Answer to Question #203067 in Microeconomics for Metu

Question

QUESTION ONE: (25 MARKS)

From a cross-sectional data of 41 countries, you want to test the hypotheses that trade taxes are positively related to trade volume but negatively related to per capita income. You estimate the following regression model:

𝑙𝑛𝑌=𝛽 +𝛽 𝑋 +𝛽 𝑋 +𝑢 (𝑖=1,2,...n) 𝐼 1 2 2𝑖 3 3𝑖 𝑖

Where;

Y = Ratio of trade taxes (import and export taxes) to government revenue; X2 = ratio of exports plus Imports to GNP;

X3 =GNP per (R'OOOs)

𝑖 =𝑖𝑡h country

1.1 If a cross section sample of large and small countries is used for the estimation of this model, explain why heteroscedasticity is almost certain to exist. (2)

1.2 Outline the problems one is likely to encounter when applying OLS in the presence of heteroscedasticity. (3)

1.3 How would you test the claim that the data suffers from heteroscedasticity using the general White test? (4)

1.4 Which remedy would you adopt if heteroscedasticity is indeed present? (2)

Answer 1

1,1

Heteroscedasticity is likely to happen because the standard deviation of the values is non-constant.

1.2

In presence of heteroscedasticity the OLS estimates is no longer blue and the estimated standard error is also wrong. Due to this the intervals and hypothesis test cannot be relied on.

1.3

To test whether the variance of the errors is constant using white test, the following are the steps;

• First estimate the model using OLS and obtain predicted Y values.
• Retain the R squared value from the regression and lastly
• calculate the F or chi-squared statistic.

1.4

Use the OLS estimates or any other estimates to estimate the parameters of the model.