Forecasting with vector autoregressive (VAR) models subject to business cycle restrictions

In the last decade VAR models have become a widely-used tool for forecasting macroeconomic time series. To improve the out-of-sample forecasting accuracy of these models, Bayesian random-walk prior restrictions are often imposed on VAR model parameters. This paper focuses on whether placing an alternative type of restriction on the parameters of unrestricted VAR models improves the out-of-sample forecasting performance of these models. The type of restriction analyzed here is based on the business cycle characteristics of U.S. macroeconomic data, and in particular, requires that the dynamic behavior of the restricted VAR model mimic the business cycle characteristics of historical data. The question posed in this paper is: would a VAR model, estimated subject to the restriction that the cyclical characteristics of simulated data from the model “match up” with the business cycle characteristics of U.S. data, generate more accurate out-of-sample forecasts than unrestricted or Bayesian VAR models?     

Inference on impulse response functions in structural VAR models

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68% posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.     

Panel data analysis of U.S. coal productivity

We analyze labor productivity in coal mining in the United States using indices of productivity change associated with the concepts of panel data modeling. This approach is valuable when there is extensive heterogeneity in production units, as with coal mines. We find substantial returns to scale for coal mining in all geographical regions, and find that smooth technical progress is exhibited by estimates of the fixed effects for coal mining. We carry out a variety of diagnostic analyses of our basic model and primary modeling assumptions, using recently proposed methods for addressing ‘errors-in-variables’ and ‘weak instrument bias’ problems in linear and nonlinear models.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

Technical efficiency in competing panel data models: a study of Norwegian grain farming

Estimation of technical efficiency is widely used in empirical research using both cross-sectional and panel data. Although several stochastic frontier models for panel data are available, only a few of them are normally applied in empirical research. In this article we chose a broad selection of such models based on different assumptions and specifications of heterogeneity, heteroskedasticity and technical inefficiency. We applied these models to a single dataset from Norwegian grain farmers for the period 2004–2008. We also introduced a new model that disentangles firm effects from persistent (time-invariant) and residual (time-varying) technical inefficiency. We found that efficiency results are quite sensitive to how inefficiency is modeled and interpreted. Consequently, we recommend that future empirical research should pay more attention to modeling and interpreting inefficiency as well as to the assumptions underlying each model when using panel data.     

Maximum likelihood estimation based on the Laplace approximation for p2 network regression models

The class of p₂ models is suitable for modeling binary relation data in social network analysis. A p₂ model is essentially a regression model for bivariate binary responses, featuring within‐dyad dependence and correlated crossed random effects to represent heterogeneity of actors. Despite some desirable properties, these models are used less frequently in empirical applications than other models for network data. A possible reason for this is due to the limited possibilities for this model for accounting for (and explicitly modeling) structural dependence beyond the dyad as can be done in exponential random graph models. Another motive, however, may lie in the computational difficulties existing to estimate such models by means of the methods proposed in the literature, such as joint maximization methods and Bayesian methods. The aim of this article is to investigate maximum likelihood estimation based on the Laplace approximation approach, that can be refined by importance sampling. Practical implementation of such methods can be performed in an efficient manner, and the article provides details on a software implementation using R . Numerical examples and simulation studies illustrate the methodology.     

Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting

Wind power forecasts with lead times of up to a few hours are essential to the optimal and economical operation of power systems and markets. Vector autoregression (VAR) is a framework that has been shown to be well suited to predicting for several wind farms simultaneously by considering the spatio-temporal dependencies in their time series. Lasso penalisation yields sparse models and can avoid overfitting the large numbers of coefficients in higher dimensional settings. However, estimation in VAR models usually does not account for changes in the spatio-temporal wind power dynamics that are related to factors such as seasons or wind farm setup changes, for example. This paper tackles this problem by proposing a time-adaptive lasso estimator and an efficient coordinate descent algorithm for updating the VAR model parameters recursively online. The approach shows good abilities to track changes in the multivariate time series dynamics on simulated data. Furthermore, in two case studies it shows clearly better predictive performances than the non-adaptive lasso VAR and univariate autoregression.     

Fixed effects demeaning in the presence of interactive effects in treatment effects regressions and elsewhere

The present paper shows that cross-section demeaning with respect to time fixed effects is more useful than commonly appreciated, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients when the number of time periods, T, is small and only the number of cross-sectional units, N, is large. This is important when using OLS but also when using more sophisticated estimators of interactive effects models whose validity does not require demeaning, a point that to the best of our knowledge has not been made before in the literature. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time-varying heterogeneity. Gobillon and Magnac (2016) recently considered this problem. They employed a principal components-based approach designed to deal with general unobserved heterogeneity, which does not require fixed effects demeaning. The approach does, however, require that T is large, which is typically not the case in practice, and the results reported here confirm that the performance can be extremely poor in small-T samples. The exception is when the approach is applied to data that have been demeaned with respect to fixed effects.     

Forecasting data vintages

This article provides a discussion of Clements and Galvão’s paper “Forecasting with vector autoregressive models of data vintages: US output growth and inflation.” Clements and Galvão argue that a multiple-vintage VAR model can be useful for forecasting data that are subject to revisions. They draw a “distinction between forecasting future observations and revisions to past data,” which focuses forecasters’ attention on yet another real time data issue. This comment discusses the importance of taking data revisions into consideration, and compares the multiple-vintage VAR approach of Clements and Galvão to a state space approach.     

On the forecasting performance of a small-scale DSGE model

Dynamic stochastic general equilibrium (DSGE) models have recently become standard tools for policy analysis. Nevertheless, their forecasting properties have still barely been explored. In this article, we address this problem by examining the quality of forecasts of the key U.S. economic variables: the three-month Treasury bill yield, the GDP growth rate and GDP price index inflation, from a small-size DSGE model, trivariate vector autoregression (VAR) models and the Philadelphia Fed Survey of Professional Forecasters (SPF). The ex post forecast errors are evaluated on the basis of the data from the period 1994–2006. We apply the Philadelphia Fed “Real-Time Data Set for Macroeconomists” to ensure that the data used in estimating the DSGE and VAR models was comparable to the information available to the SPF.Overall, the results are mixed. When comparing the root mean squared errors for some forecast horizons, it appears that the DSGE model outperforms the other methods in forecasting the GDP growth rate. However, this characteristic turned out to be statistically insignificant. Most of the SPF's forecasts of GDP price index inflation and the short-term interest rate are better than those from the DSGE and VAR models.     

Multicointegration in Stock-Flow Models

Multicointegration, in the sense of Granger and Lee (1990), frequently occurs in models of stock-flow adjustment and implies cointegration amongst I(2) variables and their differences (polynomial cointegration). The purpose of this article is two-fold. First, we demonstrate that based on a multicointegrated vector autoregression (VAR) two equivalent error correction model (ECM) representations can be derived; the first is expressed in terms of adjustments in the flows of the variables (the standard I(2) ECM), and the second is expressed in terms of adjustments in both the stocks and the flows. Secondly, we apply I(2) estimation and testing procedures for multicointegrated time series to analyze data for US housing construction. We find that stocks of housing units started and completed exhibit poly- nomial cointegration (and hence the flows are multicointegrated) and the associated ECM's are estimated. Lee (1992, 1996) also found multicointegration in this data set but without explicitly exploiting the I(2) property.     

Forecasts of market shares from VAR and BVAR models: a comparison of their accuracy

This paper develops a Bayesian vector autoregressive model (BVAR) for the leader of the Portuguese car market to forecast the market share. The model includes five marketing decision variables. The Bayesian prior is selected on the basis of the accuracy of the out-of-sample forecasts. We find that BVAR models generally produce more accurate forecasts. The out-of-sample accuracy of the BVAR forecasts is also compared with that of forecasts from an unrestricted VAR model and of benchmark forecasts produced from three univariate models. Additionally, competitive dynamics are revealed through variance decompositions and impulse response analyses.     

Estimation in Two-Stage Models with Heteroscedasticity

A surprising number of important problems can be cast in the framework of estimating a mean and variance using data arising from a two-stage structure. The first stage is a random sampling of "units" with some quantity of interest associated with the unit. The second stage produces an estimate of that quantity and usually, but not always, an estimated standard error, which may change considerably across units. Heteroscedasticity in the estimates over different units can arise for a number of reasons, including variation associated with the unit and changing sampling effort over units. This paper presents a broad discussion of the problem of making inferences for the population mean and variance associated with the unobserved true values at the first stage of sampling. A careful discussion of the causes of heteroscedasticity is given, followed by an examination of ways in which inferences can be carried out in a manner that is robust to the nature of the within unit heteroscedasticity. Among the conclusions are that under any type of heteroscedasticity, an unbiased estimate of the mean and the variance of the estimated mean can be obtained by using the estimates as if they were true unobserved values from the first stage. The issue of using the mean versus a weighted average which tries to account for the heteroscedasticity is also discussed. An unbiased estimate of the population variance is given and the variance of this estimate and its covariance with the estimated mean is provided under various types of heteroscedasticity. The two-stage setting arises in many contexts including the one-way random effects models with replication, meta-analysis, multi-stage sampling from finite populations and random coefficients models. We will motivate and illustrate the problem with data arising from these various contexts with the goal of providing a unified framework for addressing such problems.     

A copula-based time series model for global horizontal irradiation

The increasing importance of solar power for electricity generation leads to increasing demand for probabilistic forecasting of local and aggregated photovoltaic (PV) yields. Based on publicly available irradiation data, this paper uses an indirect modeling approach for hourly medium to long-term local PV yields. We suggest a time series model for global horizontal irradiation that allows for multivariate probabilistic forecasts for arbitrary time horizons. It features several important stylized facts. Sharp time-dependent lower and upper bounds of global horizontal irradiations are estimated. The parameters of the beta distributed marginals of the transformed data are allowed to be time-dependent. A copula-based time series model is introduced for the hourly and daily dependence structure based on simple vine copulas with so-called tail dependence. Evaluation methods based on scoring rules are used to compare the model’s power for multivariate probabilistic forecasting with other models used in the literature showing that our model outperforms other models in many respects.     

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.     

Economic transition and growth

Some extensions of neoclassical growth models are discussed that allow for cross‐section heterogeneity among economies and evolution in rates of technological progress over time. The models offer a spectrum of transitional behavior among economies that includes convergence to a common steady‐state path as well as various forms of transitional divergence and convergence. Mechanisms for modeling such transitions, measuring them econometrically, assessing group behavior and selecting subgroups are developed in the paper. Some econometric issues with the commonly used augmented Solow regressions are pointed out, including problems of endogeneity and omitted variable bias which arise under conditions of transitional heterogeneity. Alternative regression methods for analyzing economic transition are given which lead to a new test of the convergence hypothesis and a new procedure for detecting club convergence clusters. Transition curves for individual economies and subgroups of economies are estimated in a series of empirical applications of the methods to regional US data, OECD data and Penn World Table data. Copyright © 2009 John Wiley & Sons, Ltd.     

What drives returns to euro area housing? Evidence from a dynamic dividend–discount model

We apply a dynamic dividend–discount model to analyse housing returns for eight euro area countries comprising over 90% of euro area GDP, both individually and as a panel. A vector autoregressive model (VAR) is estimated for four variables – excess return to housing, rents, the real interest rate and real disposable per capita income – using quarterly data over the period 1978–2009. This empirical investigation – which allows for a decomposition of house price movements into movements in rent (cash-flow) and expected return news components – indicates that the bulk of the variability of euro area house price movements can be attributed to movements in fundamentals. There remains nonetheless an important but less sizeable influence of market-wide (or expected-return) variations in house prices. Country-specific estimation indicates considerable heterogeneity around the euro area result, both for what concerns long-term impacts and dynamics. Notably, changes in expected returns play a relatively strong role in the house prices of Ireland and Spain.     

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.     

COMBINING REVEALED AND STATED PREFERENCE DATA TO ESTIMATE THE NONMARKET VALUE OF ECOLOGICAL SERVICES: AN ASSESSMENT OF THE STATE OF THE SCIENCE

Abstract This paper reviews the marketing, transportation and environmental economics literature on the joint estimation of revealed preference (RP) and stated preference (SP) data. The RP and SP approaches are first described with a focus on the strengths and weaknesses of each. Recognizing these strengths and weaknesses, the potential gains from combining data are described. A classification system for combined data that emphasizes the type of data combination and the econometric models used is proposed. A methodological review of the literature is pursued based on this classification system. Examples from the environmental economics literature are highlighted. A discussion of the advantages and disadvantages of each type of jointly estimated model is then presented. Suggestions for future research, in particular opportunities for application of these models to environmental quality valuation, are presented.