Economic Models - Convex Optimization

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Inflation Control in Central and Eastern European Countries 183 Figure 4. Republic. Quarterly inflation, output gap, real exchange rate depreciation, Czech Figure 5. Slovenia. Quarterly inflation, output gap, real exchange rate depreciation, is already possible to notice that, while for Germany, the dynamics of inflation is dictated by the output gap, in the three new EU members inflation is largely dictated by the real exchange rate dynamics. Estimation was carried out using OLS equation by equation, as in Rudebush and Svensson (1999). We did not introduce any other modification to
184 Fabrizio Iacone and Renzo Orsi the AD equation, but we re-wrote the PC as π t = α 0 + ρ 0 π t−1 + ρ 1 π t−1 + ρ 2 π t−2 + ρ 3 π t−3 + ρ y y t−1 + α q (q t−1 − q t−5 ) + ε π,t PC (the term q t−1 − q t−5 does not appear in the equation for Germany). This is a re-parametrization of the original equation, with ρ 0 = (α π1 + α π2 + α π3 + α π4 − 1) ρ 1 =−(α π2 + α π3 + α π4 ), ρ 2 =−(α π3 + α π4 ), ρ 3 =−α π4 Being simply a re-parametrization, the residual sum of squares that has to be minimized is the same, so the OLS estimates are not different than the estimates that one would obtain in the original model in levels. The advantage of this specification is that long and short dynamics are explicitly separated, ∑ 4 j=1 α πj = 1 corresponding to p 0 = 0, and that, more importantly, the multi-collinearity due to the terms π t−1 to π t−4 is much less severe. Correct specification was primarily checked by looking at the tests for normality (Jarque and Bera), autocorrelation (up to the fourth lag: Breusch .Godfrey LM) and heteroskedasticity (white without cross terms) in the residuals: we referred to these tests using N for the normality, AC for the autocorrelation, and H for the heteroskedasticity. If the model appeared to be correctly specified, we then analyzed the stability of the parameters over time. If we did not reject the hypothesis of stability either, we moved to test specific restrictions on the parameters, and to estimate a more efficient version of the model. In all the tests, we used the conventional 5% size. In the tables in the Appendix, we presented both the P-values associated to the tests and a summary of the equation estimated when the restriction was imposed. We considered the normality test first, because we used its result to choose between the small or large sample version of the other tests. Since the small and large sample statistics are asymptotically equivalent in large samples, the asymptotic interpretation of the results is not affected. Admittedly, due to the asymptotic nature of the Jarque and Bera test, and to the small sample lower order bias in the estimation of autoregressive coefficients, the reader may be cautious in the interpretation of the results, especially, when only portions of the dataset are used to estimate parameters (like in the Chow stability test or in the estimates on sub-samples): notice anyway that this is a problem that depends on the dimension of the sample; so, indeed the same caveat applies to all the empirical analyzes present in
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ECONOMIC MODELS Methods, Theory and
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ECONOMIC MODELS Methods, Theory and
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This Volume is Dedicated to the Mem
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Contents Tom Oskar Martin Kronsjo:
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Tom Oskar Martin Kronsjo: A Profile
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Tom Oskar Martin Kronsjo students t
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About the Editor Prof. Dipak Basu i
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Contributors Athanasios Athanasenas
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Contributors Victoria Miroshnik, is
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xx Introduction type of model is ve
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4 Olav Bjerkholt Among these was al
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6 Olav Bjerkholt method, searching
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8 Olav Bjerkholt context, but one o
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10 Olav Bjerkholt be modified in th
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12 Olav Bjerkholt through a number
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14 Olav Bjerkholt memoranda. These
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16 Olav Bjerkholt hopelessly ineffe
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18 Olav Bjerkholt References Arrow,
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24 Alexis Lazaridis A straightforwa
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26 Alexis Lazaridis where ⎛ ⎞ j
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28 Alexis Lazaridis Estimating the
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30 Alexis Lazaridis 5.1. Testing fo
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32 Alexis Lazaridis by applying the
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34 Alexis Lazaridis Nevertheless, t
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36 Alexis Lazaridis Table 2. Residu
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38 Alexis Lazaridis Table 3. Critic
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40 Alexis Lazaridis Figure 4. The s
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42 Alexis Lazaridis Perron, P and T
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44 Dipak R. Basu and Alexis Lazarid
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70 Andrew Hughes Hallet have, there
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78 Andrew Hughes Hallet control inf
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80 Andrew Hughes Hallet Table 2. Fi
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94 Andrew Hughes Hallet Table 3. Ex
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102 Chirstophe Deissenberg and Pave
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Page 161 and 162: 138 Victoria Miroshnik 2. Corporate
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Page 175 and 176: 152 Anna-Maria Mouza of salaries of
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Page 191 and 192: 168 Anna-Maria Mouza The solution o
Page 197 and 198: 174 Fabrizio Iacone and Renzo Orsi
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Page 225 and 226: 202 Athanasios Athanasenas 2. The C
Page 227 and 228: 204 Athanasios Athanasenas to asset
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Page 245 and 246: 222 Athanasios Athanasenas Lown, C
Page 247 and 248: 224 Index fiscal expansions, 91, 92
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Economic Models - Convex Optimization

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