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Interactive Exercise 2 |
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Heteroskedasticity. This dependent variable is already per capita, is time series, and does not change substantially during the sample period. As a result, the possibility of pure heteroskedasticity is so low that most econometricians would not even bother testing for it. (If a Park test were to be run, however, a logical proportionality factor Z might be per capita disposable income.)
Serial Correlation. Serial correlation is quite another matter, however, since the data are time series and a number of the Durbin-Watson d statistics are below the critical dL value for positive serial correlation. In addition, it seems possible that short-run fads in the consumption of pork, or alternatively, supply shocks, might cause swings in consumption from year to year that would not be completely captured by the price variables or by coefficients estimated over the entire sample.
In particular, if your final equation was either regression run 6 or run 14, then there is a possibility of serial correlation. Their Durbin-Watson d's of 1.09 and 1.19 respectively are right at the edge of the critical dL for positive serial correlation for 40 observations and 6 explanatory variables.
The application of generalized least squares to regression runs 6 and 14 are contained in regression runs 2l and 22 respectively; we include these mainly for instructional purposes, since the inconclusive Durbin-Watson statistics do not justify GLS on their own.
| Regression Run 21 Dependent Variable: CONPK Method: Least Squares Sample(adjusted): 1975:2 1984:4 Included observations: 39 after adjusting endpoints Convergence achieved after 48 iterations
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| Regression Run 22 Dependent Variable: CONPK Method: Least Squares Sample(adjusted): 1975:2 1984:4 Included observations: 39 after adjusting endpoints Convergence achieved after 32 iterations
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As can be seen by comparing the GLS result with the OLS result, the correction with a 
did indeed decrease the significance of the price and income explanatory variables as would have been expected. The increase in significance of the seasonal dummies with GLS estimation raises the possibility that the seasonal pattern is not as simple as that implied by the three intercept dummies.
Note that most of the lowest Durbin-Watson statistics came with the seasonal dummy group included, supporting the hypothesis that this set of dummies did not properly capture the actual seasonality of the demand for pork; the introduction of the seasonal dummies might have deleted some but not all of the seasonal variation, leaving a serially correlated pattern in the residuals. While the equation was probably better off with the seasonal dummies than without, a better knowledge of the meat industry before estimation might have allowed a more sophisticated seasonal pattern to be chosen. Even using only intercept dummies, for example, a better overall fit might have been obtained by using only one seasonal dummy (D4, equal to one in the fourth quarter and zero otherwise). To make such a switch (or to drop one of the seasonal dummies while keeping the others) on the sole basis of the attached estimations would be a mistake, however, because the hypothesis would be tested on the same data set from which it was developed.
Finally, note that some of the Durbin-Watson statistics were greater than two when PROPK was included in the regression. This result almost surely occurred because the resulting equation included both demand-side and supply-side variables, and the residuals were no longer the residuals of just the demand-side equation. This result is one of many reasons that most econometricians go to great lengths to avoid including such a production variable in a demand-side equation. In a sense, production acts like a dominant variable; its relationship to the dependent variable is strong but is definitional with little economic content.
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