Simulated Minimum Distance Research Articles

A comparison of economic agent-based model calibration methods

Despite significant expansion in recent years, the literature on quantitative and data-driven approaches to economic agent-based model validation and calibration consists primarily of studies that have focused on the introduction of new calibration methods that are neither benchmarked against existing alternatives nor rigorously tested in terms of the quality of the estimates they produce. In response, we compare a number of prominent agent-based model calibration methods, both established and novel, through a series of computational experiments in an attempt to determine the respective strengths and weaknesses of each approach. Overall, we find that a simple, likelihood-based approach to Bayesian estimation consistently outperforms several members of the more popular class of simulated minimum distance methods and results in reasonable parameter estimates in many contexts, with a degradation in performance observed only when considering a large-scale model and attempting to fit a substantial number of its parameters.

Markov chain analysis in agent-based model calibration by classical and simulated minimum distance

Agent-based models are nowadays widely used; however, their calibration on real data still remains an open issue which prevents to exploit completely their potentiality. Rarely such a kind of models can be studied analytically; more often they are studied by simulation. Among the problems encountered in ABM calibration, the choice of the criteria to fit can appear arbitrary. Markov chain analysis can come through to identify a standard procedure able to face this issue. Indeed, Izquierdo et al. (J Artif Soc Soc Simul 12(16):1–6, 2009) show that many computer simulation models can be represented as Markov chains. Exploiting such an idea classical minimum distance and its simulated counterpart, i.e., simulated minimum distance, are discussed theoretically and applied to Kirman model, which can be reformulated as a Markov chain. Comparison with approximate Bayesian computation is also addressed.

The ABC of simulation estimation with auxiliary statistics

The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is far more popular. This paper connects these two seemingly related approaches to likelihood-free estimation by means of a Reverse Sampler that uses both optimization and importance weighting to target the posterior distribution. Its hybrid features enable us to analyze an ABC estimate from the perspective of SMD. We show that an ideal ABC estimate can be obtained as a weighted average of a sequence of SMD modes, each being the minimizer of the deviations between the data and the model. This contrasts with the SMD, which is the mode of the average deviations. Using stochastic expansions, we provide a general characterization of frequentist estimators and those based on Bayesian computations including Laplace-type estimators. Their differences are illustrated using analytical examples and a simulation study of the dynamic panel model.

Simulated Minimum Hellinger Distance Inference Methods for Count Data

In this paper, we consider simulated minimum Hellinger distance (SMHD) inferences for count data. We consider grouped and ungrouped data and emphasize SMHD methods. The approaches extend the methods based on the deterministic version of Hellinger distance for count data. The methods are general, it only requires that random samples from the discrete parametric family can be drawn and can be used as alternative methods to estimation using probability generating function (pgf) or methods based matching moments. Whereas this paper focuses on count data, goodness of fit tests based on simulated Hellinger distance can also be applied for testing goodness of fit for continuous distributions when continuous observations are grouped into intervals like in the case of the traditional Pearson’s statistics. Asymptotic properties of the SMHD methods are studied and the methods appear to preserve the properties of having good efficiency and robustness of the deterministic version.

Labour Market Effects of International Trade When Mobility is Costly

I build and estimate a dynamic structural model of sectoral choices with heterogeneous workers accumulating imperfectly transferable human capital. Utility costs provide an additional barrier to mobility. Estimated by Simulated Minimum Distance on administrative data covering the population of Danish workers, costs are found to be in the range of 10% to 19% of average annual wages. Removing permanent unobserved heterogeneity increases the utility costs by an order of magnitude. I show that both the imperfect transferability of human capital and the utility costs are important in explaining the slow adjustment of the labour market following shocks to the economy. This article is protected by copyright. All rights reserved.

Simulated minimum distance estimation of dynamic models with errors-in-variables

Empirical analysis often involves using inexact measures of the predictors suggested by economic theory. The bias created by the correlation between the mismeasured regressors and the error term motivates the need for instrumental variable estimation. This paper considers a class of estimators that can be used in dynamic models with measurement errors when external instruments may not be available or are weak. The idea is to exploit the relation between the parameters of the model and the least squares biases. In cases when the latter are not analytically tractable, a special algorithm is designed to simulate the model without completely specifying the processes that generate the latent predictors. The proposed estimators perform well in simulations of the autoregressive distributed lag model. The methodology is used to estimate the long-run risks model.

An Estimated Structural Model of Entrepreneurial Behavior

Using a rich panel of owner-operated New York dairy farms, we provide new evidence on entrepreneurial behavior. We formulate a dynamic model of farms facing uninsured risks and financial constraints. Farmers derive nonpecuniary benefits from operating their businesses. We estimate the model via simulated minimum distance, matching both production and financial data. We find that financial factors and nonpecuniary benefits are of first-order importance. Collateral constraints and liquidity restrictions inhibit borrowing and the accumulation of capital. The nonpecuniary benefits to farming are large and keep small, low-productivity farms in business. Although farmers are risk averse, eliminating uninsured risk has only modest effects on capital and output.

An Estimated Structural Model of Entrepreneurial Behavior

Using a rich panel of owner-operated New York dairy farms, we provide new evidence on entrepreneurial behavior. We formulate a dynamic model of farms facing uninsured risks and financial constraints. Farmers derive nonpecuniary benefits from operating their businesses. We estimate the model via simulated minimum distance, matching both production and financial data. We find that financial factors and nonpecuniary benefits are of first-order importance. Collateral constraints and liquidity restrictions inhibit borrowing and the accumulation of capital, especially among high-productivity firms seeking to expand. The nonpecuniary benefits to farming are large and keep small, low-productivity farms in business. Although farmers are risk averse, eliminating uninsured production risk has only modest effects on capital and output. (JEL C51, D24, G32, Q12, Q14)

Bayesian estimation of agent-based models

We consider Bayesian inference techniques for agent-based (AB) models, as an alternative to simulated minimum distance (SMD). Three computationally heavy steps are involved: (i) simulating the model, (ii) estimating the likelihood and (iii) sampling from the posterior distribution of the parameters. Computational complexity of AB models implies that efficient techniques have to be used with respect to points (ii) and (iii), possibly involving approximations. We first discuss non-parametric (kernel density) estimation of the likelihood, coupled with Markov chain Monte Carlo sampling schemes. We then turn to parametric approximations of the likelihood, which can be derived by observing the distribution of the simulation outcomes around the statistical equilibria, or by assuming a specific form for the distribution of external deviations in the data. Finally, we introduce Approximate Bayesian Computation techniques for likelihood-free estimation. These allow embedding SMD methods in a Bayesian framework, and are particularly suited when robust estimation is needed. These techniques are first tested in a simple price discovery model with one parameter, and then employed to estimate the behavioural macroeconomic model of De Grauwe (2012), with nine unknown parameters.

Assortative Matching on Income Potentials, Intra-Household Specialization and Human Capital Formation

This paper develops a novel model of marital sorting on income potentials: In the marriage market, people are matching on potential wage growth rates which differ across individuals. Gains from marriage arise from intra-household specialization as couples make joint decisions on how much time to spend on home production and how much time on labour market work. Couples' specialization decisions hence affect their human capital accumulation in the labour market and the realization of their potential income. The model is estimated by simulated minimum distance techniques with PSID data from 1968 to 2011. I find there is strong positive assortative matching on wage growth rates, which helps explain the correlated wage residuals for married couples. Households' market intensity and specialization arrangements are not affected when matching is switched to random, but the observed average wage growth rates would be higher. The estimated elasticity of substitution between market goods and home production is approximately 0.37. Husband's time and wife's time turn out to be complements in the home production function.

Estimation of ergodic agent-based models by simulated minimum distance

Two difficulties arise in the estimation of AB models: (i) the criterion function has no simple analytical expression, (ii) the aggregate properties of the model cannot be analytically understood. In this paper we show how to circumvent these difficulties and under which conditions ergodic models can be consistently estimated by simulated minimum distance techniques, both in a long-run equilibrium and during an adjustment phase.

Search and Non-Wage Job Characteristics

This paper quantifies the importance of non-wage job characteristics to workers by estimating a structural on-the-job search model. The model generalizes the standard search framework by allowing workers to search for jobs based on both wages and job-specific non-wage utility flows. Within the structure of the search model, data on accepted wages and wage changes at job transitions identify the importance of non-wage utility through revealed preference. The parameters of the model are estimated by simulated minimum distance using the 1997 cohort of the National Longitudinal Survey of Youth (NLSY97). The estimates reveal that utility from non-wage job characteristics plays an important role in determining job mobility, the value of jobs to workers, and the gains from job search. More specifically, non-wage utility accounts for approximately one-third of the total gains from job mobility. These large non-pecuniary gains from search are missed by search models which assume that the wage captures the entire value of a job to a worker.

Health Inequality Over the Life-Cycle

We investigate the evolution of health inequality over the life-course. Health is modeled as a latent variable that is determined by three factors: endowments, and permanent and transitory shocks. We employ Simulated Minimum Distance and the Panel Study of Income Dynamics to estimate the model. We estimate that permanent shocks account for under 10% of the total variation in health for the college educated, but between 35% and 70% of total health variability for people without college degrees. Consistent with this, we find that health inequality moves substantially more slowly over the life-course for the college educated.

Job Search, Bargaining, and Wage Dynamics

This article constructs and estimates a model of wage bargaining with on‐the‐job search to explore three different components of wages: general human capital, match‐specific capital, and outside options. As the workers find better job opportunities, the current employer has to compete with outside firms to retain them. This between‐firm competition results in wage growth even when productivity remains the same. The model is estimated by a simulated minimum distance estimator and data from the 1979 National Longitudinal Study of Youth. The results indicate that the improved value of the outside option raises wages by 14%–16% in the first 5 years.

Simulated minimum Hellinger distance estimation of stochastic volatility models

A simultaneously efficient and robust approach for distribution-free parametric inference, called the simulated minimum Hellinger distance (SMHD) estimator, is proposed. In the SMHD estimation, the Hellinger distance between the nonparametrically estimated density of the observed data and that of the simulated samples from the model is minimized. The method is applicable to the situation where the closed-form expression of the model density is intractable but simulating random variables from the model is possible. The robustness of the SMHD estimator is equivalent to the minimum Hellinger distance estimator. The finite sample efficiency of the proposed methodology is found to be comparable to the Bayesian Markov chain Monte Carlo and maximum likelihood Monte Carlo methods and outperform the efficient method of moments estimators. The robustness of the method to a stochastic volatility model is demonstrated by a simulation study. An empirical application to the weekly observations of foreign exchange rates is presented.

Estimating Dynamic Models of Imperfect Competition

We describe a two-step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including industry competition models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).

Entry costs and stock market participation over the life cycle

Several explanations for the observed limited stock market participation have been offered in the literature. One of the most promising is the presence of market frictions mostly in the form of fixed entry and/or transaction costs. Empirical studies point to a significant structural (state) dependence in the stock market entry decision, which is consistent with costs of this type. However, the magnitude of these costs is not yet known. This paper focuses on fixed stock market entry costs. I set up a structural estimation procedure which involves solving and simulating a life cycle intertemporal portfolio choice model augmented with a fixed stock market entry cost. Important features of household portfolio data (from the PSID) are matched to their simulated counterparts. Utilizing a Simulated Minimum Distance estimator, I estimate the coefficient of relative risk aversion, the discount factor and the stock market entry cost. Given the equity premium and the calibrated income process, I estimate a one-time entry cost of approximately two percent of the permanent component of the annual labor income. My estimated model matches the zero median holding as well as the hump-shaped age–participation profile observed in the data.

Job Search, Bargaining, and Wage Dynamics

What are the sources of rapid wage growth during a worker’s early career? To address this question, I construct and estimate a model of strategic wage bargaining with on-the-job search to explore three different components of wages: general human capital, match-specific capital, and outside option. Workers search for alternative job opportunities on the job and accumulate human capital through learning-by-doing. As the workers find better job opportunities, the current employer has to compete with outside firms to retain them. This between-firm competition improves the outside option value of the worker, which results in wage growth on the job even when productivity remains the same. The model is estimated by a simulated minimum distance estimator and data from the NLSY 79. The parameter estimates are used to simulate counterfactuals. The results indicate that the improved value of outside option raises wages of ten-year-experienced workers by 16%, which accounts for about 30% of the wage growth during the first ten years of career. I also find that human capital accumulation affects wage profile not only because it directly changes labor productivity, but also because it alters job search behavior due to low future productivity.

Job Search, Bargaining, and Wage Dynamics

What are the sources of rapid wage growth during a worker's early career? To address this question, I construct and estimate a model of strategic wage bargaining with on-the-job search to explore three different components of wages: general human capital, match-specific capital, and bargaining position. Workers search for alternative job opportunities on the job and accumulate human capital through learning-by-doing. As the workers find better job opportunities, the current employer has to compete with outside firms to retain them. This between-firm competition improves the outside option value of the worker, which results in wage growth on the job even when productivity remains the same. The model is estimated by a simulated minimum distance estimator and data from the NLSY 79. The parameter estimates are used to simulate counterfactuals. Through these simulations I find that only 60% of the observed wage growth reflects the accumulation of general human capital. The growth match-specific capital through job changes accounts for about 20%. The improved bargaining position explains the remaining 20% of the wage growth. The results suggest that labor market frictions explain a larger part of wage growth than previously considered in the literature.

Estimating Dynamic Models of Imperfect Competition

We describe a two-step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including industry competition models with both discrete and continuous controls such as the Ericson and Pakes (1995) model. We test the algorithm on a class of dynamic discrete choice models with normally distributed errors, and a class of dynamic oligopoly models similar to that of Pakes and McGuire (1994).