Effect of FDI and Time on Catching Up: New Insights from a Conditional Nonparametric Frontier Analysis

We use an appropriate nonparametric two‐step approach on conditional efficiencies to investigate how foreign direct investment (FDI) and time affect the process of catching up. By using a dataset of 44 countries over 1970–2007, we explore the channels under which FDI fosters productivity by disentangling the impact of this factor on the production process and its components: impact on the attainable production set (input–output space) and the impact on the distribution of efficiencies. We extend existing methodological tools—conditional nonparametric efficiency measures—to examine these interrelationships. We emphasize the usefulness of smoothing over time to better analyze the potential dynamic influence of FDI on efficiency. We find that both FDI and time play an important role as influencing efficiency distribution and affecting, to a smaller extend, the production set. This effect of FDI does not seem to vary much over time. By the second‐stage nonparametric regression of the conditional efficiencies over FDI and time we identify clearly the effect of time and FDI on conditional efficiency and we determine idiosyncratic efficiency, which represents the‘Solow residual’, measured by looking to the unexplained part of the conditional efficiencies. Copyright © 2014 John Wiley & Sons, Ltd.     

Semiparametric analysis of clustered survival data under nonparametric frailty

In this article a novel approach to analyze clustered survival data that are subject to extravariation encountered through clustering of survival times is proposed. This is accomplished by extending the Cox proportional hazard model to a frailty model where the cluster-specific shared frailty is modeled nonparametrically. We assume a nonparametric Dirichlet process for the distribution of frailty. In such a semiparametric setup, we propose a hybrid method to draw model-based inferences. In the framework of the proposed hybrid method, the estimation of parameters is performed by implementing Monte Carlo expected conditional maximization algorithm. A simulation study is conducted to study the efficiency of our methodology. The proposed methodology is, thereafter, illustrated by a real-life data on recurrence time to infections in kidney patient.     

Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In the literature two main approaches have been developed: one-stage approaches and two-stage approaches. Daraio and Simar (2005, J Prod Anal 24(1):93–121) propose a fully nonparametric methodology based on conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. However, convexity has always been assumed in mainstream production theory and general equilibrium. In addition, in many empirical applications, the convexity assumption can be reasonable and sometimes natural. Lead by these considerations, in this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models for convex and nonconvex technologies. Extending earlier contributions by Daraio and Simar (2005, J Prod Anal 24(1):93–121) as well as Cazals et al. (2002, J Econometrics 106:1–25), we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is proposed too. These various measures of efficiency provide also indicators of convexity which we illustrate using simulated and real data. Cinzia Daraio received Research support from the Italian Ministry of Education Research on Innovation Systems Project (iRis) “The reorganization of the public system of research for the technological transfer: governance, tools and interventions” and from the Italian Ministry of Educational Research Project (MIUR 40% 2004) “System spillovers on the competitiveness of Italian economy: quantitative analysis for sectoral policies” which are acknowledged. Léopold Simar received Research support from the “Interuniversity Attraction Pole”, Phase V (No. P5/24) from the Belgian Government (Belgian Science Policy) is acknowledged.     

Nonparametric efficiency analysis: A multivariate conditional quantile approach

This paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup (multiple inputs and multiple outputs). It introduces α-quantile efficiency scores. A nonparametric estimator is proposed achieving strong consistency and asymptotic normality. Then if α increases to one as a function of the sample size we recover the properties of the FDH estimator. But our estimator is more robust to the perturbations in data, since it attains a finite gross-error sensitivity. Environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed. Numerical examples illustrate the usefulness of the approach.     

Incorporating the Operating Environment Into a Nonparametric Measure of Technical Efficiency

The ability of a production unit to transform inputs into outputs is influenced by its technical efficiency and external operating environment. This paper introduces a nonparametric, linear programming, frontier procedure for obtaining a measure of managerial efficiency that controls for exogenous features of the operating environment. The approach also provides statistical tests of the effects of external conditions on the efficient use of each individual input (for an input oriented model) or for each individual output (for an output oriented model). The procedure is illustrated for a sample of nursing homes.     

A general framework for frontier estimation with panel data

The main objective of the paper is to present a general framework for estimating production frontier models with panel data. A sample of firms i = 1, ..., N is observed on several time periods t = 1, ... T. In this framework, nonparametric stochastic models for the frontier will be analyzed. The usual parametric formulations of the literature are viewed as particular cases and the convergence of the obtained estimators in this general framework are investigated. Special attention is devoted to the role of N and of T on the speeds of convergence of the obtained estimators. First, a very general model is investigated. In this model almost no restriction is imposed on the structure of the model or of the inefficiencies. This model is estimable from a nonparametric point of view but needs large values of T and of N to obtain reliable estimates of the individual production functions and estimates of the frontier function. Then more specific nonparametric firm effect models are presented. In these cases, only NT must be large to estimate the common production function; but again both large N and T are needed for estimating individual efficiencies and for estimating the frontier. The methods are illustrated through a numerical example with real data.     

A profit function approach to measuring productivity growth: The case of U.S. manufacturing

This article proposes a method of estimating productivity growth using an estimated profit function. The approach has the advantage of incorporating endogenous changes in profit-maximizing output levels that would result from productivity changes. As with the cost function, it can be easily adapted to accomodate the presence of quasi-fixed factors. The article first develops the methodology and shows the equivalence between the proposed measure and other measures of productivity based on cost or production functions. An empirical application to the measurement of productivity changes in the U.S. manufacturing industry is presented next. The profit-function measure is compared to a nonparametric measure based on the same data and to the results of other studies of U.S. manufacturing.The refereeing process of this paper was handled through J. deMelo.     

An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models

It is shown how to implement an EM algorithm for maximum likelihood estimation of hierarchical nonlinear models for data sets consisting of more than two levels of nesting. This upward–downward algorithm makes use of the conditional independence assumptions implied by the hierarchical model. It cannot only be used for the estimation of models with a parametric specification of the random effects, but also to extend the two-level nonparametric approach – sometimes referred to as latent class regression – to three or more levels. The proposed approach is illustrated with an empirical application.     

Separating environmental efficiency into production and abatement efficiency: a nonparametric model with application to US power plants

In this paper we present a new approach to evaluate the environmental efficiency of decision making units. We propose a model that describes a two-stage process consisting of a production and an end-of-pipe abatement stage with the environmental efficiency being determined by the efficiency of both stages. Taking the dependencies between the two stages into account, we show how nonparametric methods can be used to measure environmental efficiency and to decompose it into production and abatement efficiency. For an empirical illustration we apply our model to an analysis of US power plants.     

Count data stochastic frontier models, with an application to the patents–R&D relationship

This article introduces a new count data stochastic frontier model that researchers can use in order to study efficiency in production when the output variable is a count (so that its conditional distribution is discrete). We discuss parametric and nonparametric estimation of the model, and a Monte Carlo study is presented in order to evaluate the merits and applicability of the new model in small samples. Finally, we use the methods discussed in this article to estimate a production function for the number of patents awarded to a firm given expenditure on R&D.     

Introduction to APPC-2018, a Special Issue of the Journal of Productivity Analysis, “Novel Applications of Efficiency and Productivity Analyses in the Asia-Pacific Region”

In this study, an appropriate nonparametric two-step approach to conditional efficiencies is used to investigate how size and time affect the performance of companies. Using a dataset of Italian manufacturing firms over the period 2006–2015, we explore the effect of size on the attainable production set (input-output space) and on the efficiency distribution, without making any a priori assumptions on the role of size on efficiency. Main findings suggest that size positively affects the efficiency of companies. By exploring the idiosyncratic efficiency, an additional empirical result from the conditional efficiency approach shows that the economic disparities between North, Centre and South of Italy not only limit the foreign investment but also seem to penalize the productivity of Italian-owned companies.

     

Nonparametric stochastic frontiers: A local maximum likelihood approach

This paper proposes a new approach to handle nonparametric stochastic frontier (SF) models. It is based on local maximum likelihood techniques. The model is presented as encompassing some anchorage parametric model in a nonparametric way. First, we derive asymptotic properties of the estimator for the general case (local linear approximations). Then the results are tailored to a SF model where the convoluted error term (efficiency plus noise) is the sum of a half normal and a normal random variable. The parametric anchorage model is a linear production function with a homoscedastic error term. The local approximation is linear for both the production function and the parameters of the error terms. The performance of our estimator is then established in finite samples using simulated data sets as well as with a cross-sectional data on US commercial banks. The methods appear to be robust, numerically stable and particularly useful for investigating a production process and the derived efficiency scores.     

On the Technically Efficient Organization of an Industry: A Study of U.S. Airlines

In nonparametric analysis of production efficiency, the focus of attention is typically on the individual firm. In this article, we evaluate efficiency in resource utilization at the industry level. We propose an integer programming model to measure the extent of input saving possible if the observed output level of the industry is allocated to an optimal number of identical firms. This approach is applied to data for U.S. airlines covering the period 1970–84. Our results confirm that there were too few airlines prior to deregulation and suggest that there were too many firms during the early years of the post-deregulation era.     

Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints

The field of productive efficiency analysis is currently divided between two main paradigms: the deterministic, nonparametric Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). This paper examines an encompassing semiparametric frontier model that combines the DEA-type nonparametric frontier, which satisfies monotonicity and concavity, with the SFA-style stochastic homoskedastic composite error term. To estimate this model, a new two-stage method is proposed, referred to as Stochastic Non-smooth Envelopment of Data (StoNED). The first stage of the StoNED method applies convex nonparametric least squares (CNLS) to estimate the shape of the frontier without any assumptions about its functional form or smoothness. In the second stage, the conditional expectations of inefficiency are estimated based on the CNLS residuals, using the method of moments or pseudolikelihood techniques. Although in a cross-sectional setting distinguishing inefficiency from noise in general requires distributional assumptions, we also show how these can be relaxed in our approach if panel data are available. Performance of the StoNED method is examined using Monte Carlo simulations.     

Model‐Assisted Regression Estimators for Longitudinal Data with Nonignorable Dropout

Estimation with longitudinal Y having nonignorable dropout is considered when the joint distribution of Y and covariate X is nonparametric and the dropout propensity conditional on (Y,X) is parametric. We apply the generalised method of moments to estimate the parameters in the nonignorable dropout propensity based on estimating equations constructed using an instrument Z, which is part of X related to Y but unrelated to the dropout propensity conditioned on Y and other covariates. Population means and other parameters in the nonparametric distribution of Y can be estimated based on inverse propensity weighting with estimated propensity. To improve efficiency, we derive a model‐assisted regression estimator making use of information provided by the covariates and previously observed Y‐values in the longitudinal setting. The model‐assisted regression estimator is protected from model misspecification and is asymptotically normal and more efficient when the working models are correct and some other conditions are satisfied. The finite‐sample performance of the estimators is studied through simulation, and an application to the HIV‐CD4 data set is also presented as illustration.     

Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative

This paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables. The paper presents a test of the hypothesis that g belongs to a finite-dimensional parametric family against a nonparametric alternative. The test is not subject to the ill-posed inverse problem of nonparametric instrumental variable estimation. Under mild conditions, the test is consistent against any alternative model. In large samples, its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is proportional to n^−1/2, where n is the sample size. Monte Carlo simulations illustrate the finite-sample performance of the test.     

Nonparametric estimation of conditional VaR and expected shortfall

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya–Watson estimators. Moreover, an ad hoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical study is carried out to illustrate the finite sample performance of the proposed estimators.     

One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient,root-<Emphasis Type="Italic">n</Emphasis> consistent StoNEZD method

Understanding the effects of operational conditions and practices on productive efficiency can provide valuable economic and managerial insights. The conventional approach is to use a two-stage method where the efficiency estimates are regressed on contextual variables representing the operational conditions. The main problem of the two-stage approach is that it ignores the correlations between inputs and contextual variables. To address this shortcoming, we build on the recently developed regression interpretation of data envelopment analysis (DEA) to develop a new one-stage semi-nonparametric estimator that combines the nonparametric DEA-style frontier with a regression model of the contextual variables. The new method is referred to as stochastic semi-nonparametric envelopment of z variables data (StoNEZD). The StoNEZD estimator for the contextual variables is shown to be statistically consistent under less restrictive assumptions than those required by the two-stage DEA estimator. Further, the StoNEZD estimator is shown to be unbiased, asymptotically efficient, asymptotically normally distributed, and converge at the standard parametric rate of order n ^−1/2. Therefore, the conventional methods of statistical testing and confidence intervals apply for asymptotic inference. Finite sample performance of the proposed estimators is examined through Monte Carlo simulations.     

Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations

This paper examines the technical efficiency of US Federal Reserve check processing offices over 1980–2003. We extend results from Park et al. [Park, B., Simar, L., Weiner, C., 2000. FDH efficiency scores from a stochastic point of view. Econometric Theory 16, 855–877] and Daouia and Simar [Daouia, A., Simar, L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics 140, 375–400] to develop an unconditional, hyperbolic, α-quantile estimator of efficiency. Our new estimator is fully non-parametric and robust with respect to outliers; when used to estimate distance to quantiles lying close to the full frontier, it is strongly consistent and converges at rate root-n, thus avoiding the curse of dimensionality that plagues data envelopment analysis (DEA) estimators. Our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices.     

Stick-breaking autoregressive processes

This paper considers the problem of defining a time-dependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stick-breaking form. The processes with Poisson-Dirichlet and Dirichlet process marginals are investigated in some detail. We develop a general conditional Markov Chain Monte Carlo (MCMC) method for inference in the wide subclass of these models where the parameters of the marginal stick-breaking process are nondecreasing sequences. We derive a generalised Pólya urn scheme type representation of the Dirichlet process construction, which allows us to develop a marginal MCMC method for this case. We apply the proposed methods to financial data to develop a semi-parametric stochastic volatility model with a time-varying nonparametric returns distribution. Finally, we present two examples concerning the analysis of regional GDP and its growth.