Bootstrap and Pretest J-Type Non-Nested Tests for Orthogonal Regression Models: Some Monte Carlo Evidence

This paper compares the size and power of two J-type tests for weakly correlated or nearly orthogonal non-nested regression models: a bootstrap and a pretest test. The latter seems to outperform the former in terms of its size characteristics, especially when the alternative model has more non-nested regressors and the orthogonality between the two sets of regressors is severe. The bootstrap test does better in terms of power.

     

Testing for individual and time effects in the two-way error component model with time-invariant regressors

In this paper, we focus on testing for individual and time effects in the two-way error component model with time-invariant regressors. We present the so-called FEF estimators when time-invariant regressors are exogenous and the FEF-IV estimators when one or more of time-invariant variables are endogenous, and obtain their asymptotic properties under some mild conditions. In the light of the moment-based test methods of Wu and Li (2014), we construct several tests for the existence of individual and time effects in the two-way error component model with time-invariant regressors. The resulting tests can be shown to have some desired properties as follows: they do not need any distributional assumptions on the error components; they do not require any assumptions on the correlation among the two random effects and the time-varying regressors; they are robust to the presence of one effect when the other one is tested. Simulation study and real data analysis are carried out for illustration of the above.     

On the diffusion of inconsistencies in linear regression

We present a general result relating inconsistencies in estimating coefficients of correctly measured regressors to inconsistencies in estimating coefficients of incorrectly measured regressors. The result is reinterpreted to apply in simultaneous equation models.     

我国保险业区域发展失衡的实证研究:基于保险密度的视角

本文建立了识别我国省际保险业发展影响因素的多元线性模型和识别我国省际保险业发展失衡成因的多元离差模型并运用格兰杰因果检验和逐步回归法为模型选择了最优的解释变量。除相关关系外,保证变量间还存在因果关系,并降低了解释变量间的共线性。实证结果表明,经济发展是推动我国省际保险业发展的根本动力,省际保险业发展失衡的主要原因是经济发展水平的差异,而不是社会文化环境和法律环境的差异。     

Signs of impact effects in time series regression models

In this paper we consider the problem of interpreting the signs of the estimated coefficients in multivariate time series regressions where the regressors are correlated. Using a continuous time model, we argue that focusing on the signs of individual coefficients in such regressions could be misleading and argue in favour of allowing for the indirect effects that arise due to the historical correlations amongst the regressors. For estimation from discrete time data we show that the sign of the total impact, including the direct and indirect effects, of a regressor can be obtained using a simple regression that only includes the regressor of interest.     

Measurement error in imputation procedures

We study how estimators that are used to impute consumption in survey data are inconsistent due to measurement error in consumption. Previous research suggests instrumenting consumption to overcome this problem. We show that, if additional regressors are present, then instrumenting consumption may still produce inconsistent estimators due to the likely correlation between additional regressors and measurement error. On the other hand, low correlations between additional regressors and instruments may reduce bias due to measurement error. We apply our findings by revisiting recent research that imputes consumption data from the CEX to the PSID.     

Estimating the variance of decomposition effects

We derive the asymptotic variance of the Blinder–Oaxaca decomposition effects. We show that the delta method approach that builds on the assumption of fixed regressors understates true variability of the decomposition effects when regressors are stochastic. Our proposed variance estimator takes randomness of regressors into consideration. Our approach is applicable to both the linear and nonlinear decompositions. Previously, only a bootstrap method has been a valid option for nonlinear decompositions. As our derivation follows the general framework of m-estimation, it is straightforward to extend our variance estimator to a cluster-robust variance estimator. We demonstrate the finite-sample performance of our variance estimator with a Monte Carlo study and present a real-data application.     

Testing the null of a low dimensional growth model

Applied growth researchers face a sample with more regressors than observations when using cross-country data. In this paper, we examine simple procedures for testing if a true submodel has been found. Specifically, we examine three tests that can be used to test a low dimensional growth model against a high dimensional alternative, when there are more regressors than observations. We examine the finite sample properties of the tests using Monte Carlo simulations. We apply the tests to a specific growth dataset that has more variables than observations and find evidence against the null that no variables are important. Finally, we apply Bayesian Averaging of Classical Estimates and reach a similar conclusion.     

Avoiding arbitrary exclusion restrictions using ratios of reduced-form estimates

We show how to obtain coherent structural-form (SF) exclusion restrictions using the reduced-form (RF) parameter ratios. It will be shown that an over-identified SF corresponds to a group of regressors sharing the same RF ratio value; those regressors should be excluded jointly from the SF. If there is no group structure, then the SF is just-identified; in this case, however, it is no longer clear which regressor should be excluded. Hence, just-identified SF’s are more arbitrary than over-identified SF’s in terms of exclusion restrictions. This is in stark contrast to the notion that the former is less arbitrary than the latter, because the former excludes fewer regressors. We formalize these points, and then suggest to find the number of modes in the estimated RF ratios as a way to find groups in the ratios. For this purpose, an informal graphical method using a kernel nonparametric method and a formal modality test are employed. An empirical example with selling price in a residential real estate market and duration on the market as two endogenous variables is provided. The authors are grateful to the editor and two anonymous referees for their comments     

A test of the independence of subsets of instrumental variables and regressors

A Wald statistic is presented to test for the independence of subsets of regressors and instrumental variables and the disturbance in a regression equation. The test does not require that the equation be identified under maintained conditions.     

Instrumental variables regressions involving seasonal data

Various approaches to handling seasonal data are known to be equivalent in the context of least squares estimation of a fixed-regressor linear model. This note extends these results to models which have stochastic regressors and are estimated by the method of Instrumental Variables.     

Potential ECB reaction functions with time-varying parameters: an assessment

This paper analyses the behaviour of the European Central Bank over the period 1999–2014 through the estimation of monetary policy reaction functions with time-varying coefficients and heteroskedastic error terms. This allows to evaluate whether relevant shifts in the conduct of monetary policy occurred and whether the current financial crisis had an influence on that. The paper considers two different specifications, one with contemporaneous regressors and one with regressors from surveys. The Taylor rule is then enriched with a set of macroeconomic and financial variables with the aim of testing their significance. Results show that forward-looking variables have a better explanatory power over interest rate policy. All the coefficients are found to be stable along the sample so that no shift in the reaction function can be identified and the financial crisis is found to only lead to a change in the size of the shock. Finally, we also provide evidence about the fact that the ECB has been actually constrained by the zero lower bound during the recent crisis.     

Asymptotic inference in regression models with autoregressive errors having roots on the unit circle

An inference procedure is proposed for regression models with stationary regressors and non-stationary autoregressive errors. It is shown that the usual GLS or Cochrane–Orcutt procedure should be done in reverse order by starting the estimation from the error structure.     

Instrumental variable estimation of a nonlinear Taylor rule

This article studies nonlinear, threshold, models in which some of the regressors can be endogenous. An estimation strategy based on instrumental variables was originally developed for dynamic panel models and we extend it to time series models. We apply this methodology to a forward-looking Taylor rule, where nonlinearity is introduced via inflation thresholds.     

Endogeneity in Semiparametric Binary Response Models

This paper develops and implements semiparametric methods for estimating binary response (binary choice) models with continuous endogenous regressors. It extends existing results on semiparametric estimation in single-index binary response models to the case of endogenous regressors. It develops a control function approach to account for endogeneity in triangular and fully simultaneous binary response models. The proposed estimation method is applied to estimate the income effect in a labour market participation problem using a large micro data-set from the British Family Expenditure Survey. The semiparametric estimator is found to perform well, detecting a significant attenuation bias. The proposed estimator is contrasted to the corresponding probit and linear probability specifications.     

Estimation and testing of nonproportional Weibull hazard models

Most applications of the Weibull hazard model specify a common shape parameter. This is a proportional hazard model that imposes a common rate of duration dependence. A wide class of nonproportional Weibull models may be estimated by making the shape parameter a linear function of observable regressors. The log-likelihood function for these models is well behaved. The conditions under which this generalization is useful are essentially the same conditions under which interaction terms are useful in classical regression. Since the nonproportional model nests the proportional model, a formal test for nonproportionality may be conducted by likelihood ratio test. Estimation and testing of nonproportional models is illustrated with data sets for housing sales, out-of-court settlements and oil field exploration. Finally, estimation of a proportional Weibull model after adding temporal interaction terms to the regressors that specify the scale parameter is shown to be a fundamental misspecification. The standard log-likelihood function fails to recognize the stochastic nature of temporal interaction terms and the resulting estimates often fall outside the parameter space of the Weibull.     

Small sample properties of the two-step and three-step estimators in a heteroscedastic linear regression model and the Bayesian alternative

In this paper, we consider the heteroscedastic linear regression model in which the variance of the disturbance term is assumed to be proportional to one of the regressors raised to an unknown power. We first derive the Bayesian estimator, and compare the mean squared errors of the two-step, three-step and Bayesian estimates by Monte Carlo experiments.     

Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated

We show that previous results on the asymptotic efficiency of OLS vs. GLS in the context of trending data carry over to regressors of the fractionally integrated type.     

Gini-PLS Regressions

Journal of Quantitative Economics - Data contamination and excessive correlations between regressors (multicollinearity) constitute a standard and major problem in econometrics. Two techniques...