nep-ecm New Economics Papers
on Econometrics
Issue of 2015‒11‒01
twenty-two papers chosen by
Sune Karlsson
Örebro universitet

  1. Inference under covariate-adaptive randomization By Federico Bugni; Ivan Canay *; Azeem Shaikh
  2. Nonparametric specification testing via the trinity of tests By Abhimanyu Gupta
  3. Model averaging in semiparametric estimation of treatment effects By Toru Kitagawa; Chris Muris
  4. Characterizations of identified sets delivered by structural econometric models By Andrew Chesher; Adam Rosen
  5. Constrained conditional moment restriction models By Victor Chernozhukov; Whitney Newey; Andres Santos
  6. Welfare Consequences of Information Aggregation and Optimal Market Size By William E. Griffiths; Gholamreza Hajargasht
  7. Testing exogeneity in nonparametric instrumental variables identified by conditional quantile restrictions By Jia-Young Michael Fu; Joel Horowitz; Matthias Parey
  8. Bayesian Inference on Structural Impulse Response Functions By Mikkel Plagborg-Møller
  9. Multivariate return decomposition: theory and implications By Anatolyev, Stanislav; Gospodinov, Nikolay
  10. Testing constancy of unconditional variance in volatility models by misspecification and specification tests By Annastiina Silvennoinen; Timo Teräsvirta
  11. Econometrics of network models By Áureo de Paula
  12. Clinical trial design enabling e-optimal treatment rules By Charles F. Manski; Aleksey Tetenov
  13. Spatial Distribution Dynamics By Stefano Magrini; Margherita Gerolimetto
  14. Variable Selection for a Categorical Varying-Coefficient Model with Identifications for Determinants of Body Mass Index By Jiti Gao; Bin Peng; Zhao Ren; Xiaohui Zhang
  15. Granger-causal analysis of GARCH models: a Bayesian approach By Tomasz Wozniak
  16. Finite sample bias corrected IV estimation for weak and many instruments By Matthew Harding; Jerry Hausman; Christopher Palmer
  17. Pseudo Maximum Likelihood Estimation of Spatial Autoregressive Models with Increasing Dimension By Abhimanyu Gupta; Peter M Robinson
  18. Specification and Estimation of Bayesian Dynamic Factor Models: A Monte Carlo Analysis with an Application to Global House Price Comovement By Jackson, Laura E.; Kose, M. Ayhan; Otrok, Christopher; Owyang, Michael T.
  19. Parametric and Semiparametric IV Estimation of Network Models with Selectivity By Tiziano Arduini; Eleonora Patacchini; Edoardo Rainone
  20. Beyond Truth-Telling: Preference Estimation with Centralized School Choice By Gabrielle Fack; Julien Grenet; Yinghua He
  21. Vector quantile regression: an optimal transport approach By Guillaume Carlier; Victor Chernozhukov; Alfred Galichon
  22. Nonparametric estimation and inference under shape restrictions By Joel Horowitz; Sokbae (Simon) Lee

  1. By: Federico Bugni (Institute for Fiscal Studies and Duke University); Ivan Canay * (Institute for Fiscal Studies); Azeem Shaikh (Institute for Fiscal Studies)
    Abstract: This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that ?rst stratify according to baseline covariates and then assign treatment status so as to achieve 'balance' within each stratum. Such schemes include, for example, Efron's biased-coin design and strati?ed block randomization. When testing the null hypothesis that the average treatment effect equals a pre-speci?ed value in such settings, we ?rst show that the usual two-sample t-test is conservative in the sense that it has limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level. In a simulation study, we ?nd that the rejection probability may in fact be dramatically less than the nominal level. We show further that these same conclusions remain true for a naïve permutation test, but that a modi?ed version of the permutation test yields a test that is non-conservative in the sense that its limiting rejection probability under the null hypothesis equals the nominal level. The modi?ed version of the permutation test has the additional advantage that it has rejection probability exactly equal to the nominal level for some distributions satisfying the null hypothesis. Finally, we show that the usual t-test (on the coefficient on treatment assignment) in a linear regression of outcomes on treatment assignment and indicators for each of the strata yields a non-conservative test as well. In a simulation study, we ?nd that the non-conservative tests have substantially greater power than the usual two-sample t-test.
    Date: 2015–08
  2. By: Abhimanyu Gupta
    Abstract: Tests are developed for inference on a parameter vector whose dimension grows slowly with sample size. The statistics are based on the Lagrange Multiplier, Wald and (pseudo) Likelihood Ratio principles, admit standard normal asymptotic distributions under the null and are straightforward to compute. They are shown to be consistent and possessing non-trivial power against local alternatives. The settings considered include multiple linear regression, panel data models with fixed effects and spatial autoregressions. When a nonparametric regression function is estimated by series, we use our statistics to propose specification tests, and in semiparametric adaptive estimation we provide a test for correct error distribution specification. These tests are nonparametric but handled in practice with parametric techniques. A Monte Carlo study suggests that our tests perform well in finite samples. Two empirical examples use them to test for correct shape of an electricity distribution cost function and linearity and equality of Engel curves.
    Date: 2015–10–22
  3. By: Toru Kitagawa (Institute for Fiscal Studies and cemmap and University College London); Chris Muris (Institute for Fiscal Studies)
    Abstract: In the practice of program evaluation, choosing the covariates and the functional form of the propensity score is an important choice that the researchers make when estimating treatment e?ects. This paper proposes a data-driven way of averaging the estimators over the candidate speci?cations in order to resolve the issue of speci?cation uncertainty in the propensity score weighting estimation of the average treatment e?ects for treated (ATT). The proposed averaging procedures aim to minimize the estimated mean squared error (MSE) of the ATT estimator in a local asymptotic framework. We formulate model averaging as a statistical decision problem in a limit experiment, and derive an averaging scheme that is Bayes optimal with respect to a given prior for the localization parameters. Analytical comparisons of the Bayes asymptotic MSE show that the averaging estimator outperforms post model selection estimators and the estimators in any of the candidate models. Our Monte Carlo studies con?rm these theoretical results and illustrate the size of the MSE gains from averaging. We apply the averaging procedure to evaluate the e?ect of the labor market program analyzed in LaLonde (1986).
    Date: 2015–08
  4. By: Andrew Chesher (Institute for Fiscal Studies and University College London); Adam Rosen (Institute for Fiscal Studies and cemmap and UCL)
    Abstract: This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous and/or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can arise when there are multiple sources of heterogeneity, censored or discrete endogenous variables, or inequality restrictions on functions of observed and unobserved variables. The models generalize the class of incomplete instrumental variable (IV) models in which unobserved variables are single-valued functions of observed variables. Thus the models are referred to as Generalized IV (GIV) models, but there are important cases in which instrumental variable restrictions play no significant role. The paper provides the first formal definition of observational equivalence for incomplete models. The development uses results from random set theory which guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case-by-case proofs of sharpness. One innovation is the use of random sets defined on the space of unobserved variables. This allows identification analysis under mean and quantile independence restrictions on the distributions of unobserved variables conditional on exogenous variables as well as under a full independence restriction. It leads to a novel general characterization of identified sets of structural functions when the sole restriction on the distribution of unobserved and observed exogenous variables is that they are independently distributed. Illustrations are presented for a parametric random coefficients linear model and for a model with an interval censored outcome, in both cases with endogenous explanatory variables, and for an incomplete nonparametric model of English auctions. Numerous other applications are indicated.
    Keywords: Instrumental variables; endogeneity; excess heterogeneity; limited information; set identification; partial identification; random sets; incomplete models
    JEL: C10 C14 C24 C26
    Date: 2015–10
  5. By: Victor Chernozhukov (Institute for Fiscal Studies and MIT); Whitney Newey (Institute for Fiscal Studies and MIT); Andres Santos (Institute for Fiscal Studies and UC San Diego)
    Abstract: This paper examines a general class of inferential problems in semiparametric and nonparametric models defined by conditional moment restrictions. We construct tests for the hypothesis that at least one element of the identified set satisfies a conjectured (Banach space) “equality” and/or (a Banach lattice) “inequality” constraint. Our procedure is applicable to identified and partially identified models, and is shown to control the level, and under some conditions the size, asymptotically uniformly in an appropriate class of distributions. The critical values are obtained by building a strong approximation to the statistic and then bootstrapping a (conservatively) relaxed form of the statistic. Sufficient conditions are provided, including strong approximations using Koltchinskii's coupling. Leading important special cases encompassed by the framework we study include: (i) Tests of shape restrictions for infinite dimensional parameters; (ii) Confidence regions for functionals that impose shape restrictions on the underlying parameter; (iii) Inference for functionals in semiparametric and nonparametric models defined by conditional moment (in)equalities; and (iv) Uniform inference in possibly nonlinear and severely ill-posed problems.
    Keywords: Shape restrictions; inference on functional; conditional moment (in)equality restrictions; instrumental variables; nonparametric and semiparametric models; Banach space; Banach lattice; Koltchinskii coupling.
    Date: 2015–09
  6. By: William E. Griffiths (Department of Economics, University of Melbourne); Gholamreza Hajargasht (Department of Economics, University of Melbourne)
    Abstract: We consider mostly Bayesian estimation of stochastic frontier models where one-sided inefficiencies and/or the idiosyncratic error term are correlated with the regressors. We begin with a model where a Chamberlain-Mundlak device is used to relate a transformation of time-invariant effects to the regressors. This basic model is then extended in several directions: First an extra one-sided error term is added to allow for time-varying efficiencies. Next, a model with an equation for instrumental variables and a more general error covariance structure is introduced to accommodate correlations between both error terms and the regressors. Finally, we show how the analysis can be extended to a nonparametric technology using Bayesian penalised splines. An application of the first and second models to Philippines rice data is provided. A limited Monte Carlo experiment is used to investigate the consequences of ignoring correlation between the effects and the regressors, and choosing the wrong functional form for the technology.
    Keywords: Technical Efficiency, Penalised Splines, Gibbs Sampling
    JEL: C11 D24 C23 C12
    Date: 2015–01
  7. By: Jia-Young Michael Fu (Institute for Fiscal Studies); Joel Horowitz (Institute for Fiscal Studies and Northwestern University); Matthias Parey (Institute for Fiscal Studies and University of Essex)
    Abstract: This paper presents a test for exogeneity of explanatory variables in a nonparametric instrumental variables (IV) model whose structural function is identified through a conditional quantile restriction. Quantile regression models are increasingly important in applied econometrics. As with mean-regression models, an erroneous assumption that the explanatory variables in a quantile regression model are exogenous can lead to highly misleading results. In addition, a test of exogeneity based on an incorrectly specified parametric model can produce misleading results. This paper presents a test of exogeneity that does not assume the structural function belongs to a known finite-dimensional parametric family and does not require nonparametric estimation of this function. The latter property is important because, owing to the ill-posed inverse problem, a test based on a nonparametric estimator of the structural function has low power. The test presented here is consistent whenever the structural function differs from the conditional quantile function on a set of non-zero probability. The test has non-trivial power uniformly over a large class of structural functions that differ from the conditional quantile function by O(n-1/2) . The results of Monte Carlo experiments illustrate the usefulness of the test.
    Date: 2015–10
  8. By: Mikkel Plagborg-Møller
    Abstract: I propose to estimate structural impulse responses from macroeconomic time series by doing Bayesian inference on the Structural Vector Moving Average representation of the data. This approach has two advantages over Structural Vector Autoregressions. First, it imposes prior information directly on the impulse responses in a flexible and transparent manner. Second, it can handle noninvertible impulse response functions, which are often encountered in applications. To rapidly simulate from the posterior of the impulse responses, I develop an algorithm that exploits the Whittle likelihood. The impulse responses are partially identified, and I derive the frequentist asymptotics of the Bayesian procedure to show which features of the prior information are updated by the data. I demonstrate the usefulness of my method in a simulation study and in an empirical application that estimates the effects of technological news shocks on the U.S. business cycle.
    Date: 2015–10
  9. By: Anatolyev, Stanislav (New Economic School); Gospodinov, Nikolay (Federal Reserve Bank of Atlanta)
    Abstract: In this paper, we propose a model based on multivariate decomposition of multiplicative—absolute values and signs—components of several returns. In the m-variate case, the marginals for the m absolute values and the binary marginals for the m directions are linked through a 2m-dimensional copula. The approach is detailed in the case of a bivariate decomposition. We outline the construction of the likelihood function and the computation of different conditional measures. The finite-sample properties of the maximum likelihood estimator are assessed by simulation. An application to predicting bond returns illustrates the usefulness of the proposed method.
    Keywords: multivariate decomposition; multiplicative components; volatility and direction models; copula; dependence
    JEL: C13 C32 C51 G12
    Date: 2015–08–01
  10. By: Annastiina Silvennoinen (School of Economics and Finance, Queensland University of Technology); Timo Teräsvirta (Aarhus University and CREATES)
    Abstract: The topic of this paper is testing the hypothesis of constant unconditional variance in GARCH models against the alternative that the unconditional variance changes deterministically over time. Tests of this hypothesis have previously been performed as misspecification tests after fitting a GARCH model to the original series. It is found by simulation that the positive size distortion present in these tests is a function of the kurtosis of the GARCH process. Adjusting the size by numerical methods is considered. The possibility of testing the constancy of the unconditional variance before fitting a GARCH model to the data is discussed. The power of the ensuing test is vastly superior to that of the misspecification test and the size distortion minimal. The test has reasonable power already in very short time series. It would thus serve as a test of constant variance in conditional mean models. An application to exchange rate returns is included. JEL Classification: C32, C52
    Keywords: autoregressive conditional heteroskedasticity, modelling volatility, testing parameter constancy, time-varying GARCH
    Date: 2015–10–27
  11. By: Áureo de Paula (Institute for Fiscal Studies and University College London)
    Abstract: In this article I provide a (selective) review of the recent econometric literature on networks. I start with a discussion of developments in the econometrics of group interactions. I subsequently provide a description of statistical and econometric models for network formation and approaches for the joint determination of networks and interactions mediated through those networks. Finally, I give a very brief discussion of measurement issues in both outcomes and networks. My focus is on identification and computational issues, but estimation aspects are also discussed.
    Date: 2015–09
  12. By: Charles F. Manski (Institute for Fiscal Studies and Northwestern University); Aleksey Tetenov (Institute for Fiscal Studies and Collegio Carlo Alberto)
    Abstract: Medical research has evolved conventions for choosing sample size in randomized clinical trials that rest on the theory of hypothesis testing. Bayesians have argued that trials should be designed to maximize subjective expected utility in settings of clinical interest. This perspective is compelling given a credible prior distribution on treatment response, but Bayesians have struggled to provide guidance on specification of priors. We use the frequentist statistical decision theory of Wald (1950) to study design of trials under ambiguity. We show that e-optimal rules exist when trials have large enough sample size. An e-optimal rule has expected welfare within e of the welfare of the best treatment in every state of nature. Equivalently, it has maximum regret no larger than e. We consider trials that draw predetermined numbers of subjects at random within groups stratified by covariates and treatments. The principal analytical findings are simple sufficient conditions on sample sizes that ensure existence of e-optimal treatment rules when outcomes are bounded. These conditions are obtained by application of Hoeffding (1963) large deviations inequalities to evaluate the performance of empirical success rules.
    Date: 2015–09
  13. By: Stefano Magrini; Margherita Gerolimetto
    Abstract: It is quite common in convergence analyses across regions that data exhibit strong spatial dependence. While the literature adopting the regression approach is now fully aware that neglecting this feature may lead to inaccurate results and has therefore suggested a number of statistical tools for addressing the issue, research is only at a very initial stage within the distribution dynamics approach. In particular, in the continuous state-space framework, a few authors opted for spatial pre-filtering the data in order to guarantee the statistical properties of the estimates. In this paper we follow an alternative route that starts from the idea that spatial dependence is not just noise but can be a substantive element of the data generating process. In particular, we develop a tool that, building on the mean-bias adjustment procedure proposed by Hyndman et al. (1996), explicitly allows for spatial dependence in distribution dynamics analysis thus eliminating the need for pre-filtering. Using this tool, we then reconsider the evidence on convergence across regional economies in the US.
    Keywords: immigration; convergence; distribution dynamics; spatial effects
    JEL: J61 O47 C14 C21
    Date: 2015–10
  14. By: Jiti Gao; Bin Peng; Zhao Ren; Xiaohui Zhang
    Abstract: In this paper, we propose a variable selection procedure based on the shrinkage estimation technique for a categorical varying-coefficient model. We apply the method to identify the relevant determinants for body mass index (BMI) from a large amount of potential factors proposed in the multidisciplinary literature, using data from the 2013 National Health Interview Survey in the United States. We quantify the varying impacts of the relevant determinants of BMI across demographic groups.
    Keywords: ody Mass Index; Obesity; Varying-Coefficient; Variable Selection
    JEL: C13 C14 I15
    Date: 2015
  15. By: Tomasz Wozniak (Department of Economics, University of Melbourne)
    Abstract: A multivariate GARCH model is used to investigate Granger causality in the conditional variance of time series. Parametric restrictions for the hypothesis of noncausality in conditional variances between two groups of variables, when there are other variables in the system as well, are derived. These novel conditions are convenient for the analysis of potentially large systems of economic variables. To evaluate hypotheses of noncausality, a Bayesian testing procedure is proposed. It avoids the singularity problem that may appear in theWald test and it relaxes the assumption of the existence of higher-order moments of the residuals required in classical tests.
    Keywords: second-order noncausality, VAR-GARCH models, Bayesian hypotheses assessment
    JEL: C11 C12 C32 C53
    Date: 2015–05
  16. By: Matthew Harding (Institute for Fiscal Studies and Stanford University); Jerry Hausman (Institute for Fiscal Studies and MIT); Christopher Palmer (Institute for Fiscal Studies)
    Abstract: This paper considers the finite sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite sample unbiased k-class estimator, we introduce a double k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperforms Fuller (1977) estimators in terms of mean bias and MSE.
    Keywords: Instrumental variables; weak and many instruments; finite sample; k-class estimators
    JEL: C31 C13 C15
    Date: 2015–07
  17. By: Abhimanyu Gupta; Peter M Robinson
    Abstract: Pseudo maximum likelihood estimates are developed for higher-order spatial autoregres- sive models with increasingly many parameters, including models with spatial lags in the dependent variables and regression models with spatial autoregressive disturbances. We consider models with and without a linear or nonlinear regression component. Sucient conditions for consistency and asymptotic normality are provided, the results varying ac- cording to whether the number of neighbours of a particular unit diverges or is bounded. Monte Carlo experiments examine nite-sample behaviour.
    Date: 2015–10–22
  18. By: Jackson, Laura E. (Bentley University); Kose, M. Ayhan (World Bank); Otrok, Christopher (University of Missouri and Federal Reserve Bank of St. Louis); Owyang, Michael T. (Federal Reserve Bank of St. Louis)
    Abstract: We compare methods to measure comovement in business cycle data using multi-level dynamic factor models. To do so, we employ a Monte Carlo procedure to evaluate model performance for different specifications of factor models across three different estimation procedures. We consider three general factor model specifications used in applied work. The first is a single- factor model, the second a two-level factor model, and the third a three-level factor model. Our estimation procedures are the Bayesian approach of Otrok and Whiteman (1998), the Bayesian state space approach of Kim and Nelson (1998) and a frequentist principal components approach. The latter serves as a benchmark to measure any potential gains from the more computationally intensive Bayesian procedures. We then apply the three methods to a novel new dataset on house prices in advanced and emerging markets from Cesa-Bianchi, Cespedes, and Rebucci (2015) and interpret the empirical results in light of the Monte Carlo results.
    Keywords: principal components; Kalman filter; data augmentation; business cycles
    JEL: C3
    Date: 2015–08–26
  19. By: Tiziano Arduini (Sapienza University of Rome); Eleonora Patacchini (Cornell University, Sapienza University of Rome, EIEF, IZA and CEPR); Edoardo Rainone (Bank of Italy)
    Abstract: We propose parametric and semiparametric IV estimators for spatial autoregressive models with network data where the network structure is endogenous. We embed a dyadic network formation process in the control function approach as in Heckman and Robb (1985). In the semiparametric case, we use power series to approximate the correction terms. We establish the consistency and asymptotic normality for both parametric and semiparametric cases. We also investigate their finite sample properties via Monte Carlo simulation.
    Date: 2015
  20. By: Gabrielle Fack (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Julien Grenet (PSE - Paris-Jourdan Sciences Economiques - CNRS - Institut national de la recherche agronomique (INRA) - EHESS - École des hautes études en sciences sociales - ENS Paris - École normale supérieure - Paris - École des Ponts ParisTech (ENPC), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Yinghua He (TSE - Toulouse School of Economics - Toulouse School of Economics)
    Abstract: We propose novel approaches and tests for estimating student preferences with data from school choice mechanisms, e.g., the Gale-Shapley Deferred Acceptance. Without requiring truth-telling to be the unique equilibrium, we show that the matching is (asymptotically) stable, or justified-envy-free, implying that every student is assigned to her favorite school among those she is qualified for ex post. Having validated the methods in simulations, we apply them to data from Paris and reject truth-telling but not stability. Our estimates are then used to compare the sorting and welfare effects of alternative admission criteria prescribing how schools rank students in centralized mechanisms.
    Keywords: Gale-Shapley Deferred Acceptance Mechanism,School Choice,Stable Matching,Student Preferences,Admission Criteria,C78, D47, D50, D61, I21
    Date: 2015–10
  21. By: Guillaume Carlier (Institute for Fiscal Studies); Victor Chernozhukov (Institute for Fiscal Studies and MIT); Alfred Galichon (Institute for Fiscal Studies and Science Po, Paris)
    Abstract: We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector Y, taking values in Rd given covariates Z=z, taking values in Rk, is a map u --> QY|Z(u,z), which is monotone, in the sense of being a gradient of a convex function, and such that given that vector U follows a reference non-atomic distribution FU, for instance uniform distribution on a unit cube in Rd, the random vector QY|Z(U,z) has the distribution of Y conditional on Z=z. Moreover, we have a strong representation, Y =QY|Z(U,Z) almost surely, for some version of U. The vector quantile regression (VQR) is a linear model for CVQF of Y given Z. Under correct specification, the notion produces strong representation,Y=ß(U)Tf(Z),for f(Z) denoting a known set of transformations of Z, where u --> ß(u)T f(Z) is a monotone map, the gradient of a convex function, and the quantile regression coefficients u --> ß(u) have the interpretations analogous to that of the standard scalar quantile regression. As f(Z) becomes a richer class of transformations of Z, the model becomes nonparametric, as in series modelling. A key property of VQR is the embedding of the classical Monge-Kantorovich's optimal transportation problem at its core as a special case. In the classical case, where Y is scalar, VQR reduces to a version of the classical QR, and CVQF reduces to the scalar conditional quantile function. An application to multiple Engel curve estimation is considered.
    Keywords: Vector quantile regression; vector conditional quantile function; Monge-Kantorovich-Brenier
    Date: 2015–09
  22. By: Joel Horowitz (Institute for Fiscal Studies and Northwestern University); Sokbae (Simon) Lee (Institute for Fiscal Studies)
    Abstract: Economic theory often provides shape restrictions on functions of interest in applications, such as monotonicity, convexity, non-increasing (non-decreasing) returns to scale, or the Slutsky inequality of consumer theory; but economic theory does not provide finite-dimensional parametric models. This motivates nonparametric estimation under shape restrictions. Nonparametric estimates are often very noisy. Shape restrictions stabilize nonparametric estimates without imposing arbitrary restrictions, such as additivity or a single-index structure, that may be inconsistent with economic theory and the data. This paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions, such as the Slutsky inequality. The results of Monte Carlo experiments illustrate the finite-sample performance of the method, and an empirical example illustrates its use in an application.
    Date: 2015–10

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