First, we have run the ordinary least squares regressions of the equation (i). The results are shown in Table 2. Note that the regressions were run with constant, but the estimated constants are not reported.
Second, we have repeated the same regressions with added sectoral dummy variable i. e. we estimated the equation
The results of the second step are shown in Table 3 (constants and coefficients at dummy varables are omitted). The low Durbin-Watson statistics6 indicate presence of autocorrelation, and the residual variances calculated separately
for each sector (see Table 4) show a presence of heteroscedasticity .
Third, we have estimated the sectoral autoregression coefficients li(1) and li(2) from the second step residuals (see Table 5) and used them to transform variables according the formula:
where xit stands for any of the left or right hand variables, including the constant and dummy
variables. Then we have repeated the estimation of equation (ii) with
transformed variables, but only for one model in each country (see Table 6). As before, constant and parameters at dummy variables are not shown.
The satisfactory Durbin-Watson statistics indicated that the autocorrelation was to a large extent eliminated. The check of the sectoral residual variances (see Table 7) showed that the remaining heteroscedasticity was very small, so that no further steps for eliminating it were necessary .
Before giving the economic interpretation to our estimates, let us briefly comment on their statistical properties :
With very few exceptions estimates in all three steps are very good and seem to be quite reliable. Most of the parameters were estimated with very small standard errors so that they are significantly different from zero. The main exceptions are parameters rt in the first step [ except for Czechoslovakia’s model (2)] and the third step estimates of the model (2) for Bulgaria. The second step estimates show that the introduction of
One interesting feature of our estimates is that the estimated parameters in all three steps tell basically the same story about the dynamic behavior of the economy. The least satisfactory in this sense are estimates of the capital elasticity for Bulgaria and Rumania. This can be perhaps explained by relatively large errors in measurement of capital for these two countries, as mentioned above. The fit statistics are good in all three steps, but of course, the best they are in the third step. The R2s of the first step may seem to be somewhat low, but due to the large number of degrees of freedom they are highly significant as the F-statistics on the joint explanatory power of all right hand variables indicate. Even in the case of Rumania where R2s = .22 the computed F-statistic is about 10 times larger than the tabulated value of F-distribution for 99 per cent level of confidence and respective degrees of freedom. As could have been expected, the elimination of sectoral components from the residuals in the second step and the removal of serial correlation out of the residuals in the third step, increased substantially the R2s and the F-statistics as well as the Durbin-Watson statistics. It should be, however, mentioned here that the gain of fit statistics was paid by increased multicolinearity, which was almost nonexistent in the first step. This multicollinearity together with already mentioned errors in measurement of capital may be a cause of the “strange” third step result for Bulgaria and Rumania. It is therefore questionable whether the third step estimates are better and more reliable than the first or second step estimates. With high multicollinearity the estimated parameters are not very reliable, therefore, we are inclined to trust the first and second step estimates more than the third step results.