Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; semi-nonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in semi-nonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and non-negativity. This chapter describes estimation of semi-nonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve M-estimates, pointwise normality of series estimates of regression functions, root-n asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.

Self-selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of self-selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process. This paper develops an alternative econometric methodology which combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell, 1993). The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems. The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions. The results suggest that self-selection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in state-specific labor markets. While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states. Consistent with the finding that the corrected return to a college education differs across the U.S., the relative state-to-state migration flows of college- versus high school-educated individuals respond strongly to differences in the return to education and amenities across states.

This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to infinity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept has typically been subsumed in the nonpara-metric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the "wage gap " between unionized and nonunionized workers, decompose the wage differential between different socio-economic groups (e.g. male-female and black-white), and evaluate the net benefits of a social programme. 1.

The field of strategic management is predicated fundamentally on the idea that managements' decisions are endogenous to their expected performance implications. Yet, based on a review of more than a decade of empirical research in the SMJ, we find that few papers econometrically correct for such endogeneity. In response, we now describe the endogeneity problem for cross-sectional and panel data, referring specifically to management's choice among discrete strategies with continuous performance outcomes. We then present readily implementable econometric methods to correct for endogeneity and, when feasible, provide STATA code to ease implementation. We also discuss extensions and nuances of these models that are sometimes difficult to decipher in more standard treatments. These extensions are not typically discussed in the strategy literature, but they are, in fact, highly pertinent to empirical strategic management research. Introduction The underlying presumption of the field of strategic management is that managers can make choices to generate sustainable competitive advantage, thereby achieving superior performance outcomes for their organizations. Thus, strategic management researchers are frequently interested in understanding those decisions that influence performance. For instance, we generally think that managers' desire to achieve high levels of performance influences their decisions about whether to make or buy, to acquire or invest, to join a network or not, to choose an alliance or a joint venture, to centralize or decentralize, etc. If this presumption is correct, then managers make strategic organizational decisions not randomly, but based on expectations of how their choices affect future performance. Put more precisely, the field of strategic management is fundamentally predicated on the idea that management's decisions are endogenous to their expected performance outcomes-if not, managerial decision-making is not strategic; it is superfluous. Endogeneity has important implications for the statistical analysis of such decisions. As we more fully illuminate below, statistical analysis that does not take into account management's expectation of performance outcomes with respect to the strategy chosen can suffer from biased coefficient estimates. These biases result from omitted variables that affect both strategy choice and performance. Thus, estimating unbiased coefficients for these problems requires econometric methods that account for omitted variables. Such methods statistically correct for management's self-selection of a particular strategy. Failure to account for endogeneity can have important consequences. For instance, 1 Endogeneity problems are particularly vexing to researchers because both the direction and the size of bias are difficult to predict ex ante. Econometric techniques to correct for endogeneity when both strategy choice and performance are continuous long have been available; instrumental variable and two and three stage methods are both well known and readily implemented. This is not the case, however, for strategy choices that are discrete yet yield performance outcomes that are continuous. Since 1974, 1 Such erroneous results can greatly contaminate the empirical progress in a field. Consider Masten's discussion (1996, 52) of Capon et al's (1990) review of 320 financial performance studies. Capon et al. reported that "vertical integration was found to have positive influence on performance in 69 studies and a negative influence in 35; horizontal integration or diversification a positive effect in 107 studies and a negative effect in 174; and owner (as opposed to manager) control a positive effect in 65 and negative impact in 56. Viewed collectively, these studies cannot sustain generalization about the direction, much less the magnitude, of the effects of organizational form." Masten concludes that the "the sorry state of this research is at least partly the result of serious specification problems" in which endogeneity is not considered. 2 econometric techniques to correct for endogeneity arising from discrete strategy choices have been available Many of these econometric estimators were developed in the context of labor economics. Nonetheless, the econometric problems in that field are structurally similar to problems of strategic management. For instance, the classic illustration in labor economics Heckman and Lee's technique for econometrically analyzing this choice is based on the assumption that individuals will self-select into the profession that provides a better match with their abilities and hence a greater return. But without modeling this self-selection, a regression of income on profession choice may lead to erroneous estimates for the returns to each profession. For instance, a regression analysis that does not correct for self-selection might imply that income is independent of profession choice, whether hunting or fishing. Yet a more appropriate econometric analysis, one that incorporates the possibility of self-selection, might instead find that those individuals who chose the hunting profession earned a substantially higher income than if they had instead chosen to fish and vice-versa. An individual choosing between these two professions is the structural equivalent of a manager choosing between two alternative strategies. For instance, an analysis that regresses profitability on make versus buy will likely lead to biased coefficient estimates of the impact of this strategic choice on performance unless we control for self-selection. The fundamental question for assessing the impact of choosing to buy (or to fish, in Roy's context) is this: What profit would the manager's organization earn if he had chosen to make (or to hunt) instead? We are not likely to provide an accurate answer this question by comparing the profits of firms choosing to make 3 with the profits of those choosing to buy, since the observed outcomes may not correspond to the counterfactual performance levels of interest. For example, firms choosing to make may have particular production capabilities that make this a highly profitable choice. On the other hand, firms choosing to buy may not have these production capabilities. Consequently, had the "buy" firms instead chosen to make, they would have been much less profitable than those firms who actually chose to make. As a result, a regression of performance on the make versus buy choice that does not allow for endogeneity of the choice may not answer the strategy effect question of interest. Although the presumption that managers make decisions with respect to expected performance benefits is a foundation of strategic management, it is surprising how few empirical papers consider and econometrically correct for such endogeneity. For example, consider empirical papers published in the Strategic Management Journal (SMJ). Whether or not SMJ represents strategy research in general, SMJ is nonetheless the core journal and a key source of knowledge for the strategy field and thus is an appropriate journal to scrutinize. Of the 426 empirical papers published in the SMJ (out of 601) between January, 1990, and December, 2001, we identify only 27 papers that explicitly econometrically correct for potential endogeneity concerns. Of course, not all research involves such endogeneity concerns-an econometric model in which potential omitted variables are uncorrelated with right hand side covariates may not suffer from endogeneity bias. However, at a minimum, empirical strategy research that investigates some type of performance outcome should carefully consider correcting for endogeneity. 2 2 A conservative estimate of the number of papers that should have considered correcting for endogeneity might be all those empirical studies that directly study performance (e.g., profits, mortality, satisfaction, etc.). A total of 169 of the 196 performance-related papers (86%) do not control for endogeneity. Thus, while a variety of econometric 4 We believe that the low number of papers in SMJ that account for endogeneity may indicate a failure of empirical research in strategic management. An empirical analysis that models performance as a function of right-hand-side decision variables without correcting for the presumption that managers make decisions to achieve some level of expected performance is implicitly assuming that these decision variables are exogenous to performance and thus ignores the endogeneity of these decisions. Yet, ignoring endogeneity is perilous; as the Our paper provides value to strategic management researchers in four ways. First, we assess the diffusion of econometric methods used in empirical research published in the SMJ over the past decade. In doing so, we find a sea change over the past decade in the type of econometric techniques used to test hypotheses in the field of strategic management. Second, we identify the methodological issues associated with endogeneity specifically for strategic management phenomena for both cross-sectional and panel data. Third, we review econometrics methods for dealing with these issues and explain when different types of models are appropriately used. Unlike standard econometric treatments, our presentation and discussions are developed specifically for application to strategic management phenomena. We also discuss extensions and nuances of these models that are sometimes difficult to decipher or not readily accessible in more methods to correct for endogeneity have been introduced since the 1970s, it was not until this past decade that the early methods began to diffuse into strategic management research. This lag suggests that while strategic management research is beginning to more directly focus empirical work on correcting for endogeneity, research may not be benefiting from more recent econometric advances. 5 standard treatments and describe additional information provided by theses models about relative and absolute comparative advantages that, ironically, are typically ignored in strategic management applications. Fourth, we focus on methods that are readily implementable using standard software packages that require little in the way of programming. 3 To highlight this, we provide relevant STATA code, when feasible, in an Appendix to make it easier for researchers to implement these techniques not only in STATA but also other statistical software packages. We believe that the information provided herein goes far in bridging the gap between the state of the art in econometric theory (which is sometimes difficult to access) and empirical strategic management research practice (which presents challenges when coding econometric software packages to estimate models).

ABSTRACT 1 Several studies based on US and UK data have used market value as an indicator of the firm’s expected R&D performance. However, there exist no investigations for the continental countries in the European Union, partly because the analysis is complicated by data availability problems. In this paper we take a first step towards filling this gap using a newly constructed panel dataset of firms that are publicly traded in France, Germany, and Italy. Controlling for either permanent unobserved firm effects or sample selection due to the voluntary nature of R&D disclosure, we find that the relative shadow value of R&D in France and Germany is remarkably similar both to each other and to that in the US or the UK during the same period In contrast, we find that R&D in publicly traded Italian firms is not valued by financial markets on average. However, when we control for the presence of a single large shareholder, we find that both French and Italian firms have high R&D valuations when no single shareholder holds more than one third of the firm, but that R&D is essentially not valued in the other firms.

J71. We thank Rob Alessie for a discussion that led to this paper, and we thank Alejandro Badel and participants at the ESPE meeting in New York and the Econometric Society meetings in San Diego and at seminars at the University of British Columbia Several recent papers use the quantile regression decomposition method of Machado and Mata (2005) to analyze the gender gap in log wages across the distribution. Since employment rates often differ substantially by gender, sample selection is potentially a serious issue for such studies. To address this issue, we extend the Machado-Mata technique to account for selection. In addition, we prove that this procedure yields consistent and asymptotically normal estimates of the quantiles of the counterfactual distribution that it is designed to simulate. We illustrate our approach by analyzing the gender log wage gap between men and women who work full time in the Netherlands. Because the fraction of women working full time in the Netherlands is quite low, this is a case in which sample selection is clearly important. We find a positive selection of women into

This paper presents estimates of the changing distribution of wages that are robust to possible selection effects. We find convincing evidence of an increase in overall inequality, changes in the “return ” to education and increases in inequality within age and education groups. On the other hand we find that the increase in the relative wages of women may have been driven by selection. 1 Introduction and

working paper

This paper studies the possible existence of sample selection bias for infor-mal and formal employment in Brazil. We use semi-parametric methods that do not rely on the normality assumption and are capable of analyzing individuals at various points of the earnings distribution. We present selectivity corrected quantile regression models for earnings of both informal and formal workers. We ¯nd that in the informal sector the unobservable characteristics which cause se-lection increase the expected income for lower earnings quantiles while lowering those for higher quantiles. We also ¯nd that the earnings gaps between formal and informal workers are wider at low conditional quantiles than at high ones. Di®erences in returns to attributes explain around 30 % of their earnings gap at low quantiles, while at high quantiles of the distribution, the gap is completely explained by di®erences in their individual characteristics.

The purpose of this paper is to formulate procedures for the analysis of the time series behaviour of micro panel data subject to censoring. We assume an autoregressive model with random effects for a latent variable which is only partly observed due to a selection mechanism. Our methods are based on the observation that the subsamples which only include individuals without censored past observations are exogenously selected for the purpose of estimating features of the distribution of the censored endogenous variable conditional on its past. We apply these methods to analyze the dynamics of female labour supply and wages using PSID data. ∗ An earlier version of this paper was presented at the Mannheim Meeting on Labour