EXPRESS: Handling Endogenous Regressors using Copulas: A Generalization to Linear Panel Models with Fixed Effects and Correlated Regressors

This paper proposes a panel data generalization for a recently suggested IVfree estimation method that builds on joint estimation. The author shows how the method can be extended to linear panel models by combining fixed-effects transformations with the common GLS transformation to allow for heterogeneous intercepts. To account for between-regressor dependence, the author proposes determining the joint distribution of the error term and all explanatory variables using a Gaussian copula function, with the distinction that some variables are endogenous and the others are exogenous. The identification does not require any instrumental variables if the regressor-error relation is nonlinear. With a normally distributed error, nonnormally distributed endogenous regressors are therefore required. Monte Carlo simulations assess the finite sample performance of the proposed estimator and demonstrate its superiority to conventional instrumental variable estimation. A specific advantage of the proposed method is that the estimator is unbiased in dynamic panel models with small time dimensions and serially correlated errors; therefore, it is a useful alternative to GMM-style instrumentation. The practical applicability of the proposed method is demonstrated via an empirical example.

Revisiting Gaussian copulas to handle endogenous regressors

Marketing researchers are increasingly taking advantage of the instrumental variable (IV)-free Gaussian copula approach. They use this method to identify and correct endogeneity when estimating regression models with non-experimental data. The Gaussian copula approach’s original presentation and performance demonstration via a series of simulation studies focused primarily on regression models without intercept. However, marketing and other disciplines’ researchers mainly use regression models with intercept. This research expands our knowledge of the Gaussian copula approach to regression models with intercept and to multilevel models. The results of our simulation studies reveal a fundamental bias and concerns about statistical power at smaller sample sizes and when the approach’s primary assumptions are not fully met. This key finding opposes the method’s potential advantages and raises concerns about its appropriate use in prior studies. As a remedy, we derive boundary conditions and guidelines that contribute to the Gaussian copula approach’s proper use. Thereby, this research contributes to ensuring the validity of results and conclusions of empirical research applying the Gaussian copula approach.

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

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.

Connectivity and growth: Financial centres in investment banking networks

We investigate the effect of urban network connectivity on the growth of financial centres. While existing research recognises the importance of network connectivity to firms, clusters as well as city regions, large-sample empirical evidence is currently scarce, particularly in the context of financial services. We contribute to this debate by studying underwriting of equity and debt securities, which represent some of the core activities of financial centres. We operationalise our analysis using a proprietary dataset collated from Dealogic Equity Capital Market and Debt Capital Market databases covering over 1.7 million interactions of investment banks with issuers across 540 cities globally during the 1993–2016 period. We estimate our regression equations using the system generalised method of moments estimator, which allows us to obtain consistent coefficient estimates on potentially endogenous regressors, including network connectivity variables. We identify a clear pattern of a positive association between network centrality of financial centres and their growth. We distinguish between intracity and intercity network connectivity and find that financial centres with a larger number of intercity network ties and assortative intracity networks grow faster, while intracity network density does not appear to affect financial centre growth. Our results on intercity network ties are broadly consistent with established knowledge of cluster networks. In contrast, our findings on financial centres' intracity networks contradict previous research that suggests that dense and disassortative intracluster networks aid economic performance of clusters.

Accounting for Endogeneity in Regression Models Using Copulas: A Step-by-Step Guide for Empirical Studies

We provide a detailed presentation and guide for the use of Copulas in order to account for endogeneity in linear regression models without the need for instrumental variables. We start by developing the model from first principles of likelihood inference, and then focus on the Gaussian Copula. We discuss its merits and propose diagnostics to assess its validity. We analyze in detail and provide solutions to the various issues that may arise in empirical applications for applying the method. We treat the cases of both continuous and discrete endogenous regressors. We present simulation evidence for the performance of the proposed model in finite samples, and we illustrate its application by a short empirical study. A Supplementary File contains additional simulations and another empirical illustration.