Christopher Dougherty EC220 - Introduction to econometrics (chapter 6) Slideshow: exercise 6.7 Original citation: Dougherty, C. (2012) EC220 - Introduction.
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Christopher Dougherty
EC220 - Introduction to econometrics (chapter 6)Slideshow: exercise 6.7
Original citation:
Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 6). [Teaching Resource]
This version available at: http://learningresources.lse.ac.uk/132/
Available in LSE Learning Resources Online: May 2012
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We will start with the sample of 30 industrialized countries. In the multiple regression, the estimates of the elasticities of Y with respect to X and Z are both highly significant and have the expected signs. We will therefore adopt this as our preferred specification.
We are told that X and Z are positively correlated, so the numerator of the second factor in the bias term will be positive. The denominator must be positive. Hence the bias will be negative, accounting for the fall in the estimate of the elasticity.
Similarly, in model (3), the estimate of the elasticity of Y with respect to Z will be subject to omitted variable bias. It is reasonable to assume that 2 is positive, and we know that the numerator and the denominator of the second factor are positive, so the bias is positive.
The bias just about offsets the true value of the coefficient, with the consequence that the estimated coefficient is close to 0. It appears that log Z has very little effect on log Y, and this in turn accounts for the very low value of R2.
However, in the multiple regression, where the effect of omitted variable bias is eliminated, we see that in fact log X and log Z account for nearly half the variance in log Y.
Next we come to the sample of 30 developing countries. In the multiple regression, the estimate of the elasticity of Y with respect to X is again highly significant, but that of the elasticity with respect to Z is not.
If instead we drop log X, the estimate of the elasticity with respect to Z changes sign, suggesting that expenditure on enforcement actually encourages the growth of the shadow economy. Moreover, the effect appears to be highly significant.
As in the case of the industrialized countries, the bias is positive, and it is so large that it dominates the estimate of the elasticity. log Z is acting as a proxy for log X.
It is possible that enforcement expenditure has no effect and model (2) is the correct specification. If this is the case, the estimator of the elasticity of X in model (1) will be less efficient and this is the reason that the standard error is larger.
Alternatively, model (1) might be the correct specification. Enforcement expenditure may have an effect, but bureaucracy and corruption undermine it and account for the low and insignificant estimate of its elasticity.
In practice, in a situation like this, you would present the regression results for both models (1) and (2) in your report, giving the reader all the available information.