1. Suppose that a researcher wants to evaluate the effect of a specific job training program...

  

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1. Suppose that a researcher wants to evaluate the effect of a specific job training program on worker productivity of manufacturing firms. This job training was conducted by the grant from the government and the government chose the firms to receive the grant. He collects data on the scrap rate of firm i (i=1,..., 2750) in 2009. The data include following variables Variable scrap grant size export Pfemale Label the number of items, per 100, that is scrapped due to defects =1 if firm i received a job training grant from the government log of number of employees =1 if a firm i is exporting. proportion of female employees. Now, the researcher suspects the unobserved firm's characteristics (called 'fixed effects') that might be related to whether a firm receives a grant, and affect the scrap rate. The unobserved fixed effects might contain such factors as average employee ability, capital, and managerial skill. Thus, he assumes that the true scrap rate model is as follows scrap, = Bo + Bigrant, +Basize, + Berporti + 6 + U (M) where Bo is an intercept and d, is an unobserved fixed effect. We assume that size, export, venture are exogenous variables. (a) Explain the reason why we cannot estimate the coefficient (8₁) of grant consistently in this model (M) using OLS? (b) Suppose that the researcher collected an additional variable of proportion of female among employees (Pfemale). And he found that the government changed the selection rule for the grant, so that firms with higher proportion of female employees were more likely to have a chance to receive the grant. What kinds of conditions should be satisfied to use Pfemale as an instrumental variable for grant? Do you think the conditions are satisfied? Explain why. (For simplicity, we assume no ability difference between male and female employees.) (c) The researcher decided to use Pfemale, as an instrumental variable and estimated the following regression to see whether the conditions for IVs are satisfied, 0.381 +0.251 Pfemale, +0.078size, +0.153erzport,, 0.079 -0.031, N=2750. Do you think which condition is satisfied? Explain why and provide the test results. grant, R² (d) Given the results in (c), the researcher decided to use TSLS (two-stage least square) estimator. Write down the second-stage regression equation to estimate Bo. B1, B2. Bs. and 3 in (M) (e) The researcher obtained the following results using OLS and TSLS. If a firm receives the grant, what is the predicted ceteris paribus change in scrap for this firm? Is this change statistically significant? scrap grant BOLS -0.672 8126 OLS 0.746 export -0.635 R² 0.120 P-value of Hausman-test: 0.0447 TSLS SE(BOLS) BIVE 0.076 -1.486 0.196 0.651 0.201 -0.576 0.113 SE(BIVE) 0.554 0.240 0.228 1. Suppose that a researcher wants to evaluate the effect of a specific job training program on worker productivity of manufacturing firms. This job training was conducted by the grant from the government and the government chose the firms to receive the grant. He collects data on the scrap rate of firm i (i=1,..., 2750) in 2009. The data include following variables Variable scrap grant size export Pfemale Label the number of items, per 100, that is scrapped due to defects =1 if firm i received a job training grant from the government log of number of employees =1 if a firm i is exporting. proportion of female employees. Now, the researcher suspects the unobserved firm's characteristics (called 'fixed effects') that might be related to whether a firm receives a grant, and affect the scrap rate. The unobserved fixed effects might contain such factors as average employee ability, capital, and managerial skill. Thus, he assumes that the true scrap rate model is as follows scrap, = Bo + Bigrant, +Basize, + Berporti + 6 + U (M) where Bo is an intercept and d, is an unobserved fixed effect. We assume that size, export, venture are exogenous variables. (a) Explain the reason why we cannot estimate the coefficient (8₁) of grant consistently in this model (M) using OLS? (b) Suppose that the researcher collected an additional variable of proportion of female among employees (Pfemale). And he found that the government changed the selection rule for the grant, so that firms with higher proportion of female employees were more likely to have a chance to receive the grant. What kinds of conditions should be satisfied to use Pfemale as an instrumental variable for grant? Do you think the conditions are satisfied? Explain why. (For simplicity, we assume no ability difference between male and female employees.) (c) The researcher decided to use Pfemale, as an instrumental variable and estimated the following regression to see whether the conditions for IVs are satisfied, 0.381 +0.251 Pfemale, +0.078size, +0.153erzport,, 0.079 -0.031, N=2750. Do you think which condition is satisfied? Explain why and provide the test results. grant, R² (d) Given the results in (c), the researcher decided to use TSLS (two-stage least square) estimator. Write down the second-stage regression equation to estimate Bo. B1, B2. Bs. and 3 in (M) (e) The researcher obtained the following results using OLS and TSLS. If a firm receives the grant, what is the predicted ceteris paribus change in scrap for this firm? Is this change statistically significant? scrap grant BOLS -0.672 8126 OLS 0.746 export -0.635 R² 0.120 P-value of Hausman-test: 0.0447 TSLS SE(BOLS) BIVE 0.076 -1.486 0.196 0.651 0.201 -0.576 0.113 SE(BIVE) 0.554 0.240 0.228

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