Problem 5 (20 points) You have a dataset of the trade of 12 countries for the years 1990-2009 (20 years). The variables are: Ln(Tradet): Logarithm of the sum of country i's exports to the rest of the world, plus country i's imports from the rest of the world, in millions of dollars, in year t. Note: this value is not deflated, that is, it tends to increase over time just due to inflation. Also note: all of these countries are in the OECD, and have a similar rate of inflation each year. Ln(GDPit): Logarithm of country i's GDP (Gross Domestic Product), in year t. Note: this value is not deflated, that is, it tends to increase over time just due to inflation. Ln(Distance): Logarithm of country i's average distance to all other countries in the sample, in km. Corruptionit: An index for country i's level of corruption in year t, obtained from a global survey of business people (1-least corrupt; 10= most corrupt). Institutionsit: An index for country i's quality of institutions (government, courts, etc.), obtained from a global survey of political scientists (1-worst institutions; 10= best institutions). Democracy it: a dummy variable, taking the value 1 if the country is a democracy, 0 otherwise, obtained from a think tank. You run five models: (1)-(5), with results shown in the table below. a. (5 points) Test whether the time fixed effects are collectively significant, at the 5% significance level. State which model you used for your test. For full score, you must be precise about the actual test you are performing, and the critical value you are using. b. (5 points) Interpret the coefficient on Ln(GDP) in model (2). In particular, answer: is it an elasticity? How can you tell? Also, write something along the following lines: "if (...) rises by (...), then (...) rises / decreases by (...). REGRESSION RESULTS Dependent Variable: Ln(Trade) REGRESSOR Constant Ln(GDP) Ln(Distance) Corruption Institutions Democracy Ln(GDP) Democracy Country Fixed Effects Year Fixed Effects R Observations F-STATISTICS Country fixed effects=0 Year fixed effects=0 Corruption=0 Institutions=0 Democracy=0 (1) 2.3 (0.9) 1.13 (0.06) -1.07 (0.12) No No 0.09 201 (2) 1.02 (0.07) Yes No 0.76 201 5.85 (3) 1.02 (0.07) -0.005 (0.01) -0.05 (0.001) 0.008 (0.002) Yes No 0.76 201 5.82 3.91 0.87 (0.09) -0.01 (0.04) -0.07 (0.006) 0.03 (0.4) 0.36 (0.12) Yes No 0.77 201 5.91 3.92 (5) 0.69 (0.06) -0.01 (0.05) -0.04 (0.008) 0.01 (0.3) 0.25 (0.20) Yes Yes 0.93 201 5.77 2.30 3.89 5 REGRESSION RESULTS Dependent Variable: Ln(Trade) REGRESSOR Constant Ln(GDP) Ln(Distance) Corruption Institutions Democracy Ln(GDP) Democracy Country Fixed Effects Year Fixed Effects R Observations F-STATISTICS Country fixed effects=0 Year fixed effects=0 Corruption=0 Institutions 0 Democracy=0 (1) 2.3 (0.9) 1.13 (0.06) -1.07 (0.12) No No 0.09 201 (2) 1.02 (0.07) Yes No 0.76 201 5.85 (3) 1.02 (0.07) -0.005 (0.01) -0.05 (0.001) 0.008 (0.002) Yes No 0.76 201 5.82 3.91 (4) 0.87 (0.09) -0.01 (0.04) -0.07 (0.006) 0.03 (0.4) 0.36 (0.12) Yes No 0.77 201 5.91 3.92 (5) 0.69 (0.06) -0.01 (0.05) -0.04 (0.008) 0.01 (0.3) 0.25 (0.20) Yes Yes 0.93 201 5.77 2.30 3.89 c. (5 points) in 1999, a country's trade in millions of dollars was 345.8. The country becomes a democracy in 2000. Assuming all other variables remain the same, use model (3) to calculate the expected percentage increase in the country's trade, from 1999 to 2000, d. (5 points) Recall that the country effects are modeled by entering parameters a, into the regression, where i is the country. Suppose that acanada> aus. What does that tell you? Try to be as precise as you can in your answer. Problem 5 (20 points) You have a dataset of the trade of 12 countries for the years 1990-2009 (20 years). The variables are: Ln(Tradet): Logarithm of the sum of country i's exports to the rest of the world, plus country i's imports from the rest of the world, in millions of dollars, in year t. Note: this value is not deflated, that is, it tends to increase over time just due to inflation. Also note: all of these countries are in the OECD, and have a similar rate of inflation each year. Ln(GDPit): Logarithm of country i's GDP (Gross Domestic Product), in year t. Note: this value is not deflated, that is, it tends to increase over time just due to inflation. Ln(Distance): Logarithm of country i's average distance to all other countries in the sample, in km. Corruptionit: An index for country i's level of corruption in year t, obtained from a global survey of business people (1-least corrupt; 10= most corrupt). Institutionsit: An index for country i's quality of institutions (government, courts, etc.), obtained from a global survey of political scientists (1-worst institutions; 10= best institutions). Democracy it: a dummy variable, taking the value 1 if the country is a democracy, 0 otherwise, obtained from a think tank. You run five models: (1)-(5), with results shown in the table below. a. (5 points) Test whether the time fixed effects are collectively significant, at the 5% significance level. State which model you used for your test. For full score, you must be precise about the actual test you are performing, and the critical value you are using. b. (5 points) Interpret the coefficient on Ln(GDP) in model (2). In particular, answer: is it an elasticity? How can you tell? Also, write something along the following lines: "if (...) rises by (...), then (...) rises / decreases by (...). REGRESSION RESULTS Dependent Variable: Ln(Trade) REGRESSOR Constant Ln(GDP) Ln(Distance) Corruption Institutions Democracy Ln(GDP) Democracy Country Fixed Effects Year Fixed Effects R Observations F-STATISTICS Country fixed effects=0 Year fixed effects=0 Corruption=0 Institutions=0 Democracy=0 (1) 2.3 (0.9) 1.13 (0.06) -1.07 (0.12) No No 0.09 201 (2) 1.02 (0.07) Yes No 0.76 201 5.85 (3) 1.02 (0.07) -0.005 (0.01) -0.05 (0.001) 0.008 (0.002) Yes No 0.76 201 5.82 3.91 0.87 (0.09) -0.01 (0.04) -0.07 (0.006) 0.03 (0.4) 0.36 (0.12) Yes No 0.77 201 5.91 3.92 (5) 0.69 (0.06) -0.01 (0.05) -0.04 (0.008) 0.01 (0.3) 0.25 (0.20) Yes Yes 0.93 201 5.77 2.30 3.89 5 REGRESSION RESULTS Dependent Variable: Ln(Trade) REGRESSOR Constant Ln(GDP) Ln(Distance) Corruption Institutions Democracy Ln(GDP) Democracy Country Fixed Effects Year Fixed Effects R Observations F-STATISTICS Country fixed effects=0 Year fixed effects=0 Corruption=0 Institutions 0 Democracy=0 (1) 2.3 (0.9) 1.13 (0.06) -1.07 (0.12) No No 0.09 201 (2) 1.02 (0.07) Yes No 0.76 201 5.85 (3) 1.02 (0.07) -0.005 (0.01) -0.05 (0.001) 0.008 (0.002) Yes No 0.76 201 5.82 3.91 (4) 0.87 (0.09) -0.01 (0.04) -0.07 (0.006) 0.03 (0.4) 0.36 (0.12) Yes No 0.77 201 5.91 3.92 (5) 0.69 (0.06) -0.01 (0.05) -0.04 (0.008) 0.01 (0.3) 0.25 (0.20) Yes Yes 0.93 201 5.77 2.30 3.89 c. (5 points) in 1999, a country's trade in millions of dollars was 345.8. The country becomes a democracy in 2000. Assuming all other variables remain the same, use model (3) to calculate the expected percentage increase in the country's trade, from 1999 to 2000, d. (5 points) Recall that the country effects are modeled by entering parameters a, into the regression, where i is the country. Suppose that acanada> aus. What does that tell you? Try to be as precise as you can in your