Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 11

Use CRIME3.RAW for this exercise.

(i) In the model of Example, test the hypothesis H0: ?1 = ?2. (Hint: Define ?1 = ?1 – ?2 and write ?1 in terms of ?1 and ft. Substitute this into the equation and then rearrange. Do a t test on ?1.)

(ii) If ft = ft, show that the differenced equation can be written as

Alog(crimei) = ?0 + ?1?avgclri + ?ui, where ?1 = 2?1 and avgclr. = (clrprc4-1 + clrprc4-2)/2 is the average clear-up percentage over the previous two years.

(iii) Estimate the equation from part (ii). Compare the adjusted R-squared with that in (13.22). Which model would you finally use?

Step 1 of 3

Consider the unobserved effects model:

This model when expressed as the first-differenced equation, the result is:

Given

Substitute in the first-differenced equation, the result is:

Estimating

The result is:

Testing for the significance of the hypothesis using the Wald test which is equivalent to testing for the hypothesis using the Wald test, the result is:

Since, the p-value corresponding to F-statistic is 0.2881 which is greater than the critical p-value of 0.05 at 5% level of significance, it is indicated that .That means there is no statistical significant difference between andat 5% level of significance