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

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alecos Papadopoulos
Keyword(s):  
Regression Models ◽  
Empirical Studies ◽  
Gaussian Copula ◽  
Supplementary File ◽  
Linear Regression Models ◽  
Finite Samples ◽  
Endogenous Regressors ◽  
Proposed Model ◽  
Present Simulation ◽  
Detailed Presentation

Abstract 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.

scholarly journals Revisiting Gaussian copulas to handle endogenous regressors

2021 ◽  
Author(s):  
Jan-Michael Becker ◽  
Dorian Proksch ◽  
Christian M. Ringle
Keyword(s):  
Regression Models ◽  
Statistical Power ◽  
Multilevel Models ◽  
Gaussian Copula ◽  
Simulation Studies ◽  
Validity Of Results ◽  
Endogenous Regressors ◽  
Copula Approach ◽  
Original Presentation ◽  
And Performance

AbstractMarketing 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.

scholarly journals The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors

2021 ◽  
Author(s):  
Leo Michelis
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Regression Models ◽  
Population Distribution ◽  
Nuisance Parameter ◽  
Linear Regression Models ◽  
Null Distributions ◽  
Finite Samples ◽  
The Monte Carlo Method ◽  
Asymptotic Expressions

This paper examines the asymptotic null distributions of the <em>J</em> and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The <em>J</em> and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, <em>c</em>, a N(0,1) variate and a <em>χ</em>2(<em>q</em>) variate, where <em>q</em> is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of <em>c</em> into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.

scholarly journals SHRINKAGE ESTIMATION OF REGRESSION MODELS WITH MULTIPLE STRUCTURAL CHANGES

2015 ◽  
Vol 32 (6) ◽  
pp. 1376-1433 ◽  
Author(s):  
Junhui Qian ◽  
Liangjun Su
Keyword(s):  
Regression Models ◽  
Structural Changes ◽  
Equity Premium ◽  
Asymptotic Distributions ◽  
Regression Coefficients ◽  
Tuning Parameter ◽  
Linear Regression Models ◽  
Predictive Regression ◽  
Finite Samples ◽  
Fundamental Information

In this paper, we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso. We show that with probability tending to one, our method can correctly determine the unknown number of breaks, and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break ratios and regression coefficients. We also propose and validate a data-driven method to determine the tuning parameter. Monte Carlo simulations demonstrate that the proposed method works well in finite samples. We illustrate the use of our method with a predictive regression of the equity premium on fundamental information.

scholarly journals The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors

2021 ◽  
Author(s):  
Leo Michelis
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Regression Models ◽  
Population Distribution ◽  
Nuisance Parameter ◽  
Linear Regression Models ◽  
Null Distributions ◽  
Finite Samples ◽  
The Monte Carlo Method ◽  
Asymptotic Expressions

This paper examines the asymptotic null distributions of the <em>J</em> and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The <em>J</em> and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, <em>c</em>, a N(0,1) variate and a <em>χ</em>2(<em>q</em>) variate, where <em>q</em> is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of <em>c</em> into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.

FAKTOR DETERMINAN PENYALURAN KREDIT BANK PERSERO

2018 ◽  
Vol 23 (1) ◽  
pp. 60-71
Author(s):  
Wigiyanti Masodah
Keyword(s):  
Interest Rate ◽  
Linear Regression ◽  
Interest Rates ◽  
Regression Models ◽  
Linear Regression Models ◽  
Negative Impacts ◽  
Main Activity ◽  
The Impact ◽  
The Given ◽  
Multiple Linear Regression Models

Offering credit is the main activity of a Bank. There are some considerations when a bank offers credit, that includes Interest Rates, Inflation, and NPL. This study aims to find out the impact of Variable Interest Rates, Inflation variables and NPL variables on credit disbursed. The object in this study is state-owned banks. The method of analysis in this study uses multiple linear regression models. The results of the study have shown that Interest Rates and NPL gave some negative impacts on the given credit. Meanwhile, Inflation variable does not have a significant effect on credit given. Keywords: Interest Rate, Inflation, NPL, offered Credit.

Linear Regression Models for Interval-Valued Data using Log-transformation

2020 ◽  
Author(s):  
Nykolas Mayko Maia Barbosa ◽  
João Paulo Pordeus Gomes ◽  
César Lincoln Cavalcante Mattos ◽  
Diêgo Farias Oliveira
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Log Transformation ◽  
Interval Valued

THE PREDICTIVE CONTENT OF DISAGGREGATED NORMAL INCOME: An Empirical Study in the JSX

2003 ◽  
Vol 5 (3) ◽  
pp. 363 ◽  
Author(s):  
Slamet Sugiri
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Stock Exchange ◽  
Manufacturing Firms ◽  
Single Step ◽  
Model Parameters ◽  
Linear Regression Models ◽  
Operating Income ◽  
Predictive Content ◽  
Multiple Step

The main objective of this study is to examine a hypothesis that the predictive content of normal income disaggregated into operating income and nonoperating income outperforms that of aggregated normal income in predicting future cash flow. To test the hypothesis, linear regression models are developed. The model parameters are estimated based on fifty-five manufacturing firms listed in the Jakarta Stock Exchange (JSX) up to the end of 1997.This study finds that empirical evidence supports the hypothesis. This evidence supports arguments that, in reporting income from continuing operations, multiple-step approach is preferred to single-step one.

scholarly journals Relationships between test positivity rate, total laboratory confirmed cases of malaria, and malaria incidence in high burden settings of Uganda: an ecological analysis

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Jaffer Okiring ◽  
Adrienne Epstein ◽  
Jane F. Namuganga ◽  
Victor Kamya ◽  
Asadu Sserwanga ◽  
...  
Keyword(s):  
Regression Models ◽  
Malaria Incidence ◽  
Temporal Changes ◽  
Linear Regression Models ◽  
High Burden ◽  
Exponential Regression ◽  
Malaria Morbidity ◽  
Laboratory Test Results ◽  
Combining Data ◽  
Catchment Areas

Abstract Background Malaria surveillance is critical for monitoring changes in malaria morbidity over time. National Malaria Control Programmes often rely on surrogate measures of malaria incidence, including the test positivity rate (TPR) and total laboratory confirmed cases of malaria (TCM), to monitor trends in malaria morbidity. However, there are limited data on the accuracy of TPR and TCM for predicting temporal changes in malaria incidence, especially in high burden settings. Methods This study leveraged data from 5 malaria reference centres (MRCs) located in high burden settings over a 15-month period from November 2018 through January 2020 as part of an enhanced health facility-based surveillance system established in Uganda. Individual level data were collected from all outpatients including demographics, laboratory test results, and village of residence. Estimates of malaria incidence were derived from catchment areas around the MRCs. Temporal relationships between monthly aggregate measures of TPR and TCM relative to estimates of malaria incidence were examined using linear and exponential regression models. Results A total of 149,739 outpatient visits to the 5 MRCs were recorded. Overall, malaria was suspected in 73.4% of visits, 99.1% of patients with suspected malaria received a diagnostic test, and 69.7% of those tested for malaria were positive. Temporal correlations between monthly measures of TPR and malaria incidence using linear and exponential regression models were relatively poor, with small changes in TPR frequently associated with large changes in malaria incidence. Linear regression models of temporal changes in TCM provided the most parsimonious and accurate predictor of changes in malaria incidence, with adjusted R2 values ranging from 0.81 to 0.98 across the 5 MRCs. However, the slope of the regression lines indicating the change in malaria incidence per unit change in TCM varied from 0.57 to 2.13 across the 5 MRCs, and when combining data across all 5 sites, the R2 value reduced to 0.38. Conclusions In high malaria burden areas of Uganda, site-specific temporal changes in TCM had a strong linear relationship with malaria incidence and were a more useful metric than TPR. However, caution should be taken when comparing changes in TCM across sites.

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