Comparing features of convenient estimators for binary choice models with endogenous regressors

Abstract We discuss the relative advantages and disadvantages of four types of convenient estimators of binary choice models when regressors may be endogenous or mismeasured or when errors are likely to be heteroscedastic. For example, such models arise when treatment is not randomly assigned and outcomes are binary. The estimators we compare are the two‐stage least squares linear probability model, maximum likelihood estimation, control function estimators, and special regressor methods. We specifically focus on models and associated estimators that are easy to implement. Also, for calculating choice probabilities and regressor marginal effects, we propose the average index function (AIF), which, unlike the average structural function (ASF), is always easy to estimate.     

Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments

We observe a dependent variable and some regressors, including a mismeasured binary regressor. We provide identification of the nonparametric regression model containing this misclassified dichotomous regressor. We obtain identification without parameterizations or instruments, by assuming the model error isn't skewed.     

Unit Root Tests for Dependent Micropanels

This paper proposes a new test for the null hypothesis of panel unit roots for micropanels with short time dimensions (T) and large cross‐sections (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model allowing for cross‐sectional dependency, which is introduced by a factor structure of the initial condition. Second, the test employs the panel AR(1) model with AR(1) coefficients that are heterogeneous for finite N. Third, the test can be used both for the alternative hypothesis of stationarity and for that of explosive roots. Fourth, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, the present paper employs cross‐sectional regressions using the first time‐series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t‐ratios for the coefficient are this paper's test statistics and have a standard normal distribution in the limit. The t‐ratios are based on the OLS estimator and the instrumental variables estimator that uses reshuffled regressors as instruments. The test proposed in this paper makes it possible to test for a unit root even at T = 2 as long as N is large. Simulation results show that test statistics have reasonable empirical size and power. The test is applied to college graduates' monthly real wage in South Korea. The number of time‐series observations for this data is only two. The null hypothesis of a unit root is rejected against the alternative of stationarity.     

Exclusion Bias in Sample-Selection Model Estimators

Exclusion restrictions are routinely used in sample-selection models with "selection" and "outcome" equations. A false restriction, however, can cause an "exclusion bias" for the outcome equation estimator. In this paper, the specific form of the exclusion bias is derived for various sample-selection model estimators. Furthermore, it is shown that the outcome equation parameters for regressors with zero coefficients in the selection equation are immune to exclusion bias if only one regressor is excluded. Exclusion bias, or a lack thereof, is verified through a simulation study with the regressors taken from Mroz (1987).
JEL Classification Numbers: C24, C34     

Endogeneity bias and growth regressions

The problem of regressor endogeneity stemming from reverse casuality is one that has plagued economists working in the field of empirical economic growth for some time. This paper attempts to address the relevant magnitude of this issue in the context of growth regressions based on the Solow growth model. The paper develops a method of running Monte Carlo simulations that allows us to generate simulated data that match the moments of observed real-world data typically used in such regressions while simultaneously allowing us to impose arbitrarily high correlations between the steady-state determinants of the Solow model and the unobserved residual term of the data-generating process. After running simulations that represent a wide sample of the mathematically-possible correlations, we conclude that a between estimator or a random effects estimator will deliever a lower average absolute bias across all coefficients than alternative estimators in almost all of our simulations. Conversely, estimators that use within-country variation will generate lower biases when looking solely at rates of convergence. Furthermore, we conclude that these results are robust when restricting our sample of simulations to several subsets of the assumed parameters and to changing our assumptions about country fixed-effects terms.     

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.     

A Monte Carlo study of growth regressions

Using Monte Carlo simulations, this paper evaluates the bias properties of estimators commonly used to estimate growth regressions derived from the Solow model. We explicitly allow for measurement error, country-specific fixed effects and regressor endogeneity. An OLS estimator applied to a single cross-section of variables averaged over time (the between estimator) performs best in terms of the extent of bias on each of the estimated coefficients. Fixed-effects and the Arellano–Bond GMM estimator overstate the speed of convergence under a wide variety of assumptions, while the between estimator understates it. Finally, fixed effects and Arellano–Bond bias towards zero the slope estimates on the human and physical capital accumulation variables, while the between estimator and the Blundell–Bond system GMM estimator bias these coefficients upwards.      

Enhancing the local power of IVX-based tests in predictive regressions

IVX estimation is used increasingly often in predictive regressions with regressors of unknown persistence. While not exhibiting the second-order bias the OLS estimator has in this setup, IVX estimators have reduced rates of convergence when the regressors are highly persistent. The reduced convergence rates may sometimes lead to power losses in finite samples when testing for no predictability, for instance. The note discusses a simple way of improving the local power of IVX-based tests, consisting of augmenting the predictive regression with the lagged dependent variable. This implies a feed-back loop which strengthens the signal of the IVX instrument without changing its dynamic properties. The proposed augmentation works best when the power loss of IVX would have been maximal compared to the infeasible OLS-based test.     

Patterns and determinants of intergenerational educational mobility: Evidence across countries

This study analyses the patterns and determinants of the intergenerational persistence of education attainment. Internationally comparable data are used by age cohort for parentsʼ and childrenʼs education levels for 30 countries. The intergenerational regression coefficients are estimated by explicitly considering the bias from the censored regressor, and they show that educational mobility has worsened over generations in most countries. However, the degree of change varies considerably across countries and over time. Country-cohort panel regressions are performed using the estimates of intergenerational educational mobility and covariates. The results show that intergenerational educational mobility tends to decrease with income inequality, inflation and credit constraints. However, it increases with per capita GDP and public expenditure on primary education relative to that on tertiary education.     

The sensitivity of the RESET tests to disturbance autocorrelation in regression analysis

This paper investigates the sensitivity of the RESET tests, proposed by Ramsey (1969) and modified by Thursby and Schmidt (1977), to disturbance autocorrelation in regression analysis. Porter and Kashyap (1984) show that RESET is not robust to autocorrelated disturbance when there is a highly autocorrelated regressor in the model. We show that RESET is sensitive to disturbance autocorrelation even when the regressors are not autocorrelated. We explain the findings of Thursby (1979) and Porter and Kashyap (1984) as well as our result by showing that a spurious correlation between the regressor and the disturbance is responsible for the serious size distortion of the RESET tests. First version received: June 1999/Final version received: November 2000     

On the equivalence of indirect inference and bootstrap bias correction for linear IV estimators

This note shows that two ways of simulation based bias correction–indirect inference and bootstrap bias correction–are equivalent for two-stage-least-squares, as well as k$k$-class estimators for the standard linear model with endogenous regressors.     

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 remark on a generalized specification test

In testing orthogonality of a set of regressors when there exist other regressors known to be endogenous or exogenous, the appropriate test should be based on the difference between two estimators of the coefficients of regressors whose orthogonality is being tested.     

Use of quadratic terms in Type 2 Tobit models

A Type 2 Tobit model with a common set of regressors in the selection and regression equations is identified by the nonlinearity of the distribution function. The estimates are relatively less precise than in cases where there are at least some distinct regressors in the two equations. In an attempt to overcome this problem, some authors introduce quadratic terms into one or both equations. As this does not add any new statistical information, just a deterministic function of an existing regressor, the sceptic would question how this could improve the reliability of the estimates. This article shows that arbitrary use of quadratics is not without consequence. It increases the chances of getting either multiple roots, no root or a local root where a global does not exist. The nature of this problem is illustrated with Monte Carlo methods as well as several examples from the literature.     

PERFORMANCE OF VARIOUS ESTIMATORS FOR CENSORED RESPONSE MODELS WITH ENDOGENOUS REGRESSORS

The paper reviews four approaches (substitution (SUB), control function (CF), system reduced form (SRF) and artificial instrumental regressor (AIR)) dealing with endogenous regressors in censored response models, and compares them through a simulation. Based on mean‐squared‐error type criteria, CF and AIR perform better than SUB and SRF; in terms of computation, however, SUB and CF are the easiest, closely followed by SRF. Although CF does well in both accounts, its assumptions are restrictive, and CF provides very different results from the other estimators when a real data set is used. Therefore, although the choice of an estimator among the four should be case‐specific, for practitioners, we would recommend SUB.     

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.     

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.     

Growth with endogenous migration hump and the multiple,dynamically interacting effects of aid in poor developing countries

We show empirically that aid given to poor developing countries enhances growth and reduces emigration, once several dynamically interacting effects of aid are taken into account in a system of equations. We estimate equations for net immigration flows as a share of the labour force and Gross Domestic Product Per Capita (GDPPC) growth and also for all their regressors including remittances and official development aid. We use dynamic panel data methods for a sample of poor countries with GDPPC below $1200 (2000), for which aid is about 9.5% of GDP. The partial effects in these regressions are working against each other. Therefore, we integrate all equations into a dynamic system and run a simulation. One result is an endogenous migration hump with several peaks. In a counterfactual simulation, we double aid with the consequence that for more than a 100 years migration is reduced and the GDPPC is enhanced, because the positive effects of aid on investment and education dominate the negative direct effects of aid on growth and the unfavourable effects on savings, tax revenues and labour force growth.     

The elusive effects of trade on growth: Export diversity and economic take‐off

The hallmark of the voluminous growth determinants literature is the absence of a clear‐cut effect of trade on growth. Numerous candidate regressors have been motivated by alternative theories and tested by a multitude of empirical studies, but not one trade regressor has been robustly related to growth. In this paper, we leverage Melitz's (2003) insights regarding sectoral export dynamics and Feenstra and Kee's (2008) approach to productivity and sectoral export diversity to propose a structured approach to trade and growth determinants. Instead of relying on aggregate trade measures as previous studies have done, we examine the diversity of sectoral exports and the development of broad‐based comparative advantage as a potential growth determinant. Controlling for model uncertainty and endogeneity, we find that export diversity serves as a crucial growth determinant for low‐income countries, an effect that weakens with the level of development.     

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.