Inferential methods for elasticity estimates

Elasticities are often estimated from the results of demand analysis. However, drawing inferences from them may involve assumptions that could influence the outcome. In this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the Fieller method for the construction of confidence intervals can be used to draw inferences.     

Tikhonov regularization for nonparametric instrumental variable estimators

We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivatives. After showing its consistency in the Sobolev norm and uniform consistency under an embedding condition, we derive the expression of the asymptotic Mean Integrated Square Error and the rate of convergence. The optimal value of the regularization parameter is characterized in two examples. We illustrate our theoretical findings and the small sample properties with simulation results. Finally, we provide an empirical application to estimation of an Engel curve, and discuss a data driven selection procedure for the regularization parameter.     

Nonparametric estimation and inference about the overlap of two distributions

This paper develops methodology for nonparametric estimation of a measure of the overlap of two distributions based on kernel estimation techniques. This quantity has been proposed as a measure of economic polarization between two groups, Anderson (2004) and Anderson et al. (2010). In ecology it has been used to measure the overlap of species. We give the asymptotic distribution theory of our estimator, which in some cases of practical relevance is nonstandard due to a boundary value problem. We also propose a method for conducting inference based on estimation of unknown quantities in the limiting distribution and show that our method yields consistent inference in all cases we consider. We investigate the finite sample properties of our methods by simulation methods. We give an application to the study of polarization within China in recent years using household survey data from two provinces taken in 1987 and 2001. We find a big increase in polarization between 1987 and 2001 according to monetary outcomes but less change in terms of living space.     

Efficient estimation of a multivariate multiplicative volatility model

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series. We find that the univariate model of Engle and Rangel (2008) appears to be violated in the data whereas our multivariate model is more consistent with the data.     

What model for entry in first-price auctions? A nonparametric approach

We develop a selective entry model for first-price auctions that nests two polar models often estimated in the empirical literature on auctions, Levin and Smith (1994), and Samuelson (1985). The selective entry model features a pro-competitive selection effect. The selection effect is shown to be nonparametrically identifiable, and a nonparametric test for its presence is proposed. This test can be used to discriminate between the two polar models.     

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.     

Subsampling high frequency data

The main contribution of this paper is to propose a novel way of conducting inference for an important general class of estimators that includes many estimators of integrated volatility. A subsampling scheme is introduced that consistently estimates the asymptotic variance for an estimator, thereby facilitating inference and the construction of valid confidence intervals. The new method does not rely on the exact form of the asymptotic variance, which is useful when the latter is of complicated form. The method is applied to the volatility estimator of Aït-Sahalia et al. (2011) in the presence of autocorrelated and heteroscedastic market microstructure noise.     

A smoothed least squares estimator for threshold regression models

We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen [2000. Sample splitting and threshold estimation. Econometrica 68, 575–603] to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold effect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the slope and threshold parameters.     

Testing for non-nested conditional moment restrictions using unconditional empirical likelihood

We propose non-nested hypothesis tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional moment restrictions, we construct Kolmogorov–Smirnov and Cramér–von Mises type moment encompassing tests. Advantages of our tests over Otsu and Whang’s (2011) tests are: (i) they are free from smoothing parameters, (ii) they can be applied to weakly dependent data, and (iii) they allow non-smooth moment functions. We derive the null distributions, validity of a bootstrap procedure, and local and global power properties of our tests. The simulation results show that our tests have reasonable size and power performance in finite samples.     

Semi-nonparametric estimation and misspecification testing of diffusion models

Novel transition-based misspecification tests of semiparametric and fully parametric univariate diffusion models based on the estimators developed in [Kristensen, D., 2010. Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models. Journal of Econometrics 156, 239-259] are proposed. It is demonstrated that transition-based tests in general lack power in detecting certain departures from the null since they integrate out local features of the drift and volatility. As a solution to this, tests that directly compare drift and volatility estimators under the relevant null and alternative are also developed which exhibit better power against local alternatives.     

Robustness and inference in nonparametric partial frontier modeling

A major aim in recent nonparametric frontier modeling is to estimate a partial frontier well inside the sample of production units but near the optimal boundary. Two concepts of partial boundaries of the production set have been proposed: an expected maximum output frontier of order m=1,2,… and a conditional quantile-type frontier of order α∈]0,1]. In this paper, we answer the important question of how the two families are linked. For each m, we specify the order α for which both partial production frontiers can be compared. We show that even one perturbation in data is sufficient for breakdown of the nonparametric order-m frontiers, whereas the global robustness of the order-α frontiers attains a higher breakdown value. Nevertheless, once the α frontiers break down, they become less resistant to outliers than the order-m frontiers. Moreover, the m frontiers have the advantage to be statistically more efficient. Based on these findings, we suggest a methodology for identifying outlying data points. We establish some asymptotic results, contributing to important gaps in the literature. The theoretical findings are illustrated via simulations and real data.     

Nonparametric tests of collectively rational consumption behavior: An integer programming procedure

We present an IP-based nonparametric (revealed preference) testing procedure for rational consumption behavior in terms of a general collective model, which includes consumption externalities and public consumption. An empirical application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the practical usefulness of the procedure. Finally, we present extensions of the testing procedure to evaluate the goodness-of-fit (accounting for optimization error as well as measurement error) of the collective model subject to testing.     

Semiparametric inference in a GARCH-in-mean model

A new semiparametric estimator for an empirical asset pricing model with general nonparametric risk-return tradeoff and GARCH-type underlying volatility is introduced. Based on the profile likelihood approach, it does not rely on any initial parametric estimator of the conditional mean function, and it is under stated conditions consistent, asymptotically normal, and efficient, i.e., it achieves the semiparametric lower bound. A sampling experiment provides finite sample comparisons with the parametric approach and the iterative semiparametric approach with parametric initial estimate of Conrad and Mammen (2008). An application to daily stock market returns suggests that the risk-return relation is indeed nonlinear.     

An alternative approach to estimating demand: Neural network regression with conditional volatility for high frequency air passenger arrivals

In this paper we provide an alternative approach to analyze the demand for international tourism in the Balearic Islands, Spain, by using a neural network model that incorporates time-varying conditional volatility. We consider daily air passenger arrivals to Palma de Mallorca, Ibiza and Mahon, which are located in the islands of Mallorca, Ibiza and Menorca, respectively, as a proxy for international tourism demand for the Balearic Islands. Spain is a world leader in terms of total international tourist arrivals and receipts, and Mallorca is one of the most popular destinations in Spain. For tourism management and marketing, it is essential to forecast high frequency international tourist demand accurately. As it is important to provide sensible international tourism demand forecast intervals, it is also necessary to model their variances accurately. Moreover, time-varying variances provide useful information regarding the risks associated with variations in international tourist arrivals.