Identification Based on Difference‐in‐Differences Approaches with Multiple Treatments

This paper discusses identification based on difference‐in‐differences (DiD) approaches with multiple treatments. It shows that an appropriate adaptation of the common trend assumption underlying the DiD strategy for the comparison of two treatments restricts the possibility of effect heterogeneity for at least one of the treatments. The required assumption of effect homogeneity is likely to be violated because of non‐random assignment to treatment based on both observables and unobservables. However, this paper shows that, under certain conditions, the DiD estimate comparing two treatments identifies a lower bound in absolute values on the average treatment effect on the treated compared to the unobserved non‐treatment state, even if effect homogeneity is violated. This is possible if the treatments have ordered treatment effects, that is, in expectation, the effects of both treatments compared to no treatment have the same sign, and one treatment has a stronger effect than the other treatment on the respective recipients. Such assumptions are plausible if treatments are ordered or vary in intensity.     

Estimating panel data models in the presence of endogeneity and selection

We consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity. Assuming that appropriate instruments are available, we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors. The tests are based on the fixed effects two-stage least squares estimator, thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables. The first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed. The second procedure estimates the model parameters semiparametrically using series estimators. In the proposed testing and correction procedures, the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations. Because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables, they provide a useful alternative to the existing approaches presented in the literature.     

A semiparametric random effects approach to unobserved heterogeneity in count data models of organizational founding

The paper discusses a semiparametric random-effects approach to the problem of unobserved population heterogeneity in organizational research based on models for pooled cross-sectional time series count data. The analytical value of this approach rests in its ability to produce estimates of the structural parameters that do not depend on any specific assumption about the distribution of the heterogeneity components in the population. The practical value of the method proposed is illustrated in an empirical application to processes of organizational founding, and to the relation between density dependence and unobserved heterogeneity in spatially distributed organizational populations. The empirical evidence produced suggests that future studies of organizational founding at the population level will have to account for variation in observed as well as unmeasured (or unobservable) variables.     

Estimating systematic continuous-time trends in recidivism using a non-Gaussian panel data model

We model panel data of crime careers of juveniles from a Dutch Judicial Juvenile Institution. The data are decomposed into a systematic and an individual-specific component, of which the systematic component reflects the general time-varying conditions including the criminological climate. Within a model-based analysis, we treat (1) shared effects of each group with the same systematic conditions, (2) strongly non-Gaussian features of the individual time series, (3) unobserved common systematic conditions, (4) changing recidivism probabilities in continuous time and (5) missing observations. We adopt a non-Gaussian multivariate state-space model that deals with all these issues simultaneously. The parameters of the model are estimated by Monte Carlo maximum likelihood methods. This paper illustrates the methods empirically. We compare continuous time trends and standard discrete-time stochastic trend specifications. We find interesting common time variation in the recidivism behaviour of the juveniles during a period of 13 years, while taking account of significant heterogeneity determined by personality characteristics and initial crime records.     

Can univariate models forecast turning points in seasonal economic time series?

Based on a particular class of recently developed unobserved component models with, time varying parameters, the objectives of this paper are two-fold. On the one hand, we propose an alternative measure of underlying growth based on our estimated trend derivative with no need for any further transformations. Additionally, using the information embedded on the trend derivative, we provide a simple method for improving quantitative point forecasts in the vicinity of turning points. Empirical applications are presented for a set of seasonal monthly economic indicators of the Spanish economy.     

A Social Interactions Model with Endogenous Friendship Formation and Selectivity

This paper analyzes the endogeneity bias problem caused by associations of members within a network when the spatial autoregressive (SAR) model is used to study social interactions. When there are unobserved factors that affect both friendship decisions and economic outcomes, the spatial weight matrix (sociomatrix; adjacency matrix) in the SAR model, which represents the structure of a friendship network, might correlate with the disturbance term of the model, and consequently result in an endogenous selection problem in the outcomes. We consider this problem of selection bias with a modeling approach. In this approach, a statistical network model is adopted to explain the endogenous network formation process. By specifying unobserved components in both the network model and the SAR model, we capture the correlation between the processes of network and outcome formation, and propose a proper estimation procedure for the system. We demonstrate that the estimation of this system can be effectively done by using the Bayesian method. We provide a Monte Carlo experiment and an empirical application of this modeling approach on the friendship networks of high school students and their interactions on academic performance in the Add Health data. Copyright © 2015 John Wiley & Sons, Ltd.     

Interlocking directorates in Italy: persistent links in network dynamics

In this work we study the time evolution of interlocking directorates in Italy from 1998 to 2011 by means of dynamical networks. Our purpose is to assess if in Italy there is a connected and stable structure, due to the presence of directors with multiple mandates, like it happens in the German case. We find a very cohesive network structure, due to the presence of a few directors with multiple assignments and, unlike the German case, this structure is stable, but not connected. Moreover we propose an alternative approach to investigate the dynamics, based on temporal networks, in order to quantify the variation of links in a certain time period. We construct a unique cumulative network, where nodes are companies and the existence of an edge is related with the persistence in time of an interlock between two companies. This persistence is due on the one hand to the ownership of a few family firms, and on the other hand to cross-shareholdings between companies. To complete the analysis we also investigate whether the link stability results from the appointments of the same director or from the stepping in/out of different directors.     

A Test of the Conditional Independence Assumption in Sample Selection Models

Identification in most sample selection models depends on the independence of the regressors and the error terms conditional on the selection probability. All quantile and mean functions are parallel in these models; this implies that quantile estimators cannot reveal any—per assumption non‐existing—heterogeneity. Quantile estimators are nevertheless useful for testing the conditional independence assumption because they are consistent under the null hypothesis. We propose tests of the Kolmogorov–Smirnov type based on the conditional quantile regression process. Monte Carlo simulations show that their size is satisfactory and their power sufficient to detect deviations under plausible data‐generating processes. We apply our procedures to female wage data from the 2011 Current Population Survey and show that homogeneity is clearly rejected. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian estimation of inefficiency heterogeneity in stochastic frontier models

Estimation of the one sided error component in stochastic frontier models may erroneously attribute firm characteristics to inefficiency if heterogeneity is unaccounted for. However, unobserved inefficiency heterogeneity has been little explored. In this work, we propose to capture it through a random parameter which may affect the location, scale, or both parameters of a truncated normal inefficiency distribution using a Bayesian approach. Our findings using two real data sets, suggest that the inclusion of a random parameter in the inefficiency distribution is able to capture latent heterogeneity and can be used to validate the suitability of observed covariates to distinguish heterogeneity from inefficiency. Relevant effects are also found on separating and shrinking individual posterior efficiency distributions when heterogeneity affects the location and scale parameters of the one-sided error distribution, and consequently affecting the estimated mean efficiency scores and rankings. In particular, including heterogeneity simultaneously in both parameters of the inefficiency distribution in models that satisfy the scaling property leads to a decrease in the uncertainty around the mean scores and less overlapping of the posterior efficiency distributions, which provides both more reliable efficiency scores and rankings.     

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.     

Automatic selection of unobserved components models for supply chain forecasting

For many companies, automatic forecasting has come to be an essential part of business analytics applications. The large amounts of data available, the short life-cycle of the analysis and the acceleration of business operations make traditional manual data analysis unfeasible in such environments. In this paper, an automatic forecasting support system that comprises several methods and models is developed in a general state space framework built in the SSpace toolbox written for Matlab. Some of the models included are well-known, such as exponential smoothing and ARIMA, but we also propose a new model family that has been used only very rarely in this context, namely unobserved components models. Additional novelties include the use of unobserved components models in an automatic identification environment and the comparison of their forecasting performances with those of exponential smoothing and ARIMA models estimated using different software packages. The new system is tested empirically on a daily dataset of all of the products sold by a franchise chain in Spain (166 products over a period of 517 days). The system works well in practice and the proposed automatic unobserved components models compare very favorably with other methods and other well-known software packages in forecasting terms.     

On parameter estimation of partly observed bilinear discrete-time stochastic systems

The parameter estimation problem of a partly observed nonlinear discrete-time stochastic system is considered. The unobserved component of the system is a q-dimensional stable autoregressive process of the pth order with random parameters, observed in the presence of multiplicative and additive noises. The distributions of all the noises of the system are supposed to be unknown. The problem is to estimate the mean of the drifting parameters of the object and variances of the additive noises of the system. Asymptotic correlation estimators of all these parameters are investigated and sequential estimators with given mean square accuracy of the mean of the drifting autoregressive parameters are obtained.     

A Bayesian Semiparametric Competing Risk Model with Unobserved Heterogeneity

This paper generalizes existing econometric models for censored competing risks by introducing a new flexible specification based on a piecewise linear baseline hazard, time‐varying regressors, and unobserved individual heterogeneity distributed as an infinite mixture of generalized inverse Gaussian (GIG) densities, nesting the gamma kernel as a special case. A common correlated latent time effect induces dependence among risks. Our model is based on underlying latent exit decisions in continuous time while only a time interval containing the exit time is observed, as is common in economic data. We do not make the simplifying assumption of discretizing exit decisions—our competing risk model setup allows for latent exit times of different risk types to be realized within the same time period. In this setting, we derive a tractable likelihood based on scaled GIG Laplace transforms and their higher‐order derivatives. We apply our approach to analyzing the determinants of unemployment duration with exits to jobs in the same industry or a different industry among unemployment insurance recipients on nationally representative individual‐level survey data from the US Department of Labor. Our approach allows us to conduct a counterfactual policy experiment by changing the replacement rate: we find that the impact of its change on the probability of exit from unemployment is inelastic. Copyright © 2014 John Wiley & Sons, Ltd.     

Identification and Estimation of Engel Curves with Endogenous and Unobserved Expenditures

When dealing with the estimation of Engel curves, measurement errors in expenditure data and simultaneity are likely sources of endogeneity. In this paper we study identification of the parameters that characterize an Engel curve in the presence of both. We consider specifications where budget shares are polynomials in the logarithm of total expenditure, which is the case frequently encountered in empirical applications. We propose an estimation procedure which is an extension of that in Lewbel ( 1996 ) and exploits a control function assumption to correct for the endogeneity of the true unobserved total expenditure. Copyright © 2013 John Wiley & Sons, Ltd.     

Fertility and female employment dynamics in Europe: the effect of using alternative econometric modeling assumptions

We investigate the direct and long‐run effects of fertility on employment in Europe, estimating dynamic models of labor supply under different assumptions regarding the exogeneity of fertility and modeling assumptions related to initial conditions, unobserved heterogeneity and serial correlation in the error terms. We find overall large direct and long‐run effects of giving birth on employment probabilities, and these effects differ considerably across countries. We find that within countries the results are sensitive to the statistical assumption made on initial conditions, the inclusion of serial correlation and the assumption of strict exogeneity of children. However, the pattern across countries is robust to these assumptions. We show that such patterns are largely consistent with prevailing institutional differences related to the flexibility of the labor markets and family policies. Copyright © 2009 John Wiley & Sons, Ltd.     

Kalman filtering estimation of unobserved rational expectations with an application to the German hyperinflation

The assumption that rational expectations always lie on a convergent path is subject to an empirical test using the German hyperinflation data. The estimation technique employs a Kalman filtering algorithm. After presenting a brief background for the convergent expectations problem and a derivation of the various model specifications, a generalized expectations model and its attendant Kalman filtering estimation technique are discussed. Additional estimation details and empirical results are then presented. Based on an assumption of normally distributed errors, the null hypothesis of convergent paths is rejected in all situations involving a deterministic specification of the evolution of the unobserved parameter which characterizes the convergent path. The same null hypothesis is rejected in four of the six cases corresponding to a stochastic specification of the evolution of the unobserved parameter which characterizes the convergent path. A discussion of these findings, their economic significance, and suggestions for further research concludes the paper.     

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.     

Estimation and model selection based inference in single and multiple threshold models

This paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models. We initially proceed under the assumption that the number of regimes is known á priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly. Theoretical properties of the resulting estimators are derived and their finite sample properties investigated.     

Granger causality detection in high-dimensional systems using feedforward neural networks

This paper proposes a novel methodology to detect Granger causality on average in vector autoregressive settings using feedforward neural networks. The approach accommodates unknown dependence structures between elements of high-dimensional multivariate time series with weak and strong persistence. To do this, we propose a two-stage procedure: first, we maximize the transfer of information between input and output variables in the network in order to obtain an optimal number of nodes in the intermediate hidden layers. Second, we apply a novel sparse double group lasso penalty function in order to identify the variables that have the predictive ability and, hence, indicate that Granger causality is present in the others. The penalty function inducing sparsity is applied to the weights that characterize the nodes of the neural network. We show the correct identification of these weights so as to increase sample sizes. We apply this method to the recently created Tobalaba network of renewable energy companies and show the increase in connectivity between companies after the creation of the network using Granger causality measures to map the connections.     

集群企业捆绑式合作创新的动力机制——基于演化博弈视角

在知识经济和网络经济时代,集群企业捆绑式合作创新是常见和有效的创新模式。为描述和分析捆绑式合作创新的动力机制,本文基于演化博弈视角,建立了相应的演化博弈模型,分析了模型的演化结果、稳定性及演化路径,并通过参数分析,针对性地提出了相关政策建议。