1、HOMEWOK ONESection one1 Let the population regression function be . iii uXY21Write out the following matrices to show their elements: . Use the OLS estimator formula of 1)(,),(, XYYXand the elements of the above matrices to write out the expressions for and . Also calculate the estimated 12values of
2、 the parameters if 15,20,4,0,4822 nXYXYiiii2 A regression model is specified as , where u iiiuXYand X satisfy all the basic assumptions. Three estimators of have been proposed.Y122iX23Yiiia. Show that all three estimators are unbiased.b. Derive the variance of each of the three estimators. 3 Let X1,
3、 X2, , Xn be a random sample from a population with probability density function . Set up the likelihood function and 0exp),(ffind the maximum likelihood estimator of .4 Based on a sample of data from the U.S. population, we estimate a regression of the natural logarithm of consumption on a constant
4、 and the natural logarithm of income using least squares (LS). Selected results from this regression are presented in the following table:(a) Which of these coefficients are significantly different from zero at the 0.05 level?(b) Comment on the appropriateness of the following statement: “Other thin
5、gs equal, when income increases by 1%, we expect consumption to rise by 0.8013%.”Section two1) Give a careful interpretation of the coefficient (sign, magnitude and significance) of lifexp. 2) Give a careful interpretation of 3) Test whether the variables capturing the level of development are joint
6、ly significant. Write out the null-hypothesis and the alternative hypothesis, calculate the test and derive your conclusions. 4) True or False: based on the above estimates, we can accept the hypothesis that districts with higher life expectancy have a lower incidence of conflict in Nepal. T/F. Expl
7、ain. 5) Do you think it was a good idea to use the log of the dependent variable in this case? Explain.6) In the first model, the researcher was surprised to not to find a significant coefficient for the variable measuring income per capita. Imagine the researcher would estimate the first regression
8、 without including the life expectancy variable. a. Do you expect the coefficient of incpc to become more negative, less negative or positive? Explain why.b. Do you expect the precision of the estimate of incpc to be higher or lower than in the regression shown above? Explain why.7) The researcher d
9、oes some additional efforts and also finds data on district-level inequality in 2004. Do you think it would be a good idea to incorporate this information as an additional variable in the model? Explain. 8) At what level of significance can you reject the hypothesis that geography and forest cover together dont have an effect on conflict-related incidents. 9) Based on the regression results presented here, do you think the researcher should conclude that countries natural resource endowments do not affect the likelihood of civil war? Explain.
