Semiparametric estimation of a bivariate Tobit model

The existing semiparametric estimation literature has mainly focused on univariate Tobit models and no semiparametric estimation has been considered for bivariate Tobit models. In this paper, we consider semiparametric estimation of the bivariate Tobit model proposed by Amemiya (1974), under the independence condition without imposing any parametric restriction on the error distribution. Our estimator is shown to be consistent and asymptotically normal, and simulation results show that our estimator performs well in finite samples. It is also worth noting that while Amemiya’s (1974) instrumental variables estimator (IV) requires the normality assumption, our semiparametric estimator actually outperforms his IV estimator even when normality holds. Our approach can be extended to higher dimensional multivariate Tobit models.     

Efficiency changes in long-term care in OECD countries: A non-parametric Malmquist Index approach

Future demographic projections indicate that long-term care (LTC) demand will put significant pressures on the long-term sustainability of public finances. Efficiency gains could potentially compensate for increasing LTC expenditures. Nevertheless, among the factors that drive LTC expenditures, efficiency, or productivity discussions have received little attention. This paper provides the first analysis of the efficiency levels of LTC for a subset of OECD countries. In doing so, the study adopts a non-parametric approach and performs a Data Envelopment Analysis (DEA). The results of the DEA show that average efficiency scores have a slight tendency to increase. There was a 0.1% increase in productivity in the provision of LTC between 2009 and 2014, which mainly resulted from an increase in technological change. However, the slight increase in efficiency is insufficient to offset fiscal pressures led by the increasing number of LTC beneficiaries and amount spent on LTC. The second stage Tobit analysis results further indicate that the productivity of LTC provision does not differ across countries with different public LTC financing arrangements.     

Estimation of a simultaneous equations model with an ordinal endogenous variable: The extent of teacher bargaining and the state legal environment

This paper presents a simple two-step estimator for a simultaneous equations model that contains an ordinal endogenous variable. The estimation rules are extensions of the Heckman (1978) estimators, also considered by Amemiya (1978). Asymptotic covariance matrices of the estimators also are derived. The estimator is applied to an economic model in which the statewide extent of teacher bargaining and teacherbargaining legislation are determined jointly.     

Censored regression models with unobserved,stochastic censoring thresholds

The ‘Tobit’ model is a useful tool for estimation of regression models with truncated or limited dependent variables, but it requires a threshold which is either a known constant or an observable and independent variable. The model presented here extends the Tobit model to the censored case where the threshold is an unobserved and not necessarily independent random variable. Maximum likelihood procedures can be employed for joint estimation of both the primary regression equation and the parameters of the distribution of that random threshold.     

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.     

Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality

This paper extends the method of local instrumental variables developed by Heckman and Vytlacil [Heckman, J., Vytlacil E., 2005. Structural equations, treatment, effects and econometric policy evaluation. Econometrica 73(3), 669–738] to the estimation of not only means, but also distributions of potential outcomes. The newly developed method is illustrated by applying it to changes in college enrollment and wage inequality using data from the National Longitudinal Survey of Youth of 1979. Increases in college enrollment cause changes in the distribution of ability among college and high school graduates. This paper estimates a semiparametric selection model of schooling and wages to show that, for fixed skill prices, a 14% increase in college participation (analogous to the increase observed in the 1980s), reduces the college premium by 12% and increases the 90–10 percentile ratio among college graduates by 2%.     

Recent contributions to censored regression models

A brief survey of estimation of parameters in a censored regression model (known as the Tobit model) and some details of the properties of LAD (least absolute deviation) estimates and tests of significance of linear hypotheses are given.     

The relative importance of campaign expenditures: An application of production theory

In an election campaign a politician attempts to combine the resources at his disposal so as to maximize the percent of the votes he receives. This behavior is consistent with an economic model of production where the producer combines inputs in order to maximize output. In this paper the concept of an election campaign as a production process is applied to elections to the U.S. House of Representatives. The three inputs were campaign expenditures, years of tenure in office, and the percent of registered voters in candidate's party. Cobb-Douglas and CES versions of the production function are estimated. Each estimation indicated that the marginal productivity of campaign expenditures was very low. Further, the CES estimation indicated low elasticity of substitution between campaign expenditures and other inputs. This means that it is difficult for a candidate who faces a disadvantage—either because his opponent is an incumbent with several years experience, or because he belongs to a minority party—to overcome this disadvantage by simply spending more money.     

The role of governance in mobile phones for inclusive human development in Sub-Saharan Africa

This study assesses the synergy effects of governance in mobile phone penetration for inclusive human development in Sub-Saharan Africa with data for the period 2000–2012. It employs a battery of interactive estimation techniques, namely: Fixed effects, Generalised Method of Moments and Tobit regressions. Concepts of political (voice and accountability and political stability/no violence), economic (government effectiveness and regulation quality) and institutional (corruption-control and rule of law) governance are employed. The following findings are established. The previously apparent positive correlation between mobile phones and inclusive development can be extended to a positive effect. Although political governance is overwhelmingly not significant across estimated models, the average effects from economic governance are higher relative to institutional governance. On the interactions between mobile phones and governance variables, while none are apparent in Fixed effects regressions, there are significant synergy effects in Generalised Method of Moments and Tobit estimations, notably, from: regulation quality in the former and political stability, voice and accountability and rule of law in the latter. There is consistent evidence of convergence in inclusive human development. Policy implications are discussed.     

Least absolute deviations estimation for the censored regression model

This paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression (or censored ‘Tobit’) model. The proposed estimator is a generalization of least absolute deviations estimation for the standard linear model, and, unlike estimation methods based on the assumption of normally distributed error terms, the estimator is consistent and asymptotically normal for a wide class of error distributions, and is also robust to heteroscedasticity. The paper gives the regularity conditions and proofs of these large-sample results, and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances.     

Heterogeneous treatment effects: Instrumental variables without monotonicity?

Imbens and Angrist (1994) were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables. More recently, Heckman and Vytlacil (1999) suggested the estimation of a variety of treatment effect parameters using a local version of their approach. We investigate the sensitivity of the respective estimates to random departures from monotonicity. Approximations to the respective bias terms are derived. In an empirical application the bias is calculated and bias corrected estimates are obtained. The accuracy of the approximation is investigated in a Monte Carlo study.     

Identifying and Estimating the Distributions of Ex Post and Ex Ante Returns to Schooling

This paper surveys a recent body of research by Carneiro, Hansen, and Heckman [Carneiro, P., K. Hansen, and J.J. Heckman, 2001, Fall. Removing the veil of ignorance in assessing the distributional impacts of social policies. Swedish Economic Policy Review 8 (2), 273–301., Carneiro, P., K. Hansen, and J.J. Heckman, 2003, May. Estimating distributions of treatment effects with an application to the returns to schooling and measurement of the effects of uncertainty on college choice. International Economic Review 44 (2), 361–422. 2001 Lawrence R. Klein Lecture], Cunha and Heckman [Cunha, F. and J.J. Heckman, 2006. The evolution of earnings risk in the US economy. Presented at the 9th World Congress of the Econometric Society, London], Cunha, Heckman, and Navarro [Cunha, F., J.J. Heckman, and S. Navarro, 2004, March. Separating heterogeneity from uncertainty in an aiyagari–laitner economy. Presented at the Goldwater Conference on Labor Markets, Arizona., Cunha, F., J.J. Heckman, and S. Navarro, 2005, April. Separating uncertainty from heterogeneity in life cycle earnings, The 2004 Hicks Lecture. Oxford Economic Papers 57 (2), 191–261., Cunha, F., J.J. Heckman, and S. Navarro, 2006. Counterfactual analysis of inequality and social mobility. In S.L. Morgan, D.B. Grusky, and G.S. Fields (Eds.), Mobility and Inequality: Frontiers of Research in Sociology and Economics, Chapter 4, pp. 290–348. Stanford, CA: Stanford University Press], Heckman and Navarro [Heckman, J.J. and S. Navarro, 2007, February. Dynamic discrete choice and dynamic treatment effects. Journal of Econometrics 136 (2), 341–396] and Navarro [Navarro, S., 2005. Understanding Schooling: Using Observed Choices to Infer Agent's Information in a Dynamic Model of Schooling Choice When Consumption Allocation is Subject to Borrowing Constraints. Ph.D. Dissertation, University of Chicago, Chicago, IL] that identifies and estimates the ex post distribution of returns to schooling and determines ex ante distributions of returns on which agents base their schooling choices. We discuss methods and evidence, and state a fundamental identification problem concerning the separation of preferences, market structures and agent information sets. For a variety of market structures and preference specifications, we estimate that over 50% of the ex post variance in returns to college are forecastable at the time agents make their schooling choices.     

带未知异方差与半线性结构Tobit模型的半参数估计

本文将Tobit模型扩展至同时带未知条件异方差与半线性结构回归函数的场合,并提出一种计算简便的半参数二步估计法。该方法的关键之处在于连续两次施以成对相减变换,并先后消去第一步所得被解释变量非参数条件分位函数中的两类非线性冗余成分(非线性回归函数部分与未知异方差结构)。文章证明了估计量的n-一致性与渐近正态性,并通过Monte Carlo模拟研究了分位点对的选择、扰动项分布类型与样本删尾程度等因素对估计量小样本性质的影响。最后通过国内居民医疗服务利用不平等的实例验证了本文所提的方法。     

Institutional versus non-institutional credit to agricultural households in India: Evidence on impact from a national farmers’ survey

A goal of agricultural policy in India has been to reduce farmers’ dependence on informal credit. To that end, recent initiatives are focused explicitly on rural areas and have a positive impact on the flow of agricultural credit. Despite the significance of the above initiatives in enhancing the flow of institutional credit to agriculture, the links between institutional credit and net farm income and consumption expenditures in India are not very well documented. Using large, national farm household level data and IV 2SLS estimation methods, we investigate the role of institutional farm credit on farm income and farm household consumption expenditures. Findings show that, in India, formal credit does indeed play a critical role in increasing both net farm income and per capita monthly household expenditures of Indian farm families. Finally, we find that, in the presence of formal credit, social safety net programs like the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) may have unintended consequences. In particular, MGNREGA reduces both net farm income and per capita monthly household consumption expenditures. On the other hand, in the presence of formal credit, the Public Distribution System may increase both net farm income and per capita monthly household consumption expenditures.     

Estimation of International Demand Behaviour for Use with Input-Output Based Data

The making of projections often requires an economy-wide perspective, and the estimation of consumer demands at the international level. In this paper, an implicit, directly additive demand system (AIDADS) is estimated using cross- country data on consumer expenditures from two different sources: the International Comparison Programme (ICP), and the Global Trade Analysis Project (GTAP). The two data sets are found to produce results that are quite consistent despite their differing origins, and the fact that the former is based on consumer goods that embody wholesale/retail margins, while margin demands are treated separately in GTAP. Given the similarity of the results, the estimation based on GTAP data is favoured for economy-wide projection purposes because it can be readily matched to input-output based production and trade data. An additional benefit of the GTAP-based estimates is that they provide direct evidence concerning how aggregate margin expenditures vary with per capita income.     

Estimating a public school expenditure model under binding spending limitations

A model explaining desired expenditure on education is estimated for a sample of New Jersey school districts. Because the limit on annual increases in school spending is binding for a subsample of jurisdictions, the Tobit estimation procedure is used. We test for equality of the pre- and postlimitation structures and find substantial similarity. The cap on expenditure increases was part of a court-ordered reform of New Jersey school finance law. The results can be used to explain the failure of the existing school finance laws in lessening expenditure disparities at the lower end of the distribution.     

Correcting for bias in retrospective data

When panel data are not available, retrospective data are used in the estimation of dynamic choice models. However, retrospective data are not reliable. Previous studies of voting choices, for example, have shown that respondents misreport their past choices in order to appear more consistent with their current choice. Such retrospective bias leads to inconsistent estimates, especially when there is state dependence in choices. Specifically, observed persistence in retrospective data may be due to (a) true state dependence, (b) unobserved heterogeneity, and (c) retrospective bias in reporting previous choices. Whereas Heckman in his 1981 study deals with (a) and (b), we introduce a method to estimate true state dependence while accounting for both unobserved heterogeneity and retrospective reporting bias. Our method is based on modeling the reporting behavior and integrating it into the estimation. The identification strategy is based on the correlation between the reported previous choices and current exogenous variables. Using data on Israeli voters, we find that the probability that a respondent whose vote intention in 1991 differed from his or her past voting choices would lie about their past choices is 0.23. Copyright © 2007 John Wiley & Sons, Ltd.     

ARE IMPACTS OF EARLY INTERVENTIONS IN THE SCANDINAVIAN WELFARE STATE CONSISTENT WITH A HECKMAN CURVE? A META‐ANALYSIS

“Early intervention” has been a mantra in recent debates about human capital investment. Strong theoretical models motivate this focus by predicting that investment in children is most cost‐effective when they are young. The “Heckman curve” summarizes this idea visually (Heckman, 2006). However, hardly any reviews scrutinize this hypothesis empirically in modern welfare states such as those in Scandinavia that already invest heavily during early childhood. Any such review is ideally based on interventions conducted as randomized controlled trials (RCTs), set in the same welfare state, and comparable across ages through cost‐standardized effects. This meta‐analysis assembles cost‐standardized effect estimates from 10 RCTs, including a total of 18 intervention arms and 30,578 participants (aged 1.5–24 years), conducted by the same research center in the Scandinavian welfare state of Denmark. These interventions show significant effects relative to their costs, despite the large baseline investment level. Interventions targeted at younger children tend to produce larger effects, consistent with the Heckman curve. However, variation in the effect size within age groups is as large as it is across age groups. This indicates that both the quality and timing of investments matter and that “early interventions” are not necessarily superior to later interventions.     

Generalised residuals and heterogeneous duration models: With applications to the Weilbull model

This paper deals with models for the duration of an event that are misspecified by the neglect of random multiplicative heterogeneity in the hazard function. This type of misspecification has been widely discussed in the literature [e.g., Heckman and Singer (1982), Lancaster and Nickell (1980)], but no study of its effect on maximum likelihood estimators has been given. This paper aims to provide such a study with particular reference to the Weibull regression model which is by far the most frequently used parametric model [e.g., Heckman and Borjas (1980), Lancaster (1979)]. In this paper we define generalised errors and residuals in the sense of Cox and Snell (1968, 1971) and show how their use materially simplifies the analysis of both true and misspecified duration models. We show that multiplicative heterogeneity in the hazard of the Weibull model has two errors in variables interpretations. We give the exact asymptotic inconsistency of M.L. estimation in the Weibull model and give a general expression for the inconsistency of M.L. estimators due to neglected heterogeneity for any duration model to O(σ²), where σ² is the variance of the error term. We also discuss the information matrix test for neglected heterogeneity in duration models and consider its behaviour when σ²>0.