Phillips Curve Specification And the Decline in U. S. Output and ...

Phillips Curve Specification 

And the Decline in U. S. Output and Inflation Volatility * 

Robert J. Gordon 

Northwestern University and NBER 

First Draft to be Presented at Symposium on 

The Phillips Curve and the Natural Rate of Unemployment, 

Institut für Welwirtschaft 

Kiel, Germany 

June 3‐4, 2007 

____________________ 

*I am grateful to Rob McMenamin for excellent research assistance on this paper and to 

Ian Dew‐Becker for his insights and assistance on previous related papers.

Phillips Curve Specification 

And the Decline in U. S. Output and Inflation Volatility 

ABSTRACT 

Journalists have recently characterized the Fed’s view that the slope of the United States 

Phillips Curve (PC) has become substantially flatter, by a factor of at least half, since the mid‐ 

1980s. The flattening of the Phillips curve is documented in a particular style of PC research 

based on the New Keynesian Phillips Curve (NKPC) literature, in which PC specifications 

involve links between the current inflation rate and short lags on inflation, and on the current 

unemployment rate. The first part of this paper uses a wide variety of statistical tests to show 

that the Fed’s PC equation, as based on research by Roberts (2006), is strongly rejected both by 

traditional and nontraditional tests when compared to the Gordon “triangle” model that was 

developed in the early 1980s. The Roberts version of the NKPC is entirely nested in the triangle 

model, allowing each of its exclusion restrictions to be tested, and each is rejected at high levels 

of statistical significance. 

The remainder of the paper asks why the volatility of inflation, of output changes and of 

the output gap has declined substantially after 1984, a finding on which U. S. macroeconomists 

share an unusual consensus. Our analysis based on a small macroeconometric model concludes 

that about 1/3 of the reduction in the volatility of real GDP can be traced to the role of supply 

shocks in the triangle inflation equation. More important are errors in the output gap or “IS” 

equation that quantifies the role of monetary policy in reducing output when interest rates are 

high and stimulating output when interest rates are low. 

To highlight the role of Phillips curve specifications in the analysis of reduced U.S. 

business cycle volatility, we show that the Roberts/NKPC type Phillips curve specification 

misses much of the role of supply shocks in contributing to reduced volatility in both inflation 

and output. Finally, we find no role at all for monetary policy in reducing the volatility of 

inflation or output, unless monetary policy is more broadly defined to include the component of 

“IS stabilization” represented by the financial deregulation of the late 1970s that reduced the 

volatility of residential construction. 

Robert J. Gordon 

Department of Economics 

Northwestern University 

Evanston IL 60208‐2600 

rjg@northwestern.edu 

http://faculty‐web.at.northwestern.edu/economics/gordon

Phillips Curve Specification and Business Cycle Volatility, Page 1 

I. Introduction 

Has the slope of the American Phillips Curve (PC) become flatter in the past two 

decades? Recently the Wall Street Journal announced on its front page the finding of recent 

research at the Federal Reserve Board demonstrating a sharp flattening of the PC since the mid‐ 

1980s. The primary Fed study by Roberts (2006) attributes to monetary policy both the change 

in slope and the related marked reduction in U. S. business cycle volatility. The channel of 

monetary policy influence comes from an increased Fed responsiveness to output and inflation, 

so that any pressure for higher inflation or any movement of the output gap away from zero are 

“nipped in the bud”. A flatter PC directly contributes to the interplay between monetary policy 

and output stabilization, as movements of the output gap above zero generate less inflation 

than formerly, requiring less monetary tightening and thus a smaller subsequent downward 

adjustment in output. 1 

However, both of these two conclusions are highly controversial. The verdict that the 

PC slope has flattened is highly sensitive to specification choices, and a primary purpose of this 

paper is to examine the interplay between model specification and conclusions about the 

stability of PC parameters. Further, while all research agrees that output has become less 

volatile since the mid‐1980s, much of it contradicts Robert’s conclusion that the improved 

conduct of monetary policy is responsible. Stock and Watson (2002, 2003) were among the first 

to quantify the role of smaller shocks in contributing to improved stability, and Gordon (2005) 

1. Also representing the Fed view are Kohn (2005) and Williams (2006).


concluded that roughly two‐thirds of the improvement in stability resulted from smaller 

demand shocks, one‐third from smaller supply shocks, with no remaining role for monetary 

policy at all. 2 

The specification of the Phillips curve is integral to the analysis of declining business 

cycle volatility because Roberts, Stock‐Watson, and Gordon all based their conclusions on small 

three‐equation models of the economy in which the Phillips Curve is the first equation, joined 

together with an interest‐rate equation based on the Taylor rule and an “IS” equation relating 

the output gap to interest rates. In addition to studying the sensitivity of the PC slope 

coefficient to alternative specifications, this paper also examines the sensitivity of conclusions 

regarding output volatility in a three‐equation model to choices in the specification of the 

Phillips curve. 

Blanchard‐Simon (2001) and others have noticed the parallel decline of inflation and 

output volatility. We can quantify the role of declining inflation volatility in contributing to 

declining output volatility, and we can inquire as to the sources of the improved stability of the 

inflation rate. The Roberts approach points to a flatter slope in diminishing the transmission of 

movements in the output gap into changes of the inflation rate. A second hypothesis is that, 

even without a change in the PC slope, declining output volatility would have directly 

contributed to improved inflation stability. A third hypothesis is that inflation depends not 

only on demand shocks but on explicit supply shocks that can be identified and quantified, and 

2. Blanchard‐Simon (2001) pointed to several of the same factors as Stock‐Watson and Gordon, but they


that a reduction in the size and importance of the supply shocks contributed directly to 

improved inflation stability and indirectly to improved output stability. While all three of 

these hypotheses could in principle be complementary, the approach of Roberts (2006) and of 

Stock‐Watson (2002, 2003) does not allow for separate testing because they do not quantify the 

role of explicit supply shock variables. 

The primary emphasis in this paper is on the role of PC specification in drawing 

conclusions about shifting slope parameters and on the sources of reduced business cycle 

volatility. A sharp contrast is drawn between the New Keynesian Phillips Curve (NKPC) of 

which one version is used by Roberts, and my own long‐standing “triangle” approach dating 

back to Gordon (1977, 1982). 3 The Roberts NKPC includes only two variables, the current 

unemployment rate and four quarterly lags on inflation. In contrast, the “triangle” description 

of my model refers to its three‐sided representation of the U. S. inflation process. The base of 

the triangle is inertia, represented by long lags on inflation. The left side of the triangle is the 

representation of demand pressure on inflation, proxied by short lags on the unemployment 

gap. The right side of the triangle contains explicit variables representing supply shocks. These 

are the oil‐food shocks, changes in relative import prices, changes in the productivity growth 

trend, and dummy variables for the 1971‐75 Nixon‐era price controls. Fortunately the Robertsstyle 

NKPC is entirely nested in my more comprehensive approach, and the differences 

did not build an econometric model to quantify the shocks or the role of their decline in magnitude. 

3. The most recent published versions of the triangle model are in Gordon (1997, 1998) and Dew‐Becker 

and Gordon (2005).


between the two specifications amount to exclusion restrictions in the Roberts version that can 

be explicitly tested both individually and jointly. 

Plan of the Paper 

The paper begins by comparing two measures of output volatility based alternatively 

on the rolling standard deviation of changes in output and of the level of the output gap. As 

others have noticed, the change‐based measure declines after the mid‐1980s substantially more 

than the gap‐based measure, but even the gap‐based measure declines markedly. Then we 

compare the evolution of volatility for output change and inflation, emphasizing both the joint 

rise in volatility in the 1970s and decline after the mid‐1980s, but also the additional fact that 

output volatility was high during 1955‐65 when inflation volatility was very low. 

The next section contrasts the Roberts version of the NKPC with the more 

comprehensive triangle PC specification in which the Roberts PC equation is nested. We 

develop a “transformation” grid to translate the Roberts equation into ours, at each step testing 

the exclusion restrictions that are implicit in the Roberts approach and indeed in the rest of the 

NKPC literature. We trace the transformation between the two specifications by alternatively 

introducing the three main differences into the Roberts equation – long lags, the inclusion of 

specific supply shock variables, and the use of a time‐varying (TV‐NAIRU) instead of constant 

NAIRU. 4 At each stage in the transformation, we can examine the interplay between lag 

length, supply shock variables, and the variability of the NAIRU, i.e., is the significance of


supply‐shock variables dependent on allowing for long lags, or vice versa? 

We base our evaluation of alternative specifications on the statistical significance of 

variables and lags that are excluded in the Roberts approach and included in our approach. In 

addition, our evaluation technique includes the use of post‐sample dynamic simulations, a 

technique of model evaluation that unfortunately is rarely used in contemporary time‐series 

econometrics. For each specification to be compared, the parameters are estimated on data 

subtracting the last ten years (e.g., 1962‐96 instead of the available 1962‐2006), and then 

predicted values of that specification are generated for the final ten years (1997‐2006) by feeding 

back the lagged dependent variable endogenously rather than assuming it to be exogenous. 

Testing specifications with dynamic simulations in models where the lagged dependent 

variable plays an important role in the explanation can reveal sources of “drift” in predicted 

values away from actual values. 

The paper then turns to the three‐equation model that, as in the papers by Roberts and 

Stock‐Watson, is designed to trace the interplay among inflation, the output gap, and the 

interest rate responses of the Fed. In this paper we examine the role of alternative PC 

specifications in drawing inferences from the multiple‐equation model used by Gordon (2005) 

regarding the causes of the decline in both output and inflation volatility after the mid‐1980s. 

For instance, we can suppress the contribution of the supply shocks in the triangle inflation 

equation or suppress the error term in the Roberts NKPC equation. Our goal is to quantify the 

4 . The time‐varying NAIRU (TV‐NAIRU) was introduced by Gordon (1997) and Staiger‐Stock‐Watson


role of alternative PC specifications in the analysis of reduced post‐1984 U. S. economic 

volatility. We find that the Roberts approach greatly understates the role of declining shocks in 

achieving business cycle volatility and thus erroneously concludes that monetary policy, rather 

than the decline of shocks, was the primary mover of reduced volatility. 

II. Measures of Reduced Business‐Cycle Volatility 

Four‐quarter Changes in Real GDP 

Perhaps the clearest way to become convinced of the decline in business cycle volatility 

over the postwar era is to study the plot in the top frame of Figure 1, showing four‐quarter 

changes in the growth rate of real GDP over the 237 quarters between 1948:Q1 and 2007:Q1, 

spanning the entire quarterly data base of the U. S. National Income and Product Accounts 

(NIPA). The top frame also plots a horizontal line representing the mean growth rate of real 

GDP over this period, which is 3.35 percent per annum. 

As shown in the top frame of Figure 1, the four‐quarter percentage changes behave very 

differently before and after 1984. Prior to 1984, there are sharp zigs and zags, while after 1984 

the fluctuations are much more moderate. The pre‐1984 fluctuations are equally severe above 

and below the mean of 3.35 percent per year. In contrast, there is nothing like that experience of 

volatility after 1984. The four‐quarter growth rate of real GDP was never negative over the 

entire 22‐year period between 1983:Q1 and 2007:Q1 except in the brief interval associated with 

the 1990‐91 recession, namely 1991:Q1‐Q3. In fact, some doubt has been cast on the NBER’s 

(1997, 2001).


declaration of a recession in early 2001, because the four‐quarter change in real GDP never 

became negative in that episode and indeed in Figure 1A never fell below +0.2 percent in any 

quarter in 2001. 

Corresponding to the decline in volatility evident in the top frame of Figure 1 is a 

measure of that volatility displayed in the bottom frame, the rolling 20‐quarter standard 

deviation of the four‐quarter growth rate of real GDP. There was a sharp and apparently 

permanent decline after 1987 from a range of 1.5 to 3.5 percent down to a range of 0.5 to 1.5 

percent. Because the calculation of the rolling standard deviation as a 20‐quarter mean causes 

the post‐1983 drop in volatility to be reflected five years later, we can dramatize the movement 

toward stability by splitting the time period of the bottom frame of Figure 1 at 1987:Q4. As 

displayed in Table 1, the mean of the standard deviations plotted in the bottom frame of Figure 

1 is 2.77 percent for 1952:Q4‐1987:Q4 and a much lower 1.24 percent for 1988:Q1‐2007:Q1. 

Expressed as a percentage log change as in Table 1, the decline in the standard deviation for 

output changes is ‐80.3 percent. 

The Output Gap 

In principle part of the variance of real GDP changes could reflect changes in the growth 

rate of natural real GDP, and we would not consider these changes to reflect business cycle 

volatility. Also, some of the volatility evident in the top frame of Figure 1 could be very shortterm 

quarterly movements caused by volatile inventory changes that cancel out over two or 

three years. To check these possibilities, the top frame of Figure 2 displays the log output ratio


or “output gap” as a percent (100 times the log ratio of actual to natural real GDP). 5 

The 

dividing line of shifting output volatility at the year 1984 is not quite as stark in Figure 2 as in 

Figure 1, partly because the output gap is a level rather than a rate of change and thus cumulates 

and partially smoothes out the volatile pre‐1984 rates of change shown in Figure 1. In fact, 

Roberts (2006) points to the role of reduced short‐term volatility of inventory changes in 

explaining why the output change measure in Figure 1 appears to exhibit a greater decline in 

volatility than the output gap measure in Figure 2. 

However, there is still ample evidence of a decline in the volatility of the output gap 

after 1984. The bottom frame quantifies the shift in the volatility of the output gap by plotting 

(in parallel with Figure 1) its rolling 20‐quarter standard deviation. There is less dramatic 

evidence in the bottom frame of Figure 2 of a post‐1984 drop in output volatility than in Figure 

1. As shown in Table 1, the log ratio of the rolling standard deviation when 1988‐2007 is 

compared with 1952‐87 drops by 59 percent for the output gap as compared to 80 percent for 

four‐quarter changes of real GDP. 

Inflation and Output Volatility 

An important source of high output volatility before 1984 was high inflation volatility, 

and we show later that the reduction of inflation volatility after 1984 made a substantial 

contribution to the post‐1984 decline in output volatility. We will also show that high inflation 

5. Natural real GDP is estimated by taking an average of a Hodrick‐Prescott (parameter 6400) and a 

Kalman filter (parameter sv=15) applied to data on the quarterly change in real GDP. This method is 

developed and further explained in Gordon (2003).


volatility prior to 1984 can be linked to the behavior of an explicit set of supply shock variables. 

Figure 3 compares the 20‐quarter standard deviation of four quarter changes in real GDP and 

the GDP deflator, where the close relationship between output and inflation volatility is evident 

in the 1974‐88 period. We also note that output volatility was relatively high in 1952‐1962 

despite the low volatility of inflation, and that very low inflation volatility in 1990‐2007 did not 

prevent an increase in output volatility associated with the 1990‐91 or 2001 recessions and 

subsequent recoveries. 

Table 1 shows that the log percent measure of inflation volatility declined after 1987 by 

100 percent, as compared to 80 percent for output changes and 59 percent for the output gap. 

The bottom section of Table 1 shows that the ratio of the volatility measure for inflation to that 

for output changes was highest in 1973‐87 and a roughly similar lower value for 1952‐72 and 

1987‐2007. The fact that output volatility was as high in 1952‐72 as in 1973‐87, while inflation 

volatility was substantially lower, suggests that there was a separate component of output 

volatility unrelated to inflation behavior in the 1952‐72 period. Gordon (2005) decomposes this 

into the separate contributions of three components of instability on the demand side – 

government military spending, residential investment, and inventory investment. 

III. Contrasting the New‐Keynesian and Triangle Specifications of the Phillips 

Curve 

This section begins by comparing the generic New‐Keynesian Phillips Curve (NKPC) 

specification with the particular variant used by Roberts to arrive at his joint conclusions that


the slope of the PC has significantly flattened since the mid 1980s and that monetary policy is 

responsible for both the flatter slope and the increased stability of output. The literature 

contains two versions of the NKPC, one in which the driving force of inflation is the 

unemployment (or output) gap, and the other in which the gap is replaced by the change in 

marginal cost. 

In this paper we refer only to the unemployment‐gap version of the NKPC, both because 

it is the version used by Roberts and also because the marginal cost version requires the added 

complexity of estimating an equation for wages in addition to prices. 6 Then the triangle model 

is introduced and contrasted with the Roberts version of the NKPC, which is nested in the 

triangle model by excluding longer lags on both inflation and unemployment, by omitting all 

supply shock variables, and by assuming that the NAIRU is constant. 

The NKPC Model 

The NKPC model has emerged in the past decade as the centerpiece of macro conference 

discussions of inflation dynamics and as the ʺworkhorseʺ of the evaluation of monetary policy. 

The point of the NKPC is to derive an empirical description of inflation dynamics that is 

ʺderived from first principles in an environment of dynamically optimizing agentsʺ (Bårdsen et 

al. 2002). Most expositions of the NKPC, e.g., Mankiw (2001), begin with Calvoʹs (1983) model 

of random price adjustment. 

6. Some papers in the NKPC literature treat changes in marginal cost as exogenous, which is 

unacceptable as the change in marginal cost , e.g., the real wage divided by productivity, is inherently 

endogenous and requires separate equations for wage change and price change.


The theoretical background is that firms follow time‐contingent price‐adjustment rules. 

The firmʹs desired price depends on the overall price level and the unemployment gap. 7 Firms 

change their price only infrequently, but when they do, they set their price equal to the average 

desired price until the next price adjustment. The actual price level, in turn, is equal to a 

weighted average of all prices that firms have set in the past. The first‐order conditions for 

optimization then imply that expected future market conditions matter for todayʹs pricing 

decision. The model can be solved to yield the standard NKPC that makes the inflation rate (pt ) 

depend on expected future inflation (Et pt+1 ) and the unemployment (or output) gap: 

pt = αEt pt+1 + β(Ut ‐U*t ) + et , (1) 

where U is the unemployment rate. In our notation lower case letters represent first differences 

of logarithms and upper‐case letters represent either levels or log levels. 8 The constant term is 

suppressed, and so the NKPC has the interpretation that if α=1, then U*t represents the NAIRU. 

Much of the NKPC literature estimates the unemployment or output gap with the Hodrick‐ 

Prescott (HP) filter used to estimate the NAIRU or output trend, but Roberts sets the NAIRU 

equal to a constant, as we discuss further below. 

A central challenge to the NKPC approach is to find a proxy for the forward‐looking 

7. Most NKPC papers focus on the output gap, but the high negative correlation between the output and 

unemployment gaps allows them to be used interchangeably, see below. Mankiwʹs (2001) exposition 

followed here uses the unemployment gap. 

8. Note in particular that lower‐case p in this paper represents the first difference of the log of the price


expectations term (Et pt+1 ). Surprisingly, there is little discussion in the literature of this aspect, 

or the implications of the usual solution, which is to use instrumental variables or two‐stage 

least squares (2SLS) to estimate (1). In particular, no paper in the NKPC that I have reviewed 

contains an explicit treatment of the two stages of the 2SLS estimation and an interpretation of 

the reduced‐form equation that results when the first stage is substituted into the second stage. 

The first‐stage equation to be included in the 2SLS estimation is: 

Et pt+1 

4 

= ∑ λi pt‐i + φ(Ut ‐U*t ). (2) 

i= 

1 

Substituting the first‐stage equation (2) into the second‐stage equation (1), we obtain the 

reduced‐form 

4 

pt = ∀ ∑ λi pt‐i +(∀Ν+∃)(Ut ‐U*t ) + et (3) 

i= 

1 

Thus in practice the NKPC is simply a regression of the inflation rate on a few lags of inflation 

and the unemployment gap. As pointed out by Fuhrer (1997), the only sense in which models 

including future expectations differ from purely backward‐looking models is that they place 

restrictions on the coefficients of the backward‐looking variables that are used as proxies for the 

unobservable future expectations: 

ʺOf course, some restrictions are necessary in order to separately identify the 

effects of expected future variables. If the model is specified with unconstrained 

leads and lags, it will be difficult for the data to distinguish between the leads, 

level, not the price level itself.


which solve out as restricted combinations of lag variables, and unrestricted 

lags.ʺ (p. 338) 

And, as shown in Fuhrerʹs paper, these restrictions are implicitly rejected by the data in the 

sense that he finds that the expected inflation terms are ʺempirically unimportantʺ when 

unconstrained lagged terms are entered as well. 

The Roberts (2006) version of the NKPC is of particular interest here, because of his 

finding that the slope of the PC has declined by more than half since the mid 1980s. Roberts 

describes his equation as a “reduced form” NKPC and indeed it is identical to equation (3) 

above with two differences, the NAIRU is assumed to be constant, and the sum of coefficients 

on lagged inflation is assumed to be unity. Thus the Roberts (2006, equation 2, p. 199) version 

of (3) is: 

4 

pt = ∑ αi pt‐i + γ+∃Ut + et (4) 

i= 

1 

where the implied constant NAIRU is –γ/β. 

The “Triangle” Model of Inflation and the Role of Demand and Supply Shocks 

The inflation equation used in this paper is almost identical to that developed 25 years 

ago (Gordon, 1982). It builds on earlier work (Gordon, 1975, 1977) that combined the Friedman‐ 

Phelps natural rate hypothesis with the role of supply shocks in directly shifting the inflation 

rate and creating macroeconomic externalities in a world of nominal wage rigidity. The term 

ʺtriangleʺ model refers to a Phillips Curve that depends on three elements, inertia, demand, and


supply, and in which wages are implicitly solved out of the reduced form. The specification has 

three distinguishing characteristics — (1) the role of inertia (the bottom of the triangle) is 

broadly interpreted to go beyond any specific formulation of expectations formation to include 

other sources of inertia, e.g., wage and price contracts; (2) the driving force from the demand 

side is an unemployment or output gap; and (3) supply shock variables appear explicitly in the 

inflation equation rather than being forced into the error term as in the NKPC or Roberts 

approaches. This general framework can be written as: 

pt = a(L)pt‐1 + b(L)Dt + c(L)zt + et . (5) 

As before lower‐case letters designate first differences of logarithms, upper‐case letters 

designate logarithms of levels, and L is a polynomial in the lag operator. 

As in the NKPC and Roberts approaches, the dependent variable pt is the inflation rate. 

Inertia is conveyed by a series of lags on the inflation rate (pt‐1). Dt is an index of excess demand 

(normalized so that Dt=0 indicates the absence of excess demand), zt is a vector of supply shock 

variables (normalized so that zt=0 indicates an absence of supply shocks), and et is a serially 

uncorrelated error term. Distinguishing features in the implementation of this model include 

unusually long lags on the dependent variable, and a set of supply shock variables that are 

uniformly defined so that a zero value indicates no upward or downward pressure on inflation. 

The estimated version of equation (5) includes lags of past inflation rates, reflecting the 

influence of several past years of inflation behavior on current price setting, through some


combination of expectation formation, overlapping wage and price contracts, and buyersupplier 

relations. If the sum of the coefficients on the lagged inflation values equals unity, then 

there is a ʺnatural rateʺ of the demand variable (D N t ) consistent with a constant rate of inflation. 9 

The basic equations estimated in this paper use current and lagged values of the unemployment 

gap as a proxy for the excess demand parameter Dt, where the unemployment gap is defined as 

the difference between the actual rate of unemployment and the natural rate, and the natural 

rate (or NAIRU) is allowed to vary over time. 

The estimation of the time‐varying NAIRU combines the above inflation equation, with 

the unemployment gap serving as the proxy for excess demand, with a second equation that 

explicitly allows the NAIRU to vary with time: 

pt = a(L)pt‐1 + b(L)(Ut‐U N t ) + c(L)zt + et , (6) 

U N t = U N t‐1 + ηt , Eηt = 0, var(ηt )= τ 2 (7) 

In this formulation, the disturbance term ηt in the second equation is serially uncorrelated and is 

uncorrelated with et . When this standard deviation τη = 0, then the natural rate is constant, and 

when τη is positive, the model allows the NAIRU to vary by a limited amount each quarter. If 

no limit were placed on the ability of the NAIRU to vary each time period, then the timevarying 

NAIRU (hereafter TV‐NAIRU) would jump up and down and soak up all the residual 

9. While the estimated sum of the coefficients on lagged inflation is usually roughly equal to unity, that 

sum must be constrained to be exactly unity for a meaningful ʺnatural rateʺ of the demand variable to be


variation in the inflation equation (6). 10 

The triangle approach differs from the NKPC and Roberts approaches by including long 

lags on the dependent variable, additional lags on the unemployment gap, and explicit 

variables to represent the supply shocks (the zt variables in (5) and (6) above), namely the 

change in the relative price of non‐food non‐oil imports, the effect on inflation of changes in the 

relative price of food and energy, the acceleration in the trend rate of productivity growth, and 

dummy variables for the effect of the 1971‐74 Nixon‐era price controls. 11 Lag lengths were 

originally specified in Gordon (1982) and have not been changed since then. 

The top frame of Figure 4 displays four‐quarter moving averages of the relative import 

price variable. Its central role in explaining the spike of inflation in 1974‐75 is clearly visible, as 

is its role in the Volcker disinflation of 1982‐85, the accelerating inflation of the late 1980s, and 

the slowdown of inflation in 1997‐2001. As plotted in the bottom frame of Figure 4, the foodenergy 

effect has somewhat different timing than the import price effect. Note also the different 

orders of magnitude of the import and food‐energy effects, reflecting the fact that they are 

calculated. 

10. This method of estimating the TV‐NAIRU was introduced in simultaneous papers by Gordon (1997) 

and Staiger‐Stock‐Watson (1997). SSW developed the technique while adopting Gordon’s previous 

triangle model, and so those two papers were a merger of technique and substance. 

11. The relative import price variable is defined as the rate of change of the non‐food non‐oil import 

deflator minus the rate of change of the dependent variable, e.g., PCE deflator. The relative food‐energy 

variable is defined as the difference between the rates of change of the overall PCE deflator and the ʺcoreʺ 

PCE deflator. The Nixon control variables remain the same as originally specified in Gordon (1982). Lag 

lengths remain as in 1982 and are shown explicitly in Table 2. The productivity trend is a Hodrick‐ 

Prescott filter (using 6400 as the smoothness parameter) minus a six‐year moving average of the same H‐ 

P trend. The only changes from the previous published paper on this approach (Gordon, 1998) is in the


defined differently. 12 

The only major change in the current inflation equation involves productivity growth, 

where we follow the approach introduced in Dew‐Becker and Gordon (2005). In previous 

papers the difference in the growth rates of actual and trend productivity or “productivity 

deviation” had been entered into the inflation equation. But this misses the main impact of the 

1965‐80 productivity growth slowdown and post‐1995 productivity growth revival, which is the 

change in the growth of the trend itself. Here we create a productivity trend growth 

acceleration variable equal to a Hodrick‐Prescott filter version of the productivity growth trend 

minus a six‐year moving average of the same trend. This productivity trend acceleration 

variable is plotted in Figure 5. Its deceleration into negative territory during 1964‐1980 might be 

as important a cause of accelerating inflation in that period as its post‐1995 acceleration was a 

cause of low inflation in the late 1990s. Note also that the productivity growth trend revival of 

1980‐85 may have contributed to the success of the “Volcker disinflation,” a link that has been 

missed in most of the past PC literature. 

Estimating the TV‐NAIRU 

The time‐varying NAIRU is estimated simultaneously with the inflation equation (6) 

above. For each set of dependent variables and explanatory variables, there is a different TVtreatment 

of the productivity effect, see Dew‐Becker and Gordon (2005). 

12. Namely, the import variable is the change in the relative price of imports, which reaches a peak of 

about 15 percent in 1974‐75. The food‐energy variable is not the relative price of food and energy, but 

rather the difference between the growth rates of the PCE deflator including and excluding food and


NAIRU. For instance, when supply‐shock variables are omitted, the TV‐NAIRU soars to 8 

percent and above in the mid‐1970s, since this is the only way the inflation equation can 

“explain” why inflation was so high in the 1970s. However, when the full set of supply shocks 

is included in the inflation equation, the TV‐NAIRU is quite stable, shown by the dashed line 

plotted in Figure 6. 

The TV‐NAIRU series as plotted in Figure 6 that is associated with our basic inflation 

equation for the PCE deflator does not fall below 5.7 percent or rise above 6.5 percent over the 

period between 1962 and 1988. However, beginning in the late 1980s, the TV‐NAIRU drifts 

downwards until it reaches 5.3 percent in 1998, and then it displays a further dip in 2004‐06 to 

4.8 percent. One hypothesis to be explored below is that Roberts reaches his conclusion that 

the Phillips curve has flattened because he forces the NAIRU to be constant, and that a decline 

in the TV‐NAIRU is an alternative to a flatter PC in explaining why inflation has been relatively 

well‐behaved in the past 20 years. 13 

Some of the NKPC literature estimates the TV‐NAIRU by directly applying an H‐P filter 

to the time series of the unemployment rate. As shown in Figure 6 using two alternative H‐P 

parameters (1600 and 6400) this “direct” approach to estimating the TV‐NAIRU results in an 

unexplained increase in the TV‐NAIRU from 4 percent in 1970 to 8 percent in 1985, whereas the 

energy, and this variable peaks at 3.3 percent in 1974‐75. 

13. After developing the technique described above for estimating the TV‐NAIRU, the recent work of 

Stock and Watson has abandoned that approach in favor of using a direct Hodrick‐Prescott filter to 

estimate the NAIRU in equations which omit explicit supply shock variables. See Staigher‐Stock‐Watson 

(2001) and Stock‐Watson (2006).


triangle approach has no such unexplained increase because of its introduction of explicit 

supply shock variables. 14 

The Roberts specification forces the NAIRU to be constant. Figure 7 displays the Roberts 

estimate of the NAIRU for the PCE deflator, a constant 7.0 percent. It seems illogical for a Fed 

research paper to tell the Board of Governors that the NAIRU is 7.0 percent in 2007 when the 

actual unemployment rate is 4.5 percent. Furthermore, if the Fed Board of Governors believed 

Roberts’ research, it would have been raising interest rates continually over 2006‐07 to prevent 

inflation from accelerating as implied by the divergence between the actual unemployment rate 

and the Roberts NAIRU of 7.0 percent. The pessimism of Roberts’ specification about the 

NAIRU is reflected in its wildly exaggerated forecasts of accelerating inflation as reported in the 

simulation experiments shown below. 

Roberts vs. Triangle: Estimated Coefficients and Simulation Performance 

We next turn to the estimated coefficients, goodness of fit, and simulation performance 

of the Roberts and triangle PC specifications. Table 2 displays the estimated coefficients for 

both the Roberts and triangle specifications for the PCE deflator. Since the sample period is 

uniform across the columns of Table 2, the sum of squared residuals is the basic metric that 

allows us to compare the goodness of fit of the alternative specifications. 

In both specifications the sum of coefficients on the lagged inflation terms is always very 

14. Basthista‐Nelson (2007) are among those authors who exclude explicit supply shock variables from 

their equations and derive estimates of the TV‐NAIRU that are extremely high, e.g., 8 percent in 1975 and 

10 percent in 1981 (2007, p. 509, Figure 6).


close to unity, as in previous research. 15 The sum of the unemployment gap variables in the 

triangle approach is around ‐0.6 for the PCE deflator, which is consistent with a stylized fact 

first noticed in the 1960s that the slope of the short‐run Phillips curve is roughly minus one‐half. 

An elementary textbook on specification bias would explain why the Roberts unemployment 

coefficients are lower than in the triangle specification, namely that when supply shock 

variables are excluded that are positively correlated with inflation and negatively correlated 

with the unemployment gap, then the coefficient on the unemployment gap is biased 

downward toward zero. 

Of the supply shocks in the triangle model, the change in the relative import price effect 

has a highly significant coefficient of 0.06 in the PCE deflator equation, which is less than half of 

the 14 percent share of imports in nominal GDP. The coefficient on the change in the 

productivity trend is entered with lags 1 and 5, and the sum of these coefficients is highly 

significant at a value of about minus unity. The productivity trend effect helps to explain why 

inflation accelerated in 1965‐80 and was so well‐behaved in 1995‐2000. The coefficients for the 

Nixon control variables are highly significant and have the expected signs and magnitudes 

similar to those in past research, that is, the Nixon price controls significantly reduced inflation 

in 1971‐72 and raised inflation in 1974‐75. 

While most papers presenting time‐series regression results display coefficients, 

15. The inclusion of lags 13‐24 (years four through six) is strongly significant in an exclusion test at the 

0.0000 confidence level. As stated in the notes to Table 2, we conserve on degrees of freedom by


significance levels, and summary statistics, few go beyond that and display results of dynamic 

simulations. Yet the performance of the inflation equation, especially in the Roberts/NKPC 

version which includes no variable whatever to explain why inflation increased in 1975 while 

unemployment increased as well, the entire statistical result depends on lagged dependent 

variable terms. For the Roberts/NKPC model, inflation today is whatever it was yesterday, which is not 

a model at all. 

To unveil the heavy dependence of the Roberts/NKPC model on the “today‐isyesterday” 

methodology, dynamic simulations generate the predictions of the lagged 

dependent variable endogenously rather than feeding through the actual value of lagged 

inflation. This makes dynamic simulations the preferable method for testing. To run such 

simulations, the sample period is truncated ten years before the end of the data interval, and the 

estimated coefficients through 1996:Q4 are used to simulate the performance of the equation for 

1997‐2006, generating the lagged dependent variables endogenously. Since the simulation has 

no information on the actual value of the inflation rate, there is nothing to keep the simulated 

inflation rate from drifting far away from the actual rate in a positive or negative direction. 16 

The bottom section of Table 2 displays results of a dynamic simulation for 1997:Q1 to 2006:Q4 

based on a sample period that ends in 1996:Q4. Two statistics on simulation errors are 

including six successive four‐quarter moving averages of the lagged dependent variable at lags 1, 5, 9, 13, 

17, and 21, rather than including all 24 lags separately. 

16. I have been running dynamic simulations of Phillips curves for at least 25 years and cannot 

understand why this has not become a standard testing technique in models where there is a strong 

dependence of results on the lagged dependent variable.


provided, the mean error (ME) and the root mean‐squared error (RMSE). The simulated values 

of inflation in the triangle model are extremely close to the actual values, with a mean error over 

40 quarters of only ‐0.08. The RMSE of the simulations is lower than the standard error of 

estimate for the 1962‐96 sample period. These simulation results are substantially better than 

those reported in Gordon (1998). 

The Roberts and triangle results agree on only one aspect of the inflation process, that 

the sum of coefficients on the lagged inflation terms is always very close to unity. However, the 

Roberts coefficients on the unemployment rate are much lower than the triangle coefficients on 

the unemployment gap. As we shall see, this is an artifact of the exclusion restrictions in the 

Roberts approach which are statistically rejected in the triangle approach. 

The measures of goodness of fit in Table 2 also reject the Roberts specification by a wide 

margin. First, the triangle sum of squared residuals (SSR) is only 27 percent of the Roberts SSR. 

The triangle model explains almost four times the variance of inflation as does the Roberts 

model. 

However, the most telling indictment of the Roberts specification is in the dynamic 

simulation results shown in the bottom section of Table 2 and in Figure 8, which shows the time 

path of the four‐quarter moving average of the simulated post‐sample behavior of the inflation 

rate over 1997‐2006 in the two specifications. The Roberts specification predicts that inflation 

would soar to close to 10 percent in 2006, whereas the triangle model after ten years comes up 

with a small error, a simulated value in 2006:Q4 of 2.6 percent compared to the actual 1.9


percent. Over the entire 40‐quarter simulation period, the mean error for the triangle model 

using the PCE deflator is nearly zero (‐0.08 percent) whereas the same statistic for the Roberts 

model is several orders of magnitude higher, ‐4.67 percent. The Root Mean‐Squared Error of 

the triangle simulation is only 12 percent of the Roberts version, namely 0.60 percent in the 

second column of Table 2 compared to 5.06 percent for Roberts in the first column of Table 2. 

IV. 

The “Translation Matrix” between the Roberts/NKPC and Triangle 

Specifications 

The triangle model outperforms the Roberts/NKPC model by several orders of magnitude, 

as displayed in Table 2 and Figure 8. This raises a question central to future research on the 

U. S. Phillips curve: what are the crucial differences between the triangle and Roberts 

specifications that contribute to the superior performance of the triangle model? The three key 

differences are the inclusion in the triangle model of longer lags on both inflation and the 

unemployment gap, the inclusion of explicit supply‐shock variables, and the allowance for a 

time‐varying (TV) NAIRU in place of Roberts’ assumption of a fixed NAIRU. In this section we 

quantify the role of these differences, taking advantage of the fact that the Roberts model is fully 

nested in the triangle model. Each exclusion restriction in the Roberts model can be tested by 

standard statistical exclusion criteria, and as we will see, every one of Roberts’ exclusion criteria 

is rejected at high levels of statistical significance. 17 

Which Differences Matter in Explaining the Poor Performance of the Roberts/NKPC? 

17. Dew‐Becker (2006) has previously traced the statistical significance of stripped‐down Roberts‐type 

Phillips Curves and reached conclusions that are similar to those arrayed in Table 3.


In everything that follows, the sample period is 1962:Q1 to 2006:Q4. Subsequently we will 

look at the variability of the Phillips curve coefficient (on the unemployment rate or 

unemployment gap) in rolling regressions in order to assess Roberts’ core claim that the PC has 

become flatter since the mid‐1980s. Table 3 provides the “translation matrix” that guides us 

between the Roberts specification for the PCE deflator and the triangle specification. a There are 

24 lines that allow us to trace the role of each specification difference between triangle and 

Roberts/NKPC, and the individual lines of alternative specification are evaluated based not just 

on the SSR measure of goodness of fit, but also on the post‐sample simulation performance in 

1997‐2006 based on coefficient estimates for 1962‐1996. 

We have already seen in Table 2 that the performance of the Roberts specification for the 

PCE deflator is inferior to that of the triangle specification by both the criterion of goodness of 

fit (SSR) and also the less conventional criterion of dynamic simulation performance (ME and 

RMSE). In Table 3 the basic Roberts variant is on line 1 and the basic triangle variant is on line 

21. Roberts’ line 1 and the triangle line 21 have SSR’s of 233.3 and 63.2, exactly the same as in 

Table 2 above. 

Table 3 allows the three main differences between the Roberts/NKPC and triangle 

specifications to be evaluated, step‐by‐step. Is the crucial difference contributing to the better 

statistical performance of the triangle model dependent on the longer lags, on the supply 

shocks, on the TV‐NAIRU, or an interaction of these differences? 

In the 24 lines of Table 3, the first 12 lines exclude supply shock variables, and lines 13‐24


include the supply shock variables. Scanning down the column for “SSR”, we find that the 

variants on lines 13‐24 including supply shocks all have SSR’s below 100, while most of the 

SSR’s that exclude supply shocks have values above 200. Thus our first conclusion is that the 

exclusion of explicit supply shocks in the Roberts/NKPC research is the central reason for its 

empirical failure either to explain postwar inflation or to track the evolution of inflation in postsample 

1997‐2006 simulations. 

What difference is made by long lags and by the TV‐NAIRU? When supply shocks are 

omitted as in lines 1‐12 of Table 3, there is little difference among the alternative variants which 

yield SSR’s ranging from 172.7 to 233.3. Simulation mean errors (ME) range from ‐1.60 to ‐4.67, 

and the lower values are those that include long lags and allow the NAIRU to vary over time. 

More interesting is the set of results that include supply shocks, lines 13 to 24 in Table 3. 

The matrix in Table 3 reveals important interactions between lag lengths, the TV‐NAIRU, and 

the inclusion of supply‐shock variables. When supply shocks are included but lag lengths are 

short, as in lines 13‐14, 17‐19, and 22, the post‐sample simulation errors are very large. When 

supply shocks are included, the best results are on lines 15‐16 with a fixed NAIRU and on lines 

20‐21 with a TV‐NAIRU. Clearly, long lags on the dependent variable (inflation) matter in the 

specification of a PC including supply shocks. 

The right section of Table 3 contains a large number of significance tests on the exclusion of 

variables which are omitted in the Roberts specification and included in the triangle 

specification. Starting on line 3, even without supply shock variables, the significance value of


excluding lags 9‐24 on the lagged dependent variable is 0.00 and on lags 1‐4 of the 

unemployment gap is 0.02. Throughout lines 1‐12 of Table 3, we learn that excluding short lags 

(e.g., excluding lags 5‐8 from equations containing inflation lags 1‐4) is insignificant, whereas 

excluding lags 9‐24 yields highly significant exclusion tests. 

The most important section of Table 3 is in the bottom half, lines 13‐24. Here all lines 

have the full set of supply‐shock variables. The lines differ only in the length of lags included 

on the lagged dependent (inflation) variable and on lagged unemployment, and also on 

whether the NAIRU is forced to be fixed or is allowed to vary over time. We can interpret the 

bottom half of Table 3 by looking at blocks of four rows. 

The first group of four rows, 13 through 16, share in common the inclusion of supply 

shocks, the assumption of a fixed NAIRU, and alternative lags on the dependent variable. The 

mean error in the dynamic simulations falls by 80 percent when lags up to 24 are included, and 

the exclusion of lags 9‐24 is rejected at a 0.00 significance value. The same result occurs in lines 

22‐25 when with a time‐varying NAIRU the significance of long lags on the dependent variable 

are strongly supported at significance levels of 0.00. 

The Fragility of the Conclusion that the PC has Flattened 

Roberts’ research has been highly influential in leading the Federal Reserve to believe 

that the Phillips Curve has become flatter over the past two or more decades. Yet we have seen 

that every assumption of the Roberts (and more broadly NKPC) specification are rejected at 

high levels of statistical significance.


Has the Phillips Curve flattened? The Roberts specification says “yes” and the triangle 

specification says “no”. Figure 9 evaluates changes in coefficients by Roberts’ own preferred 

method (2006, Figure 2, p. 202), rolling regressions that shift the sample period of the regression 

through time in order to reveal changes in coefficients. The number of quarters in our basic 

results in Table 2 is 180 (1962:Q1 to 2006:Q4), and we cut this in half to 90 quarters and run 

rolling 90‐quarter regressions which alternatively start in each quarter from 1962:Q1 to 1984:Q3. 

As shown in Figure 9, the Roberts unemployment coefficient rises from ‐0.17 in 1962 to a 

peak value of ‐0.41 in 1974, and then declines back to roughly zero in 1982‐84. This appears to 

support the basic conclusion of the Roberts (2006) paper, that the Phillips Curve has flattened. 

Yet with the triangle model that fits the data so much better and provides a greatly superior 

post‐sample dynamic simulation performance, there is no evidence at all of a decline in the 

slope of the Phillips curve. As shown in Figure 9, the Phillips curve based on the triangle model 

has a roughly stable PC slope of about ‐0.6 to ‐0.7 from 1963 to 1977, and then the slope rises 

toward about ‐0.7 to about ‐0.9 in the final ten years of the rolling regressions. 

Interactions Among Specification Choices 

An important difference between the Roberts and Triangle approaches is the Roberts 

assumption that the NAIRU is constant. Figure 10 displays the different evolution of the PC 

coefficient in alternative regressions in which the NAIRU is assumed to be constant vs. timevarying. 

The two lines in Figure 10 correspond to lines 21 and 24 in Table 3. As shown in 

Figure 10 the PC coefficient is substantially more volatile when the NAIRU is assumed to be


constant than when it is allowed to vary. The volatility of the fixed‐NAIRU coefficient is not 

surprising, since some of the movements in the TV‐NAIRU are “substitutes” for the movements 

of the PC coefficient. The basic triangle specification with the TV‐NAIRU rather than a constant 

NAIRU leaves open the question of why the NAIRU changed but yields coefficients that are 

more stable over time. 

V. Properties of a Four‐Equation Macro Model 

The rest of this paper develops a small econometric model to assess the role of changes 

in demand and supply shocks and in monetary policy as causes of reduced business‐cycle 

volatility during the post‐1983 period. Our approach differs from that of Blanchard‐Simon 

(2001), who called attention to many of the same factors, including the correlation between 

output and inflation volatility (displayed in Figure 3 above), but who did not develop an 

econometric model to quantify the exact role of the different causes. Our approach is closer to 

that of Stock‐Watson (2002, 2003), who used several different macroeconometric models to 

assess the role of less volatile shocks. 

Like Stock‐Watson (S‐W)’s “SVAR” model (2002, p. 154), our model contains equations 

for the inflation rate, the short‐term interest rate following a Taylor rule specification, and 

output (what S‐W call the “IS” equation). However, we go beyond Stock‐Watson in our 

specification of the inflation process. Their SVAR model subsumes all of the supply shocks in 

the inflation equation into the error term, as in the NKPC specification used by Roberts. 

Instead, we use the triangle inflation specification described and tested above in order to


identify the role the supply shocks in achieving the stabilization of both inflation and output. 

The model developed in this paper starts with the inflation equation developed above 

and adds three extra equations, two of which are similar to those in the Stock‐Watson SVAR 

model and in the three‐equation model developed by Roberts. In addition to the inflation 

equation, the second equation explains the nominal Federal funds rate as responding to the 

output gap and to deviations of actual inflation from the Fed’s inflation target. Then the third 

equation makes the change in the output gap a function of lagged inflation and the change in 

the Federal funds rate. Since the triangle inflation equation is specified with the 

unemployment gap rather than the output gap as its demand‐side variable, we add a fourth 

equation that links the unemployment gap to current and lagged values of the output gap. 

Using a notation that is consistent with the treatment of inflation above, the four‐equation 

model can be written: 

pt = a(L)pt‐1 + b(L)(Ut‐U N t ) + c(L)zt + ept . (8) 

Ft = R* + p* + d(L)(pt ‐ p*) + f(L)Gt + eFt . (9) 

∆Gt = h(L))pt‐1 + j(L))Ft + egt . (10) 

Ut‐U N t = k(L)Gt + eUt . (11) 

The Phillips Curve equation (8) is identical to that written above as equation (6). The Taylor 

rule equation (9) for the nominal Federal Funds rate (F) includes the Fed’s target for the real


funds rate (R*), its target for the inflation rate (p*), a response including possible lags to the 

deviation of the actual inflation rate from the inflation target, and a response including possible 

lags to the level of the output gap (G), which in turn is the log ratio of actual to natural real GDP 

as plotted above in the top frame of Figure 2.. The output gap or “IS” equation (10) makes the 

change in the gap ∆G a function of one or more lags of the first difference of the inflation rate 

and of the change in the nominal Federal Funds interest rate. Finally, the Okun’s law equation 

(11) makes the level of the unemployment gap depend on the current value and one or more 

lags of the output gap. 

Much of the literature on Taylor Rule equations like (9) includes a correction for firstorder 

serial correlation. If we make the error term in (9) follow an AR(1) process: 

eFt = ρeFt‐1 +uFt, uFt~N(0,s). (12) 

then equation (9) is replaced by 

Ft = ρFt‐1 + (1‐ρ)[R* + p* + d(L)(pt ‐ p*) + f(L)Gt] + uFt . (13) 

The Roberts (2006, p. 203) specification for the Taylor Rule is identical to (13) except for the 

exclusion of lagged terms on inflation and the output gap, and for the statement of the target 

nominal interest rate as R* + pt rather than R* + p* as in (13). This means in practice that a sum 

of the d coefficients in (13) of 1.0 is equivalent to a sum for Roberts of 0.0. 

Estimated Coefficients of the Four‐Equation Model 

The columns of Table 4 list the four dependent variables in the model, with the middle 

columns providing alternative sets of results for the interest rate equation. The choice of the


three sub‐intervals reflects apparent changes in Fed reactions corresponding roughly to the 

three periods identified by Stock‐Watson (2003, Table 5), divided up in 1979:Q2 at the start of 

the Volcker period and in 1990:Q2 at end of the period in which the Fed appeared to fight 

inflation aggressively while ignoring output deviations. 

The first column of Table 4 exhibits coefficients in the inflation equation for the PCE 

deflator, which is identical to the equation already discussed in the first column of Table 2. The 

three middle columns show estimated Taylor rule equations for three periods split in 1979 and 

1990. As a shorthand, we will refer to the three sub‐intervals respectively as the “Burns,” 

“Volcker,” and “Greenspan‐Bernanke” responses. These coefficients show that before 1979 the 

Burns Fed “accommodated” inflation, raising the nominal interest rate by only 0.64 of any 

increase in the inflation rate, hence reducing the real interest rate and stimulating demand. 

After 1979 the inflation response jumped from 0.64 to 1.57, so that the Volcker Fed raised the 

nominal Federal funds rate more than the increase of inflation above its target rather than less. 

Further, the Volcker Fed did not respond at all to the output gap. The Greenspan‐Bernanke Fed 

actually responded less to inflation than the Burns Fed and put a slightly higher weight on 

output stabilization than the Burns Fed. This surprising finding that the Greenspan‐Bernanke 

Fed accommodated inflation may be an artifact of the low volatility of inflation during their 

regime, as displayed above in Figure 3. 

The “IS” equation for the first difference of the output gap, shown in the next‐to‐last 

column of Table 5, shows an insignificant positive response to the first difference of the


inflation rate, suggesting no direct feedback from a sharp increase of inflation to a sharp 

decrease in output as might have been suggested by the economy’s behavior in the 1970s. The 

responses to changes in the nominal Federal funds rate are of plausible size and highly 

significant; an increase in the funds rate by 100 basis points causes a decline in the output gap 

by one percentage point with a long lag distributed over the next 10 quarters. 18 The final 

column in Table 5 exhibits the Okun’s Law equation, showing that the unemployment gap 

responds to the output gap over the current and first two lagged quarters with a highly 

significant coefficient of ‐0.49, supporting the 2‐to‐1 responsiveness of the output gap to the 

unemployment gap endorsed by research over the past 40 years in place of the 3‐to‐1 

responsiveness originally discovered by Okun. 

Single‐Equation Model Simulations 

The aim of building the model is to use it to decompose the sources of business cycle 

volatility. For this purpose we will focus on three different sources of volatility and its post‐ 

1983 reduction, namely set of supply shocks included in the inflation equation, the error term in 

the output gap equation, and shifts in the parameters in the interest rate equation that reflect 

changes in Fed policy. 19 In this section we will examine the performance of each equation 

18. The current and first lags of the interest rate are omitted in the output gap equation because of 

simultaneity; in the short‐run changes in output and interest rates tend to be positively correlated as “IS 

shifts” move the economy along the “LM curve.” We use the nominal rather than real interest rate 

because it fits better, perhaps reflecting the role of nominal interest rate ceilings before 1980. 

19. No attention is paid to errors in the Okun’s law equation, which is viewed here as a purely 

mechanical bridge between the output and unemployment gaps. Further, because of the large role of the


without model interactions; that is, each equation’s predicted values are examined using actual 

historical values for the endogenous explanatory variables. Subsequently we will examine 

simulations that feed back simulated values of the endogenous variables. 

Figure 11 displays a dynamic simulation of the PCE deflator for the period 1965:Q1‐ 

2006:Q4 in which the coefficients are estimated through 2006 but the lagged dependent variable 

is fed back endogenously. One simulation uses the actual values of the supply‐shock variables; 

the other sets the values of all the supply shock variables equal to zero but retains the actual 

historical values of the unemployment gap. Simulated inflation with no supply shocks remains 

roughly equal to the full‐shock simulation through early 1973 and then stays consistently below 

the full‐shock simulation by a large amount through 2006. Since the only variable driving an 

acceleration or deceleration of inflation is the unemployment gap, the severe recessions of 1974‐ 

75 and 1981‐82 cause marked declines in the inflation rate, sending it close to zero in 1984‐5 and 

again in 1994‐95. Notice that the difference between the two simulations narrows in the late 

1990s, since the full‐shock simulated value of inflation fails to accelerate in 1995‐2001, due to the 

role of beneficial supply shocks that provided the Greenspan Fed with good luck and enabled it 

to avoid raising the Fed funds rate as it had in 1987‐89. 

We now turn to the single‐equation behavior of the interest rate equation, taking its 

explanatory variables as exogenous. All the simulations in this paper assume that the inflation 

target (p*) in equation (6) is 2.0 percent and that the real interest rate target (R*) is 3.0 percent. 

lagged interest rate variable in the Taylor Rule equation (13), the interest rate errors are small and


As in Table 4, the coefficients on inflation and the output gap are allowed to shift at 1979 and 

1990. The fitted values of the equation are extremely close to the actual values, which is no 

surprise in light of the correction for serial correlation, and there is no need to plot them. 

The central topic of this paper is the contribution of the Phillips Curve specification to 

explaining the reduced volatility of the output gap, as already examined above in the two 

frames of Figure 2. The predictive performance of the output gap equation is shown in Figure 

12. While the equation is estimated in first difference form, the actual and predicted values of 

the first differences are converted back to the level of the output gap for graphing in Figure 12. 20 

Clearly, the output gap has a life of its own that is not captured by the simple “IS” equation. 

The output gap equation predicts a much smaller recession in 1974‐75 than actually occurred. 

The equation’s predictions overstate the severity of the 1980‐85 slump and also fail to capture 

the output gap’s rise above zero in the late 1980s. Further, the predicted values completely miss 

the timing of the ups and downs of the output gap after 1990. 

These errors in the output gap equation are not bad news for the model. Rather, they 

remind us that output determination depends on far more than movements back and forth 

along the slope of a fixed IS curve, as is implied by our model (based in turn on the Stock‐ 

Watson SVAR) which makes changes in interest rates the only significant source of changes in 

the output gap. Obviously shifts in the IS curve matter as well, and it would take a much more 

uninteresting. 

20. The errors in the first difference equation are translated into errors in the level of the output gap by


complex model to capture the sources of these IS shifts. Missing from the predictions of the 

output gap equation in Figure 10 are such important events as Vietnam war spending in the late 

1960s and the timing of the hi‐tech investment boom of the late 1990s. In the full‐model 

simulations discussed below we will explore the effects of suppressing the error term in the 

output equation. Our interpretation of the output gap error is based on Gordon (2005), in 

which three main forces drive the increased stabilization of the output gap error term – the 

reduced share and volatility of government military spending, the increased stability of 

inventory investment, and financial reforms that reduced the volatility of residential structures 

investment. 21 

Table 5 summarizes the single‐equation results. The top four lines calculate standard 

deviations of the actual values of the inflation rate, Federal funds rate, and level and first 

difference of the output gap. The reported standard deviations for the actual inflation rate and 

output gap are similar to those in our text discussions of Figures 2 and 3 above, with a decline 

in the standard deviation of the output gap and inflation of about 76 percent in logs. In contrast 

the volatility of the interest rate declined by much less, about 40 percent in logs. 

How well do the simulations (for the inflation equation) and predicted values (for the 

other equations) replicate the lower standard deviations of the actual values? Simulated 

inflation falls by 81 percent, slightly more than the actual value, and simulated inflation declines 

forcing the level errors to have a mean of zero over the 1965‐2004 period. 

21. The role of financial market reforms in achieving reduced volatility has been studied in detail by 

Dynan, Elmendorf, and Sichel (2005).


by a smaller 61 percent when supply shock variables are excluded. However, as we have seen 

in Figure 11 above, much of the pre‐1984 inflation volatility in the “no‐shocks” scenario is due 

to the role of deep recessions in forcing inflation much lower than the actual outcome. A full 

understanding of the role of supply shocks requires us to unleash the full set of model 

interactions, since without supply shocks in the 1970s there would not have been the spikes of 

the interest rate in 1981‐82 nor the deep recession of 1981‐82. 

The single‐equation predictions for the Federal funds rate differ from the other 

equations because the error term is so small, virtually eliminated by the serial correlation 

correction. The predicted value for the interest rate has a decline in its standard deviation of 37 

percent in Table 5, very similar to the actual decline of 41 percent. The output gap equation 

yields a predicted value that has a decline in its standard deviation of 55 percent, much less 

than the actual 76 percent decline. Eliminating the error term in the output gap equation cuts 

the standard deviation by half before 1984 and by about 40 percent after 1984, indicating that a 

reduction in the variance of the output error contributed to business cycle stabilization after 

1983. 

Full‐Model Simulations 

To assess the role in achieving reduced business‐cycle volatility of supply shocks in the 

inflation equation, and of the error term in the output gap equation, we run full model 

simulations with alternative shocks set equal to zero, one at a time and then all together. Table 

6 contains five sections, one each for the standard deviation of inflation, of the interest rate, and


of the output gap, then the average value of inflation and the average absolute value of the 

output gap. Within each section there are four lines corresponding to the full model 

simulations and alternative simulations that suppress the shocks one at a time and all together. 

The contrast between the single‐equation and full‐model simulations can be seen by 

comparing Tables 5 and 6. Here is the log percent change of the standard deviations for 1984‐ 

2006 relative to 1965‐83 for each of the three variables, comparing the actual values, the singleequation 

simulation values, and the full‐model simulation values. 

Log Percent Ratio of Standard Deviations, 1984‐2004 to 1965‐83 

Four‐Quarter 

Inflation Rate Interest Rate ∆Output Gap 

Actual Values ‐76.3 ‐40.9 ‐80.2 

Single‐Equation Simulations ‐80.6 ‐37.0 ‐54.9 

Full‐Model Simulations ‐62.9 ‐7.8 ‐49.9 

The full‐model simulations share with the single‐equation simulations that they include the 

exogenous effects of the supply‐shock variables in the inflation equation, as well as the error 

terms in the interest rate and output gap equations. But they differ in that they use endogenous 

model‐generated values rather than exogenous data‐generated values for the endogenous 

variables in each equation. The switch to the full model simulations reduces the estimated post‐ 

1983 decline in the volatility of all three variables, the inflation rate, the interest rate, and the 

change in the output gap.


Counter‐Factual Full‐Model Simulation Results Supressing Supply and Demand 

Shocks 

We can now discuss the relative role of the supply and demand shocks in explaining the 

model’s simulated volatility of the economy. Because of the serial correlation correction, errors 

in the interest rate equation play no role in the explanation. We start with the alternative 

simulations for the inflation rate as described in the top section of Table 6. For the first period, 

suppressing the supply shocks eliminates about two‐thirds of the standard deviation of 

inflation in the first period, while suppressing the output gap error eliminates about 25 percent 

of the standard deviation of inflation in the first period. Suppressing supply shocks reduces the 

second‐period standard error by about half, but suppressing the output error actually raises 

volatility as compared to the “all shocks” variant. 

Figure 13 illustrates the role of supply 

shocks and the output error in explaining the behavior of the inflation rate. The dark solid line 

shows the full model simulation, which is virtually identical to the single‐equation simulation 

depicted in Figure 11. Suppressing the output error reduces the inflation rate by between three 

and four percent throughout the simulation period. Since the output equation cannot generate 

the excess demand of the late 1960s, without the output error the model forecasts less inflation 

throughout the full 40‐year simulation period. What remains when the output error is 

suppressed represents the combined contribution of the supply shocks, causing an acceleration 

of inflation of six percentage points between 1972 and 1975, and a reversal in which inflation 

decelerated by about seven percentage points between 1981 and 1987. Thus, ironically, the


“Volcker disinflation” that has usually been attributed to monetary policy actually should be 

credited in large part to the reversal of supply shocks, not just the decline in the real price of oil 

but also the effects of the dollar appreciation of 1980‐85. 

Turning to the Federal funds rate, Table 6 shows that eliminating supply shocks in 1965‐ 

83 reduces the standard deviation of the interest rate by more than one‐third, as does 

eliminating the output error. In the second period supply shocks have no impact in reducing 

volatility, but suppressing the output error reduces the standard deviation of the interest rate by 

about one‐third. Thus when we compare 1965‐83 with 1984‐2006, there was a reduction in the 

volatility of the interest rate by about two‐thirds when the effects of both supply shocks and 

output errors are combined. Yet, surprisingly, the role of these shocks was about the same in 

each period so that they contributing nothing to the stabilization of interest rates, as we can see 

in the second section of Table 6 when we compare the “All Shocks” and “No Shocks” outcomes. 

The simulations for the interest rate are displayed in Figure 14. Due to the correction 

for serial correlation, suppressing the model’s own‐equation interest rate error makes virtually 

no difference. Compared to the basic model simulation, suppressing the supply shocks makes a 

big difference in holding down the interest rate between 1974 and 1985, but after 1985 reduces 

the interest rate by very little. Suppression of the output error also makes a big difference in 

reducing the interest rate throughout the 40‐year simulation period, and particularly between 

1977 and 1992. Recall that eliminating the output error works directly through the output gap 

term in the interest rate equation and indirectly through the effect of a lower output gap in


reducing the inflation rate and hence reducing the interest rate through the inflation term in the 

interest rate equation. 

The next section of Table 6 for the standard deviation of the output gap shows that 

about half of the volatility of the output gap in the first period was caused by the output error 

but, surprisingly, none of the volatility in the second period. Suppressing the supply shocks 

eliminates about one‐third of the output gap volatility in the first period but none in the second 

period. 

The Fed’s objective as captured in the model’s interest rate equation is not the standard 

deviation of the inflation rate but rather its average value. As for the output gap, the Fed’s goal is 

for the output gap to be zero, and hence to minimize the average absolute value of the output 

gap. The bottom two sections of Table 6 report on the effect of shocks on these two central 

objectives of Fed policy. 

Suppressing the supply shocks would have converted the actual decline in the average 

inflation rate across the two periods from 5 to 2.2 percent, into an identical 3.2 percent across 

both periods. That is, supply shocks were adverse before 1983 and beneficial after 1983. Thus 

supply shocks are the whole story of why inflation declined by so much after 1984. In contrast 

the output error made inflation higher in both periods, and with no output error the inflation 

rate would have been negative after 1984. 

Overall, both the supply shocks and the output error contributed to the high volatility of 

inflation and the output gap before 1983, as well as to the high average value of inflation and


the high average absolute value of the output gap. Suppressing the supply shocks makes the 

economy’s behavior in the first period similar to its behavior in the second period, thus 

eliminating the puzzle of reduced volatility, and in fact suppressing the supply shocks makes 

average inflation in the second period slightly higher than in the first period. Suppressing the 

output error makes the economy more stable and inflation lower in both periods. Without the 

output shocks, the output gap would have been much smaller and less volatile in both periods, 

and without the output error we still would have had a puzzle of improved post‐1983 volatility 

that would have been resolved by the role of the supply shocks. 

VI. 

What Difference does PC Specification Make to Full‐Model Conclusions? 

This paper has placed primary emphasis on the contrast between the Roberts version of 

the NKPC and the alternative triangle model, which performs with orders of magnitude better 

in both standard goodness of fit measures and also in post‐sample dynamic simulations. We 

now ask how much difference the use of the triangle vs. Roberts inflation equation makes in the 

evaluation of the sources of reduced business cycle volatility since 1984. 

Table 7 is arranged with the same five vertical sections as we have already examined in 

Table 6. In each section there are four rows, so that we may contrast the impact in the triangle 

model of omitting the set of supply shock variables, with the Roberts model where the 

analogous exercise is to eliminate the error term in his inflation equation. In the next version of 

this paper, we will add an extra line for the triangle version to omit both the set of supply shock


variables and the error term in the triangle equation. An important caveat in Table 7 is that the 

only difference between the Roberts and triangle results refer to the inflation equation. The 

interest rate, output gap, and unemployment gap equations in our basic model are used 

throughout in deriving the results of Table 7. 

The top section of Table 7 shows that removing the explicit supply shock variables from 

the triangle model reduces the standard deviation of inflation much more before 1984 than after 

1983. Thus the supply shocks continue to explain most of the changed volatility of inflation 

after 1983. The third and fourth line of the top section substitute the Roberts approach. While 

the Roberts equation yields the same decline in volatility after 1984, its diagnostic ability is 

impaired. Removing the error term in the Roberts equation yields a much higher 1.48 standard 

deviation than with the triangle approach (0.82 standard deviation), and the Roberts equation 

without the error term suggests that the standard deviation of inflation should have increased 

after 1983. 

The next section of Table 7 shows that the triangle and Roberts PC specifications reach a 

similar conclusion. Suppressing the triangle supply shocks imply that interest rate volatility 

would have been higher post‐1984, and the suppression of the error term in the Roberts PC 

equation yields the same conclusion, although by a smaller amount. 

An important difference between the triangle and Roberts results appears in the third 

section of Table 7, where we examine the effect of alternative inflation equations in explaining 

changes in the standard deviation of the output gap. In the triangle model removing the supply


shocks removes about 1/3 of output volatility in the pre‐1984 period and nothing after 1984. 

Thus the supply shock variables in the triangle PC equation explain a substantial part of the 

reduction in output volatility after 1983. 

The results with the Roberts inflation equation in the multi‐equation model for the 

standard deviation of the output gap can be dismissed as perverse. With the inflation error in 

its own PC equation, the Roberts model cannot explain any of the standard deviation of the 

output gap before or after 1984. Omitting the inflation error leaves the Roberts inflation model 

clueless as to why the actual standard deviation of inflation declined after 1984. 

VI. Conclusion 

This paper began with the journalistic characterization of the Fed’s view that the slope of 

the United States Phillips Curve (PC) has become substantially flatter, by a factor of at least half, 

since the mid‐1980s. The flattening of the Phillips curve is documented in a particular style of 

PC research based on the New Keynesian Phillips Curve (NKPC) literature, in which PC 

specifications involve links between the current inflation rate and short lags on inflation, and on 

the current unemployment rate. The first part of this paper uses a wide variety of statistical 

tests to show that the Fed’s PC equation as based on research by Roberts (2006) is strongly 

rejected both by traditional and nontraditional tests when compared to the Gordon “triangle” 

model that was developed in the early 1980s. 

The remainder of the paper asks why the volatility of output changes and the output 

gap has declined substantially after 1984, a phenomenon on which U. S. macroeconomists share


an unusual consensus about its existence but not about its causes. Our analysis based on a 

small macroeconometric model concludes that about 1/3 of the reduction in the volatility of real 

GDP can be traced to the role of supply shocks in the triangle inflation equation. More 

important are errors in the output gap equation that quantifies the role of monetary policy in 

reducing output when interest rates are high and stimulating output when interest rates are 

low. 

To highlight the role of Phillips curve specifications in the analysis of reduced U.S. 

business cycle volatility, we show that the Roberts/NKPC type Phillips curve specification 

misses much of the role of supply shocks in contributing to reduced volatility in both inflation 

and output. Not only is the triangle approach necessary to understand the evolution of the U. S. 

inflation rate over the postwar era, but also the triangle approach is required to examine the 

sources of reduced business cycle volatility. Papers that omit the supply‐shock variables and 

long lags integral to the triangle approach understate the role of reduced shocks in explaining 

the lower volatility of both inflation and output changes in the postwar U. S. economy.


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26, A1. 

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Expectations,” unpublished working paper, Federal Reserve Bank of San Francisco, 

September.

Appendix 

TABLE 1 

Rolling Standard Deviations of Output Changes, Output Gap, and Inflation 

Over Selected Intervals, 1952:Q4 to 2007:Q1 

Rolling Standard Deviations 

Log Percentage 

Change 

1952:Q4- 1973:Q1- 1952:Q4- 1988:Q1- 

Variable 1972:Q4 1987:Q4 1987:Q4 2007:Q1 1988‐07 vs. 1973‐87 

Four‐Quarter Change in Real GDP 2,72 2,83 2,77 1,24 -80,3 

Four‐Quarter Change in GDP Deflator 1,14 1,59 1,33 0,49 -100,0 

Output Gap 1,85 2,42 2,09 1,16 -59,0 

Ratio GDP Deflator to Real GDP 41,9 56,2 48,1 39,5 -19,7 

Ratio Output Gap to Real GDP 68,0 85,5 75,6 93,5 21,3

TABLE 2 

Estimated Equations for Quarterly Changes in 

PCE Deflators, 1962:Q1 to 2006:Q4 

Variable Lags Roberts Triangle 

Constant 1,01 * 

Lagged Dependent Variable 1-24 a 1,00 ** 

1-4 0,96 ** 

Unemployment Gap 0-4 -0,57 ** 

Unemployment Rate 0 -0,15 * 

Relative Price of Imports 1-4 0,06 ** 

Food‐Energy Effect 0-4 0,90 ** 

Productivity Trend Change 1 5 -0,97 ** 

Nixon Controls ʺonʺ 0 -1,54 ** 

Nixon Controls ʺoffʺ 0 1,91 ** 

R2 0,79 0,94 

S.E.E 1,16 0,64 

S.S.R 233,3 63,2 

Dynamic Simulation 

1997:Q1 ‐ 2006:Q4 Note b 

Mean Error -4,67 -0,08 

Root Mean‐Square Error 5,06 0,60 

a) Lagged dependent variable is entered as the four-quarter moving 

average for lags 1, 5, 9, 13, 17, and 21, respectively 

b) Dynamic simulations are based on regressions for the sample period 

1962:Q1-1996:Q4 in which the coefficients on the lagged dependent 

variable are constrained to sum to unity.

Inf Lag 

U lag 

length 

Fixed or TV 

NAIRU 

Supply 

Table 3 

Transformation of Philips Curve 

shock R2 SEE SSR ME RMSE F Stat 

Exclude inf 

lags 5‐8 

Sig 

Level 

Exclude inf lags 

F Stat 

9‐24 

Sig 

Level 

Exclude U lags 

F Stat 

1‐4 

Sig 

Level 

Exclude Supply 

Shocks 

Sig 

1 1 to 4 0 Fixed No 0,79 1,16 233,3 -4,67 5,06 

2 1 to 8 0 Fixed No 0,79 1,16 228,0 -4,47 4,84 0,98 0,42 

3 1 to 24 0 fixed No 0,81 1,09 183,3 -3,63 3,87 2,35 0,00 

4 1 5 9 13 17 21 0 fixed No 0,79 1,16 229,8 -3,53 3,77 

5 1 to 4 0 to 4 Fixed No 0,80 1,13 217,6 -4,42 4,73 3,08 0,02 

6 1 to 4 0 to 4 TV No 0,80 1,11 211,8 -2,05 2,32 

7 1 to 8 0 to 4 TV No 0,80 1,12 209,1 -2,03 2,31 0,54 0,70 

8 1 to 24 0 to4 TV No 0,82 1,07 174,4 -1,84 2,12 1,88 0,03 

9 1 5 9 13 17 21 0 to 4 TV No 0,80 1,12 212,3 -1,60 1,92 

10 1 to 8 0 to 4 Fixed No 0,79 1,14 214,5 -4,37 4,67 0,59 0,67 

11 1 to 24 0 to 4 Fixed No 0,82 1,07 172,7 -3,92 4,15 2,27 0,01 

12 1 5 9 13 17 21 0 to 4 Fixed No 0,80 1,11 207,2 -3,62 3,84 

13 1 to 4 0 Fixed Yes 0,91 0,77 96,1 -3,84 4,37 17,68 0,00 

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 

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 

16 1 5 9 13 17 21 0 fixed Yes 0,92 0,70 78,5 -0,56 0,92 23,60 0,00 

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 

18 1 to 4 0 to 4 TV Yes 0,91 0,76 91,7 -3,05 3,33 15,93 0,00 

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 

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 

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 

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 

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 

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 

F Stat 

Level

TABLE 4 

Coefficients from Four‐Equation Model, estimated for 1962:Q1 to 2006:Q4 

Dependent Variable 

Nominal Federal Funds Rate 

1960:Q1‐ 1979:Q3‐ 1990:Q3‐ 

1979:Q2 1990:Q2 2006:Q4 

Lags 

included 

Inflation 

Rate 

Burns 

Volcker 

Bernanke 

∆ Output 

Gap 

Greenspan‐ 

Unemployment 

Gap 

Endogenous Variables 

Inflation 1-24 a 1,00 ** 

Inflation minus Inflation Target 0-1 0,64 ** 1,57 0,37 

∆ Inflation Rate 1-4 0,02 

Federal Funds Rate Error Term 1 0,79 ** 0,72 ** 0,96 ** 

∆ Federal Funds Rate 2-10 -0,95 ** 

Level of Unemployment Gap 0-4 -0,57 ** 

Level of Output Gap 0-1 0,52 ** 0,16 0,63 ** 

Level of Output Gap 0-2 -0,49 ** 

Exogenous Variables 

Relative Price of Imports 1-4 0,06 ** 

Food‐Energy Effect 0-4 0,90 ** 

Productivity Trend Change 1 5 -0,97 ** 

Nixon Controls ʺonʺ 0 -1,54 ** 

Nixon Controls ʺoffʺ 0 1,91 ** 

R2 0,94 0,91 0,82 0,94 0,20 0,71 

S.E.E 0,64 0,73 1,36 0,42 0,72 0,71 

S.S.R 63,2 38,5 70,8 10,5 87,2 89,8 

a) Lagged dependent variable is entered as the four-quarter moving 

Notes: (*) indicates that coefficient or sum of coefficients is significant at 5 percent level. (**) at 1 percent level

Table 5 

Single Equation Simulations 

1965:Q1‐1983:Q1 

1984:Q1‐2006:Q4 

Log Percent Ratio 

of 1984‐2006 to 

1965‐83 

Inflation Rate 2,66 1,24 -76,3 

FF Rate 3,65 2,43 -40,9 

Level of Output Gap 2,92 1,36 -76,4 

First Difference of Output Gap 1,09 0,49 -80,2 

Simulation Results 

Simulated Inflation 2,52 1,12 -80,6 

Simulated Inflation 1,69 0,92 -61,3 

Without Supply Shocks 

Predicted FF Rate 3,34 2,30 -37,0 

First Difference of Output Gap 0,50 0,29 -54,9

Table 6 

Standard Deviations of Full‐Model Specifications, Split‐sample 

Taylor Rule, 1965:Q1 to 2006:Q4 

1965:Q1‐1983:Q1 

1984:Q1‐2006:Q1 

Log Percent 

Ratio of 1984‐ 

2006 to 1965‐ 

Standard Deviation of Inflation Rate 

All Shocks 2,58 1,38 -62,93 

No Supply Shocks 0,82 0,62 -27,81 

No Output Error 1,95 1,52 -24,68 

No Shocks 0,44 0,61 34,08 

Standard Deviation of Fed Funds Rate 

All Shocks 3,57 3,30 -7,75 

No Supply Shocks 2,29 3,29 36,37 


No Shocks 1,21 1,15 -5,22 

Standard Deviation of Output Gap 

All Shocks 2,55 1,55 -49,89 


No Output Error 1,37 1,67 19,79 

No Shocks 0,70 0,87 22,13 

Average Inflation Rate 

All Shocks 4,98 2,22 -80,76 

No Supply Shocks 3,12 3,18 2,10 

No Output Error 2,33 -1,78 --- 

No Shocks 0,33 -0,60 --- 

Average Absolute Value of Output Gap 

All Shocks 2,06 1,31 -45,52 



No Shocks 0,84 0,75 -10,73 

83

Table 7 

Standard Deviations of Full‐Model Specifications, Substituting in Roberts 

Equations 

1965:Q1‐1983:Q1 

1984:Q1‐2006:Q1 

Log Percent 

Ratio of 1984‐ 

2006 to 1965‐ 

Standard Deviation of Inflation Rate 

Triangle with Supply Shocks 2,58 1,38 -62,93 

Triangle without Supply Shocks 0,82 0,62 -27,81 

Philips with Inflation Error 2,66 1,24 -76,31 

Phillips without Inflation Error 1,48 1,82 20,80 

Standard Deviation of Fed Funds Rate 


Triangle without Supply Shocks 2,29 3,29 36,37 


Phillips without Inflation Error 2,06 2,35 13,37 

Standard Deviation of Output Gap 




Phillips without Inflation Error 2,04 2,03 -0,45 

Average Inflation Rate 


Triangle without Supply Shocks 3,12 3,18 2,10 



Average Absolute Value of Output Gap 





83

Figure 1A. Four Quarter Growth Rate of Real GDP vs Average Real 

GDP Growth, 

1948:Q1 to 2007:Q1 

Percent per year 

14 

12 

10 

8 

6 

4 

2 

0 

Actual Real GDP 

Growth 

-2 

Average Real GDP 

-4 

Growth 

1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 

Figure 1B. Twenty Quarter Rolling Standard Deviation of Real GDP 

Growth, 

1952:Q4 to 2007:Q1 

4,5 

4 

3,5 

3 

Percent 

2,5 

2 

1,5 

1 

0,5 

0 

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Figure 2A. Output Gap, 1950:Q2 to 2006Q4 

6 

4 

2 

Log Output Ratio 

0 

-2 

-4 

-6 

-8 

-10 

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 

Figure 2B. Twenty Quarter Rolling Standard Deviation of Output Gap, 

1955:Q1 to 2006:Q4 

4 

3,5 

3 

Percent 

2,5 

2 

1,5 

1 

0,5 

0 

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 

4,5 

4 

3,5 

Output Growth 

Volatility 

3 

2,5 

2 

1,5 

1 

0,5 

Inflation Volatility 

0 

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Figure 4A. Four Quarter Average of Import Shocks, 1960:Q1 

to 2006:Q4 

20 

15 

10 

5 

0 

-5 

-10 

-15 

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 

Figure 4B. Four Quarter Average of Food and Energy 

Shocks, 1960:Q1 to 2006:Q4 

4 

3 

2 

1 

0 

-1 

-2 

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Figure 5. Acceleration of Trend Productivity Growth, 

1960:Q1 to 2006:Q4 

0,6 

0,5 

0,4 

0,3 

0,2 

0,1 

0 

-0,1 

-0,2 

-0,3 

-0,4 

-0,5 

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Figure 6. Actual Unemployment Rate vs. Time-Varying NAIRU, 1962:Q1 to 2006:Q4 

11 

10 

Unemployment rate 

9 

Unemployment HP λ=6400 

8 

Unemployment HP λ=1600 

7 

6 

TV NAIRU 

5 

4 

3 

1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006

Figure 7. Time-Varying NAIRU vs. Constant NAIRU, 1962:Q1 to 2006:Q4 

Unemployment rate 

9 

Constant NAIRU 

6 

TV NAIRU 

3 

1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006

Figure 8. Predicted and Simulated Values of Inflation from Triangle and Roberts Equations 1962:Q1 to 

2006:Q4 

12 

Inflation 

10 

Roberts 

8 

6 

4 

2 

Triangle 

0 

1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007

Figure 9. Roberts Vs. Triangle Unemployment Coefficients on 90 Quarter Rolling Regressions from 

1962:Q1 to 1984:Q3 

0 

-0,1 

-0,2 

Roberts 

-0,3 

-0,4 

-0,5 

Triangle 

-0,6 

-0,7 

-0,8 

-0,9 

-1 

1963 1966 1969 1972 1975 1978 1981 1984

Figure 10. Constant NAIRU vs. Time Varying NAIRU Unemployment Coefficients on 90 Quarter Rolling 

Regressions from 1962:Q1 to 1984:Q3 

0 

-0,2 

Constant NAIRU 

-0,4 

-0,6 

TV NAIRU 

-0,8 

-1 

-1,2 

1963 1966 1969 1972 1975 1978 1981 1984

Figure 11. Predicted Inflation with and without Supply shocks, 

1962:Q1 to 2006:Q4 

12 

Predicted Inflation with Actual 

Shocks, 1965:Q1-2006:Q4 

10 

8 

6 

4 

2 

Predicted Inflation with Shocks 

Suppressed, 1965:Q1-2006:Q4 

0 

-2 

1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

Figure 12. Actual and Predicted Level of the Output Gap 

6 

Estimated Error 

4 

Actual 

2 

0 

-2 

-4 

Predicted 

-6 

-8 

-10 

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 inflation Rate, 

1965:Q1 to 2006:Q4 

12 

10 

All Shocks 

8 

6 

No Supply Shocks 

4 

2 

0 

-2 

No Output Error 

No Shocks 

-4 

-6 

1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

Figure 14. Simulated Values of Four Quarter Moving Average of Fed Funds Rate, 

1965:Q1 to 2006:Q4 

18 

16 

All Shocks 

14 

12 

10 

No Supply Shocks 

8 

6 

4 

2 

0 

No Output Error 

-2 

No Shocks 

-4 

1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

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