Accelerated gaussian importance sampler with application to dynamic latent variable models

We propose a new generic and highly efficient Accelerated Gaussian Importance Sampler (AGIS) for the numerical evaluation of (very) high-dimensional density functions. A specific case of interest to us is the evaluation of likelihood functions for a broad class of dynamic latent variable models. The feasibility of our method is strikingly illustrated by means of an application to a first-order dynamic stochastic volatility model for daily stock returns, whose likelihood for an actual sample of size 2022 (!) is evaluated with high numerical accuracy by means of 10,000 Monte Carlo replications. The estimated model parsimoniously dominates ARCH and GARCH alternatives, one of which includes twelve lags.     

Urban search models under high-relocation costs. Theory and application to spatial mismatch

We develop a search-matching model in which mobility costs are so high that it is too costly for workers to relocate when a change in their employment status occurs. We show that, in equilibrium, wages increase with distance to jobs and commuting costs because firms need to compensate the transportation cost difference between the employed and unemployed workers at each location in the city. We also show that the equilibrium land rent is negatively affected by the unemployment benefit because an increase in the latter induce firms to create less jobs, which, in turn, reduces the competition in the land market. We then use this model to provide a mechanism for the observed spatial mismatch between where black workers live and where jobs are. We finally show that a transportation policy consisting in subsidizing the commuting costs of black workers can increase job creation and reduce unemployment if the level of the subsidy is set at a sufficiently high level.     

Some cumulative logit models for panel-data analysis: an application to a dynamic analysis of personal efficacy

This paper introduces novel cumulative logit models for the panel-data analysis of transitions among ordered states of a polytomous dependent variable. The models differ from conventional cumulative logit models in that they can distinguish between covariate effects on the odds of having an upward transition and covariate effects on the odds of having a downward transition in the ordered states of the dependent variable. The new models are applied to panel data on personal efficacy and are used to identify asymmetric patterns in the effects of divorce and unemployment on changes in the level of personal efficacy. The effects of the two events on increasing the odds of having a downward transition are shown to be greater than their effects on decreasing the odds of having an upward transition. Some distinct characteristics of the effects of each event are also reported.     

Temporary jobs and job search effort in Europe

Using longitudinal data on individuals from the European Community Household Panel (ECHP) for eleven countries during 1995-2001, I investigate temporary job contract duration and job search effort. The countries are Austria, Belgium, Denmark, Finland, France, Greece, Ireland, Italy, the Netherlands, Portugal and Spain. I construct a search model for workers in temporary jobs which predicts that shorter duration raises search intensity. Calibration of the model to the ECHP data implies that at least 75% of the increase in search intensity over the life of a 2+ year temporary contract occurs in the last six months of the contract. I then estimate regression models for search effort that control for human capital, pay, local unemployment, and individual and time fixed effects. I find that workers on temporary jobs indeed search harder than those on permanent jobs. Moreover, search intensity increases as temporary job duration falls, and roughly 84% of this increase occurs on average in the shortest duration jobs. These results are robust to disaggregation by gender and by country. These empirical results are noteworthy, since it is not necessary to assume myopia or hyperbolic discounting in order to explain them, although the data clearly also do not rule out such explanations.     

A dynamic programming approach to work force scheduling with time-dependent performance measures

An implicit enumeration algorithm is defined to obtain solutions to the commercial bank check processing encoder scheduling problem. The specific application is of particular interest because a significant factor in determining optimality is the float costs associated with checks which are unprocessed and unavailable for presentation at check clearing deadlines, thereby making the timing of the activity of crucial importance. A one day time horizon is employed to reflect those situations where banks have the scheduling flexibility afforded by part-time and/or temporary help in additon to a complement of full-time operators. Comparisons are made with other suggested approaches to daily encoder scheduling. Results indicate that dynamic programming can be an attractive methodology to attack this complex problem.     

Differentiating employment prospects by industry and returns to job search in metropolitan areas

The role of differentiating employment prospects by the industry of the employer in the job seeker's calculation of the returns to search is analyzed. It is demonstrated that returns to search can vary systematically between metropolitan areas because of differing mixes of industry employment; it is argued that an increase in a measure of dispersion in the industry mix will tend to raise returns to job search. To test this hypothesis, cross sections of census data on unemployment rates of male experienced workers in each of the seven major occupational groups were analyzed. Statistically significant regression equations were obtained for three occupational groups (craftsmen, nonfarm laborers, and operatives); in all these cases the results supported the hypothesis of the paper.     

Semiparametric binary regression models under shape constraints with an application to Indian schooling data

We consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable Δ$\Delta$ is influenced by a set of covariates that can be partitioned as (X,Z)$(X,Z)$ where Z$Z$ (real valued) is the covariate of primary interest and X$X$ (vector valued) denotes a set of control variables. For any fixed X$X$, the conditional probability of the event of interest (Δ=1$\Delta =1$) is assumed to be a non-decreasing function of Z$Z$. The effect of the control variables is captured by a regression parameter β$\beta$. We show that the baseline conditional probability function (corresponding to X=0$X=0$) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing asymptotic confidence intervals for the conditional probability function (the regression function) that avoids the need to estimate nuisance parameters. Interestingly enough, the calibration of the likelihood ratio based confidence sets for the regression function no longer involves the usual χ²${\chi }^2$ quantiles, but those of the distribution of a new random variable that can be characterized as a functional of convex minorants of Brownian motion with quadratic drift. Confidence sets for the regression parameter β$\beta$ can however be constructed using asymptotically χ²${\chi }^2$ likelihood ratio statistics. The finite sample performance of the methods are assessed via a simulation study. The techniques of the paper are applied to data sets on primary school attendance among children belonging to different socio-economic groups in rural India.     

Employment effects of extended geographic scope in job search

This paper uses a unique possibility to link unemployed individuals' stated willingness to move for work with administrative data, giving us the possibility to analyse the effects of individual willingness-to-move on labour market outcome. Those with extended geographic job search area have a higher probability of finding a job. However, the greatest effect is found on the local labour market, indicating that it is not the extended geographic scope per se that increases the likelihood of escaping unemployment, but differences in unobservable characteristics between those who use an extended search area and those who do not.     

A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

Life-cycle patterns in male/female differences in job search

We investigate whether women search longer for a job than men and whether these differences change over the life cycle. Our empirical analysis exploits German register data on highly attached displaced workers. We apply duration models to analyze gender differences in job search taking into account observed and unobserved worker heterogeneity and censoring. Simple survival functions show that displaced women take longer to find a new job than comparable men. Disaggregation by age groups reveals that these differences are driven by differential behavior of women in their prime-childbearing years. There is no significant difference in job search duration among the very young and older workers. These differential outcomes remain even after we control for differences in human capital and when unobserved heterogeneity is incorporated into the model.     

The approximate solution of finite‐horizon discrete‐choice dynamic programming models

The estimation of finite‐horizon discrete‐choice dynamic programming (DCDP) models is computationally expensive. This limits their realism and impedes verification and validation efforts. Keane and Wolpin (Review of Economics and Statistics, 1994, 76(4), 648–672) propose an interpolation method that ameliorates the computational burden but introduces approximation error. I describe their approach in detail, successfully recompute their original quality diagnostics, and provide some additional insights that underscore the trade‐off between computation time and the accuracy of estimation results.     

Discussion of dynamic programming and linear programming approaches to stochastic control and optimal stopping in continuous time

This paper seeks to highlight two approaches to the solution of stochastic control and optimal stopping problems in continuous time. Each approach transforms the stochastic problem into a deterministic problem. Dynamic programming is a well-established technique that obtains a partial/ordinary differential equation, variational or quasi-variational inequality depending on the type of problem; the solution provides the value of the problem as a function of the initial position (the value function). The other method recasts the problems as linear programs over a space of feasible measures. Both approaches use Dynkin’s formula in essential but different ways. The aim of this paper is to present the main ideas underlying these approaches with only passing attention paid to the important and necessary technical details.     

Simultaneous equations models in applied search theory

This paper shows how standard simultaneous equations models arise in the analysis of survey data on wages and unemployment durations in the light of job search theory. Log-linear approximations to the key functional relations lead to ordinary log-linear simultaneous equations in which, moreover, specification error or heterogeneity terms are absorbed into the structural form error terms. Identifiability of structural parameters by exclusion restrictions can then be examined. An illustrative application of the method to data on elapsed durations and asking wages is given with results not inconsistent with search theory.     

Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

Fitting dynamic factor models to non-stationary time series

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time by proposing a deterministic time variation of its loadings. In this respect we generalize the existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as a time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a “double-asymptotic” framework of both cross-section and time dimension tending to infinity. The performance of the estimators is illustrated by a simulation study and an application to a macroeconomic data set.     

Tailored randomized block MCMC methods with application to DSGE models

In this paper we develop new Markov chain Monte Carlo schemes for the estimation of Bayesian models. One key feature of our method, which we call the tailored randomized block Metropolis–Hastings (TaRB-MH) method, is the random clustering of the parameters at every iteration into an arbitrary number of blocks. Then each block is sequentially updated through an M–H step. Another feature is that the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing, following  and  and Chib and Ergashev (in press). We also provide an extended version of our method for sampling multi-modal distributions in which at a pre-specified mode jumping iteration, a single-block proposal is generated from one of the modal regions using a mixture proposal density, and this proposal is then accepted according to an M–H probability of move. At the non-mode jumping iterations, the draws are obtained by applying the TaRB-MH algorithm. We also discuss how the approaches of Chib (1995) and Chib and Jeliazkov (2001) can be adapted to these sampling schemes for estimating the model marginal likelihood. The methods are illustrated in several problems. In the DSGE model of Smets and Wouters (2007), for example, which involves a 36-dimensional posterior distribution, we show that the autocorrelations of the sampled draws from the TaRB-MH algorithm decay to zero within 30–40 lags for most parameters. In contrast, the sampled draws from the random-walk M–H method, the algorithm that has been used to date in the context of DSGE models, exhibit significant autocorrelations even at lags 2500 and beyond. Additionally, the RW-MH does not explore the same high density regions of the posterior distribution as the TaRB-MH algorithm. Another example concerns the model of An and Schorfheide (2007) where the posterior distribution is multi-modal. While the RW-MH algorithm is unable to jump from the low modal region to the high modal region, and vice-versa, we show that the extended TaRB-MH method explores the posterior distribution globally in an efficient manner.     

Moving average stochastic volatility models with application to inflation forecast

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical application involving US inflation we find that these moving average stochastic volatility models provide better in-sample fitness and out-of-sample forecast performance than the standard variants with only stochastic volatility.     

Indirect estimation of large conditionally heteroskedastic factor models,with an application to the Dow 30 stocks

We derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a Kalman-filter approximation with inequality constraints on the auxiliary model parameters. We also propose alternative indirect estimators for large-scale models, and explain how to apply our procedures to many other dynamic latent variable models. We analyse the small sample behaviour of our indirect estimators and several likelihood-based procedures through an extensive Monte Carlo experiment with empirically realistic designs. Finally, we apply our procedures to weekly returns on the Dow 30 stocks.     

Forecasting banking crises with dynamic panel probit models

Banking crises are rare events, but when they occur, their consequences are often dramatic. The aim of this paper is to contribute to the toolkit of early warning models that is available to policy makers by exploring the dynamics and exuberances embedded in a panel dataset that covers 22 European countries over four decades (from 1970Q1 to 2012Q4). The in- and out-of-sample forecast performances of several (dynamic) probit models are evaluated, with the objective of developing common vulnerability indicators with early warning properties. The results obtained show that adding dynamic components and exuberance indicators to the models improves the performances of early warning models significantly.