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For this exercise, we use JTRAIN to determine the effect of the job training grant on hours of job train-ing per employee. The basic model for the three years is$\begin{aligned} \text {hrsemp}_{i t}=& \beta_{0}+\delta_{1} d 88_{t}+\delta_{2} d 89_{t}+\beta_{1} g r a n t_{i t}+\beta_{2} g r a n t_{i, t-l} \\ &+\beta_{3} \log \left(e m p l o y_{i t}\right)+a_{i}+u_{i t} \end{aligned}$(i) Estimate the equation using fixed effects. How many firms are used in the FE estimation? Howmany total observations would be used if each firm had data on all variables (in particular,hrsemp) for all three years?(ii) Interpret the coefficient on grant and comment on its significance.(iii) Is it surprising that grant $_{-1}$ is insignificant? Explain.(iv) Do larger firms provide their employees with more or less training, on average? How big arethe differences? (For example, if a firm has 10$\%$ more employees, what is the change in averagehours of training?

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The difference in the training is $-0.176$ hours of training per employee if the firm is with employ10$\%$ point higher than the other firm

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Chapter 14

Advanced Panel Data Methods

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not one. We use 135 firms. In the fixed effect estimation, we would have a total of 405 observations as we have three years. If each firm had data on all variables four or three years. Yeah. However, due to missing data, we only have 390 observations in the fixed effects estimation, This is the regression result or to the estimate on variable Grant means that if a firm received a grand for the current here, a train is worker, an average of 34.2 hours more than it would have otherwise. This is a large effect. And because the T statistic is also very large, this effect is very significant. Yeah, we can say that this variable is statistically and economically significant. Part three, you can tell from the estimation result. The variable grand I t minus one is not significant. It's standard Error is way larger than its estimate. This is not surprising because mhm the grants do not carry over into more training of the next year. Lastly, we have the coefficient of lock of employee numbers. Yeah. Now this coefficient is very small. Yeah, we have the dependent variable in level and this variable is in log. So this is how we interpret the coefficient? A 10% increase in the number of employee which represents by variable Employee. That would increase the predicted hours per employee by only about 0.18 Yeah, this is a very, very small effect and given its T statistic, so you can approximate that. The T statistic is about 0.2 0.2 As three, the T statistic is virtually zero, so this variable is small and insignificant.

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