GS2SLS / SARAR Panels

Instrumental-variables estimation of SARAR panels with endogenous regressors.

SpatialEconometrics.SpatialGS2SLSPanel.GS2SLSModel — Type

GS2SLSModel

A fitted GS2SLS / SARAR panel, returned by fit_gs2sls_panel. Implements the StatsAPI.RegressionModel interface.

Carries coef and vcov, both spatial parameters rho and lambda, sigma2, the Sargan over-identification statistic with its p-value, the weight matrix, residuals, coefnames and the panel dimensions.

Estimated by instrumental variables rather than maximum likelihood, which is what lets it handle endogenous regressors alongside spatial dependence and avoids assuming normal errors.

Note

Check sargan_pval before reading anything else. A small value says the instruments are rejected, and then the coefficients are not credible whatever their standard errors look like.

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SpatialEconometrics.SpatialGS2SLSPanel.fit_gs2sls_panel — Function

fit_gs2sls_panel(fe_spec, W, X_exog, X_endog, Z_iv, y, N, T_total;
                 varnames, exog_names, endog_names)

Fit a SARAR panel with endogenous regressors by generalized spatial two-stage least squares.

Handles two problems at once: spatial dependence in both y and the errors (as in SARAR), and regressors correlated with the error for non-spatial reasons. Because it is an IV method it needs no distributional assumption, unlike the likelihood-based panel estimators.

Arguments

fe_spec: a FixedEffectsSpec.
W: N x N cross-sectional weight matrix.
X_exog: exogenous covariates.
X_endog: endogenous regressors.
Z_iv: excluded instruments — at least as many columns as X_endog, or the model is not identified.
y: stacked response.
N, T_total: units and periods; one period is consumed, so estimation uses T_total - 1.

Keywords

varnames, exog_names, endog_names: names for the output table.

Returns

A GS2SLSModel.

Warning

Same stacking convention as the other panel estimators: units vary fastest within each period. And read sargan_pval first — rejected instruments invalidate the estimates.

Examples

m = fit_gs2sls_panel(TwoWayFE(), W, X_exog, X_endog, Z_iv, y, N, T_total)
m.sargan_pval
m.rho, m.lambda

A formula interface is available, which derives N, T_total and the stacking order from the table:

fit_gs2sls_panel(
    @formula(y ~ x1 + endo(x2, z1 + z2) + fe(region) + fe(year)),
    table, W; panel = :region, time = :year)

See also endo, extract_panel_permutation.

References

Kelejian, H. & Prucha, I. (1998). Journal of Real Estate Finance and Economics, 17(1).

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