong><br />
volatility of residential construction.<br />
Robert J. Gordon<br />
Department of Economics<br />
Northwestern University<br />
Evanston IL 60208‐2600<br />
rjg@northwestern.edu<br />
http://faculty‐web.at.northwestern.edu/economics/gordon
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 1<br />
I. Introduction<br />
Has <strong>the</strong> slope of <strong>the</strong> American <strong>Phillips</strong> <strong>Curve</strong> (PC) become flatter <strong>in</strong> <strong>the</strong> past two<br />
decades? Recently <strong>the</strong> Wall Street Journal announced on its front page <strong>the</strong> f<strong>in</strong>d<strong>in</strong>g of recent<br />
research at <strong>the</strong> Federal Reserve Board demonstrat<strong>in</strong>g a sharp flatten<strong>in</strong>g of <strong>the</strong> PC s<strong>in</strong>ce <strong>the</strong> mid‐<br />
1980s. The primary Fed study by Roberts (2006) attributes to monetary policy both <strong>the</strong> change<br />
<strong>in</strong> slope <strong>and</strong> <strong>the</strong> related marked reduction <strong>in</strong> U. S. bus<strong>in</strong>ess cycle volatility. The channel of<br />
monetary policy <strong>in</strong>fluence comes from an <strong>in</strong>creased Fed responsiveness to output <strong>and</strong> <strong>in</strong>flation,<br />
so that any pressure for higher <strong>in</strong>flation or any movement of <strong>the</strong> output gap away from zero are<br />
“nipped <strong>in</strong> <strong>the</strong> bud”. A flatter PC directly contributes to <strong>the</strong> <strong>in</strong>terplay between monetary policy<br />
<strong>and</strong> output stabilization, as movements of <strong>the</strong> output gap above zero generate less <strong>in</strong>flation<br />
than formerly, requir<strong>in</strong>g less monetary tighten<strong>in</strong>g <strong>and</strong> thus a smaller subsequent downward<br />
adjustment <strong>in</strong> output. 1<br />
However, both of <strong>the</strong>se two conclusions are highly controversial. The verdict that <strong>the</strong><br />
PC slope has flattened is highly sensitive to specification choices, <strong>and</strong> a primary purpose of this<br />
paper is to exam<strong>in</strong>e <strong>the</strong> <strong>in</strong>terplay between model specification <strong>and</strong> conclusions about <strong>the</strong><br />
stability of PC parameters. Fur<strong>the</strong>r, while all research agrees that output has become less<br />
volatile s<strong>in</strong>ce <strong>the</strong> mid‐1980s, much of it contradicts Robert’s conclusion that <strong>the</strong> improved<br />
conduct of monetary policy is responsible. Stock <strong>and</strong> Watson (2002, 2003) were among <strong>the</strong> first<br />
to quantify <strong>the</strong> role of smaller shocks <strong>in</strong> contribut<strong>in</strong>g to improved stability, <strong>and</strong> Gordon (2005)<br />
1. Also represent<strong>in</strong>g <strong>the</strong> Fed view are Kohn (2005) <strong>and</strong> Williams (2006).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 2<br />
concluded that roughly two‐thirds of <strong>the</strong> improvement <strong>in</strong> stability resulted from smaller<br />
dem<strong>and</strong> shocks, one‐third from smaller supply shocks, with no rema<strong>in</strong><strong>in</strong>g role for monetary<br />
policy at all. 2<br />
The specification of <strong>the</strong> <strong>Phillips</strong> curve is <strong>in</strong>tegral to <strong>the</strong> analysis of decl<strong>in</strong><strong>in</strong>g bus<strong>in</strong>ess<br />
cycle volatility because Roberts, Stock‐Watson, <strong>and</strong> Gordon all based <strong>the</strong>ir conclusions on small<br />
three‐equation models of <strong>the</strong> economy <strong>in</strong> which <strong>the</strong> <strong>Phillips</strong> <strong>Curve</strong> is <strong>the</strong> first equation, jo<strong>in</strong>ed<br />
toge<strong>the</strong>r with an <strong>in</strong>terest‐rate equation based on <strong>the</strong> Taylor rule <strong>and</strong> an “IS” equation relat<strong>in</strong>g<br />
<strong>the</strong> output gap to <strong>in</strong>terest rates. In addition to study<strong>in</strong>g <strong>the</strong> sensitivity of <strong>the</strong> PC slope<br />
coefficient to alternative specifications, this paper also exam<strong>in</strong>es <strong>the</strong> sensitivity of conclusions<br />
regard<strong>in</strong>g output volatility <strong>in</strong> a three‐equation model to choices <strong>in</strong> <strong>the</strong> specification of <strong>the</strong><br />
<strong>Phillips</strong> curve.<br />
Blanchard‐Simon (2001) <strong>and</strong> o<strong>the</strong>rs have noticed <strong>the</strong> parallel decl<strong>in</strong>e of <strong>in</strong>flation <strong>and</strong><br />
output volatility. We can quantify <strong>the</strong> role of decl<strong>in</strong><strong>in</strong>g <strong>in</strong>flation volatility <strong>in</strong> contribut<strong>in</strong>g to<br />
decl<strong>in</strong><strong>in</strong>g output volatility, <strong>and</strong> we can <strong>in</strong>quire as to <strong>the</strong> sources of <strong>the</strong> improved stability of <strong>the</strong><br />
<strong>in</strong>flation rate. The Roberts approach po<strong>in</strong>ts to a flatter slope <strong>in</strong> dim<strong>in</strong>ish<strong>in</strong>g <strong>the</strong> transmission of<br />
movements <strong>in</strong> <strong>the</strong> output gap <strong>in</strong>to changes of <strong>the</strong> <strong>in</strong>flation rate. A second hypo<strong>the</strong>sis is that,<br />
even without a change <strong>in</strong> <strong>the</strong> PC slope, decl<strong>in</strong><strong>in</strong>g output volatility would have directly<br />
contributed to improved <strong>in</strong>flation stability. A third hypo<strong>the</strong>sis is that <strong>in</strong>flation depends not<br />
only on dem<strong>and</strong> shocks but on explicit supply shocks that can be identified <strong>and</strong> quantified, <strong>and</strong><br />
2. Blanchard‐Simon (2001) po<strong>in</strong>ted to several of <strong>the</strong> same factors as Stock‐Watson <strong>and</strong> Gordon, but <strong>the</strong>y
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 3<br />
that a reduction <strong>in</strong> <strong>the</strong> size <strong>and</strong> importance of <strong>the</strong> supply shocks contributed directly to<br />
improved <strong>in</strong>flation stability <strong>and</strong> <strong>in</strong>directly to improved output stability. While all three of<br />
<strong>the</strong>se hypo<strong>the</strong>ses could <strong>in</strong> pr<strong>in</strong>ciple be complementary, <strong>the</strong> approach of Roberts (2006) <strong>and</strong> of<br />
Stock‐Watson (2002, 2003) does not allow for separate test<strong>in</strong>g because <strong>the</strong>y do not quantify <strong>the</strong><br />
role of explicit supply shock variables.<br />
The primary emphasis <strong>in</strong> this paper is on <strong>the</strong> role of PC specification <strong>in</strong> draw<strong>in</strong>g<br />
conclusions about shift<strong>in</strong>g slope parameters <strong>and</strong> on <strong>the</strong> sources of reduced bus<strong>in</strong>ess cycle<br />
volatility. A sharp contrast is drawn between <strong>the</strong> New Keynesian <strong>Phillips</strong> <strong>Curve</strong> (NKPC) of<br />
which one version is used by Roberts, <strong>and</strong> my own long‐st<strong>and</strong><strong>in</strong>g “triangle” approach dat<strong>in</strong>g<br />
back to Gordon (1977, 1982). 3 The Roberts NKPC <strong>in</strong>cludes only two variables, <strong>the</strong> current<br />
unemployment rate <strong>and</strong> four quarterly lags on <strong>in</strong>flation. In contrast, <strong>the</strong> “triangle” description<br />
of my model refers to its three‐sided representation of <strong>the</strong> U. S. <strong>in</strong>flation process. The base of<br />
<strong>the</strong> triangle is <strong>in</strong>ertia, represented by long lags on <strong>in</strong>flation. The left side of <strong>the</strong> triangle is <strong>the</strong><br />
representation of dem<strong>and</strong> pressure on <strong>in</strong>flation, proxied by short lags on <strong>the</strong> unemployment<br />
gap. The right side of <strong>the</strong> triangle conta<strong>in</strong>s explicit variables represent<strong>in</strong>g supply shocks. These<br />
are <strong>the</strong> oil‐food shocks, changes <strong>in</strong> relative import prices, changes <strong>in</strong> <strong>the</strong> productivity growth<br />
trend, <strong>and</strong> dummy variables for <strong>the</strong> 1971‐75 Nixon‐era price controls. Fortunately <strong>the</strong> Robertsstyle<br />
NKPC is entirely nested <strong>in</strong> my more comprehensive approach, <strong>and</strong> <strong>the</strong> differences<br />
did not build an econometric model to quantify <strong>the</strong> shocks or <strong>the</strong> role of <strong>the</strong>ir decl<strong>in</strong>e <strong>in</strong> magnitude.<br />
3. The most recent published versions of <strong>the</strong> triangle model are <strong>in</strong> Gordon (1997, 1998) <strong>and</strong> Dew‐Becker<br />
<strong>and</strong> Gordon (2005).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 4<br />
between <strong>the</strong> two specifications amount to exclusion restrictions <strong>in</strong> <strong>the</strong> Roberts version that can<br />
be explicitly tested both <strong>in</strong>dividually <strong>and</strong> jo<strong>in</strong>tly.<br />
Plan of <strong>the</strong> Paper<br />
The paper beg<strong>in</strong>s by compar<strong>in</strong>g two measures of output volatility based alternatively<br />
on <strong>the</strong> roll<strong>in</strong>g st<strong>and</strong>ard deviation of changes <strong>in</strong> output <strong>and</strong> of <strong>the</strong> level of <strong>the</strong> output gap. As<br />
o<strong>the</strong>rs have noticed, <strong>the</strong> change‐based measure decl<strong>in</strong>es after <strong>the</strong> mid‐1980s substantially more<br />
than <strong>the</strong> gap‐based measure, but even <strong>the</strong> gap‐based measure decl<strong>in</strong>es markedly. Then we<br />
compare <strong>the</strong> evolution of volatility for output change <strong>and</strong> <strong>in</strong>flation, emphasiz<strong>in</strong>g both <strong>the</strong> jo<strong>in</strong>t<br />
rise <strong>in</strong> volatility <strong>in</strong> <strong>the</strong> 1970s <strong>and</strong> decl<strong>in</strong>e after <strong>the</strong> mid‐1980s, but also <strong>the</strong> additional fact that<br />
output volatility was high dur<strong>in</strong>g 1955‐65 when <strong>in</strong>flation volatility was very low.<br />
The next section contrasts <strong>the</strong> Roberts version of <strong>the</strong> NKPC with <strong>the</strong> more<br />
comprehensive triangle PC specification <strong>in</strong> which <strong>the</strong> Roberts PC equation is nested. We<br />
develop a “transformation” grid to translate <strong>the</strong> Roberts equation <strong>in</strong>to ours, at each step test<strong>in</strong>g<br />
<strong>the</strong> exclusion restrictions that are implicit <strong>in</strong> <strong>the</strong> Roberts approach <strong>and</strong> <strong>in</strong>deed <strong>in</strong> <strong>the</strong> rest of <strong>the</strong><br />
NKPC literature. We trace <strong>the</strong> transformation between <strong>the</strong> two specifications by alternatively<br />
<strong>in</strong>troduc<strong>in</strong>g <strong>the</strong> three ma<strong>in</strong> differences <strong>in</strong>to <strong>the</strong> Roberts equation – long lags, <strong>the</strong> <strong>in</strong>clusion of<br />
specific supply shock variables, <strong>and</strong> <strong>the</strong> use of a time‐vary<strong>in</strong>g (TV‐NAIRU) <strong>in</strong>stead of constant<br />
NAIRU. 4 At each stage <strong>in</strong> <strong>the</strong> transformation, we can exam<strong>in</strong>e <strong>the</strong> <strong>in</strong>terplay between lag<br />
length, supply shock variables, <strong>and</strong> <strong>the</strong> variability of <strong>the</strong> NAIRU, i.e., is <strong>the</strong> significance of
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 5<br />
supply‐shock variables dependent on allow<strong>in</strong>g for long lags, or vice versa?<br />
We base our evaluation of alternative specifications on <strong>the</strong> statistical significance of<br />
variables <strong>and</strong> lags that are excluded <strong>in</strong> <strong>the</strong> Roberts approach <strong>and</strong> <strong>in</strong>cluded <strong>in</strong> our approach. In<br />
addition, our evaluation technique <strong>in</strong>cludes <strong>the</strong> use of post‐sample dynamic simulations, a<br />
technique of model evaluation that unfortunately is rarely used <strong>in</strong> contemporary time‐series<br />
econometrics. For each specification to be compared, <strong>the</strong> parameters are estimated on data<br />
subtract<strong>in</strong>g <strong>the</strong> last ten years (e.g., 1962‐96 <strong>in</strong>stead of <strong>the</strong> available 1962‐2006), <strong>and</strong> <strong>the</strong>n<br />
predicted values of that specification are generated for <strong>the</strong> f<strong>in</strong>al ten years (1997‐2006) by feed<strong>in</strong>g<br />
back <strong>the</strong> lagged dependent variable endogenously ra<strong>the</strong>r than assum<strong>in</strong>g it to be exogenous.<br />
Test<strong>in</strong>g specifications with dynamic simulations <strong>in</strong> models where <strong>the</strong> lagged dependent<br />
variable plays an important role <strong>in</strong> <strong>the</strong> explanation can reveal sources of “drift” <strong>in</strong> predicted<br />
values away from actual values.<br />
The paper <strong>the</strong>n turns to <strong>the</strong> three‐equation model that, as <strong>in</strong> <strong>the</strong> papers by Roberts <strong>and</strong><br />
Stock‐Watson, is designed to trace <strong>the</strong> <strong>in</strong>terplay among <strong>in</strong>flation, <strong>the</strong> output gap, <strong>and</strong> <strong>the</strong><br />
<strong>in</strong>terest rate responses of <strong>the</strong> Fed. In this paper we exam<strong>in</strong>e <strong>the</strong> role of alternative PC<br />
specifications <strong>in</strong> draw<strong>in</strong>g <strong>in</strong>ferences from <strong>the</strong> multiple‐equation model used by Gordon (2005)<br />
regard<strong>in</strong>g <strong>the</strong> causes of <strong>the</strong> decl<strong>in</strong>e <strong>in</strong> both output <strong>and</strong> <strong>in</strong>flation volatility after <strong>the</strong> mid‐1980s.<br />
For <strong>in</strong>stance, we can suppress <strong>the</strong> contribution of <strong>the</strong> supply shocks <strong>in</strong> <strong>the</strong> triangle <strong>in</strong>flation<br />
equation or suppress <strong>the</strong> error term <strong>in</strong> <strong>the</strong> Roberts NKPC equation. Our goal is to quantify <strong>the</strong><br />
4 . The time‐vary<strong>in</strong>g NAIRU (TV‐NAIRU) was <strong>in</strong>troduced by Gordon (1997) <strong>and</strong> Staiger‐Stock‐Watson
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 6<br />
role of alternative PC specifications <strong>in</strong> <strong>the</strong> analysis of reduced post‐1984 U. S. economic<br />
volatility. We f<strong>in</strong>d that <strong>the</strong> Roberts approach greatly understates <strong>the</strong> role of decl<strong>in</strong><strong>in</strong>g shocks <strong>in</strong><br />
achiev<strong>in</strong>g bus<strong>in</strong>ess cycle volatility <strong>and</strong> thus erroneously concludes that monetary policy, ra<strong>the</strong>r<br />
than <strong>the</strong> decl<strong>in</strong>e of shocks, was <strong>the</strong> primary mover of reduced volatility.<br />
II. Measures of Reduced Bus<strong>in</strong>ess‐Cycle Volatility<br />
Four‐quarter Changes <strong>in</strong> Real GDP<br />
Perhaps <strong>the</strong> clearest way to become conv<strong>in</strong>ced of <strong>the</strong> decl<strong>in</strong>e <strong>in</strong> bus<strong>in</strong>ess cycle volatility<br />
over <strong>the</strong> postwar era is to study <strong>the</strong> plot <strong>in</strong> <strong>the</strong> top frame of Figure 1, show<strong>in</strong>g four‐quarter<br />
changes <strong>in</strong> <strong>the</strong> growth rate of real GDP over <strong>the</strong> 237 quarters between 1948:Q1 <strong>and</strong> 2007:Q1,<br />
spann<strong>in</strong>g <strong>the</strong> entire quarterly data base of <strong>the</strong> U. S. National Income <strong>and</strong> Product Accounts<br />
(NIPA). The top frame also plots a horizontal l<strong>in</strong>e represent<strong>in</strong>g <strong>the</strong> mean growth rate of real<br />
GDP over this period, which is 3.35 percent per annum.<br />
As shown <strong>in</strong> <strong>the</strong> top frame of Figure 1, <strong>the</strong> four‐quarter percentage changes behave very<br />
differently before <strong>and</strong> after 1984. Prior to 1984, <strong>the</strong>re are sharp zigs <strong>and</strong> zags, while after 1984<br />
<strong>the</strong> fluctuations are much more moderate. The pre‐1984 fluctuations are equally severe above<br />
<strong>and</strong> below <strong>the</strong> mean of 3.35 percent per year. In contrast, <strong>the</strong>re is noth<strong>in</strong>g like that experience of<br />
volatility after 1984. The four‐quarter growth rate of real GDP was never negative over <strong>the</strong><br />
entire 22‐year period between 1983:Q1 <strong>and</strong> 2007:Q1 except <strong>in</strong> <strong>the</strong> brief <strong>in</strong>terval associated with<br />
<strong>the</strong> 1990‐91 recession, namely 1991:Q1‐Q3. In fact, some doubt has been cast on <strong>the</strong> NBER’s<br />
(1997, 2001).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 7<br />
declaration of a recession <strong>in</strong> early 2001, because <strong>the</strong> four‐quarter change <strong>in</strong> real GDP never<br />
became negative <strong>in</strong> that episode <strong>and</strong> <strong>in</strong>deed <strong>in</strong> Figure 1A never fell below +0.2 percent <strong>in</strong> any<br />
quarter <strong>in</strong> 2001.<br />
Correspond<strong>in</strong>g to <strong>the</strong> decl<strong>in</strong>e <strong>in</strong> volatility evident <strong>in</strong> <strong>the</strong> top frame of Figure 1 is a<br />
measure of that volatility displayed <strong>in</strong> <strong>the</strong> bottom frame, <strong>the</strong> roll<strong>in</strong>g 20‐quarter st<strong>and</strong>ard<br />
deviation of <strong>the</strong> four‐quarter growth rate of real GDP. There was a sharp <strong>and</strong> apparently<br />
permanent decl<strong>in</strong>e after 1987 from a range of 1.5 to 3.5 percent down to a range of 0.5 to 1.5<br />
percent. Because <strong>the</strong> calculation of <strong>the</strong> roll<strong>in</strong>g st<strong>and</strong>ard deviation as a 20‐quarter mean causes<br />
<strong>the</strong> post‐1983 drop <strong>in</strong> volatility to be reflected five years later, we can dramatize <strong>the</strong> movement<br />
toward stability by splitt<strong>in</strong>g <strong>the</strong> time period of <strong>the</strong> bottom frame of Figure 1 at 1987:Q4. As<br />
displayed <strong>in</strong> Table 1, <strong>the</strong> mean of <strong>the</strong> st<strong>and</strong>ard deviations plotted <strong>in</strong> <strong>the</strong> bottom frame of Figure<br />
1 is 2.77 percent for 1952:Q4‐1987:Q4 <strong>and</strong> a much lower 1.24 percent for 1988:Q1‐2007:Q1.<br />
Expressed as a percentage log change as <strong>in</strong> Table 1, <strong>the</strong> decl<strong>in</strong>e <strong>in</strong> <strong>the</strong> st<strong>and</strong>ard deviation for<br />
output changes is ‐80.3 percent.<br />
The <strong>Output</strong> Gap<br />
In pr<strong>in</strong>ciple part of <strong>the</strong> variance of real GDP changes could reflect changes <strong>in</strong> <strong>the</strong> growth<br />
rate of natural real GDP, <strong>and</strong> we would not consider <strong>the</strong>se changes to reflect bus<strong>in</strong>ess cycle<br />
volatility. Also, some of <strong>the</strong> volatility evident <strong>in</strong> <strong>the</strong> top frame of Figure 1 could be very shortterm<br />
quarterly movements caused by volatile <strong>in</strong>ventory changes that cancel out over two or<br />
three years. To check <strong>the</strong>se possibilities, <strong>the</strong> top frame of Figure 2 displays <strong>the</strong> log output ratio
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 8<br />
or “output gap” as a percent (100 times <strong>the</strong> log ratio of actual to natural real GDP). 5<br />
The<br />
divid<strong>in</strong>g l<strong>in</strong>e of shift<strong>in</strong>g output volatility at <strong>the</strong> year 1984 is not quite as stark <strong>in</strong> Figure 2 as <strong>in</strong><br />
Figure 1, partly because <strong>the</strong> output gap is a level ra<strong>the</strong>r than a rate of change <strong>and</strong> thus cumulates<br />
<strong>and</strong> partially smoo<strong>the</strong>s out <strong>the</strong> volatile pre‐1984 rates of change shown <strong>in</strong> Figure 1. In fact,<br />
Roberts (2006) po<strong>in</strong>ts to <strong>the</strong> role of reduced short‐term volatility of <strong>in</strong>ventory changes <strong>in</strong><br />
expla<strong>in</strong><strong>in</strong>g why <strong>the</strong> output change measure <strong>in</strong> Figure 1 appears to exhibit a greater decl<strong>in</strong>e <strong>in</strong><br />
volatility than <strong>the</strong> output gap measure <strong>in</strong> Figure 2.<br />
However, <strong>the</strong>re is still ample evidence of a decl<strong>in</strong>e <strong>in</strong> <strong>the</strong> volatility of <strong>the</strong> output gap<br />
after 1984. The bottom frame quantifies <strong>the</strong> shift <strong>in</strong> <strong>the</strong> volatility of <strong>the</strong> output gap by plott<strong>in</strong>g<br />
(<strong>in</strong> parallel with Figure 1) its roll<strong>in</strong>g 20‐quarter st<strong>and</strong>ard deviation. There is less dramatic<br />
evidence <strong>in</strong> <strong>the</strong> bottom frame of Figure 2 of a post‐1984 drop <strong>in</strong> output volatility than <strong>in</strong> Figure<br />
1. As shown <strong>in</strong> Table 1, <strong>the</strong> log ratio of <strong>the</strong> roll<strong>in</strong>g st<strong>and</strong>ard deviation when 1988‐2007 is<br />
compared with 1952‐87 drops by 59 percent for <strong>the</strong> output gap as compared to 80 percent for<br />
four‐quarter changes of real GDP.<br />
Inflation <strong>and</strong> <strong>Output</strong> Volatility<br />
An important source of high output volatility before 1984 was high <strong>in</strong>flation volatility,<br />
<strong>and</strong> we show later that <strong>the</strong> reduction of <strong>in</strong>flation volatility after 1984 made a substantial<br />
contribution to <strong>the</strong> post‐1984 decl<strong>in</strong>e <strong>in</strong> output volatility. We will also show that high <strong>in</strong>flation<br />
5. Natural real GDP is estimated by tak<strong>in</strong>g an average of a Hodrick‐Prescott (parameter 6400) <strong>and</strong> a<br />
Kalman filter (parameter sv=15) applied to data on <strong>the</strong> quarterly change <strong>in</strong> real GDP. This method is<br />
developed <strong>and</strong> fur<strong>the</strong>r expla<strong>in</strong>ed <strong>in</strong> Gordon (2003).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 9<br />
volatility prior to 1984 can be l<strong>in</strong>ked to <strong>the</strong> behavior of an explicit set of supply shock variables.<br />
Figure 3 compares <strong>the</strong> 20‐quarter st<strong>and</strong>ard deviation of four quarter changes <strong>in</strong> real GDP <strong>and</strong><br />
<strong>the</strong> GDP deflator, where <strong>the</strong> close relationship between output <strong>and</strong> <strong>in</strong>flation volatility is evident<br />
<strong>in</strong> <strong>the</strong> 1974‐88 period. We also note that output volatility was relatively high <strong>in</strong> 1952‐1962<br />
despite <strong>the</strong> low volatility of <strong>in</strong>flation, <strong>and</strong> that very low <strong>in</strong>flation volatility <strong>in</strong> 1990‐2007 did not<br />
prevent an <strong>in</strong>crease <strong>in</strong> output volatility associated with <strong>the</strong> 1990‐91 or 2001 recessions <strong>and</strong><br />
subsequent recoveries.<br />
Table 1 shows that <strong>the</strong> log percent measure of <strong>in</strong>flation volatility decl<strong>in</strong>ed after 1987 by<br />
100 percent, as compared to 80 percent for output changes <strong>and</strong> 59 percent for <strong>the</strong> output gap.<br />
The bottom section of Table 1 shows that <strong>the</strong> ratio of <strong>the</strong> volatility measure for <strong>in</strong>flation to that<br />
for output changes was highest <strong>in</strong> 1973‐87 <strong>and</strong> a roughly similar lower value for 1952‐72 <strong>and</strong><br />
1987‐2007. The fact that output volatility was as high <strong>in</strong> 1952‐72 as <strong>in</strong> 1973‐87, while <strong>in</strong>flation<br />
volatility was substantially lower, suggests that <strong>the</strong>re was a separate component of output<br />
volatility unrelated to <strong>in</strong>flation behavior <strong>in</strong> <strong>the</strong> 1952‐72 period. Gordon (2005) decomposes this<br />
<strong>in</strong>to <strong>the</strong> separate contributions of three components of <strong>in</strong>stability on <strong>the</strong> dem<strong>and</strong> side –<br />
government military spend<strong>in</strong>g, residential <strong>in</strong>vestment, <strong>and</strong> <strong>in</strong>ventory <strong>in</strong>vestment.<br />
III. Contrast<strong>in</strong>g <strong>the</strong> New‐Keynesian <strong>and</strong> Triangle <strong>Specification</strong>s of <strong>the</strong> <strong>Phillips</strong><br />
<strong>Curve</strong><br />
This section beg<strong>in</strong>s by compar<strong>in</strong>g <strong>the</strong> generic New‐Keynesian <strong>Phillips</strong> <strong>Curve</strong> (NKPC)<br />
specification with <strong>the</strong> particular variant used by Roberts to arrive at his jo<strong>in</strong>t conclusions that
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 10<br />
<strong>the</strong> slope of <strong>the</strong> PC has significantly flattened s<strong>in</strong>ce <strong>the</strong> mid 1980s <strong>and</strong> that monetary policy is<br />
responsible for both <strong>the</strong> flatter slope <strong>and</strong> <strong>the</strong> <strong>in</strong>creased stability of output. The literature<br />
conta<strong>in</strong>s two versions of <strong>the</strong> NKPC, one <strong>in</strong> which <strong>the</strong> driv<strong>in</strong>g force of <strong>in</strong>flation is <strong>the</strong><br />
unemployment (or output) gap, <strong>and</strong> <strong>the</strong> o<strong>the</strong>r <strong>in</strong> which <strong>the</strong> gap is replaced by <strong>the</strong> change <strong>in</strong><br />
marg<strong>in</strong>al cost.<br />
In this paper we refer only to <strong>the</strong> unemployment‐gap version of <strong>the</strong> NKPC, both because<br />
it is <strong>the</strong> version used by Roberts <strong>and</strong> also because <strong>the</strong> marg<strong>in</strong>al cost version requires <strong>the</strong> added<br />
complexity of estimat<strong>in</strong>g an equation for wages <strong>in</strong> addition to prices. 6 Then <strong>the</strong> triangle model<br />
is <strong>in</strong>troduced <strong>and</strong> contrasted with <strong>the</strong> Roberts version of <strong>the</strong> NKPC, which is nested <strong>in</strong> <strong>the</strong><br />
triangle model by exclud<strong>in</strong>g longer lags on both <strong>in</strong>flation <strong>and</strong> unemployment, by omitt<strong>in</strong>g all<br />
supply shock variables, <strong>and</strong> by assum<strong>in</strong>g that <strong>the</strong> NAIRU is constant.<br />
The NKPC Model<br />
The NKPC model has emerged <strong>in</strong> <strong>the</strong> past decade as <strong>the</strong> centerpiece of macro conference<br />
discussions of <strong>in</strong>flation dynamics <strong>and</strong> as <strong>the</strong> ʺworkhorseʺ of <strong>the</strong> evaluation of monetary policy.<br />
The po<strong>in</strong>t of <strong>the</strong> NKPC is to derive an empirical description of <strong>in</strong>flation dynamics that is<br />
ʺderived from first pr<strong>in</strong>ciples <strong>in</strong> an environment of dynamically optimiz<strong>in</strong>g agentsʺ (Bårdsen et<br />
al. 2002). Most expositions of <strong>the</strong> NKPC, e.g., Mankiw (2001), beg<strong>in</strong> with Calvoʹs (1983) model<br />
of r<strong>and</strong>om price adjustment.<br />
6. Some papers <strong>in</strong> <strong>the</strong> NKPC literature treat changes <strong>in</strong> marg<strong>in</strong>al cost as exogenous, which is<br />
unacceptable as <strong>the</strong> change <strong>in</strong> marg<strong>in</strong>al cost , e.g., <strong>the</strong> real wage divided by productivity, is <strong>in</strong>herently<br />
endogenous <strong>and</strong> requires separate equations for wage change <strong>and</strong> price change.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 11<br />
The <strong>the</strong>oretical background is that firms follow time‐cont<strong>in</strong>gent price‐adjustment rules.<br />
The firmʹs desired price depends on <strong>the</strong> overall price level <strong>and</strong> <strong>the</strong> unemployment gap. 7 Firms<br />
change <strong>the</strong>ir price only <strong>in</strong>frequently, but when <strong>the</strong>y do, <strong>the</strong>y set <strong>the</strong>ir price equal to <strong>the</strong> average<br />
desired price until <strong>the</strong> next price adjustment. The actual price level, <strong>in</strong> turn, is equal to a<br />
weighted average of all prices that firms have set <strong>in</strong> <strong>the</strong> past. The first‐order conditions for<br />
optimization <strong>the</strong>n imply that expected future market conditions matter for todayʹs pric<strong>in</strong>g<br />
decision. The model can be solved to yield <strong>the</strong> st<strong>and</strong>ard NKPC that makes <strong>the</strong> <strong>in</strong>flation rate (pt )<br />
depend on expected future <strong>in</strong>flation (Et pt+1 ) <strong>and</strong> <strong>the</strong> unemployment (or output) gap:<br />
pt = αEt pt+1 + β(Ut ‐U*t ) + et , (1)<br />
where U is <strong>the</strong> unemployment rate. In our notation lower case letters represent first differences<br />
of logarithms <strong>and</strong> upper‐case letters represent ei<strong>the</strong>r levels or log levels. 8 The constant term is<br />
suppressed, <strong>and</strong> so <strong>the</strong> NKPC has <strong>the</strong> <strong>in</strong>terpretation that if α=1, <strong>the</strong>n U*t represents <strong>the</strong> NAIRU.<br />
Much of <strong>the</strong> NKPC literature estimates <strong>the</strong> unemployment or output gap with <strong>the</strong> Hodrick‐<br />
Prescott (HP) filter used to estimate <strong>the</strong> NAIRU or output trend, but Roberts sets <strong>the</strong> NAIRU<br />
equal to a constant, as we discuss fur<strong>the</strong>r below.<br />
A central challenge to <strong>the</strong> NKPC approach is to f<strong>in</strong>d a proxy for <strong>the</strong> forward‐look<strong>in</strong>g<br />
7. Most NKPC papers focus on <strong>the</strong> output gap, but <strong>the</strong> high negative correlation between <strong>the</strong> output <strong>and</strong><br />
unemployment gaps allows <strong>the</strong>m to be used <strong>in</strong>terchangeably, see below. Mankiwʹs (2001) exposition<br />
followed here uses <strong>the</strong> unemployment gap.<br />
8. Note <strong>in</strong> particular that lower‐case p <strong>in</strong> this paper represents <strong>the</strong> first difference of <strong>the</strong> log of <strong>the</strong> price
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 12<br />
expectations term (Et pt+1 ). Surpris<strong>in</strong>gly, <strong>the</strong>re is little discussion <strong>in</strong> <strong>the</strong> literature of this aspect,<br />
or <strong>the</strong> implications of <strong>the</strong> usual solution, which is to use <strong>in</strong>strumental variables or two‐stage<br />
least squares (2SLS) to estimate (1). In particular, no paper <strong>in</strong> <strong>the</strong> NKPC that I have reviewed<br />
conta<strong>in</strong>s an explicit treatment of <strong>the</strong> two stages of <strong>the</strong> 2SLS estimation <strong>and</strong> an <strong>in</strong>terpretation of<br />
<strong>the</strong> reduced‐form equation that results when <strong>the</strong> first stage is substituted <strong>in</strong>to <strong>the</strong> second stage.<br />
The first‐stage equation to be <strong>in</strong>cluded <strong>in</strong> <strong>the</strong> 2SLS estimation is:<br />
Et pt+1<br />
4<br />
= ∑ λi pt‐i + φ(Ut ‐U*t ). (2)<br />
i=<br />
1<br />
Substitut<strong>in</strong>g <strong>the</strong> first‐stage equation (2) <strong>in</strong>to <strong>the</strong> second‐stage equation (1), we obta<strong>in</strong> <strong>the</strong><br />
reduced‐form<br />
4<br />
pt = ∀ ∑ λi pt‐i +(∀Ν+∃)(Ut ‐U*t ) + et (3)<br />
i=<br />
1<br />
Thus <strong>in</strong> practice <strong>the</strong> NKPC is simply a regression of <strong>the</strong> <strong>in</strong>flation rate on a few lags of <strong>in</strong>flation<br />
<strong>and</strong> <strong>the</strong> unemployment gap. As po<strong>in</strong>ted out by Fuhrer (1997), <strong>the</strong> only sense <strong>in</strong> which models<br />
<strong>in</strong>clud<strong>in</strong>g future expectations differ from purely backward‐look<strong>in</strong>g models is that <strong>the</strong>y place<br />
restrictions on <strong>the</strong> coefficients of <strong>the</strong> backward‐look<strong>in</strong>g variables that are used as proxies for <strong>the</strong><br />
unobservable future expectations:<br />
ʺOf course, some restrictions are necessary <strong>in</strong> order to separately identify <strong>the</strong><br />
effects of expected future variables. If <strong>the</strong> model is specified with unconstra<strong>in</strong>ed<br />
leads <strong>and</strong> lags, it will be difficult for <strong>the</strong> data to dist<strong>in</strong>guish between <strong>the</strong> leads,<br />
level, not <strong>the</strong> price level itself.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 13<br />
which solve out as restricted comb<strong>in</strong>ations of lag variables, <strong>and</strong> unrestricted<br />
lags.ʺ (p. 338)<br />
<strong>And</strong>, as shown <strong>in</strong> Fuhrerʹs paper, <strong>the</strong>se restrictions are implicitly rejected by <strong>the</strong> data <strong>in</strong> <strong>the</strong><br />
sense that he f<strong>in</strong>ds that <strong>the</strong> expected <strong>in</strong>flation terms are ʺempirically unimportantʺ when<br />
unconstra<strong>in</strong>ed lagged terms are entered as well.<br />
The Roberts (2006) version of <strong>the</strong> NKPC is of particular <strong>in</strong>terest here, because of his<br />
f<strong>in</strong>d<strong>in</strong>g that <strong>the</strong> slope of <strong>the</strong> PC has decl<strong>in</strong>ed by more than half s<strong>in</strong>ce <strong>the</strong> mid 1980s. Roberts<br />
describes his equation as a “reduced form” NKPC <strong>and</strong> <strong>in</strong>deed it is identical to equation (3)<br />
above with two differences, <strong>the</strong> NAIRU is assumed to be constant, <strong>and</strong> <strong>the</strong> sum of coefficients<br />
on lagged <strong>in</strong>flation is assumed to be unity. Thus <strong>the</strong> Roberts (2006, equation 2, p. 199) version<br />
of (3) is:<br />
4<br />
pt = ∑ αi pt‐i + γ+∃Ut + et (4)<br />
i=<br />
1<br />
where <strong>the</strong> implied constant NAIRU is –γ/β.<br />
The “Triangle” Model of Inflation <strong>and</strong> <strong>the</strong> Role of Dem<strong>and</strong> <strong>and</strong> Supply Shocks<br />
The <strong>in</strong>flation equation used <strong>in</strong> this paper is almost identical to that developed 25 years<br />
ago (Gordon, 1982). It builds on earlier work (Gordon, 1975, 1977) that comb<strong>in</strong>ed <strong>the</strong> Friedman‐<br />
Phelps natural rate hypo<strong>the</strong>sis with <strong>the</strong> role of supply shocks <strong>in</strong> directly shift<strong>in</strong>g <strong>the</strong> <strong>in</strong>flation<br />
rate <strong>and</strong> creat<strong>in</strong>g macroeconomic externalities <strong>in</strong> a world of nom<strong>in</strong>al wage rigidity. The term<br />
ʺtriangleʺ model refers to a <strong>Phillips</strong> <strong>Curve</strong> that depends on three elements, <strong>in</strong>ertia, dem<strong>and</strong>, <strong>and</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 14<br />
supply, <strong>and</strong> <strong>in</strong> which wages are implicitly solved out of <strong>the</strong> reduced form. The specification has<br />
three dist<strong>in</strong>guish<strong>in</strong>g characteristics — (1) <strong>the</strong> role of <strong>in</strong>ertia (<strong>the</strong> bottom of <strong>the</strong> triangle) is<br />
broadly <strong>in</strong>terpreted to go beyond any specific formulation of expectations formation to <strong>in</strong>clude<br />
o<strong>the</strong>r sources of <strong>in</strong>ertia, e.g., wage <strong>and</strong> price contracts; (2) <strong>the</strong> driv<strong>in</strong>g force from <strong>the</strong> dem<strong>and</strong><br />
side is an unemployment or output gap; <strong>and</strong> (3) supply shock variables appear explicitly <strong>in</strong> <strong>the</strong><br />
<strong>in</strong>flation equation ra<strong>the</strong>r than be<strong>in</strong>g forced <strong>in</strong>to <strong>the</strong> error term as <strong>in</strong> <strong>the</strong> NKPC or Roberts<br />
approaches. This general framework can be written as:<br />
pt = a(L)pt‐1 + b(L)Dt + c(L)zt + et . (5)<br />
As before lower‐case letters designate first differences of logarithms, upper‐case letters<br />
designate logarithms of levels, <strong>and</strong> L is a polynomial <strong>in</strong> <strong>the</strong> lag operator.<br />
As <strong>in</strong> <strong>the</strong> NKPC <strong>and</strong> Roberts approaches, <strong>the</strong> dependent variable pt is <strong>the</strong> <strong>in</strong>flation rate.<br />
Inertia is conveyed by a series of lags on <strong>the</strong> <strong>in</strong>flation rate (pt‐1). Dt is an <strong>in</strong>dex of excess dem<strong>and</strong><br />
(normalized so that Dt=0 <strong>in</strong>dicates <strong>the</strong> absence of excess dem<strong>and</strong>), zt is a vector of supply shock<br />
variables (normalized so that zt=0 <strong>in</strong>dicates an absence of supply shocks), <strong>and</strong> et is a serially<br />
uncorrelated error term. Dist<strong>in</strong>guish<strong>in</strong>g features <strong>in</strong> <strong>the</strong> implementation of this model <strong>in</strong>clude<br />
unusually long lags on <strong>the</strong> dependent variable, <strong>and</strong> a set of supply shock variables that are<br />
uniformly def<strong>in</strong>ed so that a zero value <strong>in</strong>dicates no upward or downward pressure on <strong>in</strong>flation.<br />
The estimated version of equation (5) <strong>in</strong>cludes lags of past <strong>in</strong>flation rates, reflect<strong>in</strong>g <strong>the</strong><br />
<strong>in</strong>fluence of several past years of <strong>in</strong>flation behavior on current price sett<strong>in</strong>g, through some
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 15<br />
comb<strong>in</strong>ation of expectation formation, overlapp<strong>in</strong>g wage <strong>and</strong> price contracts, <strong>and</strong> buyersupplier<br />
relations. If <strong>the</strong> sum of <strong>the</strong> coefficients on <strong>the</strong> lagged <strong>in</strong>flation values equals unity, <strong>the</strong>n<br />
<strong>the</strong>re is a ʺnatural rateʺ of <strong>the</strong> dem<strong>and</strong> variable (D N t ) consistent with a constant rate of <strong>in</strong>flation. 9<br />
The basic equations estimated <strong>in</strong> this paper use current <strong>and</strong> lagged values of <strong>the</strong> unemployment<br />
gap as a proxy for <strong>the</strong> excess dem<strong>and</strong> parameter Dt, where <strong>the</strong> unemployment gap is def<strong>in</strong>ed as<br />
<strong>the</strong> difference between <strong>the</strong> actual rate of unemployment <strong>and</strong> <strong>the</strong> natural rate, <strong>and</strong> <strong>the</strong> natural<br />
rate (or NAIRU) is allowed to vary over time.<br />
The estimation of <strong>the</strong> time‐vary<strong>in</strong>g NAIRU comb<strong>in</strong>es <strong>the</strong> above <strong>in</strong>flation equation, with<br />
<strong>the</strong> unemployment gap serv<strong>in</strong>g as <strong>the</strong> proxy for excess dem<strong>and</strong>, with a second equation that<br />
explicitly allows <strong>the</strong> NAIRU to vary with time:<br />
pt = a(L)pt‐1 + b(L)(Ut‐U N t ) + c(L)zt + et , (6)<br />
U N t = U N t‐1 + ηt , Eηt = 0, var(ηt )= τ 2 (7)<br />
In this formulation, <strong>the</strong> disturbance term ηt <strong>in</strong> <strong>the</strong> second equation is serially uncorrelated <strong>and</strong> is<br />
uncorrelated with et . When this st<strong>and</strong>ard deviation τη = 0, <strong>the</strong>n <strong>the</strong> natural rate is constant, <strong>and</strong><br />
when τη is positive, <strong>the</strong> model allows <strong>the</strong> NAIRU to vary by a limited amount each quarter. If<br />
no limit were placed on <strong>the</strong> ability of <strong>the</strong> NAIRU to vary each time period, <strong>the</strong>n <strong>the</strong> timevary<strong>in</strong>g<br />
NAIRU (hereafter TV‐NAIRU) would jump up <strong>and</strong> down <strong>and</strong> soak up all <strong>the</strong> residual<br />
9. While <strong>the</strong> estimated sum of <strong>the</strong> coefficients on lagged <strong>in</strong>flation is usually roughly equal to unity, that<br />
sum must be constra<strong>in</strong>ed to be exactly unity for a mean<strong>in</strong>gful ʺnatural rateʺ of <strong>the</strong> dem<strong>and</strong> variable to be
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 16<br />
variation <strong>in</strong> <strong>the</strong> <strong>in</strong>flation equation (6). 10<br />
The triangle approach differs from <strong>the</strong> NKPC <strong>and</strong> Roberts approaches by <strong>in</strong>clud<strong>in</strong>g long<br />
lags on <strong>the</strong> dependent variable, additional lags on <strong>the</strong> unemployment gap, <strong>and</strong> explicit<br />
variables to represent <strong>the</strong> supply shocks (<strong>the</strong> zt variables <strong>in</strong> (5) <strong>and</strong> (6) above), namely <strong>the</strong><br />
change <strong>in</strong> <strong>the</strong> relative price of non‐food non‐oil imports, <strong>the</strong> effect on <strong>in</strong>flation of changes <strong>in</strong> <strong>the</strong><br />
relative price of food <strong>and</strong> energy, <strong>the</strong> acceleration <strong>in</strong> <strong>the</strong> trend rate of productivity growth, <strong>and</strong><br />
dummy variables for <strong>the</strong> effect of <strong>the</strong> 1971‐74 Nixon‐era price controls. 11 Lag lengths were<br />
orig<strong>in</strong>ally specified <strong>in</strong> Gordon (1982) <strong>and</strong> have not been changed s<strong>in</strong>ce <strong>the</strong>n.<br />
The top frame of Figure 4 displays four‐quarter mov<strong>in</strong>g averages of <strong>the</strong> relative import<br />
price variable. Its central role <strong>in</strong> expla<strong>in</strong><strong>in</strong>g <strong>the</strong> spike of <strong>in</strong>flation <strong>in</strong> 1974‐75 is clearly visible, as<br />
is its role <strong>in</strong> <strong>the</strong> Volcker dis<strong>in</strong>flation of 1982‐85, <strong>the</strong> accelerat<strong>in</strong>g <strong>in</strong>flation of <strong>the</strong> late 1980s, <strong>and</strong><br />
<strong>the</strong> slowdown of <strong>in</strong>flation <strong>in</strong> 1997‐2001. As plotted <strong>in</strong> <strong>the</strong> bottom frame of Figure 4, <strong>the</strong> foodenergy<br />
effect has somewhat different tim<strong>in</strong>g than <strong>the</strong> import price effect. Note also <strong>the</strong> different<br />
orders of magnitude of <strong>the</strong> import <strong>and</strong> food‐energy effects, reflect<strong>in</strong>g <strong>the</strong> fact that <strong>the</strong>y are<br />
calculated.<br />
10. This method of estimat<strong>in</strong>g <strong>the</strong> TV‐NAIRU was <strong>in</strong>troduced <strong>in</strong> simultaneous papers by Gordon (1997)<br />
<strong>and</strong> Staiger‐Stock‐Watson (1997). SSW developed <strong>the</strong> technique while adopt<strong>in</strong>g Gordon’s previous<br />
triangle model, <strong>and</strong> so those two papers were a merger of technique <strong>and</strong> substance.<br />
11. The relative import price variable is def<strong>in</strong>ed as <strong>the</strong> rate of change of <strong>the</strong> non‐food non‐oil import<br />
deflator m<strong>in</strong>us <strong>the</strong> rate of change of <strong>the</strong> dependent variable, e.g., PCE deflator. The relative food‐energy<br />
variable is def<strong>in</strong>ed as <strong>the</strong> difference between <strong>the</strong> rates of change of <strong>the</strong> overall PCE deflator <strong>and</strong> <strong>the</strong> ʺcoreʺ<br />
PCE deflator. The Nixon control variables rema<strong>in</strong> <strong>the</strong> same as orig<strong>in</strong>ally specified <strong>in</strong> Gordon (1982). Lag<br />
lengths rema<strong>in</strong> as <strong>in</strong> 1982 <strong>and</strong> are shown explicitly <strong>in</strong> Table 2. The productivity trend is a Hodrick‐<br />
Prescott filter (us<strong>in</strong>g 6400 as <strong>the</strong> smoothness parameter) m<strong>in</strong>us a six‐year mov<strong>in</strong>g average of <strong>the</strong> same H‐<br />
P trend. The only changes from <strong>the</strong> previous published paper on this approach (Gordon, 1998) is <strong>in</strong> <strong>the</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 17<br />
def<strong>in</strong>ed differently. 12<br />
The only major change <strong>in</strong> <strong>the</strong> current <strong>in</strong>flation equation <strong>in</strong>volves productivity growth,<br />
where we follow <strong>the</strong> approach <strong>in</strong>troduced <strong>in</strong> Dew‐Becker <strong>and</strong> Gordon (2005). In previous<br />
papers <strong>the</strong> difference <strong>in</strong> <strong>the</strong> growth rates of actual <strong>and</strong> trend productivity or “productivity<br />
deviation” had been entered <strong>in</strong>to <strong>the</strong> <strong>in</strong>flation equation. But this misses <strong>the</strong> ma<strong>in</strong> impact of <strong>the</strong><br />
1965‐80 productivity growth slowdown <strong>and</strong> post‐1995 productivity growth revival, which is <strong>the</strong><br />
change <strong>in</strong> <strong>the</strong> growth of <strong>the</strong> trend itself. Here we create a productivity trend growth<br />
acceleration variable equal to a Hodrick‐Prescott filter version of <strong>the</strong> productivity growth trend<br />
m<strong>in</strong>us a six‐year mov<strong>in</strong>g average of <strong>the</strong> same trend. This productivity trend acceleration<br />
variable is plotted <strong>in</strong> Figure 5. Its deceleration <strong>in</strong>to negative territory dur<strong>in</strong>g 1964‐1980 might be<br />
as important a cause of accelerat<strong>in</strong>g <strong>in</strong>flation <strong>in</strong> that period as its post‐1995 acceleration was a<br />
cause of low <strong>in</strong>flation <strong>in</strong> <strong>the</strong> late 1990s. Note also that <strong>the</strong> productivity growth trend revival of<br />
1980‐85 may have contributed to <strong>the</strong> success of <strong>the</strong> “Volcker dis<strong>in</strong>flation,” a l<strong>in</strong>k that has been<br />
missed <strong>in</strong> most of <strong>the</strong> past PC literature.<br />
Estimat<strong>in</strong>g <strong>the</strong> TV‐NAIRU<br />
The time‐vary<strong>in</strong>g NAIRU is estimated simultaneously with <strong>the</strong> <strong>in</strong>flation equation (6)<br />
above. For each set of dependent variables <strong>and</strong> explanatory variables, <strong>the</strong>re is a different TVtreatment<br />
of <strong>the</strong> productivity effect, see Dew‐Becker <strong>and</strong> Gordon (2005).<br />
12. Namely, <strong>the</strong> import variable is <strong>the</strong> change <strong>in</strong> <strong>the</strong> relative price of imports, which reaches a peak of<br />
about 15 percent <strong>in</strong> 1974‐75. The food‐energy variable is not <strong>the</strong> relative price of food <strong>and</strong> energy, but<br />
ra<strong>the</strong>r <strong>the</strong> difference between <strong>the</strong> growth rates of <strong>the</strong> PCE deflator <strong>in</strong>clud<strong>in</strong>g <strong>and</strong> exclud<strong>in</strong>g food <strong>and</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 18<br />
NAIRU. For <strong>in</strong>stance, when supply‐shock variables are omitted, <strong>the</strong> TV‐NAIRU soars to 8<br />
percent <strong>and</strong> above <strong>in</strong> <strong>the</strong> mid‐1970s, s<strong>in</strong>ce this is <strong>the</strong> only way <strong>the</strong> <strong>in</strong>flation equation can<br />
“expla<strong>in</strong>” why <strong>in</strong>flation was so high <strong>in</strong> <strong>the</strong> 1970s. However, when <strong>the</strong> full set of supply shocks<br />
is <strong>in</strong>cluded <strong>in</strong> <strong>the</strong> <strong>in</strong>flation equation, <strong>the</strong> TV‐NAIRU is quite stable, shown by <strong>the</strong> dashed l<strong>in</strong>e<br />
plotted <strong>in</strong> Figure 6.<br />
The TV‐NAIRU series as plotted <strong>in</strong> Figure 6 that is associated with our basic <strong>in</strong>flation<br />
equation for <strong>the</strong> PCE deflator does not fall below 5.7 percent or rise above 6.5 percent over <strong>the</strong><br />
period between 1962 <strong>and</strong> 1988. However, beg<strong>in</strong>n<strong>in</strong>g <strong>in</strong> <strong>the</strong> late 1980s, <strong>the</strong> TV‐NAIRU drifts<br />
downwards until it reaches 5.3 percent <strong>in</strong> 1998, <strong>and</strong> <strong>the</strong>n it displays a fur<strong>the</strong>r dip <strong>in</strong> 2004‐06 to<br />
4.8 percent. One hypo<strong>the</strong>sis to be explored below is that Roberts reaches his conclusion that<br />
<strong>the</strong> <strong>Phillips</strong> curve has flattened because he forces <strong>the</strong> NAIRU to be constant, <strong>and</strong> that a decl<strong>in</strong>e<br />
<strong>in</strong> <strong>the</strong> TV‐NAIRU is an alternative to a flatter PC <strong>in</strong> expla<strong>in</strong><strong>in</strong>g why <strong>in</strong>flation has been relatively<br />
well‐behaved <strong>in</strong> <strong>the</strong> past 20 years. 13<br />
Some of <strong>the</strong> NKPC literature estimates <strong>the</strong> TV‐NAIRU by directly apply<strong>in</strong>g an H‐P filter<br />
to <strong>the</strong> time series of <strong>the</strong> unemployment rate. As shown <strong>in</strong> Figure 6 us<strong>in</strong>g two alternative H‐P<br />
parameters (1600 <strong>and</strong> 6400) this “direct” approach to estimat<strong>in</strong>g <strong>the</strong> TV‐NAIRU results <strong>in</strong> an<br />
unexpla<strong>in</strong>ed <strong>in</strong>crease <strong>in</strong> <strong>the</strong> TV‐NAIRU from 4 percent <strong>in</strong> 1970 to 8 percent <strong>in</strong> 1985, whereas <strong>the</strong><br />
energy, <strong>and</strong> this variable peaks at 3.3 percent <strong>in</strong> 1974‐75.<br />
13. After develop<strong>in</strong>g <strong>the</strong> technique described above for estimat<strong>in</strong>g <strong>the</strong> TV‐NAIRU, <strong>the</strong> recent work of<br />
Stock <strong>and</strong> Watson has ab<strong>and</strong>oned that approach <strong>in</strong> favor of us<strong>in</strong>g a direct Hodrick‐Prescott filter to<br />
estimate <strong>the</strong> NAIRU <strong>in</strong> equations which omit explicit supply shock variables. See Staigher‐Stock‐Watson<br />
(2001) <strong>and</strong> Stock‐Watson (2006).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 19<br />
triangle approach has no such unexpla<strong>in</strong>ed <strong>in</strong>crease because of its <strong>in</strong>troduction of explicit<br />
supply shock variables. 14<br />
The Roberts specification forces <strong>the</strong> NAIRU to be constant. Figure 7 displays <strong>the</strong> Roberts<br />
estimate of <strong>the</strong> NAIRU for <strong>the</strong> PCE deflator, a constant 7.0 percent. It seems illogical for a Fed<br />
research paper to tell <strong>the</strong> Board of Governors that <strong>the</strong> NAIRU is 7.0 percent <strong>in</strong> 2007 when <strong>the</strong><br />
actual unemployment rate is 4.5 percent. Fur<strong>the</strong>rmore, if <strong>the</strong> Fed Board of Governors believed<br />
Roberts’ research, it would have been rais<strong>in</strong>g <strong>in</strong>terest rates cont<strong>in</strong>ually over 2006‐07 to prevent<br />
<strong>in</strong>flation from accelerat<strong>in</strong>g as implied by <strong>the</strong> divergence between <strong>the</strong> actual unemployment rate<br />
<strong>and</strong> <strong>the</strong> Roberts NAIRU of 7.0 percent. The pessimism of Roberts’ specification about <strong>the</strong><br />
NAIRU is reflected <strong>in</strong> its wildly exaggerated forecasts of accelerat<strong>in</strong>g <strong>in</strong>flation as reported <strong>in</strong> <strong>the</strong><br />
simulation experiments shown below.<br />
Roberts vs. Triangle: Estimated Coefficients <strong>and</strong> Simulation Performance<br />
We next turn to <strong>the</strong> estimated coefficients, goodness of fit, <strong>and</strong> simulation performance<br />
of <strong>the</strong> Roberts <strong>and</strong> triangle PC specifications. Table 2 displays <strong>the</strong> estimated coefficients for<br />
both <strong>the</strong> Roberts <strong>and</strong> triangle specifications for <strong>the</strong> PCE deflator. S<strong>in</strong>ce <strong>the</strong> sample period is<br />
uniform across <strong>the</strong> columns of Table 2, <strong>the</strong> sum of squared residuals is <strong>the</strong> basic metric that<br />
allows us to compare <strong>the</strong> goodness of fit of <strong>the</strong> alternative specifications.<br />
In both specifications <strong>the</strong> sum of coefficients on <strong>the</strong> lagged <strong>in</strong>flation terms is always very<br />
14. Basthista‐Nelson (2007) are among those authors who exclude explicit supply shock variables from<br />
<strong>the</strong>ir equations <strong>and</strong> derive estimates of <strong>the</strong> TV‐NAIRU that are extremely high, e.g., 8 percent <strong>in</strong> 1975 <strong>and</strong><br />
10 percent <strong>in</strong> 1981 (2007, p. 509, Figure 6).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 20<br />
close to unity, as <strong>in</strong> previous research. 15 The sum of <strong>the</strong> unemployment gap variables <strong>in</strong> <strong>the</strong><br />
triangle approach is around ‐0.6 for <strong>the</strong> PCE deflator, which is consistent with a stylized fact<br />
first noticed <strong>in</strong> <strong>the</strong> 1960s that <strong>the</strong> slope of <strong>the</strong> short‐run <strong>Phillips</strong> curve is roughly m<strong>in</strong>us one‐half.<br />
An elementary textbook on specification bias would expla<strong>in</strong> why <strong>the</strong> Roberts unemployment<br />
coefficients are lower than <strong>in</strong> <strong>the</strong> triangle specification, namely that when supply shock<br />
variables are excluded that are positively correlated with <strong>in</strong>flation <strong>and</strong> negatively correlated<br />
with <strong>the</strong> unemployment gap, <strong>the</strong>n <strong>the</strong> coefficient on <strong>the</strong> unemployment gap is biased<br />
downward toward zero.<br />
Of <strong>the</strong> supply shocks <strong>in</strong> <strong>the</strong> triangle model, <strong>the</strong> change <strong>in</strong> <strong>the</strong> relative import price effect<br />
has a highly significant coefficient of 0.06 <strong>in</strong> <strong>the</strong> PCE deflator equation, which is less than half of<br />
<strong>the</strong> 14 percent share of imports <strong>in</strong> nom<strong>in</strong>al GDP. The coefficient on <strong>the</strong> change <strong>in</strong> <strong>the</strong><br />
productivity trend is entered with lags 1 <strong>and</strong> 5, <strong>and</strong> <strong>the</strong> sum of <strong>the</strong>se coefficients is highly<br />
significant at a value of about m<strong>in</strong>us unity. The productivity trend effect helps to expla<strong>in</strong> why<br />
<strong>in</strong>flation accelerated <strong>in</strong> 1965‐80 <strong>and</strong> was so well‐behaved <strong>in</strong> 1995‐2000. The coefficients for <strong>the</strong><br />
Nixon control variables are highly significant <strong>and</strong> have <strong>the</strong> expected signs <strong>and</strong> magnitudes<br />
similar to those <strong>in</strong> past research, that is, <strong>the</strong> Nixon price controls significantly reduced <strong>in</strong>flation<br />
<strong>in</strong> 1971‐72 <strong>and</strong> raised <strong>in</strong>flation <strong>in</strong> 1974‐75.<br />
While most papers present<strong>in</strong>g time‐series regression results display coefficients,<br />
15. The <strong>in</strong>clusion of lags 13‐24 (years four through six) is strongly significant <strong>in</strong> an exclusion test at <strong>the</strong><br />
0.0000 confidence level. As stated <strong>in</strong> <strong>the</strong> notes to Table 2, we conserve on degrees of freedom by
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 21<br />
significance levels, <strong>and</strong> summary statistics, few go beyond that <strong>and</strong> display results of dynamic<br />
simulations. Yet <strong>the</strong> performance of <strong>the</strong> <strong>in</strong>flation equation, especially <strong>in</strong> <strong>the</strong> Roberts/NKPC<br />
version which <strong>in</strong>cludes no variable whatever to expla<strong>in</strong> why <strong>in</strong>flation <strong>in</strong>creased <strong>in</strong> 1975 while<br />
unemployment <strong>in</strong>creased as well, <strong>the</strong> entire statistical result depends on lagged dependent<br />
variable terms. For <strong>the</strong> Roberts/NKPC model, <strong>in</strong>flation today is whatever it was yesterday, which is not<br />
a model at all.<br />
To unveil <strong>the</strong> heavy dependence of <strong>the</strong> Roberts/NKPC model on <strong>the</strong> “today‐isyesterday”<br />
methodology, dynamic simulations generate <strong>the</strong> predictions of <strong>the</strong> lagged<br />
dependent variable endogenously ra<strong>the</strong>r than feed<strong>in</strong>g through <strong>the</strong> actual value of lagged<br />
<strong>in</strong>flation. This makes dynamic simulations <strong>the</strong> preferable method for test<strong>in</strong>g. To run such<br />
simulations, <strong>the</strong> sample period is truncated ten years before <strong>the</strong> end of <strong>the</strong> data <strong>in</strong>terval, <strong>and</strong> <strong>the</strong><br />
estimated coefficients through 1996:Q4 are used to simulate <strong>the</strong> performance of <strong>the</strong> equation for<br />
1997‐2006, generat<strong>in</strong>g <strong>the</strong> lagged dependent variables endogenously. S<strong>in</strong>ce <strong>the</strong> simulation has<br />
no <strong>in</strong>formation on <strong>the</strong> actual value of <strong>the</strong> <strong>in</strong>flation rate, <strong>the</strong>re is noth<strong>in</strong>g to keep <strong>the</strong> simulated<br />
<strong>in</strong>flation rate from drift<strong>in</strong>g far away from <strong>the</strong> actual rate <strong>in</strong> a positive or negative direction. 16<br />
The bottom section of Table 2 displays results of a dynamic simulation for 1997:Q1 to 2006:Q4<br />
based on a sample period that ends <strong>in</strong> 1996:Q4. Two statistics on simulation errors are<br />
<strong>in</strong>clud<strong>in</strong>g six successive four‐quarter mov<strong>in</strong>g averages of <strong>the</strong> lagged dependent variable at lags 1, 5, 9, 13,<br />
17, <strong>and</strong> 21, ra<strong>the</strong>r than <strong>in</strong>clud<strong>in</strong>g all 24 lags separately.<br />
16. I have been runn<strong>in</strong>g dynamic simulations of <strong>Phillips</strong> curves for at least 25 years <strong>and</strong> cannot<br />
underst<strong>and</strong> why this has not become a st<strong>and</strong>ard test<strong>in</strong>g technique <strong>in</strong> models where <strong>the</strong>re is a strong<br />
dependence of results on <strong>the</strong> lagged dependent variable.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 22<br />
provided, <strong>the</strong> mean error (ME) <strong>and</strong> <strong>the</strong> root mean‐squared error (RMSE). The simulated values<br />
of <strong>in</strong>flation <strong>in</strong> <strong>the</strong> triangle model are extremely close to <strong>the</strong> actual values, with a mean error over<br />
40 quarters of only ‐0.08. The RMSE of <strong>the</strong> simulations is lower than <strong>the</strong> st<strong>and</strong>ard error of<br />
estimate for <strong>the</strong> 1962‐96 sample period. These simulation results are substantially better than<br />
those reported <strong>in</strong> Gordon (1998).<br />
The Roberts <strong>and</strong> triangle results agree on only one aspect of <strong>the</strong> <strong>in</strong>flation process, that<br />
<strong>the</strong> sum of coefficients on <strong>the</strong> lagged <strong>in</strong>flation terms is always very close to unity. However, <strong>the</strong><br />
Roberts coefficients on <strong>the</strong> unemployment rate are much lower than <strong>the</strong> triangle coefficients on<br />
<strong>the</strong> unemployment gap. As we shall see, this is an artifact of <strong>the</strong> exclusion restrictions <strong>in</strong> <strong>the</strong><br />
Roberts approach which are statistically rejected <strong>in</strong> <strong>the</strong> triangle approach.<br />
The measures of goodness of fit <strong>in</strong> Table 2 also reject <strong>the</strong> Roberts specification by a wide<br />
marg<strong>in</strong>. First, <strong>the</strong> triangle sum of squared residuals (SSR) is only 27 percent of <strong>the</strong> Roberts SSR.<br />
The triangle model expla<strong>in</strong>s almost four times <strong>the</strong> variance of <strong>in</strong>flation as does <strong>the</strong> Roberts<br />
model.<br />
However, <strong>the</strong> most tell<strong>in</strong>g <strong>in</strong>dictment of <strong>the</strong> Roberts specification is <strong>in</strong> <strong>the</strong> dynamic<br />
simulation results shown <strong>in</strong> <strong>the</strong> bottom section of Table 2 <strong>and</strong> <strong>in</strong> Figure 8, which shows <strong>the</strong> time<br />
path of <strong>the</strong> four‐quarter mov<strong>in</strong>g average of <strong>the</strong> simulated post‐sample behavior of <strong>the</strong> <strong>in</strong>flation<br />
rate over 1997‐2006 <strong>in</strong> <strong>the</strong> two specifications. The Roberts specification predicts that <strong>in</strong>flation<br />
would soar to close to 10 percent <strong>in</strong> 2006, whereas <strong>the</strong> triangle model after ten years comes up<br />
with a small error, a simulated value <strong>in</strong> 2006:Q4 of 2.6 percent compared to <strong>the</strong> actual 1.9
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 23<br />
percent. Over <strong>the</strong> entire 40‐quarter simulation period, <strong>the</strong> mean error for <strong>the</strong> triangle model<br />
us<strong>in</strong>g <strong>the</strong> PCE deflator is nearly zero (‐0.08 percent) whereas <strong>the</strong> same statistic for <strong>the</strong> Roberts<br />
model is several orders of magnitude higher, ‐4.67 percent. The Root Mean‐Squared Error of<br />
<strong>the</strong> triangle simulation is only 12 percent of <strong>the</strong> Roberts version, namely 0.60 percent <strong>in</strong> <strong>the</strong><br />
second column of Table 2 compared to 5.06 percent for Roberts <strong>in</strong> <strong>the</strong> first column of Table 2.<br />
IV.<br />
The “Translation Matrix” between <strong>the</strong> Roberts/NKPC <strong>and</strong> Triangle<br />
<strong>Specification</strong>s<br />
The triangle model outperforms <strong>the</strong> Roberts/NKPC model by several orders of magnitude,<br />
as displayed <strong>in</strong> Table 2 <strong>and</strong> Figure 8. This raises a question central to future research on <strong>the</strong><br />
U. S. <strong>Phillips</strong> curve: what are <strong>the</strong> crucial differences between <strong>the</strong> triangle <strong>and</strong> Roberts<br />
specifications that contribute to <strong>the</strong> superior performance of <strong>the</strong> triangle model? The three key<br />
differences are <strong>the</strong> <strong>in</strong>clusion <strong>in</strong> <strong>the</strong> triangle model of longer lags on both <strong>in</strong>flation <strong>and</strong> <strong>the</strong><br />
unemployment gap, <strong>the</strong> <strong>in</strong>clusion of explicit supply‐shock variables, <strong>and</strong> <strong>the</strong> allowance for a<br />
time‐vary<strong>in</strong>g (TV) NAIRU <strong>in</strong> place of Roberts’ assumption of a fixed NAIRU. In this section we<br />
quantify <strong>the</strong> role of <strong>the</strong>se differences, tak<strong>in</strong>g advantage of <strong>the</strong> fact that <strong>the</strong> Roberts model is fully<br />
nested <strong>in</strong> <strong>the</strong> triangle model. Each exclusion restriction <strong>in</strong> <strong>the</strong> Roberts model can be tested by<br />
st<strong>and</strong>ard statistical exclusion criteria, <strong>and</strong> as we will see, every one of Roberts’ exclusion criteria<br />
is rejected at high levels of statistical significance. 17<br />
Which Differences Matter <strong>in</strong> Expla<strong>in</strong><strong>in</strong>g <strong>the</strong> Poor Performance of <strong>the</strong> Roberts/NKPC?<br />
17. Dew‐Becker (2006) has previously traced <strong>the</strong> statistical significance of stripped‐down Roberts‐type<br />
<strong>Phillips</strong> <strong>Curve</strong>s <strong>and</strong> reached conclusions that are similar to those arrayed <strong>in</strong> Table 3.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 24<br />
In everyth<strong>in</strong>g that follows, <strong>the</strong> sample period is 1962:Q1 to 2006:Q4. Subsequently we will<br />
look at <strong>the</strong> variability of <strong>the</strong> <strong>Phillips</strong> curve coefficient (on <strong>the</strong> unemployment rate or<br />
unemployment gap) <strong>in</strong> roll<strong>in</strong>g regressions <strong>in</strong> order to assess Roberts’ core claim that <strong>the</strong> PC has<br />
become flatter s<strong>in</strong>ce <strong>the</strong> mid‐1980s. Table 3 provides <strong>the</strong> “translation matrix” that guides us<br />
between <strong>the</strong> Roberts specification for <strong>the</strong> PCE deflator <strong>and</strong> <strong>the</strong> triangle specification. a There are<br />
24 l<strong>in</strong>es that allow us to trace <strong>the</strong> role of each specification difference between triangle <strong>and</strong><br />
Roberts/NKPC, <strong>and</strong> <strong>the</strong> <strong>in</strong>dividual l<strong>in</strong>es of alternative specification are evaluated based not just<br />
on <strong>the</strong> SSR measure of goodness of fit, but also on <strong>the</strong> post‐sample simulation performance <strong>in</strong><br />
1997‐2006 based on coefficient estimates for 1962‐1996.<br />
We have already seen <strong>in</strong> Table 2 that <strong>the</strong> performance of <strong>the</strong> Roberts specification for <strong>the</strong><br />
PCE deflator is <strong>in</strong>ferior to that of <strong>the</strong> triangle specification by both <strong>the</strong> criterion of goodness of<br />
fit (SSR) <strong>and</strong> also <strong>the</strong> less conventional criterion of dynamic simulation performance (ME <strong>and</strong><br />
RMSE). In Table 3 <strong>the</strong> basic Roberts variant is on l<strong>in</strong>e 1 <strong>and</strong> <strong>the</strong> basic triangle variant is on l<strong>in</strong>e<br />
21. Roberts’ l<strong>in</strong>e 1 <strong>and</strong> <strong>the</strong> triangle l<strong>in</strong>e 21 have SSR’s of 233.3 <strong>and</strong> 63.2, exactly <strong>the</strong> same as <strong>in</strong><br />
Table 2 above.<br />
Table 3 allows <strong>the</strong> three ma<strong>in</strong> differences between <strong>the</strong> Roberts/NKPC <strong>and</strong> triangle<br />
specifications to be evaluated, step‐by‐step. Is <strong>the</strong> crucial difference contribut<strong>in</strong>g to <strong>the</strong> better<br />
statistical performance of <strong>the</strong> triangle model dependent on <strong>the</strong> longer lags, on <strong>the</strong> supply<br />
shocks, on <strong>the</strong> TV‐NAIRU, or an <strong>in</strong>teraction of <strong>the</strong>se differences?<br />
In <strong>the</strong> 24 l<strong>in</strong>es of Table 3, <strong>the</strong> first 12 l<strong>in</strong>es exclude supply shock variables, <strong>and</strong> l<strong>in</strong>es 13‐24
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 25<br />
<strong>in</strong>clude <strong>the</strong> supply shock variables. Scann<strong>in</strong>g down <strong>the</strong> column for “SSR”, we f<strong>in</strong>d that <strong>the</strong><br />
variants on l<strong>in</strong>es 13‐24 <strong>in</strong>clud<strong>in</strong>g supply shocks all have SSR’s below 100, while most of <strong>the</strong><br />
SSR’s that exclude supply shocks have values above 200. Thus our first conclusion is that <strong>the</strong><br />
exclusion of explicit supply shocks <strong>in</strong> <strong>the</strong> Roberts/NKPC research is <strong>the</strong> central reason for its<br />
empirical failure ei<strong>the</strong>r to expla<strong>in</strong> postwar <strong>in</strong>flation or to track <strong>the</strong> evolution of <strong>in</strong>flation <strong>in</strong> postsample<br />
1997‐2006 simulations.<br />
What difference is made by long lags <strong>and</strong> by <strong>the</strong> TV‐NAIRU? When supply shocks are<br />
omitted as <strong>in</strong> l<strong>in</strong>es 1‐12 of Table 3, <strong>the</strong>re is little difference among <strong>the</strong> alternative variants which<br />
yield SSR’s rang<strong>in</strong>g from 172.7 to 233.3. Simulation mean errors (ME) range from ‐1.60 to ‐4.67,<br />
<strong>and</strong> <strong>the</strong> lower values are those that <strong>in</strong>clude long lags <strong>and</strong> allow <strong>the</strong> NAIRU to vary over time.<br />
More <strong>in</strong>terest<strong>in</strong>g is <strong>the</strong> set of results that <strong>in</strong>clude supply shocks, l<strong>in</strong>es 13 to 24 <strong>in</strong> Table 3.<br />
The matrix <strong>in</strong> Table 3 reveals important <strong>in</strong>teractions between lag lengths, <strong>the</strong> TV‐NAIRU, <strong>and</strong><br />
<strong>the</strong> <strong>in</strong>clusion of supply‐shock variables. When supply shocks are <strong>in</strong>cluded but lag lengths are<br />
short, as <strong>in</strong> l<strong>in</strong>es 13‐14, 17‐19, <strong>and</strong> 22, <strong>the</strong> post‐sample simulation errors are very large. When<br />
supply shocks are <strong>in</strong>cluded, <strong>the</strong> best results are on l<strong>in</strong>es 15‐16 with a fixed NAIRU <strong>and</strong> on l<strong>in</strong>es<br />
20‐21 with a TV‐NAIRU. Clearly, long lags on <strong>the</strong> dependent variable (<strong>in</strong>flation) matter <strong>in</strong> <strong>the</strong><br />
specification of a PC <strong>in</strong>clud<strong>in</strong>g supply shocks.<br />
The right section of Table 3 conta<strong>in</strong>s a large number of significance tests on <strong>the</strong> exclusion of<br />
variables which are omitted <strong>in</strong> <strong>the</strong> Roberts specification <strong>and</strong> <strong>in</strong>cluded <strong>in</strong> <strong>the</strong> triangle<br />
specification. Start<strong>in</strong>g on l<strong>in</strong>e 3, even without supply shock variables, <strong>the</strong> significance value of
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 26<br />
exclud<strong>in</strong>g lags 9‐24 on <strong>the</strong> lagged dependent variable is 0.00 <strong>and</strong> on lags 1‐4 of <strong>the</strong><br />
unemployment gap is 0.02. Throughout l<strong>in</strong>es 1‐12 of Table 3, we learn that exclud<strong>in</strong>g short lags<br />
(e.g., exclud<strong>in</strong>g lags 5‐8 from equations conta<strong>in</strong><strong>in</strong>g <strong>in</strong>flation lags 1‐4) is <strong>in</strong>significant, whereas<br />
exclud<strong>in</strong>g lags 9‐24 yields highly significant exclusion tests.<br />
The most important section of Table 3 is <strong>in</strong> <strong>the</strong> bottom half, l<strong>in</strong>es 13‐24. Here all l<strong>in</strong>es<br />
have <strong>the</strong> full set of supply‐shock variables. The l<strong>in</strong>es differ only <strong>in</strong> <strong>the</strong> length of lags <strong>in</strong>cluded<br />
on <strong>the</strong> lagged dependent (<strong>in</strong>flation) variable <strong>and</strong> on lagged unemployment, <strong>and</strong> also on<br />
whe<strong>the</strong>r <strong>the</strong> NAIRU is forced to be fixed or is allowed to vary over time. We can <strong>in</strong>terpret <strong>the</strong><br />
bottom half of Table 3 by look<strong>in</strong>g at blocks of four rows.<br />
The first group of four rows, 13 through 16, share <strong>in</strong> common <strong>the</strong> <strong>in</strong>clusion of supply<br />
shocks, <strong>the</strong> assumption of a fixed NAIRU, <strong>and</strong> alternative lags on <strong>the</strong> dependent variable. The<br />
mean error <strong>in</strong> <strong>the</strong> dynamic simulations falls by 80 percent when lags up to 24 are <strong>in</strong>cluded, <strong>and</strong><br />
<strong>the</strong> exclusion of lags 9‐24 is rejected at a 0.00 significance value. The same result occurs <strong>in</strong> l<strong>in</strong>es<br />
22‐25 when with a time‐vary<strong>in</strong>g NAIRU <strong>the</strong> significance of long lags on <strong>the</strong> dependent variable<br />
are strongly supported at significance levels of 0.00.<br />
The Fragility of <strong>the</strong> Conclusion that <strong>the</strong> PC has Flattened<br />
Roberts’ research has been highly <strong>in</strong>fluential <strong>in</strong> lead<strong>in</strong>g <strong>the</strong> Federal Reserve to believe<br />
that <strong>the</strong> <strong>Phillips</strong> <strong>Curve</strong> has become flatter over <strong>the</strong> past two or more decades. Yet we have seen<br />
that every assumption of <strong>the</strong> Roberts (<strong>and</strong> more broadly NKPC) specification are rejected at<br />
high levels of statistical significance.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 27<br />
Has <strong>the</strong> <strong>Phillips</strong> <strong>Curve</strong> flattened? The Roberts specification says “yes” <strong>and</strong> <strong>the</strong> triangle<br />
specification says “no”. Figure 9 evaluates changes <strong>in</strong> coefficients by Roberts’ own preferred<br />
method (2006, Figure 2, p. 202), roll<strong>in</strong>g regressions that shift <strong>the</strong> sample period of <strong>the</strong> regression<br />
through time <strong>in</strong> order to reveal changes <strong>in</strong> coefficients. The number of quarters <strong>in</strong> our basic<br />
results <strong>in</strong> Table 2 is 180 (1962:Q1 to 2006:Q4), <strong>and</strong> we cut this <strong>in</strong> half to 90 quarters <strong>and</strong> run<br />
roll<strong>in</strong>g 90‐quarter regressions which alternatively start <strong>in</strong> each quarter from 1962:Q1 to 1984:Q3.<br />
As shown <strong>in</strong> Figure 9, <strong>the</strong> Roberts unemployment coefficient rises from ‐0.17 <strong>in</strong> 1962 to a<br />
peak value of ‐0.41 <strong>in</strong> 1974, <strong>and</strong> <strong>the</strong>n decl<strong>in</strong>es back to roughly zero <strong>in</strong> 1982‐84. This appears to<br />
support <strong>the</strong> basic conclusion of <strong>the</strong> Roberts (2006) paper, that <strong>the</strong> <strong>Phillips</strong> <strong>Curve</strong> has flattened.<br />
Yet with <strong>the</strong> triangle model that fits <strong>the</strong> data so much better <strong>and</strong> provides a greatly superior<br />
post‐sample dynamic simulation performance, <strong>the</strong>re is no evidence at all of a decl<strong>in</strong>e <strong>in</strong> <strong>the</strong><br />
slope of <strong>the</strong> <strong>Phillips</strong> curve. As shown <strong>in</strong> Figure 9, <strong>the</strong> <strong>Phillips</strong> curve based on <strong>the</strong> triangle model<br />
has a roughly stable PC slope of about ‐0.6 to ‐0.7 from 1963 to 1977, <strong>and</strong> <strong>the</strong>n <strong>the</strong> slope rises<br />
toward about ‐0.7 to about ‐0.9 <strong>in</strong> <strong>the</strong> f<strong>in</strong>al ten years of <strong>the</strong> roll<strong>in</strong>g regressions.<br />
Interactions Among <strong>Specification</strong> Choices<br />
An important difference between <strong>the</strong> Roberts <strong>and</strong> Triangle approaches is <strong>the</strong> Roberts<br />
assumption that <strong>the</strong> NAIRU is constant. Figure 10 displays <strong>the</strong> different evolution of <strong>the</strong> PC<br />
coefficient <strong>in</strong> alternative regressions <strong>in</strong> which <strong>the</strong> NAIRU is assumed to be constant vs. timevary<strong>in</strong>g.<br />
The two l<strong>in</strong>es <strong>in</strong> Figure 10 correspond to l<strong>in</strong>es 21 <strong>and</strong> 24 <strong>in</strong> Table 3. As shown <strong>in</strong><br />
Figure 10 <strong>the</strong> PC coefficient is substantially more volatile when <strong>the</strong> NAIRU is assumed to be
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 28<br />
constant than when it is allowed to vary. The volatility of <strong>the</strong> fixed‐NAIRU coefficient is not<br />
surpris<strong>in</strong>g, s<strong>in</strong>ce some of <strong>the</strong> movements <strong>in</strong> <strong>the</strong> TV‐NAIRU are “substitutes” for <strong>the</strong> movements<br />
of <strong>the</strong> PC coefficient. The basic triangle specification with <strong>the</strong> TV‐NAIRU ra<strong>the</strong>r than a constant<br />
NAIRU leaves open <strong>the</strong> question of why <strong>the</strong> NAIRU changed but yields coefficients that are<br />
more stable over time.<br />
V. Properties of a Four‐Equation Macro Model<br />
The rest of this paper develops a small econometric model to assess <strong>the</strong> role of changes<br />
<strong>in</strong> dem<strong>and</strong> <strong>and</strong> supply shocks <strong>and</strong> <strong>in</strong> monetary policy as causes of reduced bus<strong>in</strong>ess‐cycle<br />
volatility dur<strong>in</strong>g <strong>the</strong> post‐1983 period. Our approach differs from that of Blanchard‐Simon<br />
(2001), who called attention to many of <strong>the</strong> same factors, <strong>in</strong>clud<strong>in</strong>g <strong>the</strong> correlation between<br />
output <strong>and</strong> <strong>in</strong>flation volatility (displayed <strong>in</strong> Figure 3 above), but who did not develop an<br />
econometric model to quantify <strong>the</strong> exact role of <strong>the</strong> different causes. Our approach is closer to<br />
that of Stock‐Watson (2002, 2003), who used several different macroeconometric models to<br />
assess <strong>the</strong> role of less volatile shocks.<br />
Like Stock‐Watson (S‐W)’s “SVAR” model (2002, p. 154), our model conta<strong>in</strong>s equations<br />
for <strong>the</strong> <strong>in</strong>flation rate, <strong>the</strong> short‐term <strong>in</strong>terest rate follow<strong>in</strong>g a Taylor rule specification, <strong>and</strong><br />
output (what S‐W call <strong>the</strong> “IS” equation). However, we go beyond Stock‐Watson <strong>in</strong> our<br />
specification of <strong>the</strong> <strong>in</strong>flation process. Their SVAR model subsumes all of <strong>the</strong> supply shocks <strong>in</strong><br />
<strong>the</strong> <strong>in</strong>flation equation <strong>in</strong>to <strong>the</strong> error term, as <strong>in</strong> <strong>the</strong> NKPC specification used by Roberts.<br />
Instead, we use <strong>the</strong> triangle <strong>in</strong>flation specification described <strong>and</strong> tested above <strong>in</strong> order to
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 29<br />
identify <strong>the</strong> role <strong>the</strong> supply shocks <strong>in</strong> achiev<strong>in</strong>g <strong>the</strong> stabilization of both <strong>in</strong>flation <strong>and</strong> output.<br />
The model developed <strong>in</strong> this paper starts with <strong>the</strong> <strong>in</strong>flation equation developed above<br />
<strong>and</strong> adds three extra equations, two of which are similar to those <strong>in</strong> <strong>the</strong> Stock‐Watson SVAR<br />
model <strong>and</strong> <strong>in</strong> <strong>the</strong> three‐equation model developed by Roberts. In addition to <strong>the</strong> <strong>in</strong>flation<br />
equation, <strong>the</strong> second equation expla<strong>in</strong>s <strong>the</strong> nom<strong>in</strong>al Federal funds rate as respond<strong>in</strong>g to <strong>the</strong><br />
output gap <strong>and</strong> to deviations of actual <strong>in</strong>flation from <strong>the</strong> Fed’s <strong>in</strong>flation target. Then <strong>the</strong> third<br />
equation makes <strong>the</strong> change <strong>in</strong> <strong>the</strong> output gap a function of lagged <strong>in</strong>flation <strong>and</strong> <strong>the</strong> change <strong>in</strong><br />
<strong>the</strong> Federal funds rate. S<strong>in</strong>ce <strong>the</strong> triangle <strong>in</strong>flation equation is specified with <strong>the</strong><br />
unemployment gap ra<strong>the</strong>r than <strong>the</strong> output gap as its dem<strong>and</strong>‐side variable, we add a fourth<br />
equation that l<strong>in</strong>ks <strong>the</strong> unemployment gap to current <strong>and</strong> lagged values of <strong>the</strong> output gap.<br />
Us<strong>in</strong>g a notation that is consistent with <strong>the</strong> treatment of <strong>in</strong>flation above, <strong>the</strong> four‐equation<br />
model can be written:<br />
pt = a(L)pt‐1 + b(L)(Ut‐U N t ) + c(L)zt + ept . (8)<br />
Ft = R* + p* + d(L)(pt ‐ p*) + f(L)Gt + eFt . (9)<br />
∆Gt = h(L))pt‐1 + j(L))Ft + egt . (10)<br />
Ut‐U N t = k(L)Gt + eUt . (11)<br />
The <strong>Phillips</strong> <strong>Curve</strong> equation (8) is identical to that written above as equation (6). The Taylor<br />
rule equation (9) for <strong>the</strong> nom<strong>in</strong>al Federal Funds rate (F) <strong>in</strong>cludes <strong>the</strong> Fed’s target for <strong>the</strong> real
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 30<br />
funds rate (R*), its target for <strong>the</strong> <strong>in</strong>flation rate (p*), a response <strong>in</strong>clud<strong>in</strong>g possible lags to <strong>the</strong><br />
deviation of <strong>the</strong> actual <strong>in</strong>flation rate from <strong>the</strong> <strong>in</strong>flation target, <strong>and</strong> a response <strong>in</strong>clud<strong>in</strong>g possible<br />
lags to <strong>the</strong> level of <strong>the</strong> output gap (G), which <strong>in</strong> turn is <strong>the</strong> log ratio of actual to natural real GDP<br />
as plotted above <strong>in</strong> <strong>the</strong> top frame of Figure 2.. The output gap or “IS” equation (10) makes <strong>the</strong><br />
change <strong>in</strong> <strong>the</strong> gap ∆G a function of one or more lags of <strong>the</strong> first difference of <strong>the</strong> <strong>in</strong>flation rate<br />
<strong>and</strong> of <strong>the</strong> change <strong>in</strong> <strong>the</strong> nom<strong>in</strong>al Federal Funds <strong>in</strong>terest rate. F<strong>in</strong>ally, <strong>the</strong> Okun’s law equation<br />
(11) makes <strong>the</strong> level of <strong>the</strong> unemployment gap depend on <strong>the</strong> current value <strong>and</strong> one or more<br />
lags of <strong>the</strong> output gap.<br />
Much of <strong>the</strong> literature on Taylor Rule equations like (9) <strong>in</strong>cludes a correction for firstorder<br />
serial correlation. If we make <strong>the</strong> error term <strong>in</strong> (9) follow an AR(1) process:<br />
eFt = ρeFt‐1 +uFt, uFt~N(0,s). (12)<br />
<strong>the</strong>n equation (9) is replaced by<br />
Ft = ρFt‐1 + (1‐ρ)[R* + p* + d(L)(pt ‐ p*) + f(L)Gt] + uFt . (13)<br />
The Roberts (2006, p. 203) specification for <strong>the</strong> Taylor Rule is identical to (13) except for <strong>the</strong><br />
exclusion of lagged terms on <strong>in</strong>flation <strong>and</strong> <strong>the</strong> output gap, <strong>and</strong> for <strong>the</strong> statement of <strong>the</strong> target<br />
nom<strong>in</strong>al <strong>in</strong>terest rate as R* + pt ra<strong>the</strong>r than R* + p* as <strong>in</strong> (13). This means <strong>in</strong> practice that a sum<br />
of <strong>the</strong> d coefficients <strong>in</strong> (13) of 1.0 is equivalent to a sum for Roberts of 0.0.<br />
Estimated Coefficients of <strong>the</strong> Four‐Equation Model<br />
The columns of Table 4 list <strong>the</strong> four dependent variables <strong>in</strong> <strong>the</strong> model, with <strong>the</strong> middle<br />
columns provid<strong>in</strong>g alternative sets of results for <strong>the</strong> <strong>in</strong>terest rate equation. The choice of <strong>the</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 31<br />
three sub‐<strong>in</strong>tervals reflects apparent changes <strong>in</strong> Fed reactions correspond<strong>in</strong>g roughly to <strong>the</strong><br />
three periods identified by Stock‐Watson (2003, Table 5), divided up <strong>in</strong> 1979:Q2 at <strong>the</strong> start of<br />
<strong>the</strong> Volcker period <strong>and</strong> <strong>in</strong> 1990:Q2 at end of <strong>the</strong> period <strong>in</strong> which <strong>the</strong> Fed appeared to fight<br />
<strong>in</strong>flation aggressively while ignor<strong>in</strong>g output deviations.<br />
The first column of Table 4 exhibits coefficients <strong>in</strong> <strong>the</strong> <strong>in</strong>flation equation for <strong>the</strong> PCE<br />
deflator, which is identical to <strong>the</strong> equation already discussed <strong>in</strong> <strong>the</strong> first column of Table 2. The<br />
three middle columns show estimated Taylor rule equations for three periods split <strong>in</strong> 1979 <strong>and</strong><br />
1990. As a shorth<strong>and</strong>, we will refer to <strong>the</strong> three sub‐<strong>in</strong>tervals respectively as <strong>the</strong> “Burns,”<br />
“Volcker,” <strong>and</strong> “Greenspan‐Bernanke” responses. These coefficients show that before 1979 <strong>the</strong><br />
Burns Fed “accommodated” <strong>in</strong>flation, rais<strong>in</strong>g <strong>the</strong> nom<strong>in</strong>al <strong>in</strong>terest rate by only 0.64 of any<br />
<strong>in</strong>crease <strong>in</strong> <strong>the</strong> <strong>in</strong>flation rate, hence reduc<strong>in</strong>g <strong>the</strong> real <strong>in</strong>terest rate <strong>and</strong> stimulat<strong>in</strong>g dem<strong>and</strong>.<br />
After 1979 <strong>the</strong> <strong>in</strong>flation response jumped from 0.64 to 1.57, so that <strong>the</strong> Volcker Fed raised <strong>the</strong><br />
nom<strong>in</strong>al Federal funds rate more than <strong>the</strong> <strong>in</strong>crease of <strong>in</strong>flation above its target ra<strong>the</strong>r than less.<br />
Fur<strong>the</strong>r, <strong>the</strong> Volcker Fed did not respond at all to <strong>the</strong> output gap. The Greenspan‐Bernanke Fed<br />
actually responded less to <strong>in</strong>flation than <strong>the</strong> Burns Fed <strong>and</strong> put a slightly higher weight on<br />
output stabilization than <strong>the</strong> Burns Fed. This surpris<strong>in</strong>g f<strong>in</strong>d<strong>in</strong>g that <strong>the</strong> Greenspan‐Bernanke<br />
Fed accommodated <strong>in</strong>flation may be an artifact of <strong>the</strong> low volatility of <strong>in</strong>flation dur<strong>in</strong>g <strong>the</strong>ir<br />
regime, as displayed above <strong>in</strong> Figure 3.<br />
The “IS” equation for <strong>the</strong> first difference of <strong>the</strong> output gap, shown <strong>in</strong> <strong>the</strong> next‐to‐last<br />
column of Table 5, shows an <strong>in</strong>significant positive response to <strong>the</strong> first difference of <strong>the</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 32<br />
<strong>in</strong>flation rate, suggest<strong>in</strong>g no direct feedback from a sharp <strong>in</strong>crease of <strong>in</strong>flation to a sharp<br />
decrease <strong>in</strong> output as might have been suggested by <strong>the</strong> economy’s behavior <strong>in</strong> <strong>the</strong> 1970s. The<br />
responses to changes <strong>in</strong> <strong>the</strong> nom<strong>in</strong>al Federal funds rate are of plausible size <strong>and</strong> highly<br />
significant; an <strong>in</strong>crease <strong>in</strong> <strong>the</strong> funds rate by 100 basis po<strong>in</strong>ts causes a decl<strong>in</strong>e <strong>in</strong> <strong>the</strong> output gap<br />
by one percentage po<strong>in</strong>t with a long lag distributed over <strong>the</strong> next 10 quarters. 18 The f<strong>in</strong>al<br />
column <strong>in</strong> Table 5 exhibits <strong>the</strong> Okun’s Law equation, show<strong>in</strong>g that <strong>the</strong> unemployment gap<br />
responds to <strong>the</strong> output gap over <strong>the</strong> current <strong>and</strong> first two lagged quarters with a highly<br />
significant coefficient of ‐0.49, support<strong>in</strong>g <strong>the</strong> 2‐to‐1 responsiveness of <strong>the</strong> output gap to <strong>the</strong><br />
unemployment gap endorsed by research over <strong>the</strong> past 40 years <strong>in</strong> place of <strong>the</strong> 3‐to‐1<br />
responsiveness orig<strong>in</strong>ally discovered by Okun.<br />
S<strong>in</strong>gle‐Equation Model Simulations<br />
The aim of build<strong>in</strong>g <strong>the</strong> model is to use it to decompose <strong>the</strong> sources of bus<strong>in</strong>ess cycle<br />
volatility. For this purpose we will focus on three different sources of volatility <strong>and</strong> its post‐<br />
1983 reduction, namely set of supply shocks <strong>in</strong>cluded <strong>in</strong> <strong>the</strong> <strong>in</strong>flation equation, <strong>the</strong> error term <strong>in</strong><br />
<strong>the</strong> output gap equation, <strong>and</strong> shifts <strong>in</strong> <strong>the</strong> parameters <strong>in</strong> <strong>the</strong> <strong>in</strong>terest rate equation that reflect<br />
changes <strong>in</strong> Fed policy. 19 In this section we will exam<strong>in</strong>e <strong>the</strong> performance of each equation<br />
18. The current <strong>and</strong> first lags of <strong>the</strong> <strong>in</strong>terest rate are omitted <strong>in</strong> <strong>the</strong> output gap equation because of<br />
simultaneity; <strong>in</strong> <strong>the</strong> short‐run changes <strong>in</strong> output <strong>and</strong> <strong>in</strong>terest rates tend to be positively correlated as “IS<br />
shifts” move <strong>the</strong> economy along <strong>the</strong> “LM curve.” We use <strong>the</strong> nom<strong>in</strong>al ra<strong>the</strong>r than real <strong>in</strong>terest rate<br />
because it fits better, perhaps reflect<strong>in</strong>g <strong>the</strong> role of nom<strong>in</strong>al <strong>in</strong>terest rate ceil<strong>in</strong>gs before 1980.<br />
19. No attention is paid to errors <strong>in</strong> <strong>the</strong> Okun’s law equation, which is viewed here as a purely<br />
mechanical bridge between <strong>the</strong> output <strong>and</strong> unemployment gaps. Fur<strong>the</strong>r, because of <strong>the</strong> large role of <strong>the</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 33<br />
without model <strong>in</strong>teractions; that is, each equation’s predicted values are exam<strong>in</strong>ed us<strong>in</strong>g actual<br />
historical values for <strong>the</strong> endogenous explanatory variables. Subsequently we will exam<strong>in</strong>e<br />
simulations that feed back simulated values of <strong>the</strong> endogenous variables.<br />
Figure 11 displays a dynamic simulation of <strong>the</strong> PCE deflator for <strong>the</strong> period 1965:Q1‐<br />
2006:Q4 <strong>in</strong> which <strong>the</strong> coefficients are estimated through 2006 but <strong>the</strong> lagged dependent variable<br />
is fed back endogenously. One simulation uses <strong>the</strong> actual values of <strong>the</strong> supply‐shock variables;<br />
<strong>the</strong> o<strong>the</strong>r sets <strong>the</strong> values of all <strong>the</strong> supply shock variables equal to zero but reta<strong>in</strong>s <strong>the</strong> actual<br />
historical values of <strong>the</strong> unemployment gap. Simulated <strong>in</strong>flation with no supply shocks rema<strong>in</strong>s<br />
roughly equal to <strong>the</strong> full‐shock simulation through early 1973 <strong>and</strong> <strong>the</strong>n stays consistently below<br />
<strong>the</strong> full‐shock simulation by a large amount through 2006. S<strong>in</strong>ce <strong>the</strong> only variable driv<strong>in</strong>g an<br />
acceleration or deceleration of <strong>in</strong>flation is <strong>the</strong> unemployment gap, <strong>the</strong> severe recessions of 1974‐<br />
75 <strong>and</strong> 1981‐82 cause marked decl<strong>in</strong>es <strong>in</strong> <strong>the</strong> <strong>in</strong>flation rate, send<strong>in</strong>g it close to zero <strong>in</strong> 1984‐5 <strong>and</strong><br />
aga<strong>in</strong> <strong>in</strong> 1994‐95. Notice that <strong>the</strong> difference between <strong>the</strong> two simulations narrows <strong>in</strong> <strong>the</strong> late<br />
1990s, s<strong>in</strong>ce <strong>the</strong> full‐shock simulated value of <strong>in</strong>flation fails to accelerate <strong>in</strong> 1995‐2001, due to <strong>the</strong><br />
role of beneficial supply shocks that provided <strong>the</strong> Greenspan Fed with good luck <strong>and</strong> enabled it<br />
to avoid rais<strong>in</strong>g <strong>the</strong> Fed funds rate as it had <strong>in</strong> 1987‐89.<br />
We now turn to <strong>the</strong> s<strong>in</strong>gle‐equation behavior of <strong>the</strong> <strong>in</strong>terest rate equation, tak<strong>in</strong>g its<br />
explanatory variables as exogenous. All <strong>the</strong> simulations <strong>in</strong> this paper assume that <strong>the</strong> <strong>in</strong>flation<br />
target (p*) <strong>in</strong> equation (6) is 2.0 percent <strong>and</strong> that <strong>the</strong> real <strong>in</strong>terest rate target (R*) is 3.0 percent.<br />
lagged <strong>in</strong>terest rate variable <strong>in</strong> <strong>the</strong> Taylor Rule equation (13), <strong>the</strong> <strong>in</strong>terest rate errors are small <strong>and</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 34<br />
As <strong>in</strong> Table 4, <strong>the</strong> coefficients on <strong>in</strong>flation <strong>and</strong> <strong>the</strong> output gap are allowed to shift at 1979 <strong>and</strong><br />
1990. The fitted values of <strong>the</strong> equation are extremely close to <strong>the</strong> actual values, which is no<br />
surprise <strong>in</strong> light of <strong>the</strong> correction for serial correlation, <strong>and</strong> <strong>the</strong>re is no need to plot <strong>the</strong>m.<br />
The central topic of this paper is <strong>the</strong> contribution of <strong>the</strong> <strong>Phillips</strong> <strong>Curve</strong> specification to<br />
expla<strong>in</strong><strong>in</strong>g <strong>the</strong> reduced volatility of <strong>the</strong> output gap, as already exam<strong>in</strong>ed above <strong>in</strong> <strong>the</strong> two<br />
frames of Figure 2. The predictive performance of <strong>the</strong> output gap equation is shown <strong>in</strong> Figure<br />
12. While <strong>the</strong> equation is estimated <strong>in</strong> first difference form, <strong>the</strong> actual <strong>and</strong> predicted values of<br />
<strong>the</strong> first differences are converted back to <strong>the</strong> level of <strong>the</strong> output gap for graph<strong>in</strong>g <strong>in</strong> Figure 12. 20<br />
Clearly, <strong>the</strong> output gap has a life of its own that is not captured by <strong>the</strong> simple “IS” equation.<br />
The output gap equation predicts a much smaller recession <strong>in</strong> 1974‐75 than actually occurred.<br />
The equation’s predictions overstate <strong>the</strong> severity of <strong>the</strong> 1980‐85 slump <strong>and</strong> also fail to capture<br />
<strong>the</strong> output gap’s rise above zero <strong>in</strong> <strong>the</strong> late 1980s. Fur<strong>the</strong>r, <strong>the</strong> predicted values completely miss<br />
<strong>the</strong> tim<strong>in</strong>g of <strong>the</strong> ups <strong>and</strong> downs of <strong>the</strong> output gap after 1990.<br />
These errors <strong>in</strong> <strong>the</strong> output gap equation are not bad news for <strong>the</strong> model. Ra<strong>the</strong>r, <strong>the</strong>y<br />
rem<strong>in</strong>d us that output determ<strong>in</strong>ation depends on far more than movements back <strong>and</strong> forth<br />
along <strong>the</strong> slope of a fixed IS curve, as is implied by our model (based <strong>in</strong> turn on <strong>the</strong> Stock‐<br />
Watson SVAR) which makes changes <strong>in</strong> <strong>in</strong>terest rates <strong>the</strong> only significant source of changes <strong>in</strong><br />
<strong>the</strong> output gap. Obviously shifts <strong>in</strong> <strong>the</strong> IS curve matter as well, <strong>and</strong> it would take a much more<br />
un<strong>in</strong>terest<strong>in</strong>g.<br />
20. The errors <strong>in</strong> <strong>the</strong> first difference equation are translated <strong>in</strong>to errors <strong>in</strong> <strong>the</strong> level of <strong>the</strong> output gap by
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 35<br />
complex model to capture <strong>the</strong> sources of <strong>the</strong>se IS shifts. Miss<strong>in</strong>g from <strong>the</strong> predictions of <strong>the</strong><br />
output gap equation <strong>in</strong> Figure 10 are such important events as Vietnam war spend<strong>in</strong>g <strong>in</strong> <strong>the</strong> late<br />
1960s <strong>and</strong> <strong>the</strong> tim<strong>in</strong>g of <strong>the</strong> hi‐tech <strong>in</strong>vestment boom of <strong>the</strong> late 1990s. In <strong>the</strong> full‐model<br />
simulations discussed below we will explore <strong>the</strong> effects of suppress<strong>in</strong>g <strong>the</strong> error term <strong>in</strong> <strong>the</strong><br />
output equation. Our <strong>in</strong>terpretation of <strong>the</strong> output gap error is based on Gordon (2005), <strong>in</strong><br />
which three ma<strong>in</strong> forces drive <strong>the</strong> <strong>in</strong>creased stabilization of <strong>the</strong> output gap error term – <strong>the</strong><br />
reduced share <strong>and</strong> volatility of government military spend<strong>in</strong>g, <strong>the</strong> <strong>in</strong>creased stability of<br />
<strong>in</strong>ventory <strong>in</strong>vestment, <strong>and</strong> f<strong>in</strong>ancial reforms that reduced <strong>the</strong> volatility of residential structures<br />
<strong>in</strong>vestment. 21<br />
Table 5 summarizes <strong>the</strong> s<strong>in</strong>gle‐equation results. The top four l<strong>in</strong>es calculate st<strong>and</strong>ard<br />
deviations of <strong>the</strong> actual values of <strong>the</strong> <strong>in</strong>flation rate, Federal funds rate, <strong>and</strong> level <strong>and</strong> first<br />
difference of <strong>the</strong> output gap. The reported st<strong>and</strong>ard deviations for <strong>the</strong> actual <strong>in</strong>flation rate <strong>and</strong><br />
output gap are similar to those <strong>in</strong> our text discussions of Figures 2 <strong>and</strong> 3 above, with a decl<strong>in</strong>e<br />
<strong>in</strong> <strong>the</strong> st<strong>and</strong>ard deviation of <strong>the</strong> output gap <strong>and</strong> <strong>in</strong>flation of about 76 percent <strong>in</strong> logs. In contrast<br />
<strong>the</strong> volatility of <strong>the</strong> <strong>in</strong>terest rate decl<strong>in</strong>ed by much less, about 40 percent <strong>in</strong> logs.<br />
How well do <strong>the</strong> simulations (for <strong>the</strong> <strong>in</strong>flation equation) <strong>and</strong> predicted values (for <strong>the</strong><br />
o<strong>the</strong>r equations) replicate <strong>the</strong> lower st<strong>and</strong>ard deviations of <strong>the</strong> actual values? Simulated<br />
<strong>in</strong>flation falls by 81 percent, slightly more than <strong>the</strong> actual value, <strong>and</strong> simulated <strong>in</strong>flation decl<strong>in</strong>es<br />
forc<strong>in</strong>g <strong>the</strong> level errors to have a mean of zero over <strong>the</strong> 1965‐2004 period.<br />
21. The role of f<strong>in</strong>ancial market reforms <strong>in</strong> achiev<strong>in</strong>g reduced volatility has been studied <strong>in</strong> detail by<br />
Dynan, Elmendorf, <strong>and</strong> Sichel (2005).
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 36<br />
by a smaller 61 percent when supply shock variables are excluded. However, as we have seen<br />
<strong>in</strong> Figure 11 above, much of <strong>the</strong> pre‐1984 <strong>in</strong>flation volatility <strong>in</strong> <strong>the</strong> “no‐shocks” scenario is due<br />
to <strong>the</strong> role of deep recessions <strong>in</strong> forc<strong>in</strong>g <strong>in</strong>flation much lower than <strong>the</strong> actual outcome. A full<br />
underst<strong>and</strong><strong>in</strong>g of <strong>the</strong> role of supply shocks requires us to unleash <strong>the</strong> full set of model<br />
<strong>in</strong>teractions, s<strong>in</strong>ce without supply shocks <strong>in</strong> <strong>the</strong> 1970s <strong>the</strong>re would not have been <strong>the</strong> spikes of<br />
<strong>the</strong> <strong>in</strong>terest rate <strong>in</strong> 1981‐82 nor <strong>the</strong> deep recession of 1981‐82.<br />
The s<strong>in</strong>gle‐equation predictions for <strong>the</strong> Federal funds rate differ from <strong>the</strong> o<strong>the</strong>r<br />
equations because <strong>the</strong> error term is so small, virtually elim<strong>in</strong>ated by <strong>the</strong> serial correlation<br />
correction. The predicted value for <strong>the</strong> <strong>in</strong>terest rate has a decl<strong>in</strong>e <strong>in</strong> its st<strong>and</strong>ard deviation of 37<br />
percent <strong>in</strong> Table 5, very similar to <strong>the</strong> actual decl<strong>in</strong>e of 41 percent. The output gap equation<br />
yields a predicted value that has a decl<strong>in</strong>e <strong>in</strong> its st<strong>and</strong>ard deviation of 55 percent, much less<br />
than <strong>the</strong> actual 76 percent decl<strong>in</strong>e. Elim<strong>in</strong>at<strong>in</strong>g <strong>the</strong> error term <strong>in</strong> <strong>the</strong> output gap equation cuts<br />
<strong>the</strong> st<strong>and</strong>ard deviation by half before 1984 <strong>and</strong> by about 40 percent after 1984, <strong>in</strong>dicat<strong>in</strong>g that a<br />
reduction <strong>in</strong> <strong>the</strong> variance of <strong>the</strong> output error contributed to bus<strong>in</strong>ess cycle stabilization after<br />
1983.<br />
Full‐Model Simulations<br />
To assess <strong>the</strong> role <strong>in</strong> achiev<strong>in</strong>g reduced bus<strong>in</strong>ess‐cycle volatility of supply shocks <strong>in</strong> <strong>the</strong><br />
<strong>in</strong>flation equation, <strong>and</strong> of <strong>the</strong> error term <strong>in</strong> <strong>the</strong> output gap equation, we run full model<br />
simulations with alternative shocks set equal to zero, one at a time <strong>and</strong> <strong>the</strong>n all toge<strong>the</strong>r. Table<br />
6 conta<strong>in</strong>s five sections, one each for <strong>the</strong> st<strong>and</strong>ard deviation of <strong>in</strong>flation, of <strong>the</strong> <strong>in</strong>terest rate, <strong>and</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 37<br />
of <strong>the</strong> output gap, <strong>the</strong>n <strong>the</strong> average value of <strong>in</strong>flation <strong>and</strong> <strong>the</strong> average absolute value of <strong>the</strong><br />
output gap. With<strong>in</strong> each section <strong>the</strong>re are four l<strong>in</strong>es correspond<strong>in</strong>g to <strong>the</strong> full model<br />
simulations <strong>and</strong> alternative simulations that suppress <strong>the</strong> shocks one at a time <strong>and</strong> all toge<strong>the</strong>r.<br />
The contrast between <strong>the</strong> s<strong>in</strong>gle‐equation <strong>and</strong> full‐model simulations can be seen by<br />
compar<strong>in</strong>g Tables 5 <strong>and</strong> 6. Here is <strong>the</strong> log percent change of <strong>the</strong> st<strong>and</strong>ard deviations for 1984‐<br />
2006 relative to 1965‐83 for each of <strong>the</strong> three variables, compar<strong>in</strong>g <strong>the</strong> actual values, <strong>the</strong> s<strong>in</strong>gleequation<br />
simulation values, <strong>and</strong> <strong>the</strong> full‐model simulation values.<br />
Log Percent Ratio of St<strong>and</strong>ard Deviations, 1984‐2004 to 1965‐83<br />
Four‐Quarter<br />
Inflation Rate Interest Rate ∆<strong>Output</strong> Gap<br />
Actual Values ‐76.3 ‐40.9 ‐80.2<br />
S<strong>in</strong>gle‐Equation Simulations ‐80.6 ‐37.0 ‐54.9<br />
Full‐Model Simulations ‐62.9 ‐7.8 ‐49.9<br />
The full‐model simulations share with <strong>the</strong> s<strong>in</strong>gle‐equation simulations that <strong>the</strong>y <strong>in</strong>clude <strong>the</strong><br />
exogenous effects of <strong>the</strong> supply‐shock variables <strong>in</strong> <strong>the</strong> <strong>in</strong>flation equation, as well as <strong>the</strong> error<br />
terms <strong>in</strong> <strong>the</strong> <strong>in</strong>terest rate <strong>and</strong> output gap equations. But <strong>the</strong>y differ <strong>in</strong> that <strong>the</strong>y use endogenous<br />
model‐generated values ra<strong>the</strong>r than exogenous data‐generated values for <strong>the</strong> endogenous<br />
variables <strong>in</strong> each equation. The switch to <strong>the</strong> full model simulations reduces <strong>the</strong> estimated post‐<br />
1983 decl<strong>in</strong>e <strong>in</strong> <strong>the</strong> volatility of all three variables, <strong>the</strong> <strong>in</strong>flation rate, <strong>the</strong> <strong>in</strong>terest rate, <strong>and</strong> <strong>the</strong><br />
change <strong>in</strong> <strong>the</strong> output gap.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 38<br />
Counter‐Factual Full‐Model Simulation Results Supress<strong>in</strong>g Supply <strong>and</strong> Dem<strong>and</strong><br />
Shocks<br />
We can now discuss <strong>the</strong> relative role of <strong>the</strong> supply <strong>and</strong> dem<strong>and</strong> shocks <strong>in</strong> expla<strong>in</strong><strong>in</strong>g <strong>the</strong><br />
model’s simulated volatility of <strong>the</strong> economy. Because of <strong>the</strong> serial correlation correction, errors<br />
<strong>in</strong> <strong>the</strong> <strong>in</strong>terest rate equation play no role <strong>in</strong> <strong>the</strong> explanation. We start with <strong>the</strong> alternative<br />
simulations for <strong>the</strong> <strong>in</strong>flation rate as described <strong>in</strong> <strong>the</strong> top section of Table 6. For <strong>the</strong> first period,<br />
suppress<strong>in</strong>g <strong>the</strong> supply shocks elim<strong>in</strong>ates about two‐thirds of <strong>the</strong> st<strong>and</strong>ard deviation of<br />
<strong>in</strong>flation <strong>in</strong> <strong>the</strong> first period, while suppress<strong>in</strong>g <strong>the</strong> output gap error elim<strong>in</strong>ates about 25 percent<br />
of <strong>the</strong> st<strong>and</strong>ard deviation of <strong>in</strong>flation <strong>in</strong> <strong>the</strong> first period. Suppress<strong>in</strong>g supply shocks reduces <strong>the</strong><br />
second‐period st<strong>and</strong>ard error by about half, but suppress<strong>in</strong>g <strong>the</strong> output error actually raises<br />
volatility as compared to <strong>the</strong> “all shocks” variant.<br />
Figure 13 illustrates <strong>the</strong> role of supply<br />
shocks <strong>and</strong> <strong>the</strong> output error <strong>in</strong> expla<strong>in</strong><strong>in</strong>g <strong>the</strong> behavior of <strong>the</strong> <strong>in</strong>flation rate. The dark solid l<strong>in</strong>e<br />
shows <strong>the</strong> full model simulation, which is virtually identical to <strong>the</strong> s<strong>in</strong>gle‐equation simulation<br />
depicted <strong>in</strong> Figure 11. Suppress<strong>in</strong>g <strong>the</strong> output error reduces <strong>the</strong> <strong>in</strong>flation rate by between three<br />
<strong>and</strong> four percent throughout <strong>the</strong> simulation period. S<strong>in</strong>ce <strong>the</strong> output equation cannot generate<br />
<strong>the</strong> excess dem<strong>and</strong> of <strong>the</strong> late 1960s, without <strong>the</strong> output error <strong>the</strong> model forecasts less <strong>in</strong>flation<br />
throughout <strong>the</strong> full 40‐year simulation period. What rema<strong>in</strong>s when <strong>the</strong> output error is<br />
suppressed represents <strong>the</strong> comb<strong>in</strong>ed contribution of <strong>the</strong> supply shocks, caus<strong>in</strong>g an acceleration<br />
of <strong>in</strong>flation of six percentage po<strong>in</strong>ts between 1972 <strong>and</strong> 1975, <strong>and</strong> a reversal <strong>in</strong> which <strong>in</strong>flation<br />
decelerated by about seven percentage po<strong>in</strong>ts between 1981 <strong>and</strong> 1987. Thus, ironically, <strong>the</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 39<br />
“Volcker dis<strong>in</strong>flation” that has usually been attributed to monetary policy actually should be<br />
credited <strong>in</strong> large part to <strong>the</strong> reversal of supply shocks, not just <strong>the</strong> decl<strong>in</strong>e <strong>in</strong> <strong>the</strong> real price of oil<br />
but also <strong>the</strong> effects of <strong>the</strong> dollar appreciation of 1980‐85.<br />
Turn<strong>in</strong>g to <strong>the</strong> Federal funds rate, Table 6 shows that elim<strong>in</strong>at<strong>in</strong>g supply shocks <strong>in</strong> 1965‐<br />
83 reduces <strong>the</strong> st<strong>and</strong>ard deviation of <strong>the</strong> <strong>in</strong>terest rate by more than one‐third, as does<br />
elim<strong>in</strong>at<strong>in</strong>g <strong>the</strong> output error. In <strong>the</strong> second period supply shocks have no impact <strong>in</strong> reduc<strong>in</strong>g<br />
volatility, but suppress<strong>in</strong>g <strong>the</strong> output error reduces <strong>the</strong> st<strong>and</strong>ard deviation of <strong>the</strong> <strong>in</strong>terest rate by<br />
about one‐third. Thus when we compare 1965‐83 with 1984‐2006, <strong>the</strong>re was a reduction <strong>in</strong> <strong>the</strong><br />
volatility of <strong>the</strong> <strong>in</strong>terest rate by about two‐thirds when <strong>the</strong> effects of both supply shocks <strong>and</strong><br />
output errors are comb<strong>in</strong>ed. Yet, surpris<strong>in</strong>gly, <strong>the</strong> role of <strong>the</strong>se shocks was about <strong>the</strong> same <strong>in</strong><br />
each period so that <strong>the</strong>y contribut<strong>in</strong>g noth<strong>in</strong>g to <strong>the</strong> stabilization of <strong>in</strong>terest rates, as we can see<br />
<strong>in</strong> <strong>the</strong> second section of Table 6 when we compare <strong>the</strong> “All Shocks” <strong>and</strong> “No Shocks” outcomes.<br />
The simulations for <strong>the</strong> <strong>in</strong>terest rate are displayed <strong>in</strong> Figure 14. Due to <strong>the</strong> correction<br />
for serial correlation, suppress<strong>in</strong>g <strong>the</strong> model’s own‐equation <strong>in</strong>terest rate error makes virtually<br />
no difference. Compared to <strong>the</strong> basic model simulation, suppress<strong>in</strong>g <strong>the</strong> supply shocks makes a<br />
big difference <strong>in</strong> hold<strong>in</strong>g down <strong>the</strong> <strong>in</strong>terest rate between 1974 <strong>and</strong> 1985, but after 1985 reduces<br />
<strong>the</strong> <strong>in</strong>terest rate by very little. Suppression of <strong>the</strong> output error also makes a big difference <strong>in</strong><br />
reduc<strong>in</strong>g <strong>the</strong> <strong>in</strong>terest rate throughout <strong>the</strong> 40‐year simulation period, <strong>and</strong> particularly between<br />
1977 <strong>and</strong> 1992. Recall that elim<strong>in</strong>at<strong>in</strong>g <strong>the</strong> output error works directly through <strong>the</strong> output gap<br />
term <strong>in</strong> <strong>the</strong> <strong>in</strong>terest rate equation <strong>and</strong> <strong>in</strong>directly through <strong>the</strong> effect of a lower output gap <strong>in</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 40<br />
reduc<strong>in</strong>g <strong>the</strong> <strong>in</strong>flation rate <strong>and</strong> hence reduc<strong>in</strong>g <strong>the</strong> <strong>in</strong>terest rate through <strong>the</strong> <strong>in</strong>flation term <strong>in</strong> <strong>the</strong><br />
<strong>in</strong>terest rate equation.<br />
The next section of Table 6 for <strong>the</strong> st<strong>and</strong>ard deviation of <strong>the</strong> output gap shows that<br />
about half of <strong>the</strong> volatility of <strong>the</strong> output gap <strong>in</strong> <strong>the</strong> first period was caused by <strong>the</strong> output error<br />
but, surpris<strong>in</strong>gly, none of <strong>the</strong> volatility <strong>in</strong> <strong>the</strong> second period. Suppress<strong>in</strong>g <strong>the</strong> supply shocks<br />
elim<strong>in</strong>ates about one‐third of <strong>the</strong> output gap volatility <strong>in</strong> <strong>the</strong> first period but none <strong>in</strong> <strong>the</strong> second<br />
period.<br />
The Fed’s objective as captured <strong>in</strong> <strong>the</strong> model’s <strong>in</strong>terest rate equation is not <strong>the</strong> st<strong>and</strong>ard<br />
deviation of <strong>the</strong> <strong>in</strong>flation rate but ra<strong>the</strong>r its average value. As for <strong>the</strong> output gap, <strong>the</strong> Fed’s goal is<br />
for <strong>the</strong> output gap to be zero, <strong>and</strong> hence to m<strong>in</strong>imize <strong>the</strong> average absolute value of <strong>the</strong> output<br />
gap. The bottom two sections of Table 6 report on <strong>the</strong> effect of shocks on <strong>the</strong>se two central<br />
objectives of Fed policy.<br />
Suppress<strong>in</strong>g <strong>the</strong> supply shocks would have converted <strong>the</strong> actual decl<strong>in</strong>e <strong>in</strong> <strong>the</strong> average<br />
<strong>in</strong>flation rate across <strong>the</strong> two periods from 5 to 2.2 percent, <strong>in</strong>to an identical 3.2 percent across<br />
both periods. That is, supply shocks were adverse before 1983 <strong>and</strong> beneficial after 1983. Thus<br />
supply shocks are <strong>the</strong> whole story of why <strong>in</strong>flation decl<strong>in</strong>ed by so much after 1984. In contrast<br />
<strong>the</strong> output error made <strong>in</strong>flation higher <strong>in</strong> both periods, <strong>and</strong> with no output error <strong>the</strong> <strong>in</strong>flation<br />
rate would have been negative after 1984.<br />
Overall, both <strong>the</strong> supply shocks <strong>and</strong> <strong>the</strong> output error contributed to <strong>the</strong> high volatility of<br />
<strong>in</strong>flation <strong>and</strong> <strong>the</strong> output gap before 1983, as well as to <strong>the</strong> high average value of <strong>in</strong>flation <strong>and</strong>
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 41<br />
<strong>the</strong> high average absolute value of <strong>the</strong> output gap. Suppress<strong>in</strong>g <strong>the</strong> supply shocks makes <strong>the</strong><br />
economy’s behavior <strong>in</strong> <strong>the</strong> first period similar to its behavior <strong>in</strong> <strong>the</strong> second period, thus<br />
elim<strong>in</strong>at<strong>in</strong>g <strong>the</strong> puzzle of reduced volatility, <strong>and</strong> <strong>in</strong> fact suppress<strong>in</strong>g <strong>the</strong> supply shocks makes<br />
average <strong>in</strong>flation <strong>in</strong> <strong>the</strong> second period slightly higher than <strong>in</strong> <strong>the</strong> first period. Suppress<strong>in</strong>g <strong>the</strong><br />
output error makes <strong>the</strong> economy more stable <strong>and</strong> <strong>in</strong>flation lower <strong>in</strong> both periods. Without <strong>the</strong><br />
output shocks, <strong>the</strong> output gap would have been much smaller <strong>and</strong> less volatile <strong>in</strong> both periods,<br />
<strong>and</strong> without <strong>the</strong> output error we still would have had a puzzle of improved post‐1983 volatility<br />
that would have been resolved by <strong>the</strong> role of <strong>the</strong> supply shocks.<br />
VI.<br />
What Difference does PC <strong>Specification</strong> Make to Full‐Model Conclusions?<br />
This paper has placed primary emphasis on <strong>the</strong> contrast between <strong>the</strong> Roberts version of<br />
<strong>the</strong> NKPC <strong>and</strong> <strong>the</strong> alternative triangle model, which performs with orders of magnitude better<br />
<strong>in</strong> both st<strong>and</strong>ard goodness of fit measures <strong>and</strong> also <strong>in</strong> post‐sample dynamic simulations. We<br />
now ask how much difference <strong>the</strong> use of <strong>the</strong> triangle vs. Roberts <strong>in</strong>flation equation makes <strong>in</strong> <strong>the</strong><br />
evaluation of <strong>the</strong> sources of reduced bus<strong>in</strong>ess cycle volatility s<strong>in</strong>ce 1984.<br />
Table 7 is arranged with <strong>the</strong> same five vertical sections as we have already exam<strong>in</strong>ed <strong>in</strong><br />
Table 6. In each section <strong>the</strong>re are four rows, so that we may contrast <strong>the</strong> impact <strong>in</strong> <strong>the</strong> triangle<br />
model of omitt<strong>in</strong>g <strong>the</strong> set of supply shock variables, with <strong>the</strong> Roberts model where <strong>the</strong><br />
analogous exercise is to elim<strong>in</strong>ate <strong>the</strong> error term <strong>in</strong> his <strong>in</strong>flation equation. In <strong>the</strong> next version of<br />
this paper, we will add an extra l<strong>in</strong>e for <strong>the</strong> triangle version to omit both <strong>the</strong> set of supply shock
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 42<br />
variables <strong>and</strong> <strong>the</strong> error term <strong>in</strong> <strong>the</strong> triangle equation. An important caveat <strong>in</strong> Table 7 is that <strong>the</strong><br />
only difference between <strong>the</strong> Roberts <strong>and</strong> triangle results refer to <strong>the</strong> <strong>in</strong>flation equation. The<br />
<strong>in</strong>terest rate, output gap, <strong>and</strong> unemployment gap equations <strong>in</strong> our basic model are used<br />
throughout <strong>in</strong> deriv<strong>in</strong>g <strong>the</strong> results of Table 7.<br />
The top section of Table 7 shows that remov<strong>in</strong>g <strong>the</strong> explicit supply shock variables from<br />
<strong>the</strong> triangle model reduces <strong>the</strong> st<strong>and</strong>ard deviation of <strong>in</strong>flation much more before 1984 than after<br />
1983. Thus <strong>the</strong> supply shocks cont<strong>in</strong>ue to expla<strong>in</strong> most of <strong>the</strong> changed volatility of <strong>in</strong>flation<br />
after 1983. The third <strong>and</strong> fourth l<strong>in</strong>e of <strong>the</strong> top section substitute <strong>the</strong> Roberts approach. While<br />
<strong>the</strong> Roberts equation yields <strong>the</strong> same decl<strong>in</strong>e <strong>in</strong> volatility after 1984, its diagnostic ability is<br />
impaired. Remov<strong>in</strong>g <strong>the</strong> error term <strong>in</strong> <strong>the</strong> Roberts equation yields a much higher 1.48 st<strong>and</strong>ard<br />
deviation than with <strong>the</strong> triangle approach (0.82 st<strong>and</strong>ard deviation), <strong>and</strong> <strong>the</strong> Roberts equation<br />
without <strong>the</strong> error term suggests that <strong>the</strong> st<strong>and</strong>ard deviation of <strong>in</strong>flation should have <strong>in</strong>creased<br />
after 1983.<br />
The next section of Table 7 shows that <strong>the</strong> triangle <strong>and</strong> Roberts PC specifications reach a<br />
similar conclusion. Suppress<strong>in</strong>g <strong>the</strong> triangle supply shocks imply that <strong>in</strong>terest rate volatility<br />
would have been higher post‐1984, <strong>and</strong> <strong>the</strong> suppression of <strong>the</strong> error term <strong>in</strong> <strong>the</strong> Roberts PC<br />
equation yields <strong>the</strong> same conclusion, although by a smaller amount.<br />
An important difference between <strong>the</strong> triangle <strong>and</strong> Roberts results appears <strong>in</strong> <strong>the</strong> third<br />
section of Table 7, where we exam<strong>in</strong>e <strong>the</strong> effect of alternative <strong>in</strong>flation equations <strong>in</strong> expla<strong>in</strong><strong>in</strong>g<br />
changes <strong>in</strong> <strong>the</strong> st<strong>and</strong>ard deviation of <strong>the</strong> output gap. In <strong>the</strong> triangle model remov<strong>in</strong>g <strong>the</strong> supply
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 43<br />
shocks removes about 1/3 of output volatility <strong>in</strong> <strong>the</strong> pre‐1984 period <strong>and</strong> noth<strong>in</strong>g after 1984.<br />
Thus <strong>the</strong> supply shock variables <strong>in</strong> <strong>the</strong> triangle PC equation expla<strong>in</strong> a substantial part of <strong>the</strong><br />
reduction <strong>in</strong> output volatility after 1983.<br />
The results with <strong>the</strong> Roberts <strong>in</strong>flation equation <strong>in</strong> <strong>the</strong> multi‐equation model for <strong>the</strong><br />
st<strong>and</strong>ard deviation of <strong>the</strong> output gap can be dismissed as perverse. With <strong>the</strong> <strong>in</strong>flation error <strong>in</strong><br />
its own PC equation, <strong>the</strong> Roberts model cannot expla<strong>in</strong> any of <strong>the</strong> st<strong>and</strong>ard deviation of <strong>the</strong><br />
output gap before or after 1984. Omitt<strong>in</strong>g <strong>the</strong> <strong>in</strong>flation error leaves <strong>the</strong> Roberts <strong>in</strong>flation model<br />
clueless as to why <strong>the</strong> actual st<strong>and</strong>ard deviation of <strong>in</strong>flation decl<strong>in</strong>ed after 1984.<br />
VI. Conclusion<br />
This paper began with <strong>the</strong> journalistic characterization of <strong>the</strong> Fed’s view that <strong>the</strong> slope of<br />
<strong>the</strong> United States <strong>Phillips</strong> <strong>Curve</strong> (PC) has become substantially flatter, by a factor of at least half,<br />
s<strong>in</strong>ce <strong>the</strong> mid‐1980s. The flatten<strong>in</strong>g of <strong>the</strong> <strong>Phillips</strong> curve is documented <strong>in</strong> a particular style of<br />
PC research based on <strong>the</strong> New Keynesian <strong>Phillips</strong> <strong>Curve</strong> (NKPC) literature, <strong>in</strong> which PC<br />
specifications <strong>in</strong>volve l<strong>in</strong>ks between <strong>the</strong> current <strong>in</strong>flation rate <strong>and</strong> short lags on <strong>in</strong>flation, <strong>and</strong> on<br />
<strong>the</strong> current unemployment rate. The first part of this paper uses a wide variety of statistical<br />
tests to show that <strong>the</strong> Fed’s PC equation as based on research by Roberts (2006) is strongly<br />
rejected both by traditional <strong>and</strong> nontraditional tests when compared to <strong>the</strong> Gordon “triangle”<br />
model that was developed <strong>in</strong> <strong>the</strong> early 1980s.<br />
The rema<strong>in</strong>der of <strong>the</strong> paper asks why <strong>the</strong> volatility of output changes <strong>and</strong> <strong>the</strong> output<br />
gap has decl<strong>in</strong>ed substantially after 1984, a phenomenon on which U. S. macroeconomists share
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 44<br />
an unusual consensus about its existence but not about its causes. Our analysis based on a<br />
small macroeconometric model concludes that about 1/3 of <strong>the</strong> reduction <strong>in</strong> <strong>the</strong> volatility of real<br />
GDP can be traced to <strong>the</strong> role of supply shocks <strong>in</strong> <strong>the</strong> triangle <strong>in</strong>flation equation. More<br />
important are errors <strong>in</strong> <strong>the</strong> output gap equation that quantifies <strong>the</strong> role of monetary policy <strong>in</strong><br />
reduc<strong>in</strong>g output when <strong>in</strong>terest rates are high <strong>and</strong> stimulat<strong>in</strong>g output when <strong>in</strong>terest rates are<br />
low.<br />
To highlight <strong>the</strong> role of <strong>Phillips</strong> curve specifications <strong>in</strong> <strong>the</strong> analysis of reduced U.S.<br />
bus<strong>in</strong>ess cycle volatility, we show that <strong>the</strong> Roberts/NKPC type <strong>Phillips</strong> curve specification<br />
misses much of <strong>the</strong> role of supply shocks <strong>in</strong> contribut<strong>in</strong>g to reduced volatility <strong>in</strong> both <strong>in</strong>flation<br />
<strong>and</strong> output. Not only is <strong>the</strong> triangle approach necessary to underst<strong>and</strong> <strong>the</strong> evolution of <strong>the</strong> U. S.<br />
<strong>in</strong>flation rate over <strong>the</strong> postwar era, but also <strong>the</strong> triangle approach is required to exam<strong>in</strong>e <strong>the</strong><br />
sources of reduced bus<strong>in</strong>ess cycle volatility. Papers that omit <strong>the</strong> supply‐shock variables <strong>and</strong><br />
long lags <strong>in</strong>tegral to <strong>the</strong> triangle approach understate <strong>the</strong> role of reduced shocks <strong>in</strong> expla<strong>in</strong><strong>in</strong>g<br />
<strong>the</strong> lower volatility of both <strong>in</strong>flation <strong>and</strong> output changes <strong>in</strong> <strong>the</strong> postwar U. S. economy.
<strong>Phillips</strong> <strong>Curve</strong> <strong>Specification</strong> <strong>and</strong> Bus<strong>in</strong>ess Cycle Volatility, Page 45<br />
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Appendix<br />
TABLE 1<br />
Roll<strong>in</strong>g St<strong>and</strong>ard Deviations of <strong>Output</strong> Changes, <strong>Output</strong> Gap, <strong>and</strong> Inflation<br />
Over Selected Intervals, 1952:Q4 to 2007:Q1<br />
Roll<strong>in</strong>g St<strong>and</strong>ard Deviations<br />
Log Percentage<br />
Change<br />
1952:Q4- 1973:Q1- 1952:Q4- 1988:Q1-<br />
Variable 1972:Q4 1987:Q4 1987:Q4 2007:Q1 1988‐07 vs. 1973‐87<br />
Four‐Quarter Change <strong>in</strong> Real GDP 2,72 2,83 2,77 1,24 -80,3<br />
Four‐Quarter Change <strong>in</strong> GDP Deflator 1,14 1,59 1,33 0,49 -100,0<br />
<strong>Output</strong> Gap 1,85 2,42 2,09 1,16 -59,0<br />
Ratio GDP Deflator to Real GDP 41,9 56,2 48,1 39,5 -19,7<br />
Ratio <strong>Output</strong> Gap to Real GDP 68,0 85,5 75,6 93,5 21,3
TABLE 2<br />
Estimated Equations for Quarterly Changes <strong>in</strong><br />
PCE Deflators, 1962:Q1 to 2006:Q4<br />
Variable Lags Roberts Triangle<br />
Constant 1,01 *<br />
Lagged Dependent Variable 1-24 a 1,00 **<br />
1-4 0,96 **<br />
Unemployment Gap 0-4 -0,57 **<br />
Unemployment Rate 0 -0,15 *<br />
Relative Price of Imports 1-4 0,06 **<br />
Food‐Energy Effect 0-4 0,90 **<br />
Productivity Trend Change 1 5 -0,97 **<br />
Nixon Controls ʺonʺ 0 -1,54 **<br />
Nixon Controls ʺoffʺ 0 1,91 **<br />
R2 0,79 0,94<br />
S.E.E 1,16 0,64<br />
S.S.R 233,3 63,2<br />
Dynamic Simulation<br />
1997:Q1 ‐ 2006:Q4 Note b<br />
Mean Error -4,67 -0,08<br />
Root Mean‐Square Error 5,06 0,60<br />
a) Lagged dependent variable is entered as <strong>the</strong> four-quarter mov<strong>in</strong>g<br />
average for lags 1, 5, 9, 13, 17, <strong>and</strong> 21, respectively<br />
b) Dynamic simulations are based on regressions for <strong>the</strong> sample period<br />
1962:Q1-1996:Q4 <strong>in</strong> which <strong>the</strong> coefficients on <strong>the</strong> lagged dependent<br />
variable are constra<strong>in</strong>ed to sum to unity.
Inf Lag<br />
U lag<br />
length<br />
Fixed or TV<br />
NAIRU<br />
Supply<br />
Table 3<br />
Transformation of Philips <strong>Curve</strong><br />
shock R2 SEE SSR ME RMSE F Stat<br />
Exclude <strong>in</strong>f<br />
lags 5‐8<br />
Sig<br />
Level<br />
Exclude <strong>in</strong>f lags<br />
F Stat<br />
9‐24<br />
Sig<br />
Level<br />
Exclude U lags<br />
F Stat<br />
1‐4<br />
Sig<br />
Level<br />
Exclude Supply<br />
Shocks<br />
Sig<br />
1 1 to 4 0 Fixed No 0,79 1,16 233,3 -4,67 5,06<br />
2 1 to 8 0 Fixed No 0,79 1,16 228,0 -4,47 4,84 0,98 0,42<br />
3 1 to 24 0 fixed No 0,81 1,09 183,3 -3,63 3,87 2,35 0,00<br />
4 1 5 9 13 17 21 0 fixed No 0,79 1,16 229,8 -3,53 3,77<br />
5 1 to 4 0 to 4 Fixed No 0,80 1,13 217,6 -4,42 4,73 3,08 0,02<br />
6 1 to 4 0 to 4 TV No 0,80 1,11 211,8 -2,05 2,32<br />
7 1 to 8 0 to 4 TV No 0,80 1,12 209,1 -2,03 2,31 0,54 0,70<br />
8 1 to 24 0 to4 TV No 0,82 1,07 174,4 -1,84 2,12 1,88 0,03<br />
9 1 5 9 13 17 21 0 to 4 TV No 0,80 1,12 212,3 -1,60 1,92<br />
10 1 to 8 0 to 4 Fixed No 0,79 1,14 214,5 -4,37 4,67 0,59 0,67<br />
11 1 to 24 0 to 4 Fixed No 0,82 1,07 172,7 -3,92 4,15 2,27 0,01<br />
12 1 5 9 13 17 21 0 to 4 Fixed No 0,80 1,11 207,2 -3,62 3,84<br />
13 1 to 4 0 Fixed Yes 0,91 0,77 96,1 -3,84 4,37 17,68 0,00<br />
14 1 to 8 0 Fixed Yes 0,90 0,78 95,1 -3,88 4,39 0,43 0,79 16,89 0,00<br />
15 1 to 24 0 fixed Yes 0,92 0,70 70,0 -0,57 0,97 3,16 0,00 17,57 0,00<br />
16 1 5 9 13 17 21 0 fixed Yes 0,92 0,70 78,5 -0,56 0,92 23,60 0,00<br />
17 1 to 4 0 to 4 Fixed Yes 0,90 0,77 94,1 -4,15 4,64 0,85 0,50 15,85 0,00<br />
18 1 to 4 0 to 4 TV Yes 0,91 0,76 91,7 -3,05 3,33 15,93 0,00<br />
19 1 to 8 0 to 4 TV Yes 0,91 0,76 89,9 -2,79 3,03 0,75 0,56 15,70 0,00<br />
20 1 to 24 0 to4 TV Yes 0,93 0,65 57,8 -0,08 0,67 4,79 0,00 21,41 0,00<br />
21 1 5 9 13 17 21 0 to 4 TV Yes 0,94 0,64 63,2 -0,08 0,60 28,30 0,00<br />
22 1 to 8 0 to 4 Fixed Yes 0,90 0,78 93,4 -4,03 4,48 0,27 0,90 15,26 0,00<br />
23 1 to 24 0 to 4 Fixed Yes 0,93 0,68 63,6 -0,76 1,09 4,01 0,00 18,07 0,00<br />
24 1 5 9 13 17 21 0 to 4 Fixed Yes 0,93 0,67 70,3 -0,78 1,05 23,20 0,00<br />
F Stat<br />
Level
TABLE 4<br />
Coefficients from Four‐Equation Model, estimated for 1962:Q1 to 2006:Q4<br />
Dependent Variable<br />
Nom<strong>in</strong>al Federal Funds Rate<br />
1960:Q1‐ 1979:Q3‐ 1990:Q3‐<br />
1979:Q2 1990:Q2 2006:Q4<br />
Lags<br />
<strong>in</strong>cluded<br />
Inflation<br />
Rate<br />
Burns<br />
Volcker<br />
Bernanke<br />
∆ <strong>Output</strong><br />
Gap<br />
Greenspan‐<br />
Unemployment<br />
Gap<br />
Endogenous Variables<br />
Inflation 1-24 a 1,00 **<br />
Inflation m<strong>in</strong>us Inflation Target 0-1 0,64 ** 1,57 0,37<br />
∆ Inflation Rate 1-4 0,02<br />
Federal Funds Rate Error Term 1 0,79 ** 0,72 ** 0,96 **<br />
∆ Federal Funds Rate 2-10 -0,95 **<br />
Level of Unemployment Gap 0-4 -0,57 **<br />
Level of <strong>Output</strong> Gap 0-1 0,52 ** 0,16 0,63 **<br />
Level of <strong>Output</strong> Gap 0-2 -0,49 **<br />
Exogenous Variables<br />
Relative Price of Imports 1-4 0,06 **<br />
Food‐Energy Effect 0-4 0,90 **<br />
Productivity Trend Change 1 5 -0,97 **<br />
Nixon Controls ʺonʺ 0 -1,54 **<br />
Nixon Controls ʺoffʺ 0 1,91 **<br />
R2 0,94 0,91 0,82 0,94 0,20 0,71<br />
S.E.E 0,64 0,73 1,36 0,42 0,72 0,71<br />
S.S.R 63,2 38,5 70,8 10,5 87,2 89,8<br />
a) Lagged dependent variable is entered as <strong>the</strong> four-quarter mov<strong>in</strong>g<br />
Notes: (*) <strong>in</strong>dicates that coefficient or sum of coefficients is significant at 5 percent level. (**) at 1 percent level
Table 5<br />
S<strong>in</strong>gle Equation Simulations<br />
1965:Q1‐1983:Q1<br />
1984:Q1‐2006:Q4<br />
Log Percent Ratio<br />
of 1984‐2006 to<br />
1965‐83<br />
Inflation Rate 2,66 1,24 -76,3<br />
FF Rate 3,65 2,43 -40,9<br />
Level of <strong>Output</strong> Gap 2,92 1,36 -76,4<br />
First Difference of <strong>Output</strong> Gap 1,09 0,49 -80,2<br />
Simulation Results<br />
Simulated Inflation 2,52 1,12 -80,6<br />
Simulated Inflation 1,69 0,92 -61,3<br />
Without Supply Shocks<br />
Predicted FF Rate 3,34 2,30 -37,0<br />
First Difference of <strong>Output</strong> Gap 0,50 0,29 -54,9
Table 6<br />
St<strong>and</strong>ard Deviations of Full‐Model <strong>Specification</strong>s, Split‐sample<br />
Taylor Rule, 1965:Q1 to 2006:Q4<br />
1965:Q1‐1983:Q1<br />
1984:Q1‐2006:Q1<br />
Log Percent<br />
Ratio of 1984‐<br />
2006 to 1965‐<br />
St<strong>and</strong>ard Deviation of Inflation Rate<br />
All Shocks 2,58 1,38 -62,93<br />
No Supply Shocks 0,82 0,62 -27,81<br />
No <strong>Output</strong> Error 1,95 1,52 -24,68<br />
No Shocks 0,44 0,61 34,08<br />
St<strong>and</strong>ard Deviation of Fed Funds Rate<br />
All Shocks 3,57 3,30 -7,75<br />
No Supply Shocks 2,29 3,29 36,37<br />
No <strong>Output</strong> Error 2,35 2,19 -6,80<br />
No Shocks 1,21 1,15 -5,22<br />
St<strong>and</strong>ard Deviation of <strong>Output</strong> Gap<br />
All Shocks 2,55 1,55 -49,89<br />
No Supply Shocks 1,77 1,52 -15,35<br />
No <strong>Output</strong> Error 1,37 1,67 19,79<br />
No Shocks 0,70 0,87 22,13<br />
Average Inflation Rate<br />
All Shocks 4,98 2,22 -80,76<br />
No Supply Shocks 3,12 3,18 2,10<br />
No <strong>Output</strong> Error 2,33 -1,78 ---<br />
No Shocks 0,33 -0,60 ---<br />
Average Absolute Value of <strong>Output</strong> Gap<br />
All Shocks 2,06 1,31 -45,52<br />
No Supply Shocks 1,71 1,32 -26,13<br />
No <strong>Output</strong> Error 1,97 1,32 -40,03<br />
No Shocks 0,84 0,75 -10,73<br />
83
Table 7<br />
St<strong>and</strong>ard Deviations of Full‐Model <strong>Specification</strong>s, Substitut<strong>in</strong>g <strong>in</strong> Roberts<br />
Equations<br />
1965:Q1‐1983:Q1<br />
1984:Q1‐2006:Q1<br />
Log Percent<br />
Ratio of 1984‐<br />
2006 to 1965‐<br />
St<strong>and</strong>ard Deviation of Inflation Rate<br />
Triangle with Supply Shocks 2,58 1,38 -62,93<br />
Triangle without Supply Shocks 0,82 0,62 -27,81<br />
Philips with Inflation Error 2,66 1,24 -76,31<br />
<strong>Phillips</strong> without Inflation Error 1,48 1,82 20,80<br />
St<strong>and</strong>ard Deviation of Fed Funds Rate<br />
Triangle with Supply Shocks 3,57 3,30 -7,75<br />
Triangle without Supply Shocks 2,29 3,29 36,37<br />
Philips with Inflation Error 3,82 2,37 -47,73<br />
<strong>Phillips</strong> without Inflation Error 2,06 2,35 13,37<br />
St<strong>and</strong>ard Deviation of <strong>Output</strong> Gap<br />
Triangle with Supply Shocks 2,55 1,55 -49,89<br />
Triangle without Supply Shocks 1,77 1,52 -15,35<br />
Philips with Inflation Error 0,58 0,25 -83,13<br />
<strong>Phillips</strong> without Inflation Error 2,04 2,03 -0,45<br />
Average Inflation Rate<br />
Triangle with Supply Shocks 4,98 2,22 -80,76<br />
Triangle without Supply Shocks 3,12 3,18 2,10<br />
Philips with Inflation Error 5,59 2,60 -76,68<br />
<strong>Phillips</strong> without Inflation Error 3,88 2,30 -52,47<br />
Average Absolute Value of <strong>Output</strong> Gap<br />
Triangle with Supply Shocks 2,06 1,31 -45,52<br />
Triangle without Supply Shocks 1,71 1,32 -26,13<br />
Philips with Inflation Error 0,45 0,20 -80,31<br />
<strong>Phillips</strong> without Inflation Error 2,97 2,87 -3,35<br />
83
Figure 1A. Four Quarter Growth Rate of Real GDP vs Average Real<br />
GDP Growth,<br />
1948:Q1 to 2007:Q1<br />
Percent per year<br />
14<br />
12<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
Actual Real GDP<br />
Growth<br />
-2<br />
Average Real GDP<br />
-4<br />
Growth<br />
1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005<br />
Figure 1B. Twenty Quarter Roll<strong>in</strong>g St<strong>and</strong>ard Deviation of Real GDP<br />
Growth,<br />
1952:Q4 to 2007:Q1<br />
4,5<br />
4<br />
3,5<br />
3<br />
Percent<br />
2,5<br />
2<br />
1,5<br />
1<br />
0,5<br />
0<br />
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Figure 2A. <strong>Output</strong> Gap, 1950:Q2 to 2006Q4<br />
6<br />
4<br />
2<br />
Log <strong>Output</strong> Ratio<br />
0<br />
-2<br />
-4<br />
-6<br />
-8<br />
-10<br />
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005<br />
Figure 2B. Twenty Quarter Roll<strong>in</strong>g St<strong>and</strong>ard Deviation of <strong>Output</strong> Gap,<br />
1955:Q1 to 2006:Q4<br />
4<br />
3,5<br />
3<br />
Percent<br />
2,5<br />
2<br />
1,5<br />
1<br />
0,5<br />
0<br />
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Figure 3. Real GDP Growth Volatility vs Inflation Volatility, 1952:Q3 to 2007:Q1<br />
4,5<br />
4<br />
3,5<br />
<strong>Output</strong> Growth<br />
Volatility<br />
3<br />
2,5<br />
2<br />
1,5<br />
1<br />
0,5<br />
Inflation Volatility<br />
0<br />
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Figure 4A. Four Quarter Average of Import Shocks, 1960:Q1<br />
to 2006:Q4<br />
20<br />
15<br />
10<br />
5<br />
0<br />
-5<br />
-10<br />
-15<br />
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005<br />
Figure 4B. Four Quarter Average of Food <strong>and</strong> Energy<br />
Shocks, 1960:Q1 to 2006:Q4<br />
4<br />
3<br />
2<br />
1<br />
0<br />
-1<br />
-2<br />
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Figure 5. Acceleration of Trend Productivity Growth,<br />
1960:Q1 to 2006:Q4<br />
0,6<br />
0,5<br />
0,4<br />
0,3<br />
0,2<br />
0,1<br />
0<br />
-0,1<br />
-0,2<br />
-0,3<br />
-0,4<br />
-0,5<br />
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Figure 6. Actual Unemployment Rate vs. Time-Vary<strong>in</strong>g NAIRU, 1962:Q1 to 2006:Q4<br />
11<br />
10<br />
Unemployment rate<br />
9<br />
Unemployment HP λ=6400<br />
8<br />
Unemployment HP λ=1600<br />
7<br />
6<br />
TV NAIRU<br />
5<br />
4<br />
3<br />
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
Figure 7. Time-Vary<strong>in</strong>g NAIRU vs. Constant NAIRU, 1962:Q1 to 2006:Q4<br />
Unemployment rate<br />
9<br />
Constant NAIRU<br />
6<br />
TV NAIRU<br />
3<br />
1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006
Figure 8. Predicted <strong>and</strong> Simulated Values of Inflation from Triangle <strong>and</strong> Roberts Equations 1962:Q1 to<br />
2006:Q4<br />
12<br />
Inflation<br />
10<br />
Roberts<br />
8<br />
6<br />
4<br />
2<br />
Triangle<br />
0<br />
1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007
Figure 9. Roberts Vs. Triangle Unemployment Coefficients on 90 Quarter Roll<strong>in</strong>g Regressions from<br />
1962:Q1 to 1984:Q3<br />
0<br />
-0,1<br />
-0,2<br />
Roberts<br />
-0,3<br />
-0,4<br />
-0,5<br />
Triangle<br />
-0,6<br />
-0,7<br />
-0,8<br />
-0,9<br />
-1<br />
1963 1966 1969 1972 1975 1978 1981 1984
Figure 10. Constant NAIRU vs. Time Vary<strong>in</strong>g NAIRU Unemployment Coefficients on 90 Quarter Roll<strong>in</strong>g<br />
Regressions from 1962:Q1 to 1984:Q3<br />
0<br />
-0,2<br />
Constant NAIRU<br />
-0,4<br />
-0,6<br />
TV NAIRU<br />
-0,8<br />
-1<br />
-1,2<br />
1963 1966 1969 1972 1975 1978 1981 1984
Figure 11. Predicted Inflation with <strong>and</strong> without Supply shocks,<br />
1962:Q1 to 2006:Q4<br />
12<br />
Predicted Inflation with Actual<br />
Shocks, 1965:Q1-2006:Q4<br />
10<br />
8<br />
6<br />
4<br />
2<br />
Predicted Inflation with Shocks<br />
Suppressed, 1965:Q1-2006:Q4<br />
0<br />
-2<br />
1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004
Figure 12. Actual <strong>and</strong> Predicted Level of <strong>the</strong> <strong>Output</strong> Gap<br />
6<br />
Estimated Error<br />
4<br />
Actual<br />
2<br />
0<br />
-2<br />
-4<br />
Predicted<br />
-6<br />
-8<br />
-10<br />
1965:01 1970:01 1975:01 1980:01 1985:01 1990:01 1995:01 2000:01 2005:01
Figure 13. Simulated Values of Four Quarter <strong>in</strong>flation Rate,<br />
1965:Q1 to 2006:Q4<br />
12<br />
10<br />
All Shocks<br />
8<br />
6<br />
No Supply Shocks<br />
4<br />
2<br />
0<br />
-2<br />
No <strong>Output</strong> Error<br />
No Shocks<br />
-4<br />
-6<br />
1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004
Figure 14. Simulated Values of Four Quarter Mov<strong>in</strong>g Average of Fed Funds Rate,<br />
1965:Q1 to 2006:Q4<br />
18<br />
16<br />
All Shocks<br />
14<br />
12<br />
10<br />
No Supply Shocks<br />
8<br />
6<br />
4<br />
2<br />
0<br />
No <strong>Output</strong> Error<br />
-2<br />
No Shocks<br />
-4<br />
1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004