Estimation of Engel Curves from Survey Data with Zero Expenditures*

The objective of this article is to propose a Bayesian method for estimating a system of Engel functions using survey data that include zero expenditures. We deal explicitly with the problem of zero expenditures in the model and estimate a system of Engel functions that satisfy the adding‐up condition. Furthermore, using Markov chain Monte Carlo method, we estimate unobservable parameters, including consumption of commodities, total consumption and equivalence scale, and use their posterior distributions to calculate inequality measures and total consumption elasticities.     

Quadratic Engel Curves with Measurement Error: Evidence from a Budget Survey*

This paper examines the importance of accounting for measurement error in total expenditure in the estimation of Engel curves, based on the 1994 Ethiopian Urban Household Survey. Using Lewbel's [Review of Economics and Statistics (1996 ), Vol. 78, pp. 718–725] estimator for demand models with correlated measurement errors in the dependent and independent variables, we find robust evidence of a quadratic relationship between food share and total expenditure in the capital city, and significant biases in various estimators that do not correct for correlated measurement errors.     

Contemporaneous threshold autoregressive models: Estimation,testing and forecasting

This paper proposes a contemporaneous smooth transition threshold autoregressive model (C-STAR) as a modification of the smooth transition threshold autoregressive model surveyed in Teräsvirta [1998. Modelling economic relationships with smooth transition regressions. In: Ullah, A., Giles, D.E.A. (Eds.), Handbook of Applied Economic Statistics. Marcel Dekker, New York, pp. 507–552.], in which the regime weights depend on the ex ante probability that a latent regime-specific variable will exceed a threshold value. We argue that the contemporaneous model is well suited to rational expectations applications (and pricing exercises), in that it does not require the initial regimes to be predetermined. We investigate the properties of the model and evaluate its finite-sample maximum likelihood performance. We also propose a method to determine the number of regimes based on a modified Hansen [1992. The likelihood ratio test under nonstandard conditions: testing the Markov switching model of GNP. Journal of Applied Econometrics 7, S61–S82.] procedure. Furthermore, we construct multiple-step ahead forecasts and evaluate the forecasting performance of the model. Finally, an empirical application of the short term interest rate yield is presented and discussed.     

Estimating high-dimensional demand systems in the presence of many binding non-negativity constraints

Two econometric issues arise in the structural estimation of consumer or producer demand systems in the presence of many binding non-negativity constraints. Firstly, most existing methods entail the evaluation of multivariate probability integrals. Secondly, the issue of statistical coherency must be addressed. We circumvent both of these issues using Gibbs’ Sampling, along with data augmentation and rejection sampling. We illustrate our method using several simulated data sets.     

Generalized empirical likelihood tests in time series models with potential identification failure

We introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models. The test statistics generalize those in Guggenberger and Smith [2005. Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21 (4), 667–709] from the i.i.d. to the time series context and are alternatives to those in Kleibergen [2005a. Testing parameters in GMM without assuming that they are identified. Econometrica 73 (4), 1103–1123] and Otsu [2006. Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22 (3), 513–527]. The main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification. More precisely, we show that the statistics are asymptotically distributed as chi-square under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright [2000. GMM with weak identification. Econometrica 68 (5), 1055–1096]. We also introduce a modification to Otsu's (2006) statistic that is computationally more attractive. A Monte Carlo study reveals that the finite-sample performance of the suggested tests is very competitive.     

Nonlinear models for strongly dependent processes with financial applications

This paper is motivated by recent evidence that many univariate economic and financial time series have both nonlinear and long memory characteristics. Hence, this paper considers a general nonlinear, smooth transition regime autoregression which is embedded within a strongly dependent, long memory process. A time domain MLE$MLE$ with simultaneous estimation of the long memory, linear AR$AR$ and nonlinear parameters is shown to have desirable asymptotic properties. The Bayesian and Hannan–Quinn information criteria are shown to provide consistent model selection procedures. The paper also considers an alternative two step estimator where the original time series is fractionally filtered from an initial semi-parametric estimate of the long memory parameter. Simulation evidence indicates that the time domain MLE$MLE$ is generally superior to the two step estimator. The paper also includes some applications of the methodology and estimation of a fractionally integrated, nonlinear autoregressive-ESTAR$ESTAR$ model to forward premium and real exchange rates.     

Twin Data vs. Longitudinal Data to Control for Unobserved Variables in Earnings Functions – Which Are the Differences?*

This paper compares two different approaches empirically to control for unobserved characteristics when estimating the effect of marriage on male and female earnings: the longitudinal and the twins approach. The estimates were obtained by exploiting the longitudinal dimension of a large sample of Swedish twins, so that longitudinal and twin‐based estimates could be obtained in the same sample. The two approaches lead to different conclusions both regarding the role of unobserved characteristics in the cross‐sectional earnings–marriage relationship and the effect of marriage on earnings. The paper investigates three potential explanations of this difference.     

Testing and imposing Slutsky symmetry in nonparametric demand systems

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non- and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they offer powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the differing convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and finite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We find that our nonparametric analysis yields statistically significantly and qualitatively different results from traditional parametric estimators and tests.     

Who Benefits from Marriage?*

The phenomenon that married men earn higher average wages than unmarried men – the marriage premium – is well known. However, the robustness of the premium across the wage distribution and the underlying causes of the marriage premium are unclear. Focusing on the entire wage distribution and employing recently developed semi‐non‐parametric tests for quantile treatment effects, our findings cast doubt on the robustness of the premium. We find that the premium is explained by selection above the median, whereas a positive premium is obtained only at very low wages. The causal effect at low wages may be attributable to employer discrimination.     

Bayesian hypothesis testing in latent variable models

Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on the decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function. In addition, it is easy to interpret. The method is illustrated using a one-factor asset pricing model and a stochastic volatility model with jumps.     

Endogenous household interaction

Most econometric models of intrahousehold behavior assume that household decision making is efficient, i.e., utility realizations lie on the Pareto frontier. In this paper, we investigate this claim by adding a number of participation constraints to the household allocation problem. Short-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize under (inefficient) Nash equilibrium. Long-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize by cheating on the efficient allocation and receiving Nash equilibrium payoffs in all successive periods. Given household characteristics and the (common) discount factor of the spouses, not all households may be able to attain payoffs on the Pareto frontier. We estimate these models using a Method of Simulated Moments estimator and data from one wave of the Panel Study of Income Dynamics. We find that both short- and long-run constraints are binding for sizable proportions of households in the sample. We conclude that it is important to carefully model the constraint sets household members face when modeling household allocation decisions, and to allow for the possibility that efficient outcomes may not be implementable for some households.     

Estimation of Markov regime-switching regression models with endogenous switching

Following Hamilton [1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384], estimation of Markov regime-switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous. We relax this assumption and develop a parsimonious model of endogenous Markov regime-switching. Inference via maximum likelihood estimation is possible with relatively minor modifications to existing recursive filters. The model nests the exogenous switching model, yielding straightforward tests for endogeneity. In Monte Carlo experiments, maximum likelihood estimates of the endogenous switching model parameters were quite accurate, even in the presence of certain model misspecifications. As an application, we extend the volatility feedback model of equity returns given in Turner et al. [1989. A Markov model of heteroskedasticity, risk, and learning in the stock market. Journal of Financial Economics 25, 3–22] to allow for endogenous switching.     

Reliable inference for the Gini index

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference based on the approximation is checked in a number of simulation experiments, and is found to be very good unless the tail of the underlying distribution is heavy. Bootstrap methods are presented which alleviate this problem except in cases in which the variance is very large or fails to exist. Similar methods can be used to find reliable standard errors of other indices which are not simply linear functionals of the distribution function, such as Sen’s poverty index and its modification known as the Sen–Shorrocks–Thon index.     

How Does Childbirth Alter Intrahousehold Resource Allocation? Evidence from Japan*

Exploiting unique panel data that include direct measurements of resource allocation within households, we investigated the impact of childbirth on intrahousehold allocation for married Japanese couples. Based on a collective model of the household, we developed reduced‐form and structural‐form estimation equations that allow us to focus on private goods to track the changes in intrahousehold resource allocation. We found one additional child is associated with a reduction in the wife's private expenditure share by at least two percentage points. This may be because she substitutes more say in decisions on the children for her own private expenditure share.     

Bayesian identification,selection and estimation of semiparametric functions in high-dimensional additive models

In this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions. Each function is written as a linear combination of basis terms, with coefficients regularized by a proper linearly constrained Gaussian prior. Given any potentially rank deficient prior precision matrix, we show how to derive linear constraints so that the corresponding effect is identified in the additive model. This allows for the use of a wide range of bases and precision matrices in priors for regularization. By introducing indicator variables, each constrained Gaussian prior is augmented with a point mass at zero, thus allowing for function selection. Posterior inference is calculated using Markov chain Monte Carlo and the smoothness in the functions is both the result of shrinkage through the constrained Gaussian prior and model averaging. We show how using non-degenerate priors on the shrinkage parameters enables the application of substantially more computationally efficient sampling schemes than would otherwise be the case. We show the favourable performance of our approach when compared to two contemporary alternative Bayesian methods. To highlight the potential of our approach in high-dimensional settings we apply it to estimate two large seemingly unrelated regression models for intra-day electricity load. Both models feature a variety of different univariate and bivariate functions which require different levels of smoothing, and where component selection is meaningful. Priors for the error disturbance covariances are selected carefully and the empirical results provide a substantive contribution to the electricity load modelling literature in their own right.     

Learning and the value of information: Evidence from health plan report cards

This paper develops a framework to analyze the value of information in the context of health plan choice. We use a Bayesian learning model to estimate the impact and value of information using data from a large employer, which started distributing health plan ratings to its employees in 1997. We estimate the parameters of the model with simulated maximum likelihood, and use the estimates to quantify the value of the report card information. We model both continuous specifications with Gaussian priors and signals, and discrete specifications with Beta priors and Binomial signals. We find that the release of information had a statistically significant effect on health plan choices. Consumers were willing to pay about $330 per year per below expected performance rating avoided, and the average value of the report card per employee was about $20 per year. We find large variation in valuations across different performance domains, but no significant evidence of heterogeneity based on observable employee characteristics or unobservable dimensions.     

Finite sample multivariate structural change tests with application to energy demand models

This paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models, in which case commonly used structural change tests remain asymptotic. As in Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68], we account for intervening nuisance parameters through a two-stage maximized Monte Carlo test procedure. Our contributions can be classified into five categories: (i) we extend tests for which a finite-sample theory has been supplied for Gaussian distributions to the non-Gaussian context; (ii) we show that Bai et al. [1998. Testing and dating common breaks in multi-variate time series. The Review of Economic Studies 65 (3), 395–432] test severely over-rejects and propose exact variants of this test; (iii) we consider predictive break test approaches which generalize tests in Dufour [1980. Dummy variables and predictive tests for structural change. Economics Letters 6, 241–247] and Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68]; (iv) we propose exact (non-Bonferonni based) extensions of the multivariate outliers test from Wilks [1963. Multivariate statistical outliers. Sankhya Series A 25, 407–426] to models with covariates; (v) we apply these tests to the energy demand system analyzed by Arsenault et al. [1995. A total energy demand model of Québec: forecasting properties. Energy Economics 17 (2), 163–171]. For two out of the six industrial sectors analyzed over the 1962–2000 period, break and further goodness-of-fit and diagnostic tests allow to identify (and correct) specification problems arising from historical regulatory changes or (possibly random) industry-specific effects. The procedures we propose have potential useful applications in statistics, econometrics and finance (e.g. event studies).     

Maximum likelihood estimation of partially observed diffusion models

This paper develops a maximum likelihood (ML) method to estimate partially observed diffusion models based on data sampled at discrete times. The method combines two techniques recently proposed in the literature in two separate steps. In the first step, the closed form approach of Aït-Sahalia (2008) is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states. In the second step, the efficient importance sampling technique of Richard and Zhang (2007) is used to integrate out the latent states, thereby yielding the likelihood function. Using both simulated and real data, we show that the proposed ML method works better than alternative methods. The new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations. Therefore, the method has a wide range of applicability and its computational cost is moderate.     

Estimation of technical and allocative inefficiency: A primal system approach

The estimation of technical and allocative inefficiencies using a flexible (translog) cost system is found to be quite difficult, especially when both the inefficiencies are random. In this paper we use the alternative primal system consisting of the production function (translog) and the first-order conditions of cost minimization. The estimation of the primal system is more straightforward and it enables us to estimate observation-specific technical and allocative inefficiencies, and their impact on input demand and cost. We use data on steam-electric generating plants from the U.S. to estimate the model using both Cobb–Douglas and translog production functions.