Lecture29-30 - 113 Lecture 29 - Things to be careful about...

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113 Lecture 29 - Things to be careful about when doing regression analysis 1) Doing what theory suggests. We have seen that the inclusion of irrelevant variables will cause the variance of estimators to increase and hence lower the value of their t-statistics. Thus, when a researcher encounters low t-statistics, he or she may be tempted to simply leave out the variables concluding that they were irrelevant. But note that there are other reasons for obtaining low t- values than the inclusion of irrelevant variables. For instance, we could have multicollinearity, which means the independent variables are correlated with one another. We will study multicollinearity in a few lectures from now. As we have seen, leaving out a variable, even one with a low t-value, will caused bias in the remaining coefficients if the independent variable left out is correlated with other independent variables in the regression equation. The example on page 183 of your textbook is an excellent illustration of this point. Suppose we let: C = quantity of Brazilian coffee demanded P P Y P bc = the price of Brazilian coffee cc = the price of Colombian coffee d = income of U.S. citizens. t = price of Tea Suppose we estimate and obtain the following regression results: $ Y d t .. . . . ( $ ). , . , . .,,. ., CP P SE B t Rn tb c t t =+ + + = = == 91 7 8 2 4 0035 156 12 001 5235 62 5 2 Because the coefficient on the price of Brazilian coffee has an insignificant t-value (.5) the researcher decides to drop the variable, believing that coffee demand is in-elastic with respect to price. So he/she drops the variable and re-estimates the equation obtaining: $ . Y d t ... ( $ ), . .., SE B t tt + = = 9 3 2 6 00036 1 0009 264 61 25 2 Was it a good idea to drop the variable? Let us see how it fits in with our 4 criteria for judging regression results.
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114 1) Theory - it is possible that the demand for coffee could be price inelastic (though price not mattering at all is a bit unlikely!). 2) t-test - the t-value is insignificant 3) R-BAR SQUARED - R-BAR SQUARED does increase when the variable is dropped, indicating that the variable is irrelevant. (Since the t-value <1, this is to be expected. Recall that R-BAR SQUARED penalizes you when you add a variable with low explanatory power, in practice this translates into an independent variable with a t-value <1. If the t-value is > 1, R-BAR SQUARED will increase when the independent variable is added even if the variable is statistically insignificant.). 4) Bias - the remaining coefficients change only a small amount when the price of Brazilian coffee is dropped, suggesting that there is little if any bias caused by excluding the variable. However, this is a case of poorly thought-out theory. There is no variable in either of the above equations for the price of competitive coffee, such as Colombian coffee. Theory would always suggest that competitive goods be included in the specification of the model. And, if the price of Brazilian coffee and the price of Colombian coffee are correlated, as they almost certainly are, then leaving out the price of Colombian coffee will have caused bias in the coefficient for Brazilian coffee in the above 2 equations.
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Lecture29-30 - 113 Lecture 29 - Things to be careful about...

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