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Instrumental variables estimation using heteroskedasticity-based instruments

Description

ivreg2hestimates an instrumental variables regression model providing the option to generate instruments using Lewbel's (2012) method. This technique allows the identification of structural parameters in regression models with endogenous or mismeasured regressors in the absence of traditional identifying information, such as external instruments or repeated measurements. Identification is achieved in this context by having regressors that are uncorrelated with the product of heteroskedastic errors, which is a feature of many models where error correlations are due to an unobserved common factor. The greater the degree of scale heteroskedasticity in the error process, the higher will be the correlation of the generated instruments with the included endogenous variables which are the regressands in the auxiliary ('first stage') regressions.Using this form of Lewbel's method, instruments may be constructed as simple functions of the model's data. This approach may thus be applied when no external instruments are available, or, alternatively, used to supplement external instruments to improve the efficiency of the IV estimator. Supplementing external instruments can also allow Sargan-Hansen tests of the orthogonality conditions or overidentifying restrictions to be performed, which would not be available in the case of exact identification by external instruments.

This implementation has been built using the existing

xtivreg2(Schaffer) andivreg2(Baum, Schaffer, Stillman) routines. At present it does not provide any explicit support for panel data. Asivreg2his a variant ofivreg2, essentially all of the features and options of that program are available inivreg2h. For that reason, you should consult help ivreg2 for details of the available options.

ivreg2hcan be invoked to estimate a traditionally identified single equation, or a single equation that--before augmentation with the generated instruments--fails the order condition for identification: either (i) by having no excluded instruments, or (ii) by having fewer excluded instruments than needed for traditional identification.In the former case, of external instruments augmented by generated instruments, the program provides three sets of estimates: the traditional IV estimates, estimates using only generated instruments, and estimates using both generated and excluded instruments.

ivreg2hautomatically produces a Hayashi "C" test of the excluded instruments' validity (equivalent to use of theorthogoption in {cmd{ivreg2}). The results of the third estimation (that including both generated and excluded instruments) are saved in the ereturn list. All three sets of estimates are saved, namedStdIV,GenInstandGenExtInst, respectively.In the latter case, of an underidentified equation, the only the estimates using generated instruments are displayed. Unlike

ivreg2orivregress,ivreg2hallows the syntaxivreg2h depvar exogvar (endogvar=), as after augmentation with the generated regressors, the order condition for identification will be satisfied. The resulting estimates are saved in the ereturn list and as a set of estimates namedGenInst.

Saved ResultsNote that in the

estimates tableoutput, the displayed resultsj,jdfandjprefer to the Hansen J statistic, its degrees of freedom, and its p-value. If i.i.d. errors are assumed, and a Sargan test is displayed in the standard output, the Sargan statistic, degrees of freedom and p-value are displayed inj,jdfandjpval, as the Hansen and Sargan statistics coincide in that case.The results of the most recent estimation are saved in the ereturn list. Please see

help ivreg2for details.

ExamplesExample from Lewbel (2012). Note that centering of regressors is only used to match the results.

. ssc install center // (if needed)

. ssc install bcuse // (if needed)

. bcuse engeldat

. center age-twocars, prefix(z_)

. ivreg2h foodshare z_* (lrtotexp=), small robust

. ivreg2h foodshare z_* (lrtotexp = lrinc), small robust

. ivreg2h foodshare z_* (lrtotexp = lrinc), small robust gmm2s

Example using panel data and HAC standard errors. Centering used to remove firm fixed effects.

. webuse grunfeld

. by company: center invest kstock mvalue

. ivreg2h c_invest L(1/2).c_kstock (c_mvalue=)

. ivreg2h c_invest L(1/2).c_kstock (c_mvalue=L(1/4).c_mvalue), robust gmm2s bw(3)

AcknowledgementsWe thank participants in the 2012 UK Stata Users Group meetings for their constructive comments.

ReferencesBaum CF, Lewbel A, Schaffer ME, Talavera O, 2012. Instrumental variables estimation using heteroskedasticity-based instruments. http://repec.org/usug2012/UK12_baum.pdf.

Lewbel, A, 2012. Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models. Journal of Business and Economic Statistics, 30:1, 67-80. http://fmwww.bc.edu/EC-P/wp587.pdf.

Citation

ivreg2his not an official Stata command. It is a free contribution to the research community, like a paper. Please cite it as such:Baum, CF, Schaffer, ME, 2012. ivreg2h: Stata module to perform instrumental variables estimation using heteroskedasticity-based instruments. http://ideas.repec.org/c/boc/bocode/s457555.html

AuthorsChristopher F Baum, Boston College, USA baum@bc.edu Mark E Schaffer, Heriot-Watt University, UK M.E.Schaffer@hw.ac.uk