*Example 10.5 READ (DATA9-2) Year r M D * Replicate Figure 10.7 GRAPH M YEAR /LINEONLY * Generate the variables in Step 1 of the example GENR Y=LOG(M) GENR Y1=LAG(Y) GENR DY=Y-Y1 GENR DY1=LAG(DY) * Step 2-3 * Generate a time trend t. GENR T=TIME(0) * The first observation on Y1 is not known, since it is a lagged variable. * DY depends on Y1, so the first observation on DY is not known either. * Since DY1 is a lagged DY, the first TWO observations are not known. * Suppress the first two observations. SAMPLE 3 36 * Estimate the unrestricted model. OLS DY T Y1 DY1 * The output reports the T RATIOs for all coefficients, including Y1 * Step 4 * Save the ESS in the variable ESSU, for use in calculating the Fc statistic. * Use the temporary variable $sse. GEN1 ESSU=$SSE * Also save n-k in the variable df. Use the temporary variable $df. gen1 df=$df * Estimate the restricted model. OLS DY DY1 * Calculate the value of Fc, using the formula at the bottom of p. 458. * The ESS of the restricted model is in the temporary variable $sse. GEN1 F=($SSE-ESSU)/2/(ESSU/DF) PRINT F * * Alternatively, the Dickey-Fuller tests can be generated automatically * using the COINT command. * COINT automatically adjusts the sample for the appropriate lags. SAMPLE 1 36 * We can specify the number of lagged dependent variables DY by the NLAG option. COINT Y /NLAG=1 * The appropriate specification is CONSTANT TREND (since there is a * time trend in the model). * The first test statistic reported here is the t-test. * The third test statistic is the F-test on the null hypotheis that the coefficient * for both t and Y1 is zero. * The critical values reported in COINT are asymptotic critical values, while those * in the text are small-sample critical values for n=25 and n=50 respectvely. As a * result, these critical values are not the same. STOP