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 (hrsengo) from two consecutive years at n=420 manufacturing rms. To control for time and rms' fixed effects, we difference the data. This way we can safely remove the potential biases that could be caused by unobservables that either chance over time or across rms. We then run the following OLS regression: Aln(scrapit) = [30 + Blhrsempit + An\" where the estimated 31 coefcient is equal to 40.0076 (HAC std error = 0.0045). Econ 213a Fall 2021 Prof. Pettenuzzo (a) We are afraid that Ann and dhrsempit may be correlated. For example, it is possible that a rm 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. (11-) Suppose we have data on whether firms received job training grants in the two years, and use this data to dene a new regressor, Agrantit. Let's assume that Agrantit and Au\" are uncorrelated. Write down the rst stage model of the resulting TSLS regression. (c) The estimated coefcients from the first stage regression described in (b) are given by: 30 = 0.51 (HAC std. err. = 1.56) and 31 = 27.88 (HAC std. err. = 12.13). Do you conclude that Agrantit is a relevant instrument? (d) How would you test in this case whether the proposed instrument is in fact exogenous