Appendices. Chile models. Appendix

Transcription

1 Appendices Appendix Chile models Table 1 New Philips curve Dependent Variable: DLCPI Date: 11/15/04 Time: 17:23 Sample(adjusted): 1997:2 2003:4 Included observations: 27 after adjusting endpoints Kernel: Bartlett, Bandwidth: Fixed (2), No prewhitening Convergence achieved after: 18 weight matrices, 19 total coef iterations Instrument list: DLCPI(-1 TO -4) SHLAB GDPGAP DLWPXC DLUSD Variable LABGAP DLCPI(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Table 2 Non-linear estimation of the structural parameters c(1) share of firms which do not change prices; c(2) the discount factor Date: 11/17/04 Time: 08:48 Sample(adjusted): 1997:2 2003:4 Included observations: 27 after adjusting endpoints Kernel: Bartlett, Bandwidth: Fixed (2), No prewhitening Convergence achieved after: 14 weight matrices, 15 total coef iterations C(1)*DLCPI - (1-C(1))*(1-C(2)*C(1))*LABGAP-C(1)*C(2)*DLCPI(1) Instrument list: DLCPI(-1 TO -4) SHLAB GDPGAP DLUSD DLWPXC C(1) C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Table 3 Hybrid Philips curve estimation Date: 11/17/04 Time: 10:32 Sample(adjusted): 1997:2 2003:4 Included observations: 27 after adjusting endpoints Kernel: Bartlett, Bandwidth: Fixed (2), No prewhitening Convergence achieved after: 28 weight matrices, 29 total coef iterations (C(1)+C(3)*(1-C(1)*(1-C(2))))*DLCPI -(1-C(3))*(1-C(1))*(1-C(1)*C(2)) *LABGAP -C(1)*C(2)*DLCPI(1) -C(3)*DLCPI(-1) Instrument list: DLDEFL96SA(-1 TO -4) SHLAB GDPGAP DLWPXC DLUSD SI

2 C(1) C(3) C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Data description: Data sources: IFS; Statistical office of Chile ( ), Central Bank of Chile ( Quarterly data E-views variable Description Stationarity cpi CPI index I(2) dlcpi Dlcpi=lcpi-lcpi(-1) I(0) gdp96 GDP at 1996 prices I(1) gdpc GDP current prices I(2) M1 M1 aggregate current prices I(2) empl People employed I(2) policy_rate Policy rate of the Central bank I(1) wage Nominal average monthly wage I(1) wpxc World price index I(1) *Unit root tests performed with ADF Monthly data E-views variable Description Stationarity cpi Monthly CPI I(1) policy rate CB policy rate wage Average monthly wage (nominal) I(2) m1 m1 aggregate (nominal) I(2) *All unit root tests were performed by a combined ADF and KPSS test. 2

3 Switzerland Appendix S1: DLPGDP first difference of the log GDPdeflator DLPGDPSA first difference of the log GDPdeflator (s.a.) DLUSD first difference of the log USD/CHF DLWPXC first difference of the log world commodity price index GDPGAP trend deviation of the real seasonally adjusted GDP (in 2000 prices) IS interest rate spread (lending minus deposits rate) DLM3 first difference of the log M3 (broad money aggregate) Appendix S2 (SW estim. of eq. Baseline NKPC) Appendix S3 (SW estim of non-linear GMM with mom. Cond. (3) ) Specification (3) Date: 11/17/04 Time: 18:00 Sample(adjusted): 1982:1 2003:4 Included observations: 88 after adjusting endpoints Convergence achieved after: 23 weight matrices, 24 total coef iterations C(1)*DLPGDPSA-(1-C(1))*(1-C(1)*C(2))*GDPGAP-C(1)*C(2) *DLPGDPSA(1) Instrument list: DLPGDPSA(-1 TO -7) IS GDPGAP DLWPXC DLUSD C(1) C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Specification (4) Date: 11/17/04 Time: 18:00 Sample(adjusted): 1981:2 2003:4 Included observations: 91 after adjusting endpoints Convergence not achieved after: 499 weight matrices, 500 total coef iterations DLPGDPSA-((1-C(1))*(1-C(1)*C(2))/C(1))*GDPGAP-C(1)*C(2) *DLPGDPSA(1) Instrument list: DLPGDPSA(-1 TO -4) IS GDPGAP DLWPXC DLUSD C(1) C(2) S.E. of regression Sum squared resid

4 Durbin-Watson stat J-statistic Appendix S4 (SW estim of hybrid NKPC with BOTH mom. Conds) Specification (6) Date: 11/17/04 Time: 18:15 Sample(adjusted): 1982:1 2003:4 Included observations: 88 after adjusting endpoints Convergence achieved after: 15 weight matrices, 16 total coef iterations (C(1)+C(3)*(1-C(1)*(1-C(2))))*DLPGDPSA-(1-C(3))*(1-C(1))*(1- C(1)*C(2)) *GDPGAP-C(1)*C(2)*DLPGDPSA(1)-C(3)*DLPGDPSA(-1) Instrument list: DLPGDPSA(-1 TO -7) IS GDPGAP DLWPXC DLUSD C(1) C(3) C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Specification (7) Date: 11/12/04 Time: 18:03 Sample(adjusted): 1982:1 2003:4 Included observations: 88 after adjusting endpoints Convergence achieved after: 20 weight matrices, 21 total coef iterations DLPGDPSA-(1-C(3))*(1-C(1))*(1-C(1)*C(2))/(C(1)+C(3)*(1-C(1)*(1- C(2)))) *GDPGAP-C(1)*C(2)/(C(1)+C(3)*(1-C(1)*(1-C(2))))*DLPGDPSA(1) -C(3)/(C(1)+C(3)*(1-C(1)*(1-C(2))))*DLPGDPSA(-1) Instrument list: DLPGDPSA(-1 TO -7) IS GDPGAP DLWPXC DLUSD C(3) C(1) C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic

5 Appendices for Thailand Appendix T1: Thailand Variables Description Code Description of the Variable Measure Data Period Frequency No of observations cpi Consumer Price Index, CPI 2000 = :1-2004:3 quarterly 159 dlcpi Difference of the logs of the CPI ~ (% deviation) / 100, for small 1965:2-2004:3 quarterly 158 values dlcpisa Difference of the logs of the CPI seasonally adjusted :2-2004:3 quarterly 158 dlm1 Difference of the logs of M :2-2004:2 quarterly 157 dlm3 Difference of the logs of M :2-2004:2 quarterly 157 dlpgdpsa Difference of the logs of the seasonally adjusted GDP deflator :2-2004:2 quarterly 45 dlusd Difference of the logs of USD :2-2004:3 quarterly 158 dlwage Difference of the logs of wages :2-2004:3 quarterly 22 dlwagesa Difference of the logs of wages, seasonally adjusted :2-2004:3 quarterly 22 dlwpxc Difference of the logs of WPXC :2-2003:4 quarterly 135 empl Employment Thousands, p.a. 1998:1-2004:3 quarterly 27 emplsa Employment, seasonally adjusted Thousands, p.a. 1998:1-2004:3 quarterly 27 gdp Gross Domestic Product, GDP Billions of Baht 1993:1-2004:2 quarterly 46 gdpgap Trend deviation of the real seasonally adjusted GDP Millions of Baht, 2000 prices 1993:1-2004:2 quarterly 46 gdpr Real GDP Millions of Baht, 2000 prices 1993:1-2004:2 quarterly 46 gdprsa Real GDP, seasonally adjusted :1-2004:2 quarterly 46 gdprsahp H-P filter applied to the seasonally adjusted real GDP :1-2004:2 quarterly 46 gdpsa Seasonally adjusted GDP Billions of Baht 1993:1-2004:2 quarterly 46 is Interest spread = lending - deposit banking rates % 1977:1-2004:3 quarterly 111 lcpi log of CPI 1965:1-2004:3 quarterly 159 lcpisa log of CPI, s.a. 1965:1-2004:3 quarterly 159 lm1 log of M1 1965:1-2004:2 quarterly 159 lm3 log of M3 1965:1-2004:2 quarterly 159 lpgdp log of GDP deflator 1993:1-2004:2 quarterly 46 lpgdpsa log of GDP deflator, s.a. 1993:1-2004:2 quarterly 46 lppi log of PPI 1965:1-2004:3 quarterly 159 lusd log of USD 1965:1-2004:3 quarterly 159 lwage log of wages 1999:1-2004:3 quarterly 23 lwagesa log of wages, s.a. 1999:1-2004:3 quarterly 23 lwpxc log of WPXC 1970:1-2003:4 quarterly 136 m1 M1, "Money" from IFS Billions of Baht, e.p. 1965:1-2004:2 quarterly 158 m3 M3, "Money + Quasi Money" from IFS Billions of Baht, e.p. 1965:1-2004:2 quarterly 158 pgdp GDP deflator 2000 = :1-2004:2 quarterly 46 ppi Producer Price Index, PPI 2000 = :1-2004:3 quarterly 159 shgap Labor Share Gap = trend deviation of shlabsa (% / 100) 1999:1-2004:2 quarterly 22 shlabsa Labor Share, s.a. = (emplsa*wagesa)/(gdpsa* ) (% / 100) 1999:1-2004:2 quarterly 22 shlabsahp H-P filter of Labor Share, s.a. (% / 100) 1999:1-2004:2 quarterly 22 usd Official Exchange Rate, p.a. Baht / USD 1965:1-2004:3 quarterly 159 wage Wages Baht, p.a. 1999:1-2004:3 quarterly 23 wagesa Wages, s.a. Baht, p.a. 1999:1-2004:3 quarterly 23 wpxc World Price Index of Commodities, WPXC 2002 = :1-2003:4 quarterly 136 Notes: All the data is at quarterly frequency 5

6 Code Description of the Variable Measure Data Period Frequency p.a. - period average e.p. - end of period s.a. - seasonally adjusted No of observations Appendix T2: Thailand Unit Root Tests Variables ADF in levels ADF in 1 differences ADF in 2 differences Determined order t-statistic p-value` t-statistic p-value` t-statistic p-value` of integration GDPGAP I(0) IS I(0) LCPI I(1) LM I(1) LM I(2) LPGDP I(1)* LPGDPSA I(1) LPPI I(1) LUSD I(1) LWPXC I(1) SHGAP I(0) Notes: `MacKinnon (1996) one-sided p-values ``The test is performed with or without a constant and/or a trend term according to the most appropriate specification for the variable. Generally the trend term is excluded and the constant not. ADF test-statistic is significant at 1%, * ADF test-statistic is significant at 5% Appendix T3: Reduced form of the NKPC Dependent Variable: DLPGDPSA Date: 11/17/04 Time: 14:29 Sample(adjusted): 1993:4 2003:4 Included observations: 41 after adjusting endpoints Convergence achieved after: 8 weight matrices, 9 total coef iterations Instrument list: C DLPGDPSA(-1 TO -2) IS DLWPXC DLUSD Variable GDPGAP -5.41E E DLPGDPSA(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Test for the validity of the overidentifying restrictions: test statistic=2.17, p-value=0.30, i.e. the overidentifying restrictions are valid. Appendix T4: Non-linear GMM, specification 1 6

7 Date: 11/17/04 Time: 18:36 Sample(adjusted): 1994:4 2003:4 Included observations: 37 after adjusting endpoints Convergence achieved after: 38 weight matrices, 39 total coef iterations C(1)*DLPGDPSA-(1-C(1))*(1-C(1)*C(2))*GDPGAP-C(1)*C(2) *DLPGDPSA(1) Instrument list: C DLPGDPSA(-1 TO -6) IS DLWPXC DLUSD C(1) E C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Test for the validity of the overidentifying restrictions: test statistic=3.10, p-value=0.07, i.e. the overidentifying restrictions are valid. Appendix T5: Non-linear GMM, specification 2 Date: 11/17/04 Time: 18:38 Sample(adjusted): 1994:4 2003:4 Included observations: 37 after adjusting endpoints Convergence achieved after: 17 weight matrices, 18 total coef iterations DLPGDPSA-(1-C(1))*(1-C(1)*C(2))/C(1)*GDPGAP-C(2)*DLPGDPSA(1) Instrument list: C DLPGDPSA(-1 TO -6) IS DLWPXC DLUSD C(1) E C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Test for the validity of the overidentifying restrictions: test statistic=3.10, p-value=0.07, i.e. the overidentifying restrictions are valid. 7

8 Appendix T6: Wald Coefficient Restrictions Test Wald Test: Equation: EQ02A Test Statistic Value df Probability F-statistic (1, 35) Chi-square Null Hypothesis Summary: Normalized Restriction (= 0) Value Std. Err. (1 - C(1)) * (1 - C(1)*C(2)) / C(1) -9.92E E-08 Delta method computed using analytic derivatives. Appendix T7: Hybrid NKPC, specification 1 Date: 11/17/04 Time: 19:17 Sample(adjusted): 1994:4 2003:4 Included observations: 37 after adjusting endpoints Convergence achieved after: 94 weight matrices, 95 total coef iterations (C(1)+C(3)*(1-C(1)*(1-C(2))))*DLPGDPSA-(1-C(3))*(1-C(1))*(1-C(1)*C(2)) *GDPGAP-C(1)*C(2)*DLPGDPSA(1)-C(3)*DLPGDPSA(-1) Instrument list: C DLPGDPSA(-1 TO -6) IS DLWPXC DLUSD C(1) E C(3) C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Test for the validity of the overidentifying restrictions: test statistic=3.10, p-value=0.12, i.e. the overidentifying restrictions are valid. 8

9 Appendix T8: Hybrid NKPC, specification 2 Date: 11/18/04 Time: 11:37 Sample(adjusted): 1994:3 2003:4 Included observations: 38 after adjusting endpoints Convergence achieved after: 54 weight matrices, 55 total coef iterations DLPGDPSA-(1-C(3))*(1-C(1))*(1-C(1)*C(2))/(C(1)+C(3)*(1-C(1)*(1- C(2)))) *GDPGAP-C(1)*C(2)/(C(1)+C(3)*(1-C(1)*(1-C(2))))*DLPGDPSA(1) -C(3)/(C(1)+C(3)*(1-C(1)*(1-C(2))))*DLPGDPSA(-1) Instrument list: C DLPGDPSA(-1 TO -5) IS DLWPXC DLUSD C(3) C(1) E C(2) S.E. of regression Sum squared resid Durbin-Watson stat J-statistic Test for the validity of the overidentifying restrictions: test statistic=3.61, p-value=0.27, i.e. the overidentifying restrictions are valid. 9

10 Appendix TF1: Correlogram of DLCPI Date: 11/18/04 Time: 13:50 Sample: Included observations: 158 Autocorrelation Partial Correlation AC PAC Q-Stat Prob. *****. ***** ****. * *** ***. * ** * * * * * *. * * * *. * *. * * Appendix TF2: ARMA(6,5) Dependent Variable: DLCPI Method: Least Squares Date: 11/18/04 Time: 14:02 Sample(adjusted): 1966:4 2004:3 Included observations: 152 after adjusting endpoints Convergence achieved after 14 iterations Backcast: 1965:3 1966:3 Variable C AR(1) AR(2) AR(3) AR(4) AR(5) AR(6) MA(5) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted AR Roots i i i i -.99 Inverted MA Roots i i i i

11 Appendix TF3: ARMA Dynamic, In-Sample Forecast Forecast: DLCPI_ARMA Actual: DLCPI Forecast sample: 2003:1 2004:2 Included observations: 6 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion :1 2003:2 2003:3 2003:4 2004:1 2004:2 DLCPI_ARMA Appendix TF4: ARMAX(3,3,3) Dependent Variable: DLCPI Method: Least Squares Date: 11/18/04 Time: 16:32 Sample(adjusted): 1966:4 2004:3 Included observations: 152 after adjusting endpoints Convergence achieved after 24 iterations Backcast: 1966:1 1966:3 Variable C DLM1(-1) DLM1(-2) DLM1(-3) AR(1) AR(2) AR(3) MA(1) MA(2) MA(3) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted AR Roots i i Inverted MA Roots i i 11

12 Appendix TF5: ARMAX(3,3,3) Dynamic, In-Sample Forecast Forecast: DLCPI_ARMAX Actual: DLCPI Forecast sample: 2003:1 2004:2 Included observations: 6 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion :1 2003:2 2003:3 2003:4 2004:1 2004:2 DLCPI_ARMAX Appendix TF6: VAR Vector Autoregression Estimates Date: 11/18/04 Time: 14:37 Sample(adjusted): 1993:2 2004:2 Included observations: 45 after adjusting endpoints Standard errors in ( ) & t-statistics in [ ] DLCPI GDPGAP DLUSD DLM1 DLCPI(-1) ( ) ( ) ( ) ( ) [ ] [ ] [ ] [ ] GDPGAP(-1) 4.95E E E-07 (2.0E-08) ( ) (1.8E-07) (2.7E-07) [ ] [ ] [ ] [ ] DLUSD(-1) ( ) ( ) ( ) ( ) [ ] [ ] [ ] [ ] DLM1(-1) ( ) ( ) ( ) ( ) [ ] [ ] [ ] [ ] C ( ) ( ) ( ) ( ) [ ] [ ] [ ] [ ] R-squared Adj. R-squared Sum sq. resids E S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant Residual Covariance

13 Log Likelihood (d.f. adjusted) Akaike Information Criteria Schwarz Criteria Appendix TF7: AR Roots Graph 1.5 Inverse Roots of AR Characteristic Polynomial Appendix TF8: VAR Lag order selection criteria VAR Lag Order Selection Criteria Endogenous variables: DLCPI GDPGAP DLUSD DLM1 Exogenous variables: C Date: 11/18/04 Time: 16:54 Sample: 1965:1 2005:4 Included observations: 41 Lag LogL LR FPE AIC SC HQ NA * * * * * * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion 13

14 Appendix TF9: Serial Correlation LM Test VAR Residual Serial Correlation LM Tests H0: no serial correlation at lag order h Date: 11/18/04 Time: 16:55 Sample: 1965:1 2005:4 Included observations: 45 Lags LM-Stat Prob Probs from chi-square with 16 df. Appendix TF10: Residual Heteroskedasticity Test VAR Residual Heteroskedasticity Tests: No Cross Terms (only levels and squares) Date: 11/18/04 Time: 16:57 Sample: 1965:1 2005:4 Included observations: 45 Joint test: Chi-sq df Prob Individual components: Dependent R-squared F(8,36) Prob. Chi-sq(8) Prob. res1*res res2*res res3*res res4*res res2*res res3*res res3*res res4*res res4*res res4*res