Determinant residual covariance 490782.3
Log likelihood (df adjusted) -300.4722
Akaike information criterion 19.90451
preceding two equations, which are given in Table 22.2. Note that although our sample runs from 1979-1 to 1988-4, we used the sample for the period 1979-1 to 1987-4 and saved the last four observations to check the forecasting accuracy of the fitted VAR.
Since the preceding equations are OLS regressions, the output of the regression given in Table 22.2 is to be interpreted in the usual fashion. Of course, with several lags of the same variables, each estimated coefficient will not be statistically significant, possibly because of multicollinearity. But collectively, they may be significant on the basis of the standard F test.
Let us examine the results presented in Table 22.2. First consider the M1 regression. Individually, only M1 at lag 1 and R at lags 1 and 2 are statistically significant. But the F value is so high that we cannot reject the hypothesis that collectively all the lagged terms are statistically significant. Turning to the interest rate regression, we see that all the four lagged money
CHAPTER TWENTY-TWO: TIME SERIES ECONOMETRICS: FORECASTING 851
terms are individually statistically significant (at 10 percent or better level), whereas only the 1-period lagged interest rate variable is significant.
For comparative purposes, we present in Table 22.3 the VAR results based on only 2 lags of each endogenous variable. Here you will see that in the money regression the 1-period-lagged money variable and both lagged interest rate terms are individually statistically significant. In the interest rate regression, both lagged money terms (at about 5 percent level) and one lagged interest term are individually significant.
If we have to make a choice between the model given in Table 22.2 and that given in Table 22.3, which would we choose? The Akaike and Schwarz information values for the model in Table 22.2 are, respectively, 15.32 and 15.73, whereas the corresponding values for Table 22.3 are 15.10 and 15.33. Since the lower the values of Akaike and Schwarz statistics, the better the model, on that basis it seems the more parsimonious model given in Table 22.3 is preferable. We also considered 6 lags of each of the endogenous variables and found that the values of Akaike and Schwarz statistics were 15.37 and 15.98, respectively. Again, the choice seems to be the model with two lagged terms of each endogenous variable, that is, the model in Table 22.3.
TABLE 22.3 VECTOR AUTOREGRESSION ESTIMATES BASED ON 2 LAGS Sample (adjusted): 1979-III to 1987-IV Included observations: 34 after adjusting endpoints Standard errors in ( ) and t statistics in [ ]
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