*! version 2.1 14jun2016
help xtewreg

Title

[XT] xtewreg -- Erickson-Whited linear errors-in-variables panel regression with identification from higher order cumulants/moments

Syntax

xtewreg
depvar misindepvars [indepvars]
[if] [in]
,
maxdeg
[options]

Main
maxdeg Highest cumulant/moment order to use. Required

mismeasured The number of mismeasured regressors

method Use high order cumulants (CML) or moments (MOM)

panmethod Which panel method to use

bxint Starting guess for the coefficients on misindepvars. Requires method=MOM

centmom Support centering moment conditions for bootstrap estimation of standard errors

hascons Indicate that indepvars already contains a constant variable

nocons Indicate that indepvars should not contain a constant variable - see warning below

noprn Supress printing of results

Description

Model

xtewreg estimates a classical linear errors-in-variables model with arbitrarily many mismeasured regressors and perfectly measured regressors on panel data.
It uses information in the higher order cumulants/moments of the observable variables to identify the regression coefficient.

Yit = Xit*b + Zit*a + uit

xit = Xit + vit

In which Yit is the dependent variable, Xit is a vector of unobservable mismeasured regressors, Zit is a vector of perfectly measured regressors,
uit is the regression disturbance, xit are the proxies for Xit, and vit are the measurement errors.

This procedure implements the estimators from Erickson and Whited (2000, 2002) and Erickson, Jiang and Whited (2014).
Panel data can be analyzed by using either a clustered weighting matrix (panmethod=CLS, recommended) or a minimum distance procedure (panmethod=CMD),
in which estimates are attained for each cross section in the panel and then pooled using the classical minimum distance estimator for unbalanced panels in Erickson and Whited (2012).

As xtewreg requires de-meaned data (and does not compute fixed effects internally), the researcher must de-mean the data appropriately before using xtewreg.

Note: The Erickson-Whited estimators are unidentified if the coefficients on the mismeasured regressors are equal to zero, or if the mismeasured regressors are normally distributed.

Choosing maxdeg

xtewreg does not provide a default value for maxdeg, the highest order of cumulants/moments to use.
This choice is left to the researcher and is an empirical choice.
Generally speaking, the more data one has, the higher the order one can use.
A reasonable starting value for applied work is maxdeg=5, but the sensetivity of the estimates to different values of maxdeg should be explored on a case by case basis.

Description of MOM and CMD

While xtewreg supports both high order cumulants (CML) and moments (MOM), using high order moments is not advised.
High order moments require a minimization procedure when computing the GMM objective, whereas the cumulants are linear and so have a closed-form minimum.
Thus, using high order moments adds a level of complexity absent from high order cumulant based estimation.
Similarly, xtewreg supports panel data using both clustered weighting matrices (CLS) and using classical minimum distance (CMD).
Using classical minimum distance is not advised due to the high computational cost invloved and the finite-sample properties of the estimator.
Both options are nevertheless provided for completeness and backward compatability.

Additional statistics

Like any regression estimator, the xtewreg command returns estimates of regression coefficients, standard errors, and the R2 of the regression, denoted here rho2.
Additionally, the command returns the R2 of each measurement equation, denoted tau2, which is an index of measurement quality.
This index ranges between zero and one, with zero indicating a worthless proxy and one indicating a perfect proxy.

The xtewreg command also provides the test of the overidentifying restrictions of the model (the Sargan-Hansen J-statistic).

Technical considerations

To prevent unneccesary computations, xtewreg saves the structure of a problem (the estimation equations associated with a given maxdeg and mismeasured between executions.
This is especially useful when using bootstrap, to avoid constructing the equations for every bootstrap iteration.

This procedure requires Stata 12 or higher.

Options

maxdeg sets the highest order of cumulants/moments to use. The minimum value is 3, which corresponds to an exactly identified Geary (1942) estimator.
Very high values (above 8) are not advised, as the computational time for these models is exponential in maxdeg. See comment above regarding choosing maxdeg values.

mismeasured declares the number of mismeasured regressors in the model. The defualt value is 1.
xtewreg uses this value to distinguish between misindepvars and indepvars.
The first <mismeasured> independant variables are taken to be misindepvars, and the rest are taken to be indepvars.

method chooses whether to use high order cumulants (CML, the default) or high order moments (MOM). See comment above regarding the deprecation of high order moments.

panmethod chooses whether to perform panel estimation by using clustered weighting matrices in the GMM (CLS, the default) or combine cross-sections using a minimum distance estimator (CMD).
See comment above regarding the deprecation of classical minimum distance estimators.

bxint is a numlist of starting values for the coefficients on misindepvars. This option requires setting metod=MOM.
The high order moment estimators require numerical minimization of a nonlinear objective function and thus require starting values.
The default is to use both the OLS coefficients and the coefficients from maxdeg=3 as possible starting values.

centmom is a directive supporting centering moment conditions for bootstrap estimation of standard errors.
The option takes one of the values [set, use, reset].
centmom=set saves the value of the moment conditions for the entire sample, and should be used before using the bootstrap command.
centmom=use should be specified when using bootstrap along with xtewreg.
centmom=reset resets the value of saved moment conditions, and is rarely used.

hascons indicates that indepvar already contains a constant variable, and so a constant should not be added by the estimation procedure.

nocons indicates that indepvars should not contain a constant variable. Using this option requires that all variables have zero mean.

noprn disables printing of results table.

Examples

. xtset gvkey

. xtewreg ik q , max(5)

. xtewreg ik q cfk oik, max(5) mis(2) cent(set)

. bootstrap : xtewreg ik q cfk oik, max(5) mis(2) cent(use)

Saved results

xtewreg saves the following in e():

Scalars

e(N) number of observations

e(rho) estimate of rho^2

e(SErho) standard error for rho^2

e(Jstat) Sargan-Hansen J statistic for overidentifying restrictions

e(Jval) p-value for Jstat

e(dfree) degrees of freedom for Jstat

e(obj) minimized value of the gmm objective function

Macros

e(bxint) numlist of initial guesses for beta

e(method) method used for estimation (CML or MOM)

e(panmethod) panel method used for estimation (CMD or CLS)

Matrices

e(b) regression coeffiecients

e(V) variance-covariance matrix for e(b)

e(serr) standard errors for e(b)

e(tau) estimates of tau^2, the proxy accuracy indices

e(SEtau) standard errors for tau^2

e(vcrhotau) variance-covariance matrix for rho and all of the tau^2

e(w) the weighting matrix used in the gmm estimation

References

Erickson, T. and T. M. Whited. 2000. Measurement error and the relationship between investment and q. Journal of Political Economy 108: 1027-1057.

Erickson, T. and T. M. Whited. 2002. Two-step GMM estimation of the errors-in-variables model using high-order moments. Econometric Theory 18: 776-799.

Erickson, T. and T. M. Whited. 2012. Treating measurement error in Tobin's q. Review of Financial Studies 25: 1286-1329

Erickson, T. C. H. Jiang, and T. M. Whited. 2014. Minimum Distance Estimation of the Errors-in-Variables Model Using Linear Cumulant Equations. Journal of Econometrics, forthcoming.

Geary, R. C., 1942. Inherent relations between random variables. Proceedings of the Royal Irish Academy A 47: 63-76.

Remark

This is version 2.1 of the xtewreg command. Please send bug reports and feature requests to robert.parham@simon.rochester.edu. Adapted to Stata by Robert Parham, based on code provided by Toni M. Whited.

Also see

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