Economics 123B
Econometrics II Winter 2019
Homework 3
Due on 2/28/2019
Problems and Derivations
Problem 1: Suppose that we want to evaluate the effect of several variables on
annual saving and that we have a panel data set on individuals collected in January
1990 and January 1992. If we include a year dummy variable for 1992 and use first
differencing, can we also include age in the original model? Please explain.
Problem 2: Consider a data set consisting of observations on i = 1, . . . , n units
over t = 1, . . . , T time periods and suppose that n is large and T is small (e.g., you
have n = 5000 patients observed over T = 10 years). Write down an econometric
model that can be used to analyze the data and explain its components. What
problems arise if in your regression you ignore the fact that patients are potentially
heterogeneous? Show an example of this graphically. Discuss one approach to
estimating the parameters of this model, listing the necessary steps.
Problem 3: The mock dataset hw3 data.csv on the course website includes observations
on i = 1, . . . , 100 California counties over t = 1, . . . , 4 time periods. The

Economics 123B作业代做
dependent variable y, stored in column 1, is a measure of pollution. The next three
columns include determinants of y, and a county indicator appears in column 5.
1. Load the data into your favorite statistics software. Without using panel data
packages or toolboxes, implement the mean-differncing and first-differcing fixed
effects estimators. Show your code and report your point estimates. Are the
estimates under mean-differencing and first-differencing comparable? (Note: to
confirm the accuracy of your code, you may wish to compare your results to
those obtained from the panel data analysis tools in your software, e.g., if using
R, install package plm and enable it with the command library(plm) at the top
of your script).
2. Provide a forecast of pollution if x1 = 1.1, x2 = 1.5, and x3 = .2. Because you
have removed the county specific intercepts, what is the proper interpretation
of your forecast?

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