INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 67 It will be confined to the slope coefficient, , but exactly the same procedures are applied to the constant term, . We will take the general case, where you have defined a null hypothesis that is equal to some specific value, say , and the alternative hypothesis is that is not equal to this value (H 0 ); you maybe attempting to attack or defend the null hypothesis as it suits your purpose. We will assume that the four Gauss–Markov conditions are satisfied. 2.2.3.6.2 Developing the Implications of a Hypothesis If H 0 is correct, values of b 2 obtained using regression analysis in repeated samples will be distributed with mean and ( we will now introduce the assumption that u has a normal distribution. If this is the case, b 2 will also be normally distributed, In view of the structure of the normal distribution, most values of b 2 will lie within two standard deviations of if is true. 2.2.3.7 Compatibility, Freakiness, and the Significance Level Now, suppose that we take an actual sample of observations on average rates of price inflation and wage inflation over the past five years fora sample of countries and estimate using regression analysis. If the estimate is close to 1.0, we should almost certainly be satisfied with the null hypothesis, since it and the sample result are compatible with one another. But suppose, on the other hand, that the estimate is along way from 1.0. Suppose that it is equal to 0.7. This is three standard deviations below 1.0. If the null hypothesis is correct, the probability of being three standard deviations away from the mean, positive or negative, is only 0.0027, which is very low. You could come to either of two conclusions about this worrisome result You could continue to maintain that your null hypothesis H 0 : = 1 is correct, and that the experiment has given a freak result. You concede that the probability of such a low value of b 2 is very small, nevertheless it does occur 0.27 percent of the time and you reckon that this is one of those times.
