
on Econometrics 
By:  Sun, Yixiao 
Abstract:  The paper develops the Ã–xedsmoothing asymptotics in a twostep GMM framework. Under this type of asymptotics, the weighting matrix in the secondstep GMM criterion function converges weakly to a random matrix and the twostep GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic and the LM statistic remain asymptotically pivotal. It is shown that critical values from the fixedsmoothing asymptotic distribution are high order correct under the conventional increasingsmoothing asymptotics. When an orthonormal series covariance estimator is used, the critical values can be approximated very well by the quantiles of a noncentral F distribution. A simulation study shows that the new statistical tests based on the fixedsmoothing critical values are much more accurate in size than the conventional chisquare test. 
Keywords:  Social and Behavioral Sciences, Physical Sciences and Mathematics, Fdistribution, Fixedsmoothing Asymptotics, Heteroskedasticity and Autocorrelation Robust, Increasingsmoothing Asymptotics, Noncentral F Test, Twostep GMM Estimation 
Date:  2013–06–01 
URL:  http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt64x4z265&r=ecm 
By:  Joel Horowitz (Institute for Fiscal Studies and Northwestern University) 
Abstract:  In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g say, is discontinuous and must be regularised (that is, modified) to make consistent estimation possible. The amount of modification is contolled by a regularisation parameter. The optimal value of this parameter depends on unknown population characteristics and cannot be calculated in applications. Theoretically justified methods for choosing the regularisatoin parameter empirically in applications are not yet available. This paper presents such a method for use in series estimation, where the regularisation parameter is the number of terms in a series approximation to g. The method does not required knowledge of the smoothness of g or of other unknown functions. It adapts to their unknown smoothness. The estimator of g based on the empirically selected regularisation parameter converges in probabillity at a rate that is at least as fast as the asymptotically optimal rate multiplied by (logn)1/2, where n is the sample size. The asymptotic integrated meansquare error (AIMSE) of the estimator is within a specified factor of the optimal AIMSE. 
Keywords:  illposed inverse problem. regularisatoin, sieve estimation, series estimation, nonparametric estimation 
JEL:  C13 C14 C21 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:30/13&r=ecm 
By:  J. Miguel Marín; M. T. Rodríguez Bernal; Eva Romero 
Abstract:  GARCH models include most of the stylized facts of financial time series and they have been largely used to analyze discrete financial time series. In the last years, continuous time models based on discrete GARCH models have been also proposed to deal with nonequally spaced observations, as COGARCH model based on Lévy processes. In this paper, we propose to use the data cloning methodology in order to obtain estimators of GARCH and COGARCH model parameters. Data cloning methodology uses a Bayesian approach to obtain approximate maximum likelihood estimators avoiding numerically maximization of the pseudolikelihood function. After a simulation study for both GARCH and COGARCH models using data cloning, we apply this technique to model the behavior of some NASDAQ time series 
Keywords:  GARCH, Continuoustime GARCH process, Lévy process, COGARCH, Data cloning, Bayesian inference, MCMC algorithm 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:cte:wsrepe:ws132723&r=ecm 
By:  Grote, Claudia; Sibbertsen, Philipp 
Abstract:  This paper investigates the finitesample properties of the smooth transitionbased cointegration test proposed by Kapetanios et al. (2006) when the data generating process under the alternative hypothesis is a globally stationary second order LSTR model. The provided procedure describes an application to longrun equilibrium relations involving real exchange rates with symmetric behaviour. We utilise the properties of the double LSTR transition function that features unit root behaviour within the inner regime and symmetric behaviour in the outer regimes. Hence, under the null hypothesis we imply no cointegration and globally stationary DLSTR cointegration under the alternative. As a result of the identification problem the limiting distribution derived under the null hypothesis is nonstandard. The Double LSTR is capable of producing threeregime TAR nonlinearity when the transition parameter tends to infinity as well as generating exponentialtype nonlinearity that closely approximates ESTR nonlinearity. Therefore, we find that the Double LSTR error correction model has power against both of these alternatives. 
Keywords:  Cointegration tests, LSTR, Monte carlo simulation, Nonlinear error correction 
JEL:  C12 C32 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:han:dpaper:dp514&r=ecm 
By:  Stéphane Bonhomme (CEMFI); Koen Jochmans (Département d'économie); JeanMarc Robin (Département d'économie) 
Abstract:  The aim of this paper is to provide simple nonparametric methods to estimate finitemixture models from data with repeated measurements. Three measurements suffice for the mixture to be fully identified and so our approach can be used even with very short panel data. We provide distribution theory for estimators of the mixing proportions and the mixture distributions, and various functionals thereof. We also discuss inference on the number of components. These estimators are found to perform well in a series of Monte Carlo exercises. We apply our techniques to document heterogeneity in log annual earnings using PSID data spanning the period 1969–1998. 
Keywords:  finitemixture model, nonparametric estimation, series expansion, simultaneousdiagonalization system. 
Date:  2013–03 
URL:  http://d.repec.org/n?u=RePEc:spo:wpecon:info:hdl:2441/7o52iohb7k6srk09n8t4k21sm&r=ecm 
By:  Susanne Schennach (Institute for Fiscal Studies and Brown University) 
Abstract:  This paper introduces a general method to convert a model defined by moment conditions involving both observed and unobserved variables into equivalent moment conditions involving only observable variables. This task can be accomplished without introducing infinitedimensional nuisance parameters using a leastfavourable entropymaximising distribution. We demonstrate, through examples and simulations, that this approach covers a wide class of latent variables models, including some gametheoretic models and models with limited dependent variables, intervalvalued data, errorsinvariables, or combinations thereof. Both point and setidentified models are transparently covered. In the latter case, the method also complements the recent literature on generic setinference methods by providing the moment conditions needed to construct a GMMtype objective function for a wide class of models. Extensions of the method that cover conditional moments, independence restrictions and some statespace models are also given. 
Keywords:  method of moments, latent variables, unobservables, partial indentification, entropy, simulations, leastfavourable family 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:32/13&r=ecm 
By:  Huang, Meng; Sun, Yixiao; White, Hal 
Abstract:  This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves rootn local power. The test statistic is based on an estimator of the topological "distance" between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in Ã–nite samples. As an application, we test the key assumption of unconfoundedness in the context of estimating the returns to schooling. 
Keywords:  Social and Behavioral Sciences, Physical Sciences and Mathematics, Conditional Independence, Generically Comprehensively Revealing, Nonparametric Test 
Date:  2013–05–01 
URL:  http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt3pt89204&r=ecm 
By:  Arthur Lewbel (Boston College); Thomas Tao Yang (Boston College) 
Abstract:  Assume individuals are treated if a latent variable, containing a continuous instrument, lies between two thresholds. We place no functional form restrictions on the latent errors. Here unconfoundedness does not hold and identification at infinity is not possible. Yet we still show nonparametric point identification of the average treatment effect. We provide an associated rootn consistent estimator. We apply our model to reinvestigate the invertedU relationship between competition and innovation, estimating the impact of moderate competitiveness on innovation without the distributional assumptions required by previous analyses. We find no evidence of an invertedU in US data. 
Keywords:  Average treatment effect, Ordered choice model, Special regressor, Semiparametric, Competition and innovation, Identification. 
JEL:  C14 C21 C26 
Date:  2013–07–01 
URL:  http://d.repec.org/n?u=RePEc:boc:bocoec:825&r=ecm 
By:  Andres AradillasLopez; Adam Rosen (Institute for Fiscal Studies and University College London) 
Abstract:  We study econometric models of complete information games with ordered action spaces, such as the number of store fronts operated in a market by a firm, or the daily number of flights on a citypair offered by an airline. The model generalises single agent models such as ordered probit and logit to a simultaneous model of ordred response. We characterise identified sets for model parameters under mild shape restrictions on agents' payoff functions. We then propose a novel inference method for a parametric version of our model based on a test statistic that embeds conditional moment inequalities implied by equilibrium behaviour. Using maximal inequalities for Uprocesses, we show that an asymptotically valid confidence set is attained by employing an easy to compute fixed critical value, namely the appropriate quantile of a chisquare random variable. We apply our method to study capacity decisions measured as the number of stores operated by Lowe's and Home Depot in geographic markets. We demonstrate how our confidence sets for model parameters can be used to perform inference on other quantities of economic interest, such as the probability that any given outcome is an equilibrium and the propensity with which any particular outcome is selected when it is one of multiple equilibria. 
Keywords:  discrete games, ordered response, partial identification, conditional moment inequalities 
JEL:  C01 C31 C35 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:33/13&r=ecm 
By:  Oliver Linton (Institute for Fiscal Studies and Cambridge University); YoonJae Whang (Institute for Fiscal Studies and Seoul National University); YuMin Yen 
Abstract:  The socalled leverage hypothesis is that negative shocks to prices/ returns affect volatility more than equal positive shocks. Whether this is attributable to changing financial leverage is still subject to dispute but the terminology is in wide use. There are many tests of the leverage hypothesis using discrete time data. These typically involve the fitting of a general parametric or semiparametric model to conditional volatility and then testing the implied restrictions on parameters or curves. We propose an alternative way of testing this hypothesis using realised volatility as an alternative direct nonparametric measure. Our null hypothesis is of conditional distributional dominance and so is much stronger than the usual hypotheses considered previously. We implement our test on a number of stock return datasets using intraday data over a long span. We find powerful evidence in favour or our hypothesis. 
Keywords:  distribution function; leverage effect; gaussian process 
JEL:  C14 C15 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:28/13&r=ecm 
By:  Eric Ghysels; J. Isaac Miller (Department of Economics, University of MissouriColumbia) 
Abstract:  We examine the effects of mixed sampling frequencies and temporal aggregation on standard tests for cointegration. While it is well known that aggregation and sampling frequency do not affect the longrun properties of time series, we find that the effects of aggregation on the size of the tests may be severe. Matching sampling schemes of all series generally reduces size, and the nominal size is obtained when all series are skipsampled in the same way  e.g., endofperiod sampling. When matching all schemes is not feasible, the size of the likelihoodbased trace test may be improved by using a mixedfrequency model rather than an aggregated model. However, a mixedfrequency strategy may not improve the size distortion of residualbased cointegration tests compared to aggregated series. We test stock prices and dividends for cointegration as an empirical demonstration of the size distortion. 
Keywords:  temporal aggregation, mixed sampling frequencies, cointegration, trace test, residualbased cointegration test 
JEL:  C12 C32 
Date:  2013–06–28 
URL:  http://d.repec.org/n?u=RePEc:umc:wpaper:1307&r=ecm 
By:  Sun, Yixiao 
Abstract:  In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the smallb asymptotics and the fixedb asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixedb asymptotic approximation provides a higher order refinement to the first order smallb asymptotics. This result provides a theoretical justification on the use of the fixedb asymptotics in empirical applications. On the basis of the fixedb asymptotics and higher order smallb asymptotics, the paper introduces a new and easytouse asymptotic F test that employs a finite sample corrected Wald statistic and uses an Fdistribution as the reference distribution. Finally, the paper develops a bandwidth selection rule that is testingoptimal in that the bandwidth minimizes the type II error of the asymptotic F test while controlling for its type I error. Monte Carlo simulations show that the asymptotic F test with the testingoptimal bandwidth works very well in finite samples. 
Keywords:  Physical Sciences and Mathematics, Social and Behavioral Sciences, Asymptotic expansion, Fdistribution, Heteroskedasticity and Autocorrelation Robust, longrun variance, robust standard error, testingoptimal smoothing parameter choice, type I and type II errors. 
Date:  2013–05–01 
URL:  http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt8x8307rz&r=ecm 
By:  M. Caivano; A. Harvey 
Abstract:  We compare two EGARCH models which belong to a new class of models in which the dynamics are driven by the score of the conditional distribution of the observations. Models of this kind are called dynamic conditional score (DCS) models and their form facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The EGB2 distribution is lighttailed, but with higher kurtosis than the normal. Hence it is complementary to the fattailed t. The EGB2EGARCH model gives a good fit to many exchange rate return series, prompting an investigation into the misleading conclusions liable to be drawn from tail index estimates. 
Keywords:  Exchange rates; heavy tails; Hill's estimator, score; robustness; Student's t; tail index 
JEL:  C22 G17 
Date:  2013–07–29 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:1326&r=ecm 
By:  Fosgerau, Mogens; Frejinger, Emma; Karlstrom, Anders 
Abstract:  This paper considers the path choice problem, formulating and discussing an econometric random utility model for the choice of path in a network with no restriction on the choice set. Starting from a dynamic specification of link choices we show that it is equivalent to a static model of the multinomial logit form but with infinitely many alternatives. The model can be consistently estimated and used for prediction in a computationally efficient way. Similarly to the path size logit model, we propose an attribute called link size that corrects utilities of overlapping paths but that is link additive. The model is applied to data recording path choices in a network with more than 3,000 nodes and 7,000 links. 
Keywords:  discrete choice; recursive logit; networks; route choice; infinite choice set 
JEL:  C25 C5 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:48707&r=ecm 
By:  Michael Greenacre; Patrick J.F. Groenen 
Abstract:  We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular casesbyvariables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimensionreduction methods that are based on the singularvalue decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weightestimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots. 
Keywords:  biplot, correspondence analysis, distance, majorization, multidimensional scaling, singularvalue decomposition, weighted least squares 
JEL:  C19 C88 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:708&r=ecm 
By:  Christian Westphal (University of Marburg) 
Abstract:  School shootings are often used in public policy debate as a justification for increased regulation, based on qualitative arguments. However, to date, no effort has been made to find valid quantitative evidence for the claims bolstering the regulation recommendations. In defense of this absence of evidence, it is usually argued that the rarity of such events does not allow the employment of quantitative methods. This paper, using a simulation study, shows that, based on the number of shool shootings in the United States and Germany combined, the wellknown method of logistic regression can be applied to a casecontrol study, making it possible to at least test for an association between hypothesized influential variables and the occurrences. Moderate relative risks, explained by an observed variable, would lead to a high power of the appropriate test. A moderate numbers of cases generated by such a variable would suffice to show a significant association. 
Keywords:  Rare Events; Logistic Regression; CaseControl Studies; School Shootings 
JEL:  C25 C35 I18 K14 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:mar:magkse:20135&r=ecm 
By:  Barbara Sianesi (Institute for Fiscal Studies and IFS) 
Abstract:  We highlight the importance of randomisation bias, a situation where the process of participation in a social experiment has been affected by randomisation per se. We illustrate how this has happened in the case of the UK Employment Retention and Advancement (ERA) experiment, in which over one quarter of the eligible population was not represented. Our objective is to quantify the impact that the ERA eligible population would have experienced under ERA, and to assess how this impact relates to the experimental impact estimated on the potentially selected subgroup of study participants. We show that the typical matching assumption required to identify the average treatment effect of interest is made up of two parts. One part remains testable under the experiment even in the presence of randomisation bias, and offers a way to correct the nonexperimental estimates should they fail to pass the test. The other part rests on what we argue is a very weak assumption, at least in the case of ERA. We implement these ideas to the ERA program and show the power of this strategy. Further exploiting the experiment we assess the validity in our application of the claim often made in the literature that knowledge of long and detailed labour market histories can control for most selection bias in the evaluation of labour market interventions. Finally, for the case of surveybased outcomes, we develop a reweighting estimator which takes account of both nonparticipation and nonresponse. 
Keywords:  social experiments, sample selection, treatment effects, matching methods, reweighting estimators 
JEL:  C21 J18 J38 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:ifsewp:13/15&r=ecm 