What must be true for the reduced form parameters to be identified?

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1.

Week 5 - Problem Set

Consider the two-equation structural model

3171 92 +218 +1

32 72 91 +22182 +uzi

Solve for the reduced forms. What must be true for the reduced form parameters to be identified? What must be true for the structural coefficients to be identified?

2.

This problem considers some practical ways to develop instruments for nonlinear endoge- nous regressors using interaction terms and fitted values. Consider the model estimated in Problem 5c of Problem Set 3 using the card.xlsx data. In that model, log(wage) is regressed on educ, exper, exper2, black, south, smsa, sm sa66, and all but one of the regional dummies using 2SLS; educ is endogenous and instrumented with near 4c.

(a) Add educ2 as an endogenous regressor to the model in 8e) and, in addition to nearc4 alone, use interaction terms with nearc4 as the instruments, i.e., nearc4 exper, nearc4 exper2, nearch black, etc. Perform a robust t-test of the significance of educ2 in the model.

(b) Add educ2 as an endogenous regressor to the model in 5c and use (educ)2 as its instru- ment, where educ is the fitted value from a reduced form regression of educ on all exogenous variables (including nearc4). Perform a robust t-test of the significance of educ2 in the model.

(c) Add black educ as an endogenous regressor to the model in 5c and use interaction terms with black as the instruments, i.e., black nearc4, black exper, black exper2, black south, etc. Perform a robust t-test of the significance of black educ in the model.

(d) Add black educ as an endogenous regressor to the model in 5c and use black educ as its instrument, where educ is defined as in (b). Perform a robust t-test of the significance of black educ in the model.

3.

This problem uses data from openness.xlsx, which contains 114 observations about import and inflation rates by country. These data were used by Romer (1993) ("Openness and Infla- tion: Theory and Evidence," Quarterly Journal of Economics 108, 869-903) to examine whether the openness of an economy leads to lower inflation rates. The variables include:

Variable Name Variable Label

open

inf

pcinc

land

oil

good

imports as a percentage of GDP, 1973- average annual inflation, 1973-

per capita income in US dollars, 1980 land area in square miles

=1 if major oil producer

=1 if "good" data

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