Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

The demand for gasoline: a two stage approach

The demand for gasoline has typically been estimated using a reduced-form equation model. The simplicity of the approach is attractive, but has proven to be costly in terms of the insights lost as to the nature of the processes governing the interdependence between fuel efficiency and the overall demand for gasoline. On the other hand, disaggregating the overall demand for gasoline into all of its components produces an enormous amount of detail and many insights, but increases commensurately the complexity of the system and reduces its usefulness in forecasting.A two stage simple demand equation is used which first involves an estimation of the level of fuel efficiency of the fleet stock in terms of price induced technical change. In the second stage, the first equation is coupled with other typical demand variables to determine the overall demand for gasoline. The procedure provides an excellent forecasting equation of both the short-and long-term demand for gasoline.     

On the existence of moments of the partially restricted reduced-form estimators from a simultaneous-equation model

This article proves the existence of all moments of the partially restricted reduced-form estimator. It highlights this estimation method as it appears to be the only reduced-form estimator to possess finite moments, and is thus a valid alternative to restricted reduced-form estimation (where the moments do not exist). The estimation method is described briefly and then the existence proof is formulated, first, for the case of two included endogenous variables in the structural equation and then, we extend the result for any number of included endogenous variables.     

Index

We study two Durbin-Watson type tests for serial correlation of errors inregression models when observations are missing. We derive them by applying standard methods used in time series and linear models to deal with missing observations. The first test may be viewed as a regular Durbin-Watson test in the context of an extended model. We discuss appropriate adjustments that allow one to use all available bounds tables. We show that the test is locally most powerful invariant against the same alternative error distribution as the Durbin-Watson test. The second test is based on a modified Durbin-Watson statistic suggested by King (1981a) and is locally most powerful invariant against a first-order autoregressive process.     

Dragon Children: Identifying the Causal Effect of the First Child on Female Labour Supply with the Chinese Lunar Calendar*

Instrumental variables (IV) estimates of the effect of fertility on female labour supply have only been able to identify the causal effect of second and higher parity children. This study uses exogenous variation in fertility caused by the Chinese lunar calendar to identify the effect of the first child. Additionally, weighting formulas are presented to interpret IV estimates as weighted average treatment effects in the case of multiple endogenous variables, which are useful when children vary in intensity by both number and age. The effect of the first child is found to be much greater than that of other children.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity

We extend the identification results for nonparametric simultaneous equations models in Matzkin (2008) to situations where the observations on the vector of dependent variables might be limited, and where the number of exogenous unobservable variables is larger than the number of dependent variables.     

Sparse Partial Least Squares in Time Series for Macroeconomic Forecasting

Factor models have been applied extensively for forecasting when high‐dimensional datasets are available. In this case, the number of variables can be very large. For instance, usual dynamic factor models in central banks handle over 100 variables. However, there is a growing body of literature indicating that more variables do not necessarily lead to estimated factors with lower uncertainty or better forecasting results. This paper investigates the usefulness of partial least squares techniques that take into account the variable to be forecast when reducing the dimension of the problem from a large number of variables to a smaller number of factors. We propose different approaches of dynamic sparse partial least squares as a means of improving forecast efficiency by simultaneously taking into account the variable forecast while forming an informative subset of predictors, instead of using all the available ones to extract the factors. We use the well‐known Stock and Watson database to check the forecasting performance of our approach. The proposed dynamic sparse models show good performance in improving efficiency compared to widely used factor methods in macroeconomic forecasting. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparing Time Series Cross-Section Model Specifications: The Case of Welfare State Development

In recent years, an impressive number of pooled time series (TSCS) cross-section models have been estimated in order to test hypotheses on welfare state development. Although most of these models share several of the variables, they can often be distinguished by the model specification adopted. This begs the question: what is the appropriate specification for modeling welfare state development? In order to answer this question some leading specifications are evaluated with respect to their ability to meet the theoretical assumptions about the theory of welfare state evolution in addition to the econometric canons on panel analysis. The main conclusions of this paper are the following. First, all specifications in levels are econometrically unfounded because most of the variables typically used for analyzing this topic cannot be considered to be stationary. Second, although a first difference model performs better from an econometric point of view, it is unable to test the hypothesized long-term relationships underlying welfare state dynamics. Third, and more importantly, the single equation error correction model represents the best pooled TSCS specification for modeling welfare state development since it is able tocapture long-run effects even in the presence of nonstationary processes.     

Statistical properties of data stretching

This research examines the properties of an estimation procedure frequently used because observations on some variables are available only at higher levels of aggregation than others. When this occurs, data are often stretched by repeating observations on variables at higher levels of aggregation. We show that this procedure results in biased estimators of coefficients and error variances. Under some circumstances the estimation based on stretched data has a smaller covariance matrix than that based on aggregated data. Comparisons of mean squared errors depend on unknown coefficients.     

FRED-SD: A real-time database for state-level data with forecasting applications

We construct a real-time dataset (FRED-SD) with vintage data for the U.S. states that can be used to forecast both state-level and national-level variables. Our dataset includes approximately 28 variables per state, including labor-market, production, and housing variables. We conduct two sets of real-time forecasting exercises. The first forecasts state-level labor-market variables using five different models and different levels of industrially disaggregated data. The second forecasts a national-level variable exploiting the cross-section of state data. The state-forecasting experiments suggest that large models with industrially disaggregated data tend to have higher predictive ability for industrially diversified states. For national-level data, we find that forecasting and aggregating state-level data can outperform a random walk but not an autoregression. We compare these real-time data experiments with forecasting experiments using final-vintage data and find very different results. Because these final-vintage results are obtained with revised data that would not have been available at the time the forecasts would have been made, we conclude that the use of real-time data is essential for drawing proper conclusions about state-level forecasting models.     

Residential choice,hedonic prices,and the demand for urban air quality

This paper uses a two-step estimation procedure suggested by Sherwin Rosen to estimate structural demand and supply equations for urban air quality. In the first step, a hedonic price equation is estimated for residential property values for the Washington, D. C., SMSA for 1970. In the second step, a set of marginal hedonic prices is generated. These prices and the quantity of clean air (reciprocal of air pollution) are used as endogenous variables in a simultaneous equation model. Empirical results indicate a price elasticity of demand between ?1.2 and ?1.4 and a unitary income elasticity.     

Search for relevant sets of variables in a high-dimensional setup keeping the familywise error rate

Two multiple procedures for the detection of relevant sets of variables in a high-dimensional problem are suggested. Multivariate tests for significance are combined with the search for interpretable multivariate structures. Thus, groups of highly correlated variables are investigated. The emphasis lies on managing the huge number of possible subsets, for example, in gene expression analysis. The first procedure is based on parametric spherical tests and an order relation of the subsets. The second procedure is a non-parametric method utilizing Westfall–Young principles.     

The effects of entrepreneurial personality, background and network activities on venture growth*

This study investigates the effects of entrepreneurial personality traits, background and networking activities on venture growth among 168 Chinese entrepreneurs in small and medium sized businesses in Singapore. Personality traits include need for achievement, internal locus of control, self-reliance and extroversion; background comprises education and experience; networking activities consist of size and frequency of communication networks. A structural equation modelling technique – partial least squares (PLS) – is used to estimate a path model with latent variables. The results indicate that experience, networking activities, and number of partners as well as internal locus of control and need for achievement all have positive impact on venture growth. Two other personality traits, self-reliance and extroversion have negative impact on number of partners and positive impact on networking activities, respectively. The impact of education on venture growth, however, is moderated by firm size, positive for larger firms and negative for smaller firms. Our findings indicate that among all the factors that we have considered, an entrepreneur's industrial and managerial experience is the dominating factor affecting venture growth.     

A Better Understanding of Granger Causality Analysis: A Big Data Environment

This paper aims to provide a better understanding of the causal structure in a multivariate time series by introducing several statistical procedures for testing indirect and spurious causal effects. In practice, detecting these effects is a complicated task, since the auxiliary variables that transmit/induce indirect/spurious causality are very often unknown. The availability of hundreds of economic variables makes this task even more difficult since it is generally infeasible to find the appropriate auxiliary variables among all the available ones. In addition, including hundreds of variables and their lags in a regression equation is technically difficult. The paper proposes several statistical procedures to test for the presence of indirect/spurious causality based on big data analysis. Furthermore, it suggests an identification procedure to find the variables that transmit/induce the indirect/spurious causality. Finally, it provides an empirical application where 135 economic variables were used to study a possible indirect causality from money/credit to income.     

Semiparametric Bayesian inference in multiple equation models

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal–Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two‐equation structural model drawn from the labour and returns to schooling literatures. Copyright © 2005 John Wiley & Sons, Ltd.     

Health and economic growth in high-income countries revisited: evidence from an augmented production function for the period 1980–2009

This paper uses time series data for seven industrialized countries from 1980–2009 to explore the causality between health care expenditure (HCE) and economic growth. We have set up a classical Cobb–Douglas production function including HCE, labor, capital, and an augmented function additionally including the number of patent applications (as a proxy for technology and research) and the total number of tertiary education students (as a proxy for education). Our results show that there is a long-run relationship between growth and HCE. As regards causality, in the classical production function, evidence for mutual causality between GDP and HCE is noted only in France, Germany and England, causality from HCE to GDP is noted in Italy and Japan, while no causality whatsoever is evidenced in Canada and USA. However, a completely different situation is unveiled when the augmented production function is used with mutual causality being noted in all perused variables. The novelty of our study lies first in that it contributes to the health-growth nexus literature for high-income countries which has been quite controversial and second it sets off new variables whose omission might be one of the reasons of the result dichotomy. Results of this study will be very useful for high-income countries currently afflicted by the economic crisis and embark on HCE curtailments or revisions.     

Two–step sequential sampling

Choosing the sample size in advance is a familiar problem: often, additional observations appear to be desirable. The final sample size then becomes a random variable, which has rather serious consequences.
Two such sample extension situations will be considered here. In the first situation, the observed sample variance determines whether or not to double the original sample size. In the second situation, the variances observed in two independent samples are compared; their ratio determines the number of additional observations.     

Consistent selection of explanatory variables

We consider a linear regression model where some explanatory variables are unknown members of sets of alternative explanatory variables. It will be shown that under weak conditions the minimum residual variance criterion for selecting these explanatory variables has the property that the probability of selecting wrong explanatory variables vanishes if the number of observations increases to infmity. Moreover, the O.L.S. estimator of the resulting "specified" model turns out to be consistent, while in the case that all the parameters are nonzero it can be shown that this O.L.S. estimator has the same limiting distribution as the O.L.S. estimator of the true model.     

Investigating the Number of Non-linear and Multi-modal Relationships Between Observed Variables Measuring Growth-oriented Atmosphere

This study investigates the number of non-linear and multi-modal relationships between observed variables measuring the Growth-oriented Atmosphere. The sample (N = 726) represents employees of three vocational high schools in Finland. The first stage of analysis showed that only 22% of all dependencies between variables were purely linear. In the second stage two sub samples of the data were identified as linear and non-linear. Both bivariate correlations and confirmatory factor analysis (CFA) parameter estimates were found to be higher in the linear sub sample. Results showed that some of the highest bivariate correlations in both sub samples were explained via third variable in the non-linear Bayesian dependence modeling (BDM). Finally, the results of CFA and BDM led in different substantive interpretations in two out of four research questions concerning organizational growth.