CROSS‐SECTIONAL DEPENDENCE AND SPILLOVERS IN SPACE AND TIME: WHERE SPATIAL ECONOMETRICS AND GLOBAL VAR MODELS MEET

To enhance the measurement of economic and financial spillovers, we bring together the spatial and global vector autoregressive (GVAR) classes of econometric models by providing a detailed methodological review where they meet in terms of structure, interpretation, and estimation. We discuss the structure of connectivity (weight) matrices used by these models and its implications for estimation. To anchor our work within the dynamic literature on spillovers, we define a general yet measurable concept of spillovers. We formalize it analytically through the indirect effects used in the spatial literature and impulse responses used in the GVAR literature. Finally, we propose a practical step‐by‐step approach for applied researchers who need to account for the existence and strength of cross‐sectional dependence in the data. This approach aims to support the selection of the appropriate modeling and estimation method and of choices that represent empirical spillovers in a clear and interpretable form.     

Information Measures in Perspective

Information-theoretic methodologies are increasingly being used in various disciplines. Frequently an information measure is adapted for a problem, yet the perspective of information as the unifying notion is overlooked. We set forth this perspective through presenting information-theoretic methodologies for a set of problems in probability and statistics. Our focal measures are Shannon entropy and Kullback–Leibler information. The background topics for these measures include notions of uncertainty and information, their axiomatic foundation, interpretations, properties, and generalizations. Topics with broad methodological applications include discrepancy between distributions, derivation of probability models, dependence between variables, and Bayesian analysis. More specific methodological topics include model selection, limiting distributions, optimal prior distribution and design of experiment, modeling duration variables, order statistics, data disclosure, and relative importance of predictors. Illustrations range from very basic to highly technical ones that draw attention to subtle points.     

Space-varying Coefficient Simultaneous Autoregressive Models for the Structural Analysis of Residential Water Demand

Abstract

This study develops two space-varying coefficient simultaneous autoregressive (SVC-SAR) models for areal data and applies them to the discrete/continuous choice model, which is an econometric model based on the consumer's utility maximization problem. The space-varying coefficient model is a statistical model in which the coefficients vary depending on their location. This study introduces the simultaneous autoregressive model for the underlying spatial dependence across coefficients, where the coefficients for one observation are affected by the sum of those for the other observations. This model is named the SVC-SAR model. Because of its flexibility, we use the Bayesian approach and construct its estimation method based on the Markov chain Monte Carlo simulation. The proposed models are applied to estimate the Japanese residential water demand function, which is an example of the discrete/continuous choice model.     

Modeling regional economic dynamics: Spatial dependence,spatial heterogeneity and nonlinearities

Spatial modeling of economic phenomena requires the adoption of complex econometric tools, which allow us to deal with important methodological issues, such as spatial dependence, spatial unobserved heterogeneity and nonlinearities. In this paper we describe some recently developed econometric approaches (i.e. Spatial Autoregressive Semiparametric Geoadditive Models), which address the three issues simultaneously. We also illustrate the relative performance of these methods with an application to the case of house prices in the Lucas County.     

Rank-based Tests for Cross-sectional Dependence in Large (N,T) Fixed Effects Panel Data Models

Most existing methods for testing cross-sectional dependence in fixed effects panel data models are actually conducting tests for cross-sectional uncorrelation, which are not robust to departures of normality of the error distributions as well as nonlinear cross-sectional dependence. To this end, we construct two rank-based tests for (static and dynamic) fixed effects panel data models, based on two very popular rank correlations, that is, Kendall's tau and Bergsma–Dassios’ τ*, respectively, and derive their asymptotic distributions under the null hypothesis. Monte Carlo simulations demonstrate applicability of these rank-based tests in large (N,T) case, and also the robustness to departures of normality of the error distributions and nonlinear cross-sectional dependence.     

A nonlinear panel data model of cross-sectional dependence

This paper proposes a nonlinear panel data model which can endogenously generate both ‘weak’ and ‘strong’ cross-sectional dependence. The model’s distinguishing characteristic is that a given agent’s behaviour is influenced by an aggregation of the views or actions of those around them. The model allows for considerable flexibility in terms of the genesis of this herding or clustering type behaviour. At an econometric level, the model is shown to nest various extant dynamic panel data models. These include panel AR models, spatial models, which accommodate weak dependence only, and panel models where cross-sectional averages or factors exogenously generate strong, but not weak, cross sectional dependence. An important implication is that the appropriate model for the aggregate series becomes intrinsically nonlinear, due to the clustering behaviour, and thus requires the disaggregates to be simultaneously considered with the aggregate. We provide the associated asymptotic theory for estimation and inference. This is supplemented with Monte Carlo studies and two empirical applications which indicate the utility of our proposed model as a vehicle to model different types of cross-sectional dependence.     

Models of representation of social mobility and inequality systems. A neural network approach

This paper reports on the results of the application of an innovative technique, i.e. neural network models, to mobility data. Our primary aim is to show that the technique is more flexible than traditional statistical modeling, and that it entails less strong methodological assumptions concerning the phenomenon which they are intended to represent. Two kinds of networks have been applied: heteroassociative networks, used for prevision and class membership recognition; and autoassociative networks, used for simulation tasks. Results obtained from experiments with neural networks on Italian data are highly consistent with the body of knowledge derived from previous classical analysis. The explicative power of neural network models proved to be higher than that of path analysis given their capacity to uncover any kind or relation between variables, whether linear or nonlinear. When compared to log-linear models, they enable the reconstruction of mobility processes within a global frame, controlling all relevant variables at once.     

Family planning,gender differences and infant mortality: evidence from Uttar Pradesh,India

This paper modeled the proximate determinants of infant survival using the National Family Health Survey data on 11,500 women from the most populous Indian state Uttar Pradesh in the period 1982–1992. A methodological framework was developed for analyzing the inter-relationships between high fertility and infant mortality, gender differences in mortality, and for modeling the effects of health care and family planning variables. Probit models were estimated by maximum likelihood taking into account simultaneity of regressors and unobserved household differences. The proximate determinants of infant survival included maternal education and age at first birth, birth interval, the number of children before family planning was first used, maternal tetanus vaccination, and child's vaccinations. Indicator variables for a boy (girl) born at a birth order higher than the “ideal” number showed that unwanted births exacerbated female mortality.     

Small Area Estimation-New Developments and Directions

The purpose of this paper is to provide a critical review of the main advances in small area estimation (SAE) methods in recent years. We also discuss some of the earlier developments, which serve as a necessary background for the new studies. The review focuses on model dependent methods with special emphasis on point prediction of the target area quantities, and mean square error assessments. The new models considered are models used for discrete measurements, time series models and models that arise under informative sampling. The possible gains from modeling the correlations among small area random effects used to represent the unexplained variation of the small area target quantities are examined. For review and appraisal of the earlier methods used for SAE, see Ghosh & Rao (1994).     

The analysis of residence histories and other longitudinal panel data: A continuous time mixed markov renewal model incorporating exogeneous variables

The analysis of residence histories and other longitudinal panel data is fraught with methodological problems. Much recent progress has been made in methods of analysis within discrete time. This paper extends the development of empirically tractable mixed continuous time stochastic models. Analysis of a sample of intra-urban residential histories identifies the effect of tenure type, age of household head, size of household and duration of stay on movement probabilities. Surprisingly, no further variation, as represented by a gamma mixing distribution over a hazard rate parameter, may be identified.     

Investment decisions in manufacturing: assessing the effects of real oil prices and their uncertainty

We investigate the effects of real oil prices and their uncertainty on investment decisions. Making use of plant‐level data, we estimate dynamic, discrete‐choice models that allow modeling investment inaction, under different assumptions related to initial conditions and unobserved heterogeneity. We find that increases in real oil price changes and in real oil price uncertainty significantly reduce the likelihood of investment action, in line with the predictions of irreversible investment theory. We also document that investment decisions exhibit strong, pure state dependence and are also significantly affected by initial conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Some aspects of modeling and statistical inference for financial models

Modeling the stock price development as a geometric Brownian motion or, more generally, as a stochastic exponential of a diffusion, requires the use of specific statistical methods. For instance, the observations seldom reach us in the form of a continuous record and we are led to infer about diffusion coefficients from discrete time data. Next, often the classical assumption that the volatility is constant has to be dropped. Instead, a range of various stochastic volatility models is formed by the limiting transition from known volatility models in discrete time towards their continuous time counterparts. These are the main topics of the present survey. It is closed by a quick look beyond the usual Gaussian world in continuous time modeling by allowing a Levy process to be the driving process.     

Socio‐economic distance and spatial patterns in unemployment

This paper examines the spatial patterns of unemployment in Chicago between 1980 and 1990. We study unemployment clustering with respect to different social and economic distance metrics that reflect the structure of agents' social networks. Specifically, we use physical distance, travel time, and differences in ethnic and occupational distribution between locations. Our goal is to determine whether our estimates of spatial dependence are consistent with models in which agents' employment status is affected by information exchanged locally within their social networks. We present non‐parametric estimates of correlation across Census tracts as a function of each distance metric as well as pairs of metrics, both for unemployment rate itself and after conditioning on a set of tract characteristics. Our results indicate that there is a strong positive and statistically significant degree of spatial dependence in the distribution of raw unemployment rates, for all our metrics. However, once we condition on a set of covariates, most of the spatial autocorrelation is eliminated, with the exception of physical and occupational distance. Racial and ethnic composition variables are the single most important factor in explaining the observed correlation patterns. Copyright © 2002 John Wiley & Sons, Ltd.     

Tempus volat,hora fugit: A survey of tie-oriented dynamic network models in discrete and continuous time

Given the growing number of available tools for modeling dynamic networks, the choice of a suitable model becomes central. The goal of this survey is to provide an overview of tie-oriented dynamic network models. The survey is focused on introducing binary network models with their corresponding assumptions, advantages, and shortfalls. The models are divided according to generating processes, operating in discrete and continuous time. First, we introduce the temporal exponential random graph model (TERGM) and the separable TERGM (STERGM), both being time-discrete models. These models are then contrasted with continuous process models, focusing on the relational event model (REM). We additionally show how the REM can handle time-clustered observations, that is, continuous-time data observed at discrete time points. Besides the discussion of theoretical properties and fitting procedures, we specifically focus on the application of the models on two networks that represent international arms transfers and email exchange, respectively. The data allow to demonstrate the applicability and interpretation of the network models.     

Testing for serial correlation,spatial autocorrelation and random effects using panel data

This paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time. In addition, the model allows for heterogeneity across the spatial units using random effects. The paper then derives several Lagrange multiplier tests for this panel data regression model including a joint test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin and Bera [1998. Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York] and in the panel data context by Baltagi et al. [2003. Testing panel data regression models with spatial error correlation. Journal of Econometrics 117, 123–150]. The second is the LM tests for the error component panel data model with serial correlation derived by Baltagi and Li [1995. Testing AR(1) against MA(1) disturbances in an error component model. Journal of Econometrics 68, 133–151]. Hence, the joint LM test derived in this paper encompasses those derived in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests become marginal LM tests that ignore either serial correlation over time or spatial error correlation. The paper then derives conditional LM and LR tests that do not ignore these correlations and contrast them with their marginal LM and LR counterparts. The small sample performance of these tests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is significant can lead to misleading inference.     

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.     

Growth,unemployment and heterogeneity

The paper analyzes unemployment in a medium-run growth model, where aggregate demand and supply interact, using a top-down approach. The aim of the essay is the study of a nonlinear system where both aggregate demand and supply are endogenous and generate bounded unemployment, followed by a methodological effort direct to identify possible lines of convergence with the agent based models (ABM) approach. This is a by-product of the presence of heterogeneity in the model. Heterogeneity acts through two different channels and operates among class of agents: it comes into the aggregate consumption function where households are assumed employed or unemployed; it changes the learning process of pessimists and optimists. The analysis is carried on through simulations. The resulting system is fairly stable to changes in main structural parameters. On one hand, autonomous demand drives the dynamics of the system, while heterogeneity in the consumption function, due to the presence of unemployment, strengthens the links with supply aspects. On the other hand, both the rate of growth of labor productivity and labor supply are endogenous. Two major results are obtained. First, unemployment allows the so called Harrodian reconciliation between aggregate demand and supply. Second, unemployment remains bounded meaning that the interaction between aggregate demand and supply thwarts instability. These results are in keeping with those obtained by means of a bottom-up approach, typical of ABM. Possible explanations and implications of this convergence are put forward and open the venue to further deepening of complementarities among the two modeling strategies.

     

Spatio-temporal probabilistic forecasting of wind power for multiple farms: A copula-based hybrid model

Accurate probabilistic forecasting of wind power output is critical to maximizing network integration of this clean energy source. There is a large literature on temporal modeling of wind power forecasting, but considerably less work combining spatial dependence into the forecasting framework. Through the careful consideration of the temporal modeling component, complemented by support vector regression of the temporal model residuals, this work demonstrates that a DVINE copula model most accurately represents the residual spatial dependence. Additionally, this work proposes a complete set of validation mechanisms for multi-h-step forecasts that, when considered together, comprehensively evaluate accuracy. The model and validation mechanisms are demonstrated in two case studies, totaling ten wind farms in the Texas electric grid. The proposed method outperforms baseline and competitive models, with an average Continuous Ranked Probability Score of less than 0.15 for individual farms, and an average Energy Score of less than 0.35 for multiple farms, over the 24-hour-ahead horizon. Results show the model’s ability to replicate the power output dynamics through calibrated and sharp predictive densities.