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Economics 329 Econometrics Sanjay DeSilva Midterm Exam Fall 2006 Name: _______________________ Question 1 An economist interested in studying the effect of trade policy on GDP growth runs the following cross-country regression for a sample of 26 countries. Yi ˆ0 ˆ1 X i ei Y = GDP growth rate in percentage points. X = Average tariff rate in percentage points. The following is a partial list of results she obtains by running an OLS regression. ˆ1 0.15 y e x 2 i (Yi Y ) 2 200 2 i 168 2 i ( X i X ) 2 1000 a. Based on the information above, construct the ANOVA table for this regression. Sums Degrees of Freedom Means Explained/Regression Residual Total b. Calculate R 2 , Adjusted R 2 and the F-statistic for overall significance of the regression. R2 Adjusted R 2 F-statistic Economics 329 Econometrics Sanjay DeSilva Midterm Exam Fall 2006 c. Calculate the variance of ˆ1 , the slope coefficient. d. Carry out a hypothesis test to verify that tariffs do in fact reduce economic growth. Denote the null and alternative hypotheses, compute the relevant test statistics, and write the decision rule. H0 : H1 : Test Statistic: Decision Rule: Reject H 0 if ________________________ Economics 329 Econometrics Sanjay DeSilva Midterm Exam Fall 2006 Question 2 A more sophisticated multiple regression model that attempts to answer the same question, i.e. the effect of trade policy on economic growth, is shown below. GROWTH i ˆ0 ˆ1.TARIFFi ˆ2 .QUOTAi ˆ3 .GDPi ˆ4 .SSAi ˆ5 .EAi ei GROWTH TARIFF QUOTA GDP SSA EA = GDP growth rate in percentage points = Average tariff rate in percentage points = Index of trade quotas = GDP per capita = Dummy variable for Sub Saharan African countries = Dummy variable for East Asian counties. a. In this model, TARIFF and QUOTA are both measures of trade policy. Set up a hypothesis test that would help to establish whether trade policies significantly influence economic growth. Note the null hypothesis, construct the test statistic and report the decision rule (Don’t attempt to find numerical answers). H0 : Test Statistic: Decision Rule: Reject H 0 if ________________________ Economics 329 Econometrics Sanjay DeSilva Midterm Exam Fall 2006 b. When the QUOTA variable was added, the economist reports that the absolute value of the coefficient ˆ1 decreases (say, for example, to -0.05) but its standard error increased. Briefly explain why this may have happened. Decrease of ˆ1 : Increase of Var ( ˆ1 ): c. Suppose both ˆ1 and ˆ2 become statistically insignificant but the SSA dummy is significantly negative and the EA dummy is significantly positive. Draw a scatter plot of a relationship between tariffs and growth that is consistent with this finding. Economics 329 Econometrics Sanjay DeSilva Midterm Exam Fall 2006 d. Suppose the economist wants to find out whether the effect of tariff reduction on economic growth is greater from island nations than for countries with land borders. Sketch how this test can be carried out using a regression. Write out the regression equation/s and the set-up of a hypothesis test (null hypothesis and the test statistic). e. Suppose you want to find out whether tariffs impede growth less than quotas. Set up a hypothesis test (report the null hypothesis and the test statistic) Question 3 Consider the theoretical (population) regression Yi 0 1 X i ui . The OLS method obtains the following estimate for the slope coefficient, ˆ1 a. Show that ̂1 x y kY x i i 2 i i i where ki x y x i i 2 i xi (Note: y and Y are different). xi2 Economics 329 Econometrics Sanjay DeSilva Midterm Exam Fall 2006 b. Using the equation for the population regression, show that ˆ1 kiYi 1 ki ui c. 2 Starting from the definition of variance, show that Var ( ˆ1 ) = E k i ui 2 d. In order to simplify Var ( ˆ1 ) = E k i ui to the more familiar form that we use for a simple classical regression, what additional assumptions are needed?