kinkyreg: Instrument-free inference for linear regression models with endogenous regressors

Abstract

In models with endogenous regressors, a standard regression approach is to exploit just-identifying or overidentifying orthogonality conditions by using instrumental variables. In just-identified models, the identifying orthogonality assumptions cannot be tested without the imposition of other nontestable assumptions. While formal testing of overidentifying restrictions is possible, its interpretation still hinges on the validity of an initial set of untestable just-identifying orthogonality conditions. We present the kinkyreg command for kinky least-squares inference, which adopts an alternative approach to identification. By exploiting nonorthogonality conditions in the form of bounds on the admissible degree of endogeneity, feasible test procedures can be constructed that do not require instrumental variables. The kinky least-squares confidence bands can be more informative than confidence intervals obtained from instrumental-variables estimation, especially when the instruments are weak. Moreover, the approach facilitates a sensitivity analysis for standard instrumental-variables inference. In particular, it allows the user to assess the validity of previously untestable just-identifying exclusion restrictions. Further instrument-free tests include linear hypotheses, functional form, heteroskedasticity, and serial correlation tests.

Distributional Effects of Freedom and Income on Life Satisfaction: Evidence from East Asian Chinese Societies

“…Second, due to data limitations, the endogeneity issue is not explored in the empirical model of the present paper. Extending the analysis of Kiviet (2020) and Kripfganz and Kiviet (2021) to the ordinal regression setup is outside the scope of the present paper. It is suggested that future studies take these issues into account.…”

“…In other words, the bias of endogeneity due to positive correlation between regression errors and endogenous variables might not be prevalent. That being said, our arguments here are based on the presumption that the linear regression framework of Kiviet (2020) and Kripfganz and Kiviet (2021) is a good approximation to the ordinal regression context of the present paper. Therefore, the evidence discussed here is meant to be supportive but not confirmative.…”

“…There is a potential endogeneity issue between income and happiness. We address the endogeneity using the instrument-free inferences of Kripfganz and Kiviet (2021) and Kiviet (2020). The results suggest that the bias of endogeneity should not be prevalent, and at least, it would not change the signs of estimated coefficients of income and freedom (see Appendix 5).…”

A comparative study of the policy response to COVID-19 in the ASEAN region: A dynamic simulated ARDL approach

“…The ARDL bounds test approach proposed by [ 36 ] for a level relationship is examined using [ 37 ] tabulated values and p-values based on the response of the surface regression. The decision rule here is that, if the F-statistic of the joint zero estimation is greater than the upper bound critical values I(1) of all coefficients of the lagged independent variables at level and the coefficient of lagged dependent variable coefficient, then the null hypothesis of no level correlation (H 0 : ø 0 =ø 1 = ø 2 = ø 3 =0) will be rejected.…”

The reciprocal relationship between mathematics self-efficacy and mathematics performance in US high school students: Instrumental variables estimates and gender differences

“…From IV estimation of the Model 1, I assessed the relevance and exclusion restrictions associated with the excluded instruments using tests based on Sargan’s J-statistic. In addition, I used the recently developed kinky least-squares (KLS) approach by Jan Kiviet, 4 which yields statistical inference on the validity of exclusion restrictions regarding candidate external instrument/s (single, or as a set) when a plausible range of endogeneity correlations is available, whereas these unavoidable restrictions were always supposed to be non-testable ( Kiviet, 2020 ; Kripfganz and Kiviet, 2021 ).…”