ECON 3313 Homework 1
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ECON 3313
Homework 1
Question 1: Basic Features of the Data.
(Important: The xlim and ylim arguments I set in the in-class R example are changeable. You need to change them based on your own needs. If you keep the in-class setting for these two arguments, you might end with weird plots and lose points on it.)
1. Draw the histograms for (1)WAGE with option breaks = 20 and title “Breaks=20”;
(2) WAGE with option breaks = 40 and title “Breaks=40” . Combine these two plots into one graph. Which one would you prefer? breaks = 20 or breaks = 40?
2. Draw density plot for WAGE and LNWAGE. Fit each of them with the normal density [Hint: remember to set the number of draws equal to your 7-digit student ID]. Combine these two plots into one graph. Based on the density plots of WAGE and LNWAGE, discuss the advantage of converting WAGE into LNWAGE.
3. Draw the histograms for EDUC, EXPER, and AGE with breaks = 40 on one graph.
4. Assessing the relationship between wage and age by plotting LNWAGE against AGE. Fit the data by OLS on the same graph.
Question 2: Building the Cross-Sectional Forecasting Model.
5. Run OLS for the following model:
LNWAGE = β0 + β1 EDUC + β2 EXPER + β3 AGE2 + β4 FEMALE + ϵ
Report the coefficients and standard errors. Are those coefficients significant individually? At what level?
6. Generate the in-sample forecasts and plot LNWAGE against the in-sample forecasts on a graph. Based on this graph, discuss the performance of our model in terms of the in-sample forecasts.
7. Generate the residuals by computing the difference between LNWAGE and LN—WAGE . Then, calculate the standard error of the residuals using R programming
based on the following formula
4 d f(王ni=1) .ei(2) ,
where ei is the residual. Verify the standard error of the residuals you just calculated is the same as the one you obtained in the regression summary table.
8. Construct the density forecast for (EDUC = youryrsofeduc;
EXPER = youryrsofworkingexper; AGE2 = (yourage)2 ; FEMALE = 1 if female; 0 if male) without considering estimation uncertainty. Plot the estimated density of wage on a graph and use two vertical lines to indicate 90% CI. Construct a point forecast based on this density forecast. [Hint: remember to set the number of draws equal to your 7-digit student ID.]
9. Repeat Question 8 with parameter estimation uncertainty. Plot the estimated density of wage on a graph and use two vertical lines to indicate 99% CI. Construct a point forecast based on this density forecast.
2022-12-12