Economics 5310 Lecture 26 Causality, VAR

Causality Question: Can one statistically determine the direction of causality when temporally there is a lead-lag relationship between two variables. Granger test Sims test

Granger Test

Granger Test

Example Granger Causality Interest Rates cause housing starts housing starts cause interest rates

Interest causes housing |_ols hgrth hgrth1 hgrth2 hgrth3 rate1 rate2 rate3 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 29 DF P-VALUE CORR. COEFFICIENT AT MEANS HGRTH1 -0.31318 0.1785 -1.755 0.090-0.310 -0.3132 0.0000 HGRTH2 -0.24469 0.2238 -1.093 0.283-0.199 -0.2447 0.0000 HGRTH3 -0.39541 0.2144 -1.844 0.075-0.324 -0.3954 0.0000 RATE1 0.17777E-03 0.3018E-03 0.5890 0.560 0.109 0.2252 0.0000 RATE2 0.45781E-04 0.3705E-03 0.1236 0.903 0.023 0.0583 0.0000 RATE3 -0.23412E-03 0.2826E-03 -0.8285 0.414-0.152 -0.2995 0.0000 CONSTANT 0.15062E-02 0.5179E-01 0.2908E-01 0.977 0.005 0.0000 0.0000 |_test |_test rate1 |_test rate2 |_test rate3 |_end F STATISTIC = 0.32867447 WITH 3 AND 29 D.F. P-VALUE= 0.80462 WALD CHI-SQUARE STATISTIC = 0.98602340 WITH 3 D.F. P-VALUE= 0.80463 UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 1.00000

Housing Causes Interest Rate |_ols rate rate1 rate2 rate3 hgrth1 hgrth2 hgrth3 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 29 DF P-VALUE CORR. COEFFICIENT AT MEANS RATE1 0.72490 0.1667 4.350 0.000 0.628 0.7249 0.7493 RATE2 0.62909E-01 0.2046 0.3075 0.761 0.057 0.0632 0.0644 RATE3 0.41174E-01 0.1560 0.2639 0.794 0.049 0.0416 0.0417 HGRTH1 409.03 98.56 4.150 0.000 0.610 0.3229 0.0000 HGRTH2 245.66 123.6 1.988 0.056 0.346 0.1939 0.0000 HGRTH3 147.79 118.4 1.248 0.222 0.226 0.1167 0.0000 CONSTANT 32.321 28.60 1.130 0.268 0.205 0.0000 0.1446 |_test |_test hgrth1 |_test hgrth2 |_test hgrth3 |_end F STATISTIC = 6.0127120 WITH 3 AND 29 D.F. P-VALUE= 0.00258 WALD CHI-SQUARE STATISTIC = 18.038136 WITH 3 D.F. P-VALUE= 0.00043 UPPER BOUND ON P-VALUE BY CHEBYCHEV INEQUALITY = 0.16631 |_stop

Logic of Vector Autoregressive Models SIM’s criticism of traditional simultaneous equation models. Seed for VAR lies with Granger causality testing. Term autoregressive comes from fact that lagged values of dependent variable appear on RHS. Term vector comes from fact that we are discussing at least two variables.

Basic VAR model

Example VAR-Exchange Rate lag 6 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 272 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEX1 0.98276 0.1985E-01 49.51 0.000 0.949 0.9834 0.9831 TWEX2 0.11805E-01 0.2902E-01 0.4068 0.685 0.025 0.0129 0.0118 TWEX3 0.21203E-02 0.2986E-01 0.7102E-01 0.943 0.004 0.0025 0.0021 TWEX4 0.19340E-02 0.2985E-01 0.6479E-01 0.948 0.004 0.0024 0.0019 TWEX5 -0.25240E-01 0.2920E-01 -0.8644 0.388-0.052 -0.0332 -0.0249 TWEX6 0.41456E-02 0.1913E-01 0.2168 0.829 0.013 0.0057 0.0041 BA6M1 0.33559 0.1826 1.837 0.067 0.111 0.0742 0.0255 BA6M2 -0.40163 0.3102 -1.295 0.197-0.078 -0.0898 -0.0305 BA6M3 -0.69931E-01 0.3291 -0.2125 0.832-0.013 -0.0158 -0.0053 BA6M4 0.39043E-01 0.3291 0.1187 0.906 0.007 0.0089 0.0029 BA6M5 0.41974 0.3102 1.353 0.177 0.082 0.0966 0.0316 BA6M6 -0.19530 0.1829 -1.068 0.287-0.065 -0.0454 -0.0146 CONSTANT 1.1981 0.7537 1.590 0.113 0.096 0.0000 0.0123

Example VAR – Banker’s Acceptance Rate–lag 6 month VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 272 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEX1 -0.31468E-01 0.6742E-02 -4.667 0.000-0.272 -0.1424 -0.4139 TWEX2 0.40684E-01 0.9857E-02 4.128 0.000 0.243 0.2002 0.5333 TWEX3 -0.14832E-01 0.1014E-01 -1.463 0.145-0.088 -0.0784 -0.1937 TWEX4 0.79366E-02 0.1014E-01 0.7829 0.434 0.047 0.0446 0.1033 TWEX5 -0.15246E-01 0.9917E-02 -1.537 0.125-0.093 -0.0906 -0.1978 TWEX6 0.11043E-01 0.6495E-02 1.700 0.090 0.103 0.0689 0.1428 BA6M1 1.4049 0.6203E-01 22.65 0.000 0.808 1.4050 1.4048 BA6M2 -0.64200 0.1054 -6.093 0.000-0.347 -0.6488 -0.6401 BA6M3 0.24210 0.1118 2.166 0.031 0.130 0.2471 0.2407 BA6M4 -0.16870 0.1118 -1.510 0.132-0.091 -0.1739 -0.1673 BA6M5 0.30816 0.1054 2.925 0.004 0.175 0.3207 0.3047 BA6M6 -0.16312 0.6212E-01 -2.626 0.009-0.157 -0.1713 -0.1608 CONSTANT 0.32744 0.2560 1.279 0.202 0.077 0.0000 0.0441

Problems VAR VAR model is a-theoretic. Less suited for policy analysis since emphasis is forecasting. Problem of selecting lag length. In theory variables should be stationary, but many use levels for interpretation. Quite often look at impulse response function (IRF).

Selecting the lag length AIC-Ex Scwartz-Ex AIC-Int Scwartz-Int 1 2.900 3.013 0.395 0.411 2 2.915 3.108 0.353 0.376 3 2.924 3.198 0.342 0.374 4 2.920 3.277 0.346 0.388 5 2.951 3.398 0.347 0.400 6 2.977 3.517 0.343 0.406

Exchange rate – lag 2 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 280 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEX1 0.98915 0.1936E-01 51.09 0.000 0.950 0.9898 0.9895 TWEX2 -0.73728E-02 0.1845E-01 -0.3995 0.690-0.024 -0.0080 -0.0074 BA6M1 0.27871 0.1670 1.669 0.096 0.099 0.0616 0.0212 BA6M2 -0.17325 0.1675 -1.034 0.302-0.062 -0.0387 -0.0131 CONSTANT 0.95312 0.7394 1.289 0.198 0.077 0.0000 0.0098

Interest Rate – lag 2 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 280 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEX1 -0.27241E-01 0.6735E-02 -4.045 0.000-0.235 -0.1232 -0.3583 TWEX2 0.25923E-01 0.6419E-02 4.038 0.000 0.235 0.1276 0.3398 BA6M1 1.3328 0.5809E-01 22.94 0.000 0.808 1.3329 1.3327 BA6M2 -0.35789 0.5826E-01 -6.142 0.000-0.345 -0.3617 -0.3568 CONSTANT 0.31661 0.2572 1.231 0.219 0.073 0.0000 0.0426

1st Difference exchange rate SCHWARZ (1978) CRITERION - SC = 2.7835 AKAIKE (1974) INFORMATION CRITERION - AIC = 2.6796 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 286 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEXDIF1 0.29295 0.5879E-01 4.983 0.000 0.283 0.2929 0.3033 BA6MDIF1 0.13370 0.1605 0.8331 0.405 0.049 0.0490 -0.0161 CONSTANT -0.23110E-01 0.9582E-01 -0.2412 0.810-0.014 0.0000 0.7129

1st difference interest rate SCHWARZ (1978) CRITERION - SC = 0.36331 AKAIKE (1974) INFORMATION CRITERION - AIC = 0.34974 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 286 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEXDIF1 -0.55467E-01 0.2124E-01 -2.611 0.009-0.153 -0.1514 0.4339 BA6MDIF1 0.36143 0.5798E-01 6.234 0.000 0.346 0.3614 0.3294 CONSTANT 0.10160E-02 0.3462E-01 0.2935E-01 0.977 0.002 0.0000 0.2368

1st difference exchange rate – 2 lags SCHWARZ (1978) CRITERION - SC = 2.8678 AKAIKE (1974) INFORMATION CRITERION - AIC = 2.6916 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 284 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEXDIF1 0.30799 0.6250E-01 4.928 0.000 0.281 0.3080 0.3188 TWEXDIF2 -0.32299E-01 0.6337E-01 -0.5097 0.611-0.030 -0.0322 -0.0409 BA6MDIF1 0.18812 0.1730 1.087 0.278 0.064 0.0689 -0.0227 BA6MDIF2 -0.22252 0.1713 -1.299 0.195-0.077 -0.0815 0.0240 CONSTANT -0.23367E-01 0.9573E-01 -0.2441 0.807-0.014 0.0000 0.7208

1st difference interest rate – 2 lags SCHWARZ (1978) CRITERION - SC = 0.35906 AKAIKE (1974) INFORMATION CRITERION - AIC = 0.33699 VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY NAME COEFFICIENT ERROR 284 DF P-VALUE CORR. COEFFICIENT AT MEANS TWEXDIF1 -0.50290E-01 0.2212E-01 -2.274 0.024-0.134 -0.1373 0.3934 TWEXDIF2 -0.44321E-02 0.2242E-01 -0.1977 0.843-0.012 -0.0121 0.0424 BA6MDIF1 0.42529 0.6122E-01 6.947 0.000 0.381 0.4253 0.3876 BA6MDIF2 -0.21635 0.6061E-01 -3.570 0.000-0.207 -0.2163 -0.1762 CONSTANT 0.15140E-02 0.3387E-01 0.4470E-01 0.964 0.003 0.0000 0.3529