The Heckman Correction for Sample Selection and Its Critique

This paper gives a short overview of Monte Carlo studies on the usefulness of Heckman's (1976, 1979) two-step estimator for estimating selection models. Such models occur frequently in empirical work, especially in microeconometrics when estimating wage equations or consumer expenditures.
It is shown that exploratory work to check for collinearity problems is strongly recommended before deciding on which estimator to apply. In the absence of collinearity problems, the full-information maximum likelihood estimator is preferable to the limited-information two-step method of Heckman, although the latter also gives reasonable results. If, however, collinearity problems prevail, subsample OLS (or the Two-Part Model) is the most robust amongst the simple-to-calculate estimators.     

Conditional regression analysis

This article deals with the question of whether the inclusion of multiplicative terms to model conditional effects in multiple regression is legitimate. The major arguments in the controversy relating to this subject are reviewed. The main conclusion is that most of the objections against multiplicative terms are based on misinterpretations of the coefficients of conditional models. For the often-ignored possible numerical problems in the estimation of these models, due to multicollinearity, an indirect estimation technique is proposed. The potentials of conditional regression analysis are demonstrated on a concrete example.     

Estimation of Dynamic Nonlinear Random Effects Models with Unbalanced Panels

This paper presents estimation methods for dynamic nonlinear models with correlated random effects (CRE) when having unbalanced panels. Unbalancedness is often encountered in applied work and ignoring it in dynamic nonlinear models produces inconsistent estimates even if the unbalancedness process is completely at random. We show that selecting a balanced panel from the sample can produce efficiency losses or even inconsistent estimates of the average marginal effects. We allow the process that determines the unbalancedness structure of the data to be correlated with the permanent unobserved heterogeneity. We discuss how to address the estimation by maximizing the likelihood function for the whole sample and also propose a Minimum Distance approach, which is computationally simpler and asymptotically equivalent to the Maximum Likelihood estimation. Our Monte Carlo experiments and empirical illustration show that the issue is relevant. Our proposed solutions perform better both in terms of bias and RMSE than the approaches that ignore the unbalancedness or that balance the sample.     

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

Foreign capital inflows,domestic savings and the price of political stability in the sudan: Weisskopf revisited

This paper reworks Weisskopf's estimates of the effect of foreign capital inflow on domestic savings for a later time period. The Sudan is presented as an example of a public sector dominated economy, dependent on one major export crop and politically unstable. While Weisskopf's savings function had an indication of a negative relationship between public sector savings and official foreign capital inflow, problems of collinearity between the independent variables cast doubt on its utility for analysis of economies dependent on limited primary exports. The negative relationship between public sector savings and official is explained in terms of the expansion of the state's bureaucracy and military.     

Variance Decomposition Analysis for Nonlinear Economic Models1

In this paper, we propose a new method called the total variance method and algorithms to compute and analyse variance decomposition for nonlinear economic models. We provide theoretical and empirical examples to compare our method with the only existing method called generalized forecast error variance decomposition (GFEVD). We find that the results from the two methods are different when shocks are multiplicative or interacted in nonlinear models. We recommend that when working with nonlinear models researchers should use the total variance method in order to see the importance of indirect variance contributions and to quantify correctly the relative variance contribution of each structural shock.     

Variance Decomposition Analysis for Nonlinear Economic Models1

In this paper, we propose a new method called the total variance method and algorithms to compute and analyse variance decomposition for nonlinear economic models. We provide theoretical and empirical examples to compare our method with the only existing method called generalized forecast error variance decomposition (GFEVD). We find that the results from the two methods are different when shocks are multiplicative or interacted in nonlinear models. We recommend that when working with nonlinear models researchers should use the total variance method in order to see the importance of indirect variance contributions and to quantify correctly the relative variance contribution of each structural shock.     

Bias corrections for two-step fixed effects panel data estimators

This paper introduces large-T bias-corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity. These models include systems of equations with limited dependent variables and unobserved individual effects, and sample selection models with unobserved individual effects. Our two-step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity/selection bias. We then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable. The fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity. Since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem. This problem is exacerbated by the two-step nature of the procedure. As these two-step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large-T bias adjustments to an important class of models. Simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator.     

Simultaneous equations models in applied search theory

This paper shows how standard simultaneous equations models arise in the analysis of survey data on wages and unemployment durations in the light of job search theory. Log-linear approximations to the key functional relations lead to ordinary log-linear simultaneous equations in which, moreover, specification error or heterogeneity terms are absorbed into the structural form error terms. Identifiability of structural parameters by exclusion restrictions can then be examined. An illustrative application of the method to data on elapsed durations and asking wages is given with results not inconsistent with search theory.     

Adjusting for differential misclassification in multilevel models: the relationship between child exposure to smoke and cognitive development

Misclassification is found in many of the variables used in social sciences and, in practice, tends to be ignored in statistical analyses, and this can lead to biased results. This paper shows how to correct for differential misclassification in multilevel models and illustrates the extent to which this changes fixed and random parameter estimates. Reliability studies on self-reported behaviour of pregnant women suggest that there may be differential misclassification related to smoking and, thus, to child exposure to smoke. Models are applied to the Millennium Cohort Study data. The response variable is the child cognitive development assessed by the British Ability Scales at 3 years of age and explanatory variables are child exposure to smoke and family income. The proposed method allows a correction for misclassification when the specificity and sensitivity are known, and the assessment of potential biases occurring in the multilevel model parameter estimates if a validation data sample is not available, which is often the case.     

Common correlated effect cross‐sectional dependence corrections for nonlinear conditional mean panel models

This paper provides an approach to estimation and inference for nonlinear conditional mean panel data models, in the presence of cross‐sectional dependence. We modify Pesaran's (Econometrica, 2006, 74(4), 967–1012) common correlated effects correction to filter out the interactive unobserved multifactor structure. The estimation can be carried out using nonlinear least squares, by augmenting the set of explanatory variables with cross‐sectional averages of both linear and nonlinear terms. We propose pooled and mean group estimators, derive their asymptotic distributions, and show the consistency and asymptotic normality of the coefficients of the model. The features of the proposed estimators are investigated through extensive Monte Carlo experiments. We also present two empirical exercises. The first explores the nonlinear relationship between banks' capital ratios and riskiness. The second estimates the nonlinear effect of national savings on national investment in OECD countries depending on countries' openness.     

Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension

Pseudo maximum likelihood estimates are developed for higher-order spatial autoregressive models with increasingly many parameters, including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component, and regression models with spatial autoregressive disturbances. Consistency and asymptotic normality of the estimates are established. Monte Carlo experiments examine finite-sample behaviour.     

Using Single-Equation Models of Function-of-Functions Type in Sociological Research

This paper argues that single-equation explanatorymodels of many types of social phenomena should not be built in accordance with establishedsociological ways of thinking. In sociological research, the focus is often on the causal mechanisms behindphenomena, and it is often interesting to use models that show the hierarchical causal structure,that is, how influences are nested in the causal process. I propose such a model with a form that reflectsa two-step structure. According to this model, the dependent factor is a product of independentfactors that are linear functions of variables. The model, which should be used with the factor product inunexpanded form, can be assumed to have wide application. However, the models used insociological research and discussed in textbooks are generally very different. They do not have afunction-of-functions form, but take a form in which variables are directly entered. Furthermore,even if they take interaction into consideration, they are linear in an extended sense because they construeit as one or more terms that are products of single variables. In comparison with the proposed typeof model, these models are technically simpler. However, this paper argues that the proposed typeof model is superior in many contexts because it better reflects the causal process.     

Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects

Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables. The models can include several nested random effects (intercepts and coefficients) representing unobserved heterogeneity at different levels of a hierarchical dataset. The required multivariate integrals are evaluated efficiently using spherical quadrature rules. Simulations show that adaptive quadrature performs well in a wide range of situations.     

Current practice in the modelling of age,period and cohort effects with panel data: a commentary on Tawfik et al. (2012), Clarke et al. (2009), and McCulloch (2012)

This comment assesses how age, period and cohort (APC) effects are modelled with panel data in the social sciences. It considers variations on a 2-level multilevel model which has been used to show apparent evidence for simultaneous APC effects. We show that such an interpretation is often misleading, and that the formulation and interpretation of these models requires a better understanding of APC effects and the exact collinearity present between them. This interpretation must draw on theory to justify the claims that are made. By comparing two papers which over-interpret such a model, and another that in our view interprets it appropriately, we outline best practice for researchers aiming to use panel datasets to find APC effects, with an understanding that it is impossible for any statistical model to find and separate all three effects.     

Econometric models of asymmetric ascending auctions

We develop econometric models of ascending (English) auctions which allow for both bidder asymmetries as well as common and/or private value components in bidders’ underlying valuations. We show that the equilibrium inverse bid functions in each round of the auction are implicitly defined (pointwise) by a system of nonlinear equations, so that conditions for the existence and uniqueness of an increasing-strategy equilibrium are essentially identical to those which ensure a unique and increasing solution to the system of equations. We exploit the computational tractability of this characterization in order to develop an econometric model, thus extending the literature on structural estimation of auction models. Finally, an empirical example illustrates how equilibrium learning affects bidding during the course of the auction.     

The stochastic lake game: A numerical solution

In this paper, we numerically solve a stochastic dynamic programming problem for the solution of a stochastic dynamic game for which there is a potential function. The players select a mean level of control. The state transition dynamics is a function of the current state of the system and a multiplicative noise factor on the control variables of the players. The particular application is for lake water usage. The control variables are the levels of phosphorus discharged (typically by farmers) into the watershed of the lake, and the random shock is the rainfall that washes the phosphorus into the lake. The state of the system is the accumulated level of phosphorus in the lake. The system dynamics are sufficiently nonlinear so that there can be two Nash equilibria. A Skiba-like point can be present in the optimal control solution.We analyze (numerically) how the dynamics and the Skiba-like point change as the variance of the noise (the rain) increases. The numerical analysis uses a result of Dechert (1978. Optimal control problems from second order difference equations. Journal of Economic Theory 19, 50–63) to construct a potential function for the dynamic game. This greatly reduces the computational burden in finding Nash equilibria solutions for the dynamic game.     

A modified GMDH approach for social science research: exploring patterns of relationships in the data

Group Method of Data Handling (GMDH) is a way with which a system of models self-organize themselves by forming higher-order polynomials and selecting the ones with best power of prediction by certain criterion. This method is helpful when we explore patterns of relationships in the data under investigation. In this paper the author presents a modified version of the GMDH algorithm emphasizing the parsimony of models and the behavior of individual parameter estimates as well as of the whole model, and utilizing the consistency and accuracy of bootstrap estimates. This approach is suitable for most research social scientists conduct. An example, the 1907 Romanian Peasant Rebellion, is used to illustrate how to employ the GMDH algorithm when the research topic has been theory-laden. The findings show that GMDH is an appropriate method that social scientists can utilize in their pursuit of a model that is most parsimonious and theoretically meaningful at the same time. Possible extensions of the modified approach, which in its present form works on linear regression type of models, to logit and probit models are also considered.     

Masking identification of discrete choice models under simulation methods

We present examples based on actual and synthetic datasets to illustrate how simulation methods can mask identification problems in the estimation of discrete choice models such as mixed logit. Simulation methods approximate an integral (without a closed form) by taking draws from the underlying distribution of the random variable of integration. Our examples reveal how a low number of draws can generate estimates that appear identified, but in fact, are either not theoretically identified by the model or not empirically identified by the data. For the particular case of maximum simulated likelihood estimation, we investigate the underlying source of the problem by focusing on the shape of the simulated log-likelihood function under different conditions.     

A New Measure of Multicollinearity in Linear Regression Models

Databases with a lot of data very often mean little information. It is because of the collinearity of variables which consist of the data of the database. This collinearity is in fact a kind of redundancy of the database.
In the study a new indicator is given. With this indicator, which contains the eigenvalues of the variables' correlation matrix, it is possible to quantify the percentage of collinearity: from 0% (all the eigenvalues are equal to 1) to 100% (all the eigenvalues, except the first, are equal to 0).