I just released a brand-new Stata package called kinkyreg, which I developed jointly with Jan Kiviet and which I will present tomorrow at the virtual UK Stata Conference. This command implements the instrument-free inference approach named "kinky least squares" (KLS) estimation which was proposed by Jan Kiviet in a sequence of recent papers. The KLS estimator analytically corrects the bias of the inconsistent OLS estimator when one or more of the regressors are endogenous. It does so by making an assumption about the admissible degree of endogeneity. By constraining the endogeneity correlations within reasonably narrow bounds, set identification of the coefficients is achieved. By considering the union of confidence intervals over a grid of endogeneity correlations, asymptotically conservative inference can be performed.

The main output of the kinkyreg package is graphical. The main graphs display the coefficient estimates over a grid of postulated endogeneity correlations including their confidence bands, possibly in comparison to the conventional 2SLS estimates if the user specifies instrumental variables. Often, and especially in the presence of weak (or invalid) instruments, KLS confidence intervals can be more informative than 2SLS intervals.

A main benefit of the KLS approach is that it enables testing of the exclusion restrictions for excluded (instrumental) variables, which is not possible with the 2SLS approach. (Note that 2SLS-based overidentifying restrictions tests still maintain the untested assumption that a subset of instruments is validly excluded.) This is implemented as a kinkyreg postestimation feature (estat exclusion).

Further postestimation features include tests for linear hypotheses (estat test), Ramsey's RESET test (estat reset), heteroskedasticity tests (estat hettest) and Durbin's alternative test for serial correlation (estat durbinalt).

The package is available for installation from my personal website. Type the following in Stata's command window:

The basic command syntax is similar to ivregress, although the specification of instrumental variables is optional. (The latter are only used to compare the KLS to the 2SLS estimates.) For example,

The range() option specifies the admissible range of correlations of the endogenous regressor iq with the error term. The inference() option produces graphical output with KLS estimates over the specified range and corresponding confidence intervals for the specified regressors iq and s as a function of the endogeneity correlation. The results are compared to the 2SLS estimates with instruments age and mrt. (To see the graphs, just run the above example in Stata.) Exclusion restriction tests for the two instruments can then simply be obtained in a postestimation step:

Again, the output will be primarily graphical.

The help files explain the details of the command syntax and the available options:

Examples are included in the help file. Detailed background information and a more extensive example can also be found in an accompanying manuscript (see references below). Comments are welcome.

References:

The main output of the kinkyreg package is graphical. The main graphs display the coefficient estimates over a grid of postulated endogeneity correlations including their confidence bands, possibly in comparison to the conventional 2SLS estimates if the user specifies instrumental variables. Often, and especially in the presence of weak (or invalid) instruments, KLS confidence intervals can be more informative than 2SLS intervals.

A main benefit of the KLS approach is that it enables testing of the exclusion restrictions for excluded (instrumental) variables, which is not possible with the 2SLS approach. (Note that 2SLS-based overidentifying restrictions tests still maintain the untested assumption that a subset of instruments is validly excluded.) This is implemented as a kinkyreg postestimation feature (estat exclusion).

Further postestimation features include tests for linear hypotheses (estat test), Ramsey's RESET test (estat reset), heteroskedasticity tests (estat hettest) and Durbin's alternative test for serial correlation (estat durbinalt).

The package is available for installation from my personal website. Type the following in Stata's command window:

Code:

net install kinkyreg, from(http://www.kripfganz.de/stata/)

Code:

. use http://www.stata-press.com/data/imeus/griliches . kinkyreg lw s expr tenure rns smsa _I* (iq = age mrt), range(-0.7 0.7) inference(iq s)

Code:

. estat exclusion

The help files explain the details of the command syntax and the available options:

Code:

help kinkyreg help kinkyreg postestimation

References:

- Kiviet, J. F. (2020a). Testing the impossible: Identifying exclusion restrictions.
*Journal of Econometrics*, forthcoming. - Kiviet, J. F. (2020b). Instrument-free inference under confined regressor endogeneity; derivations and applications. Stellenbosch Economic Working Papers WP09/2020, Department of Economics, Stellenbosch University.
- Kripfganz, S., and J. F. Kiviet (2020). kinkyreg: Instrument-free inference for linear regression models with endogenous regressors. Manuscript.

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