# ARCHIVED: In Stata, how do I test overidentification using xtoverid?

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In Stata, `xtoverid` is used on a test of overidentifying restrictions (orthogonality conditions) for a panel data estimation after `xtreg`, `xtivreg`, `xtivreg2`, or `xthtaylor`.

Essentially, `xtoverid` can be used in three cases: to test on excluded instruments in IV estimations, to test on model specification (FE or RE), and to test on the strong assumption in an xthtaylor estimation.

## Testing on excluded instruments in IV estimations

In an IV estimation, `xtoverid` conducts a test on whether the excluded instruments are valid IVs or not (i.e., whether they are uncorrelated with the error term and correctly excluded from the estimated equation).

Rejection implies that some of the IVs are not valid. For example:

```    . webuse nlswork
. tsset idcode year
. gen age2=age^2
. gen black=(race==2)
. xtivreg ln_wage age (tenure = union south), fe i(idcode)
. xtoverid, cluster(idcode)```

Supplying this gives you the following result:

```      Test of overidentifying restrictions:
Cross-section time-series model: xtivreg fe  robust cluster(idcode)
Sargan-Hansen statistic   0.495  Chi-sq(1)    P-value = 0.4818```

## Testing on model specification (FE or RE)

A test of fixed vs. random effects can also be seen as a test of overidentifying restrictions:

• The fixed effects (FE) estimator uses the orthogonality conditions that the regressors are uncorrelated with the idiosyncratic error eit, i.e., E(Xit*eit)=0.
• The random effects (RE) estimator uses the additional orthogonality conditions that the regressors are uncorrelated with the group-specific error ui (the "random effect"), i.e., E(Xit*ui)=0.

These additional orthogonality conditions are overidentifying restrictions. The test is implemented by xtoverid using the artificial regression approach described by Arellano (1993) and Wooldridge (2002, pp. 290-91), in which a random effects equation is re-estimated by being augmented with additional variables consisting of the original regressors transformed into deviations-from-mean form. Rejection implies that the fixed effect model is more reasonable or preferred. For example:

```    . webuse abdata, clear
. sum
* (Balanced panel)
. xtreg n w k if year>=1978 & year<=1982, re
*(Artificial regression overid test of fixed-vs-random effects)
. xtoverid```

Supplying this will give the following result:

```      Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re
Sargan-Hansen statistic  19.845  Chi-sq(2)    P-value = 0.0000```

Note: Under conditional homoskedasticity, this test statistic is asymptotically equivalent to the usual Hausman fixed-vs-random effects test. Unlike the Hausman test, the xtoverid test extends straightforwardly to heteroskedastic- and cluster-robust versions.

## Testing on the strong assumption in an xthtaylor estimation

For the Hausman-Taylor estimator to be consistent, it is necessary to argue that all regressors are uncorrelated with the idiosyncratic errors, eit, and also that a specified subset of the regressors is uncorrelated with the fixed effect term, ai. This additional strong assumption can be tested by the `xtoverid` command. Rejection implies that some variables of the subset are not exogenous or correlated with the fixed effect term. For example:

```     . webuse psidextract, clear
. xthtaylor lwage wks south smsa ms exp exp2 occ ind union fem blk ed, ///
endog(exp exp2 wks ms union ed) constant(fem blk ed)
. xtoverid```

Supplying this will give the following result:

```      Test of overidentifying restrictions:
Cross-section time-series model: xthtaylor htaylor
Sargan-Hansen statistic   5.229  Chi-sq(3)    P-value = 0.1558```

Note: In order to perform the xtoverid test, the statistic must have `ranktest` (version 01.3.02 or greater) and `xtoverid` ado files installed.

For more on xthtaylor regression, see ARCHIVED: In Stata, how do I estimate the coefficients of time-invariant variables in the Panel FE model, using the xthtaylor command?

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