Use the data in MINWAGE for this exercise. In particular, use the employment and wage series for sector 232 (Men's and Boys' Furnishings). The variable gwage232 is the monthly growth (change in logs) in the average wage in sector $232,$ gemp232 is the growth in employment in sector $232,$ gmwage is the growth in the federal minimum wage, and $g c p i$ is the growth in the (urban) Consumer Price Index.
(i) Run the regression gwage232 on gmwage, gcpi. Do the sign and magnitude of $\hat{\beta}_{g m m a g e}$ make sense to you? Explain. Is gmwage statistically significant?
(ii) Add lags 1 through 12 of gmwage to the equation in part (i). Do you think it is necessary to include these lags to estimate the long-run effect of minimum wage growth on wage growth in sector 232$?$ Explain.
(iii) Run the regression gemp232 on gmwage, gcpi. Does minimum wage growth appear to have a contemporaneous effect on $g e m p 232 ?$
(iv) Add lags 1 through 12 to the employment growth equation. Does growth in the minimum wage have a statistically significant effect on employment growth, either in the short run or long run Explain.

Answer

(i) See video (ii) Yes (iii) No (iv) No

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Introductory Econometrics

Chapter 10

Basic Regression Analysis with Time Series Data

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Video Transcript

part one, Theis estimated equation is as follows. The coefficient on the growth of the minimum wage is 0.151 It implies that a 1% point growth in the minimum wage is estimated to increase the growth in wage of sector 2 32 by about point on 51% points. Part two Yeah, we add the 12 legs of GM wage the growth of minimum wage. We find that the sum of all the coefficient is somewhat higher than what we got from the aesthetic regression. We will use an F test to test for the joint significance of the legs. The P value of the F test is 0.58 showing that these legs are jointly significant at the 10% level. Okay, Yeah, we evaluate the joint significance of the legs, but we also look at the individual significance of each leg. We find that legs number eight to number 12, yeah, have quite large coefficient. And some of the individual T statistic are significant at the 5% level. In part three, we have a new estimated equation. The coefficient on the growth of minimum wage is very small and the teeth statistic is also very small. Okay, Okay. Remember that the T start for the beta coefficient is estimated by taking beta coefficient divided by its standard error. Yeah, another signal is the are square. The art square is almost zero. Meaning neither the growth of minimum wish. And what is the other thing? The other thing, G c p i. So neither of these variables can explain the variation in the growth of employment in sector 2 32 in part four, we will act will add the legs of the growth of minimum wage into the above equation. We find that doing so does not improve the fit of the model. The F test of joint significance of mhm should fix this The joint significance of growth of minimum wage and its lax. The F statistic has a P value of 0.439 Yeah, which means we cannot reject the non hypothesis. Yeah, the coefficients also change sign, and none of the coefficient of the legs is individually statistically significant at the 5% level. Okay. Therefore, there is little evidence that minimum wage growth affect employment growth either in short run or long run

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