A comparison of treatment effects estimators using a structural model of AMI treatment choices and severity of illness information from hospital charts

We compare the performance of various matching estimators using a novel approach that is feasible in the absence of experimental data. We estimate a structural model of hospital choices and catheterization for Medicare heart attack victims using hospital chart data on patient heterogeneity. With the estimated structural parameters, we simulate data for which the treatment effect is known. We find that as measures of individual heterogeneity are added to the controls, matching estimators perform well. However, the estimators do a poor job recovering the true treatment effect when measures of individual heterogeneity are unavailable. Copyright © 2010 John Wiley & Sons, Ltd.     

Statistical Inference under Symmetry

We explore the consequences of adjoining a symmetry group to a statistical model. Group actions are first induced on the sample space, and then on the parameter space. It is argued that the right invariant measure induced by the group on the parameter space is a natural non-informative prior for the parameters of the model. The permissible sub-parameters are introduced, i.e., the subparameters upon which group actions can be defined. Equivariant estimators are similarly defined. Orbits of the group are defined on the sample space and on the parameter space; in particular the group action is called transitive when there is only one orbit. Credibility sets and confidence sets are shown (under right invariant prior and assuming transitivity on the parameter space) to be equal when defined by permissible sub-parameters and constructed from equivariant estimators. The effect of different choices of transformation group is illustrated by examples, and properties of the orbits on the sample space and on the parameter space are discussed. It is argued that model reduction should be constrained to one or several orbits of the group. Using this and other natural criteria and concepts, among them concepts related to design of experiments under symmetry, leads to links towards chemometrical prediction methods and towards the foundation of quantum theory.     

Nonparametric identification and estimation of sample selection models under symmetry

Under a conditional mean restriction Das et al. (2003) considered nonparametric estimation of sample selection models. However, their method can only identify the outcome regression function up to a constant. In this paper we strengthen the conditional mean restriction to a symmetry restriction under which selection biases due to selection on unobservables can be eliminated through proper matching of propensity scores; consequently we are able to identify and obtain consistent estimators for the average treatment effects and the structural regression functions. The results from a simulation study suggest that our estimators perform satisfactorily.     

On Maximum Likelihood Estimation of Dynamic Panel Data Models

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.     

Information criteria for impulse response function matching estimation of DSGE models

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse Response Selection Criterion (VIRSC). The criterion is especially useful for mis-specified models. Second, we propose a criterion to select the impulse responses that are most informative about DSGE model parameters: the Relevant Impulse Response Selection Criterion (RIRSC). These criteria can be used in combination to select the subset of valid impulse response functions with minimal dimension that yields asymptotically efficient estimators. The criteria are general enough to apply to impulse responses estimated by VARs, local projections, and simulation methods. We show that the use of our criteria significantly affects estimates and inference about key parameters of two well-known new Keynesian DSGE models. Monte Carlo evidence indicates that the criteria yield gains in terms of finite sample bias as well as offering tests statistics whose behavior is better approximated by the first order asymptotic theory. Thus, our criteria improve existing methods used to implement IRFMEs.     

Expected Precision of Estimation and Probability of Ruling Out a Hypothesis Based on a Confidence Interval

Interval estimation is an important objective of most experimental and observational studies. Knowing at the design stage of the study how wide the confidence interval (CI) is expected to be and where its limits are expected to fall can be very informative. Asymptotic distribution of the confidence limits can also be used to answer complex questions of power analysis by computing power as probability that a CI will exclude a given parameter value. The CI‐based approach to power and methods of calculating the expected size and location of asymptotic CIs as a measure of expected precision of estimation are reviewed in the present paper. The theory is illustrated with commonly used estimators, including unadjusted risk differences, odds ratios and rate ratios, as well as more complex estimators based on multivariable linear, logistic and Cox regression models. It is noted that in applications with the non‐linear models, some care must be exercised when selecting the appropriate variance expression. In particular, the well‐known ‘short‐cut’ variance formula for the Cox model can be very inaccurate under unequal allocation of subjects to comparison groups. A more accurate expression is derived analytically and validated in simulations. Applications with ‘exact’ CIs are also considered.     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.     

Design‐based Estimators Calibrated on Estimated Totals from Multiple Surveys

The use of auxiliary variables to improve the efficiency of estimators is a well‐known strategy in survey sampling. Typically, the auxiliary variables used are the totals of appropriate measurement that are exactly known from registers or administrative sources. Increasingly, however, these totals are estimated from surveys and are then used to calibrate estimators and improve their efficiency. We consider different types of survey structures and develop design‐based estimators that are calibrated on known as well as estimated totals of auxiliary variables. The optimality properties of these estimators are studied. These estimators can be viewed as extensions of the Montanari generalised regression estimator adapted to the more complex situations. The paper studies interesting special cases to develop insights and guidelines to properly manage the survey‐estimated auxiliary totals.     

Matching and semi-parametric IV estimation, a distance-based measure of migration, and the wages of young men

Our paper estimates the effect of US internal migration on wage growth for young men between their first and second job. Our analysis of migration extends previous research by: (i) exploiting the distance-based measures of migration in the National Longitudinal Surveys of Youth 1979 (NLSY79); (ii) allowing the effect of migration to differ by schooling level and (iii) using propensity score matching to estimate the average treatment effect on the treated (ATET) for movers and (iv) using local average treatment effect (LATE) estimators with covariates to estimate the average treatment effect (ATE) and ATET for compliers.We believe the Conditional Independence Assumption (CIA) is reasonable for our matching estimators since the NLSY79 provides a relatively rich array of variables on which to match. Our matching methods are based on local linear, local cubic, and local linear ridge regressions. Local linear and local ridge regression matching produce relatively similar point estimates and standard errors, while local cubic regression matching badly over-fits the data and provides very noisy estimates.We use the bootstrap to calculate standard errors. Since the validity of the bootstrap has not been investigated for the matching estimators we use, and has been shown to be invalid for nearest neighbor matching estimators, we conduct a Monte Carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching. The data generating processes in our Monte Carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values. The estimated standard errors from the bootstrap are very close to those from the Monte Carlo experiments, which lends support to our using the bootstrap to calculate standard errors in our setting.From the matching estimators we find a significant positive effect of migration on the wage growth of college graduates, and a marginally significant negative effect for high school dropouts. We do not find any significant effects for other educational groups or for the overall sample. Our results are generally robust to changes in the model specification and changes in our distance-based measure of migration. We find that better data matters; if we use a measure of migration based on moving across county lines, we overstate the number of moves, while if we use a measure based on moving across state lines, we understate the number of moves. Further, using either the county or state measures leads to much less precise estimates.We also consider semi-parametric LATE estimators with covariates (Frölich 2007), using two sets of instrumental variables. We precisely estimate the proportion of compliers in our data, but because we have a small number of compliers, we cannot obtain precise LATE estimates.     

Combining Matching and Nonparametric Instrumental Variable Estimation: Theory and An Application to the Evaluation of Active Labour Market Policies

We show how instrumental variable and matching estimators can be combined in order to identify a broader array of treatment effects. Instrumental variable (IV) estimators are known to estimate effects only for the compliers, representing a subset of the entire population. By combining IV with matching, we can estimate the treatment effects for the always‐ and never‐takers as well. Since in many cases these groups are the (endogenous) outcome of some assignment process, such estimates also help in judging the implications of such a selection process. In our application to the effects of participation in active labour market programmes in Switzerland, we find large and lasting positive employment effects for the compliers, whereas the effects for the always‐ and never‐participants are small. In addition, the compliers have worse employment outcomes without treatment than those who participate in the programme with or without the intervention under investigation. This suggests that the earlier assignment policy of the caseworkers was inefficient in that the always‐participants were neither those unemployed who would experience the highest expected treatment effects nor those unemployed who had the largest need for assistance. Copyright © 2014 John Wiley & Sons, Ltd.     

Imputation methods of missing data for estimating the population mean using simple random sampling with known correlation coefficient

This paper considers three ratio estimators of the population mean using known correlation coefficient between the study and auxiliary variables in simple random sample when some sample observations are missing. The suggested estimators are compared with the estimators of Singh and Horn (Metrika 51:267–276, 2000), Singh and Deo (Stat Pap 44:555–579, 2003) and Kadilar and Cingi (Commun Stat Theory Methods 37:2226–2236, 2008). They are compared with other imputation estimators based on the mean or a ratio. It is found that the suggested estimators are approximately unbiased for the population mean. Also, it turns out that the suggested estimators perform well when compared with the other estimators considered in this study.     

SELECTION BIAS CORRECTIONS BASED ON THE MULTINOMIAL LOGIT MODEL: MONTE CARLO COMPARISONS

Abstract.  This survey presents the set of methods available in the literature on selection bias correction, when selection is specified as a multinomial logit model. It contrasts the underlying assumptions made by the different methods and shows results from a set of Monte Carlo experiments. We find that, in many cases, the approach initiated by Dubin and MacFadden (1984) as well as the semi-parametric alternative recently proposed by Dahl (2002) are to be preferred to the most commonly used Lee (1983) method. We also find that a restriction imposed in the original Dubin and MacFadden paper can be waived to achieve more robust estimators. Monte Carlo experiments also show that selection bias correction based on the multinomial logit model can provide fairly good correction for the outcome equation, even when the IIA hypothesis is violated.     

Dynamic Panel Data Models With Irregular Spacing: With an Application to Early Childhood Development

With the increased availability of longitudinal data, dynamic panel data models have become commonplace. Moreover, the properties of various estimators of such models are well known. However, we show that these estimators break down when the data are irregularly spaced along the time dimension. Unfortunately, this is an increasingly frequent occurrence as many longitudinal surveys are collected at non‐uniform intervals and no solution is currently available when time‐varying covariates are included in the model. In this paper, we propose two new estimators for dynamic panel data models when data are irregularly spaced and compare their finite‐sample performance to the näive application of existing estimators. We illustrate the practical importance of this issue in an application concerning early childhood development. Copyright © 2016 John Wiley & Sons, Ltd.     

出口贸易是否促进了我国劳动生产率的持续增长——基于工业企业微观数据的实证检验

本文采用2000～2006年持续经营的工业企业数据实证分析了我国企业的出口行为对其劳动生产率增长率的作用。倍差法的Kernel倾向评分匹配估计结果表明,我国企业的出口行为能在出口后的1年或2年内将显著提高其劳动生产率增长率,但此后该影响作用并不显著,出口贸易未能促进我国劳动生产率的持续增长。进一步的实证分析发现,企业出口活动的"干中学"效应与出口加工贸易度和技术水平均密切相关,而通过出口贸易而产生的"扩张陷阱"只存在于出口加工贸易度高的(中)低技术行业以及金属制品业中。     

On the estimation of location parameters in the multivariate one sample and two sample problems

Summary In this paper we consider the problem of estimating the vectors of location parameters in the multivariate one sample and two sample problems. These estimators are obtained through the use of the multivariate rank order statistics such as theWilcoxon or the normal scores statistic considered by the authors inPuri, Sen [1966] andSen, Puri [1967] for the corresponding testing problems. The distribution of these estimators is shown to be symmetric with respect to the parameters being estimated. These estimators are translation invariant, robust and asymptotically normal. Their asymptotic relative efficiencies with respect to the estimators based on the vector of means and medians are discussed by applying the criterion ofWilks generalized variance [Anderson, p. 166]. In particular, it is shown that the estimators based on the multivariate normal scores statistics are asymptotically as efficient as the ones based on the method of least squares when the parent distributions are normal. Research sponsored by National Science Foundation Grant No. GP-12462, and by Research Grant, GM-12868 from the N.I.H., Public Health Service.     

GMM estimation of social interaction models with centrality

This paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous, contextual, correlated, and group fixed effects. When the network structure in a group is captured by a graph in which the degrees of nodes are not all equal, the different positions of group members as measured by the Bonacich (1987) centrality provide additional information for identification and estimation. In this case, the Bonacich centrality measure for each group can be used as an instrument for the endogenous social effect, but the number of such instruments grows with the number of groups. We consider the 2SLS and GMM estimation for the model. The proposed estimators are asymptotically efficient, respectively, within the class of IV estimators and the class of GMM estimators based on linear and quadratic moments, when the sample size grows fast enough relative to the number of instruments.     

When do stable roommate matchings exist? A review

We compare different preference restrictions that ensure the existence of a stable roommate matching. Some of these restrictions are generalized to allow for indifferences as well as incomplete preference lists, in the sense that an agent may prefer remaining single to matching with some agents. We also introduce a new type of cycles and in greater detail investigate the domain of preferences that have no such cycles. In particular, we show how the absence of these cycles relates to the “symmetric utilities hypothesis” by Rodrigues-Neto (J Econ Theory 135:545–550, 2007) when applied to roommate problems with weak preferences.     

固定交互效应面板截取模型的ECM算法

交互效应面板数据模型在社会经济问题的实证分析中具有很强的适用性,但现有研究主要集中于线性面板模型。本文将交互效应引入非线性的面板截取模型,并基于ECM算法,建立了有效估计量和识别程序。基于不同因子类型的仿真实验结果显示,ECM算法可以很好地识别面板截取样本中的非观测因子。ECM估计量具有良好的有限样本性质,与其他估计量相比具有更小的偏误和更快的收敛速度。尤其是当共同因子为低频平滑因子时,其表现最为理想。     

Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables

The aim of this paper is to convey to a wider audience of applied statisticians that nonparametric (matching) estimation methods can be a very convenient tool to overcome problems with endogenous control variables. In empirical research one is often interested in the causal effect of a variable X on some outcome variable Y . With observational data, i.e. in the absence of random assignment, the correlation between X and Y generally does not reflect the treatment effect but is confounded by differences in observed and unobserved characteristics. Econometricians often use two different approaches to overcome this problem of confounding by other characteristics. First, controlling for observed characteristics, often referred to as selection on observables, or instrumental variables regression, usually with additional control variables. Instrumental variables estimation is probably the most important estimator in applied work. In many applications, these control variables are themselves correlated with the error term, making ordinary least squares and two-stage least squares inconsistent. The usual solution is to search for additional instrumental variables for these endogenous control variables, which is often difficult. We argue that nonparametric methods help to reduce the number of instruments needed. In fact, we need only one instrument whereas with conventional approaches one may need two, three or even more instruments for consistency. Nonparametric matching estimators permit     consistent estimation without the need for (additional) instrumental variables and permit arbitrary functional forms and treatment effect heterogeneity.     

A semiparametric model for binary response and continuous outcomes under index heteroscedasticity

This paper formulates a likelihood‐based estimator for a double‐index, semiparametric binary response equation. A novel feature of this estimator is that it is based on density estimation under local smoothing. While the proofs differ from those based on alternative density estimators, the finite sample performance of the estimator is significantly improved. As binary responses often appear as endogenous regressors in continuous outcome equations, we also develop an optimal instrumental variables estimator in this context. For this purpose, we specialize the double‐index model for binary response to one with heteroscedasticity that depends on an index different from that underlying the ‘mean response’. We show that such (multiplicative) heteroscedasticity, whose form is not parametrically specified, effectively induces exclusion restrictions on the outcomes equation. The estimator developed exploits such identifying information. We provide simulation evidence on the favorable performance of the estimators and illustrate their use through an empirical application on the determinants, and affect, of attendance at a government‐financed school. Copyright © 2009 John Wiley & Sons, Ltd.