使用人口的种族和语言构成作为腐败的工具变量

1、Endogeneity in Econometrics:Instrumental Variable EstimationMing LUEndogeneity Omitting variable bias Simultaneity Measurement error Can we ignore the omitted variables bias? It can be satisfactory if the estimates are coupled with the direction of the biases for the key parameters. Can we use proxy

2、 to eliminate omitted variable bias? Sometimes. Can FE estimation solve omitting variable problem? First differencing or fixed effects estimation eliminates time-constant variables. In addition, the panel data methods do not solve the problem of time-varying omitted variablesIdea of IV Estimation Ex

3、ogenous variable. Indirect effects of IV.Example What can serve as IV for edu? Mothers education? Number of siblings? The report of others? A dummy variable that is equal to 1 if a man is born in the first quarter of the year. Angrist and Krueger (1991). (Problematic.) In China, the years of primary

4、 edu?IV for skipped class? The distance from home to school.Other examples of IV IV for institution: Language? History? Mauro (1995) 使用人口的种族和语言构成作为腐败的工具变量，Hall and Jones (1999) 用距离赤道的距离和以西欧语言为第一语言的程度作为制度质量的工具变量，La Porta et al. (1997, 1998, 1999)把法律的起源作为各种法律结构的工具变量。Acemoglu, Johnson, and Robinson (20

5、01, 2002)使用殖民地时代(1500年前后)的死亡率和人口密度作为制度的工具变量 IV for school choice: Number of steams?Identification Refer to (15.9) and (15.10)The (asymptotic) standard error of SST is the total sum of squares of the xiSelf-selection Angrist (1990) studied the effect that being a veteran in the Vietnam war had on lif

6、etime earnings. Draft lottery number is a good IV candidate for veteran. Some additional words about natural experiment and DIDProperties of IV with a Poor Instrumental Variable Poor IV can cause serious bias.R2 Most regression packages compute an R-squared after IV estimation, using the standard fo

7、rmula: R2= 1- SSR/SST, where SSR is the sum of squared IV residuals, and SST is the total sum of squares of y. R2 can be negative in this case.IV ESTIMATION OF THE MULTIPLE REGRESSIONMODEL structural equationEstimationEfficient IVEquation (15.26) is an example of a , which means that we have written

8、 an endogenous variable in terms of exogenous variables.TWO STAGE LEAST SQUARES2SLS in words The first stage is to run the regression in (15.36), where we obtain the fitted values y2. The second stage is the OLS regression (15.38). Because we use y2 in place of y2, the 2SLS estimates can differ subs

9、tantially from the OLS estimates. Another interpretation:Multiple Endogenous Explanatory Variables ORDER CONDITION FOR IDENTIFICATION OF AN EQUATION: We need at least as many excluded exogenous variables as there are included endogenous explanatory variables in the structural equation.IV SOLUTIONS T

10、O ERRORS-IN-VARIABLES PROBLEMSOne possibility is to obtain a second measurement on X*1, say, z1, as IV.An alternative is to use other exogenous variables as IVs for a potentially mismeasured variable.TESTING FOR ENDOGENEITY AND TESTING OVERIDENTIFYING RESTRICTIONS The 2SLS estimator is less efficien

11、t than OLS when the explanatory variables are exogenous; as we have seen, the 2SLS estimates can have very large standard errors.How to test endogeneity? 1. Comparing the OLS and 2SLS estimates and determining whether the differences are statistically significant. (Hausman, 1978) 2. A regression tes

12、t:Another interpretation of 2SLS Including v2 in the OLS regression (15.51) clears up the endogeneity of y2. We can also test for endogeneity of multiple explanatory variables. For each suspected endogenous variable, we obtain the reduced form residuals. Then, we test for joint significance of these

13、 residuals in the structural equation, using an F test.Testing Overidentification Restrictions If we have more than one instrumental variable, we can effectively test whether some of them are uncorrelated with the structural error. Use one IV and get the predicted residual, then test the correlation

14、 between other IVs and the residual.TESTING OVERIDENTIFYING RESTRICTIONS: (i) Estimate the structural equation by 2SLS and obtain the 2SLS residuals, u1. (ii) Regress u1 on all exogenous variables. Obtain the R-squared, say R12. (iii) Under the null hypothesis that all IVs are uncorrelated with u1,

15、nR12 X 2(q) , where q is the number of instrumental variables from outside the model minus the total number of endogenous explanatory variables. If nR12 exceeds (say) the 5% critical value in the X 2(q) distribution, we reject H0 and conclude that at least some of the IVs are not exogenous.Is it bet

16、ter to have more IVs? Adding instruments to the list improves the asymptotic efficiency of the 2SLS. But this requires that any new instruments are in fact exogenous. With the typical sample sizes available, adding too many instrumentsthat is, increasing the number of overidentifying restrictionscan

17、 cause severe biases in 2SLS.2 Omitted Topics 2SLS WITH HETEROSKEDASTICITY APPLYING 2SLS TO TIME SERIES EQUATIONSAPPLYING 2SLS TO POOLED CROSS SECTIONSAND PANEL DATA For pooled cross sections data: add time dummy. For panel data: In the first stage, use the differenced IV to get an estimate of the endogenous variable. Question: If the panel model is a FE one, how to check the ef