You have an i.i.d. sample {(, X, X2i): i = 1,...,n). You want to estimate the...

 

    

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You have an i.i.d. sample {(₁, X₁, X2i): i = 1,...,n). You want to estimate the causal effect of X, on Y. a) You first run a regression Y₁ = a + a₁X₁ +u, and get the following result: = 0.5 +1.2X₁ (0.2) (0.6) where the numbers in parentheses are standard errors. Construct a 90% confidence interval for a₁. (The critical value for a t-test at 1%, 5% and 10% levels are 2.58, 1.96 and 1.64. respectively). b) You worry about omitted variable bias (OVB), so you are considering whether to put X₂, into the regression. The only condition you can check is that whether X, and X₂ are correlated. Propose a test with the null Ho: Px,x₂ = 0 based on regression. Describe what regression you would run and what the test procedure would be. Explain why the proposed test works. c) Now you find X₁ and X₂ are indeed correlated with covariance equal to 0.7. You decide to include X₂ in the regression: Y = Bo + B₂X₁ + B2X2 + e. The results are as follows: 0.6 + - 4Xzi 1.4X₁1 (0.3) (0.875) (2.67) Construct 90% confidence intervals for B, and for B₂. Is B, significantly different from 0 at 10% level? How about B₂? (1) d) You want to further conduct a Wald test for Ho: B₁ B₂ = 0. Based on the information in c), can you calculate the Wald statistic? If so, provide the derivation and the test statistic value. If not, explain why. e) Suppose the Wald statistic is equal to 4.76. Is the null in d) rejected at 10% level? f) Does parte) yield the same result as part e)? g) Suppose the difference between the estimates in a) and c) is only due to OVB. If the model in c) is the true model, provide a method to compute (estimate) the OVB based on the information given so far and the regression you run in b). You have an i.i.d. sample {(₁, X₁, X2i): i = 1,...,n). You want to estimate the causal effect of X, on Y. a) You first run a regression Y₁ = a + a₁X₁ +u, and get the following result: = 0.5 +1.2X₁ (0.2) (0.6) where the numbers in parentheses are standard errors. Construct a 90% confidence interval for a₁. (The critical value for a t-test at 1%, 5% and 10% levels are 2.58, 1.96 and 1.64. respectively). b) You worry about omitted variable bias (OVB), so you are considering whether to put X₂, into the regression. The only condition you can check is that whether X, and X₂ are correlated. Propose a test with the null Ho: Px,x₂ = 0 based on regression. Describe what regression you would run and what the test procedure would be. Explain why the proposed test works. c) Now you find X₁ and X₂ are indeed correlated with covariance equal to 0.7. You decide to include X₂ in the regression: Y = Bo + B₂X₁ + B2X2 + e. The results are as follows: 0.6 + - 4Xzi 1.4X₁1 (0.3) (0.875) (2.67) Construct 90% confidence intervals for B, and for B₂. Is B, significantly different from 0 at 10% level? How about B₂? (1) d) You want to further conduct a Wald test for Ho: B₁ B₂ = 0. Based on the information in c), can you calculate the Wald statistic? If so, provide the derivation and the test statistic value. If not, explain why. e) Suppose the Wald statistic is equal to 4.76. Is the null in d) rejected at 10% level? f) Does parte) yield the same result as part e)? g) Suppose the difference between the estimates in a) and c) is only due to OVB. If the model in c) is the true model, provide a method to compute (estimate) the OVB based on the information given so far and the regression you run in b).

Answer rating: 100% (QA)

ANSWER The total cost of producing and selling 500 bags is Cost of materials 100... View the full answer