help for ivreg2h

Instrumental variables estimation using heteroskedasticity-based instruments

Description

ivreg2h estimates 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 be (a) applied when no external instruments are available, or, alternatively,
(b) 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.

Lewbel (2016, 2018) discusses how this estimation technique may be used, under certain conditions,
where an endogenous regressor is binary rather than continuous, such as an endogenous treatment
indicator. Under the same assumptions, the technique could be employed where both the outcome
and regressor are binary.

This implementation has been built using the existing xtivreg2 (Schaffer)
and ivreg2 (Baum, Schaffer, Stillman) routines. It can be used on panel data using the
within transformation of a fixed effects model: see the fe option described below.
As ivreg2h is a variant of ivreg2, essentially
all of the features and options of that program are available in ivreg2h. For that
reason, you should consult help ivreg2 for details of the available options.

ivreg2h provides four additional options: gen, gen(string[,replace]), fe and z().
If the gen option is given, the generated instruments are saved, with names built from
the original variable names suffixed with _g.
If greater control over the naming
of the generated instruments is desired, use the gen(string[,replace] option.
The string argument allows the specification of a stub, or prefix, for the generated variable names,
which will also be suffixed with _g.
You may remove earlier instruments with those same names with the replace suboption.
If the data have been declared as a panel, you can use the fe option to specify that
a fixed-effects model should be estimated, as in xtivreg2.
In order to use a subset of the included exogenous variables to construct instruments, include
them in the z() option. Make sure that the variables listed here are in the list of included
instruments.

ivreg2h can 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 (a) by having no excluded instruments,
or (b) by having fewer excluded instruments than needed for
traditional identification.

In the former case (a), of adequate 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.
ivreg2h automatically produces a Hayashi "C" test of the excluded instruments' validity
(equivalent to use of the orthog option in 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, named StdIV, GenInst and GenExtInst, respectively.

In the latter case (b), of an underidentified equation, either one or two sets
of estimates will be produced and displayed.
If there are no excluded instruments, only the estimates using
generated instruments are displayed.
If there are excluded instruments but too few to produce identification by
the order condition, the estimates using only generated instruments and those produced by
generated and excluded instruments will be displayed.
Unlike ivreg2 or ivregress, ivreg2h allows the syntax
ivreg2h 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 named GenInst and, optionally, GenExtInst.

Saved Results

Note that in the estimates table output, the displayed results j, jdf and
jp refer 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 in j, jdf and
jpval, 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 ivreg2 for details.

Examples

Example 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

. ivreg2h foodshare z_* (lrtotexp = lrinc), small robust gmm2s z(z_age-z_agesp2)

Example using panel data and HAC standard errors.

. webuse grunfeld

. ivreg2h invest L(1/2).kstock (mvalue=), fe

. ivreg2h invest L(1/2).kstock (mvalue=L(1/4).mvalue), fe robust bw(2)

Acknowledgements

We thank participants in the 2012 UK Stata Users Group, 2013 Mexican Stata Users Group
and 2013 German Stata Users Group meetings for their constructive comments.
We are grateful to Federico Belotti for diagnosing and providing corrected code for the -generate- option.

References

Baum 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.

Lewbel, A, 2016. Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case.
Boston College Economics Working Paper 927. http://fmwww.bc.edu/EC-P/wp927.pdf

Lewbel, A, 2018. Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case.
Economics Letters, 165, 10-12.

Citation

ivreg2h is 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

Authors

Christopher F Baum, Boston College, USA

baum@bc.edu

Mark E Schaffer, Heriot-Watt University, UK

M.E.Schaffer@hw.ac.uk