Please answer and show steps for solving these questions

Suppose we want to estimate the effect of another hour of job training on workers' productivity. We collect data on the scrap rate (percentage of failed output from the production process that needs to be discarded) and hours of job training per employee (hrsemp) from two consecutive years at n=420 manufacturing firms. (a) [5 points] To control for time and firms' fixed effects, we difference the data. This way we can safely remove the potential biases that could be caused by unobservables that either change over time or across firms. Write down the model specification you would be estimating in this case, to control for both types of unobservables. (b) [10 points] Using OLS, you estimate the model you specified in (a). The estimated OLS 1 coefficient is equal to -0.0076 (HAC standard error =0.0045 ). We are however afraid that uit and hrsempit may be correlated. For example, it is possible that a firm may decide to hire more skilled worked and at the same time reduce the number of hours of job training for its employees. Describe the direction of the bias that would result from this situation. (c) [5 points] Suppose we have data on whether or not firms received job training grants in the two years, and use this data to define a new regressor, grantit. Let's assume that grantit and uit are uncorrelated. Write down the first stage model of the resulting TSLS regression. (d) [10 points] The estimated coefficients from the first stage regression described in (c) are given by: ^0=0.51 ( HAC std.err. =1.56) and 1=9.88 ( HAC std. err. =3.13). Do you conclude that grant it is a relevant instrument? In addition, how would you test in this case whether the proposed instrument is exogenous