Estimating Derivatives in Nonseparable Models With Limited Dependent Variables

We present a simple way to estimate the effects of changes in a vector of observable variables X on a limited dependent variable Y when Y is a general nonseparable function of X and unobservables, and X is independent of the unobservables. We treat models in which Y is censored from above, below, or both. The basic idea is to first estimate the derivative of the conditional mean of Y given X at x with respect to x on the uncensored sample without correcting for the effect of x on the censored population. We then correct the derivative for the effects of the selection bias. We discuss nonparametric and semiparametric estimators for the derivative. We also discuss the cases of discrete regressors and of endogenous regressors in both cross section and panel data contexts.     

The Time Series and Cross‐Section Asymptotics of Dynamic Panel Data Estimators

In this paper we derive the asymptotic properties of within groups (WG), GMM, and LIML estimators for an autoregressive model with random effects when both T and N tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When T/N→ 0 the fixed T results for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. When T/N tends to a positive constant, the WG, GMM, and LIML estimators exhibit negative asymptotic biases of order 1/T, 1/N, and 1/(2N−T), respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent as T/N→c>0, despite being consistent for fixed T. Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when both T and N tend to infinity.     

Inference in Censored Models with Endogenous Regressors

This paper analyzes the linear regression model y = xβ+ε with a conditional median assumption med (ε| z) = 0, where z is a vector of exogenous instrument random variables. We study inference on the parameter β when y is censored and x is endogenous. We treat the censored model as a model with interval observation on an outcome, thus obtaining an incomplete model with inequality restrictions on conditional median regressions. We analyze the identified features of the model and provide sufficient conditions for point identification of the parameter β. We use a minimum distance estimator to consistently estimate the identified features of the model. We show that under point identification conditions and additional regularity conditions, the estimator based on inequality restrictions is normal and we derive its asymptotic variance. One can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring. A Monte Carlo analysis illustrates our estimator in the censored and the uncensored case.     

Panel Data Discrete Choice Models with Lagged Dependent Variables

In this paper, we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables, lags of the endogenous dependent variable as well as unobservable individual‐specific effects. For the binary logit model with the dependent variable lagged only once, Chamberlain (1993) gave conditions under which the model is not identified. We present a stronger set of conditions under which the parameters of the model are identified. The identification result suggests estimators of the model, and we show that these are consistent and asymptotically normal, although their rate of convergence is slower than the inverse of the square root of the sample size. We also consider identification in the semiparametric case where the logit assumption is relaxed. We propose an estimator in the spirit of the conditional maximum score estimator (Manski (1987)) and we show that it is consistent. In addition, we discuss an extension of the identification result to multinomial discrete choice models, and to the case where the dependent variable is lagged twice. Finally, we present some Monte Carlo evidence on the small sample performance of the proposed estimators for the binary response model.     

Average and Quantile Effects in Nonseparable Panel Models

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time‐homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial‐identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed‐effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial‐identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete‐choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.     

Bounds on Parameters in Panel Dynamic Discrete Choice Models

Identification of dynamic nonlinear panel data models is an important and delicate problem in econometrics. In this paper we provide insights that shed light on the identification of parameters of some commonly used models. Using these insights, we are able to show through simple calculations that point identification often fails in these models. On the other hand, these calculations also suggest that the model restricts the parameter to lie in a region that is very small in many cases, and the failure of point identification may, therefore, be of little practical importance in those cases. Although the emphasis is on identification, our techniques are constructive in that they can easily form the basis for consistent estimates of the identified sets.     

Linear Regression Limit Theory for Nonstationary Panel Data

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section (n) and time series (T) observations. The limit theory allows for both sequential limits, wherein T→∞ followed by n→∞, and joint limits where T, n→∞ simultaneously; and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence of long-run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parameterized in terms of the matrix regression coefficient of the long-run average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.     

Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices

In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for it. This paper studies nonparametric identifiability of type probabilities and type‐specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under different assumptions on the Markov property, stationarity, and type‐invariance in the transition process. Three elements emerge as the important determinants of identification: the time‐dimension of panel data, the number of values the covariates can take, and the heterogeneity of the response of different types to changes in the covariates. For example, in a simple case where the transition function is type‐invariant, a time‐dimension of T = 3 is sufficient for identification, provided that the number of values the covariates can take is no smaller than the number of types and that the changes in the covariates induce sufficiently heterogeneous variations in the choice probabilities across types. Identification is achieved even when state dependence is present if a model is stationary first‐order Markovian and the panel has a moderate time‐dimension (T 6).     

Instrumental Variable Models for Discrete Outcomes

Single equation instrumental variable models for discrete outcomes are shown to be set identifying, not point identifying, for the structural functions that deliver the values of the discrete outcome. Bounds on identified sets are derived for a general nonparametric model and sharp set identification is demonstrated in the binary outcome case. Point identification is typically not achieved by imposing parametric restrictions. The extent of an identified set varies with the strength and support of instruments, and typically shrinks as the support of a discrete outcome grows. The paper extends the analysis of structural quantile functions with endogenous arguments to cases in which there are discrete outcomes.     

Wavelet‐Based Testing for Serial Correlation of Unknown Form in Panel Models

Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet‐based tests for serial correlation of unknown form in the estimated residuals of a panel regression model, where error components can be one‐way or two‐way, individual and time effects can be fixed or random, and regressors may contain lagged dependent variables or deterministic/stochastic trending variables. Our tests are applicable to unbalanced heterogenous panel data. They have a convenient null limit N(0,1) distribution. No formulation of an alternative model is required, and our tests are consistent against serial correlation of unknown form even in the presence of substantial inhomogeneity in serial correlation across individuals. This is in contrast to existing serial correlation tests for panel models, which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative, and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero. We propose and justify a data‐driven method to choose the smoothing parameter—the finest scale in wavelet spectral estimation, making the tests completely operational in practice. The data‐driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative, ensuring the consistency of our tests. Simulation shows that our tests perform well in small and finite samples relative to some existing tests.     

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given.     

Binary Response Models for Panel Data: Identification and Information

This paper considers a panel data model for predicting a binary outcome. The conditional probability of a positive response is obtained by evaluating a given distribution function (F) at a linear combination of the predictor variables. One of the predictor variables is unobserved. It is a random effect that varies across individuals but is constant over time. The semiparametric aspect is that the conditional distribution of the random effect, given the predictor variables, is unrestricted. This paper has two results. If the support of the observed predictor variables is bounded, then identification is possible only in the logistic case. Even if the support is unbounded, so that (from Manski (1987)) identification holds quite generally, the information bound is zero unless F is logistic. Hence consistent estimation at the standard pn rate is possible only in the logistic case.     

Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

This paper extends the conditional logit approach (Rasch, Andersen, Chamberlain) used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two‐period two‐state model, necessary and sufficient conditions on the joint distribution function of the individual‐and‐period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. By extending a result of Chamberlain, it is shown that root‐n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds. In applied work, the estimation method amounts to quasi‐differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross‐section model. Semiparametric approaches can then be readily applied.     

GMM Estimation of Autoregressive Roots Near Unity with Panel Data

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak instruments. The two moment conditions in the GMM approach are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is shown that the moment condition under GLS detrending corresponds to taking the projected score on the Bhattacharya basis, linking the approach to recent work on projected score methods for models with infinite numbers of nuisance parameters (Waterman and Lindsay (1998)). Assuming that the localizing parameter takes a nonpositive value, we establish consistency of the GMM estimator and find its limiting distribution. A notable new finding is that the GMM estimator has convergence rate , slower than , when the true localizing parameter is zero (i.e., when there is a panel unit root) and the deterministic trends in the panel are linear. These results, which rely on boundary point asymptotics, point to the continued difficulty of distinguishing unit roots from local alternatives, even when there is an infinity of additional data.     

基于面板数据模型的能耗与固定资产投资关系的实证研究

首先,对我国固定资产投资与能源消费之间的关系进行了机理分析,认为大规模的固定资产投资活动是造成能耗快速增长的主要原因,并且固定资产投资与能源消费之间存在一种循环关系.然后,采用面板数据模型对我国8个主要行业的固定资产投资与能源消费关系进行了实证研究.研究结果表明,固定资产投资是我国能耗增长的格兰杰原因,固定资产投资与能耗增长之间存在显著的正相关性.最后,对遏制我国能耗高速增长给出了相应的政策建议.     

科技财政与自主创新:基于中国省级DPD模型的实证研究

文章通过知识生产函数,利用中国省级动态面板数据模型,重点实证考察科技财政对自主创新的影响。结果发现:(1)科技财政对代表技术创新的发明专利产出有显著的正向影响,而对代表技术模仿的实用新型和外观设计无显著影响;(2)在发明这种技术创新活动中,非政府科技资金的产出弹性高于科技财政资金的产出弹性;(3)在发明专利这种技术创新活动中,科技财政资金与非政府科技资金有一定显著的替代关系,但从总体效果看,加上政府科技财政支持的产出弹性高于仅只有非政府科技资金的产出弹性;(4)非政府科技资金在发明活动中的产出弹性低于其在实用新型和外观设计的技术模仿活动中的产出弹性;(5)人力资本的产出弹性高于科技财政资金和非政府科技资金的产出弹性;(6)从短期看,代表技术创新的发明过程呈现报酬递增特征,而代表技术模仿的实用新型和外观设计活动呈现明显的报酬递减特征。但从长期看,则均呈现出明显的报酬递增性质,且发明活动具有最突出的报酬递增特征。     

金融发展与经济增长关系的理论与实证研究——基于中国省际面板数据的协整分析

本文推导了存在金融中介的情况下稳态经济增长的路径,阐述了金融发展对经济增长正向推动作用的理论依据。根据中国省际面板数据,采用面板单位根、面板协整和向量误差修正模型实证分析了金融对于中国经济增长的影响。研究表明,金融发展程度是经济增长的Granger原因,经济增长、固定资产投资、劳动力投入和金融发展之间存在显著的协整关系。从完全修正普通最小二乘回归和向量误差修正模型的结果来看,金融发展对经济增长具有明显的正向推动作用。     

西部城市人均经济增长的面板数据测度及理论分析

西部城市经济处于快速稳定增长的阶段。本文运用人均财政收入、人均GDP和相应的人均指数增长率测度城市经济发展水平和增长趋势。人均财政收入和人均GDP作为经济发展水平的两个重要参数。同时,论文采用人均财政收入作为经济发展水平的排序依据,是因为财政收入与GDP直接相关,且前者有更强的约束性和可靠性。在论文中,论文运用1998-2007年10年的人口、地方财政收入、GDP数据,西部48个城市的人均地方财政收入、人均GDP分3组进行面板数据测度,测度了人均GDP对人均地方财政收入的贡献率,人均地方财政收入年增长率和人均GDP年增长率。测度结果表明,人均财政收入年增长率、人均GDP对人均财政收入的贡献率是城市经济发展的良性指标。测度结果表明,西部城市经济的规模效应表现为两种,一种是超大城市规模公共服务的人口规模效应,一种是中等城市的优势主导产业的产业规模效应。同时,西部城市经济发展水平差距很大。低水平发展的城市宜调整发展战略,并得到相关的政策支持。     

Simulation of Longitudinal Exposure Data with Variance‐Covariance Structures Based on Mixed Models

Longitudinal data are important in exposure and risk assessments, especially for pollutants with long half‐lives in the human body and where chronic exposures to current levels in the environment raise concerns for human health effects. It is usually difficult and expensive to obtain large longitudinal data sets for human exposure studies. This article reports a new simulation method to generate longitudinal data with flexible numbers of subjects and days. Mixed models are used to describe the variance‐covariance structures of input longitudinal data. Based on estimated model parameters, simulation data are generated with similar statistical characteristics compared to the input data. Three criteria are used to determine similarity: the overall mean and standard deviation, the variance components percentages, and the average autocorrelation coefficients. Upon the discussion of mixed models, a simulation procedure is produced and numerical results are shown through one human exposure study. Simulations of three sets of exposure data successfully meet above criteria. In particular, simulations can always retain correct weights of inter‐ and intrasubject variances as in the input data. Autocorrelations are also well followed. Compared with other simulation algorithms, this new method stores more information about the input overall distribution so as to satisfy the above multiple criteria for statistical targets. In addition, it generates values from numerous data sources and simulates continuous observed variables better than current data methods. This new method also provides flexible options in both modeling and simulation procedures according to various user requirements.     

基于专利数据测度我国技术能力的计量方法与模型研究

综述了应用专利数据测度技术能力的理论和方法的演化,并分析了专利数据计量技术能力的优缺点。通过引入专利数据,构建了专利数据计量我国技术能力的模型,并且进行了实证分析。利用单位检验、协整检验和效度检验等方法,建立误差修正模型,分析专利数据与技术能力的关系。结果表明,我国专利数据具有可靠的计量技术能力的功能,专利数据测度技术能力不仅存在长期的稳定性,而且短期内具有很好的均衡修正作用。