Show transcribed image text uestion You want to examine whether a firm's performance (Y) is related with its employers' salary (X) and its employers' working hour (Z). You collect the data on 1000 firms and each firm has 500 monthly observations. A sample regression equation based is estimated based on OLS and given as Y,–0.40 + 0.48 Xt-0.42 Zit (0.22) (0.40) (0.2) i= 1, , 1000, 1-1, ,500, R=0.09, SER-4.8 The figures in parentheses below show the Heteroskedasticity- and-autocorrelation consistent standard errors for coefficient estimates 3.1) Calculate the t-statistic for two slope coefficients. Would you reject the null hypothesis that the coefficients are zero in the population, using a two-sided test and a 5% significance level? [1096] 3.2)When you re-estimate the regression with OLS using homoskedasticity-only standard errors, the standard error of the slope coefficient on the variable of X drops to 0.06. Calculate the t-statistic for the coefficient of variable X. Discuss your results by comparting the results in part (3.1) and justify which of the two standard errors (Heteroskedasticity- and-autocorrelation-consistent or homoskedasticity-only) should you use for statistical inference [20%] 3.3)Because you use the panel data in this case, you consider to include firm fixed effects and time fixed effects. Discuss the purpose of adding the entity fixed effect and the time fixed effect when we use panel data [10%] 3.4) Discuss whether the testing result is plausible in the OLS regression based on using the clustered standard errors in this case. And explain the purpose of using the clustered standard errors [10%] [Total 50%)

uestion You want to examine whether a firm's performance (Y) is related with its employers' salary (X) and its employers' working hour (Z). You collect the data on 1000 firms and each firm has 500 monthly observations. A sample regression equation based is estimated based on OLS and given as Y,–0.40 + 0.48 Xt-0.42 Zit (0.22) (0.40) (0.2) i= 1, , 1000, 1-1, ,500, R=0.09, SER-4.8 The figures in parentheses below show the Heteroskedasticity- and-autocorrelation consistent standard errors for coefficient estimates 3.1) Calculate the t-statistic for two slope coefficients. Would you reject the null hypothesis that the coefficients are zero in the population, using a two-sided test and a 5% significance level? [1096] 3.2)When you re-estimate the regression with OLS using homoskedasticity-only standard errors, the standard error of the slope coefficient on the variable of X drops to 0.06. Calculate the t-statistic for the coefficient of variable X. Discuss your results by comparting the results in part (3.1) and justify which of the two standard errors (Heteroskedasticity- and-autocorrelation-consistent or homoskedasticity-only) should you use for statistical inference [20%] 3.3)Because you use the panel data in this case, you consider to include firm fixed effects and time fixed effects. Discuss the purpose of adding the entity fixed effect and the time fixed effect when we use panel data [10%] 3.4) Discuss whether the testing result is plausible in the OLS regression based on using the clustered standard errors in this case. And explain the purpose of using the clustered standard errors [10%] [Total 50%)