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on Econometrics |
| By: | Sun, Yixiao |
| Abstract: | The paper develops the Öxed-smoothing asymptotics in a two-step GMM framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step 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 fixed-smoothing critical values are much more accurate in size than the conventional chi-square test. |
| Keywords: | Social and Behavioral Sciences, Physical Sciences and Mathematics, F-distribution, Fixed-smoothing Asymptotics, Heteroskedasticity and Autocorrelation Robust, Increasing-smoothing Asymptotics, Noncentral F Test, Two-step 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 mean-square error (AIMSE) of the estimator is within a specified factor of the optimal AIMSE. |
| Keywords: | ill-posed 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 non-equally 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 pseudo-likelihood 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, Continuous-time 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 finite-sample properties of the smooth transition-based 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 long-run 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 D-LSTR cointegration under the alternative. As a result of the identification problem the limiting distribution derived under the null hypothesis is non-standard. The Double LSTR is capable of producing three-regime TAR nonlinearity when the transition parameter tends to infinity as well as generating exponential-type 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:dp-514&r=ecm |
| By: | Stéphane Bonhomme (CEMFI); Koen Jochmans (Département d'économie); Jean-Marc 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: | finite-mixture 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 infinite-dimensional nuisance parameters using a least-favourable entropy-maximising distribution. We demonstrate, through examples and simulations, that this approach covers a wide class of latent variables models, including some game-theoretic models and models with limited dependent variables, interval-valued data, errors-in-variables, or combinations thereof. Both point- and set-identified models are transparently covered. In the latter case, the method also complements the recent literature on generic set-inference methods by providing the moment conditions needed to construct a GMM-type objective function for a wide class of models. Extensions of the method that cover conditional moments, independence restrictions and some state-space models are also given. |
| Keywords: | method of moments, latent variables, unobservables, partial indentification, entropy, simulations, least-favourable 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 root-n 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 Önite 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 root-n consistent estimator. We apply our model to reinvestigate the inverted-U 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 inverted-U 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 Aradillas-Lopez; 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 city-pair 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 U-processes, 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 chi-square 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); Yoon-Jae Whang (Institute for Fiscal Studies and Seoul National University); Yu-Min Yen |
| Abstract: | The so-called 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 Missouri-Columbia) |
| 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 long-run 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 skip-sampled in the same way -- e.g., end-of-period sampling. When matching all schemes is not feasible, the size of the likelihood-based trace test may be improved by using a mixed-frequency model rather than an aggregated model. However, a mixed-frequency strategy may not improve the size distortion of residual-based 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, residual-based 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 small-b asymptotics and the fixed-b asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixed-b asymptotic approximation provides a higher order refinement to the first order small-b asymptotics. This result provides a theoretical justification on the use of the fixed-b asymptotics in empirical applications. On the basis of the fixed-b asymptotics and higher order small-b asymptotics, the paper introduces a new and easy-to-use asymptotic F test that employs a finite sample corrected Wald statistic and uses an F-distribution as the reference distribution. Finally, the paper develops a bandwidth selection rule that is testing-optimal 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 testing-optimal bandwidth works very well in finite samples. |
| Keywords: | Physical Sciences and Mathematics, Social and Behavioral Sciences, Asymptotic expansion, F-distribution, Heteroskedasticity and Autocorrelation Robust, long-run variance, robust standard error, testing-optimal 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 light-tailed, but with higher kurtosis than the normal. Hence it is complementary to the fat-tailed t. The EGB2-EGARCH 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 cases-by-variables 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 dimension-reduction methods that are based on the singular-value 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 weight-estimation 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, singular-value 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 well-known method of logistic regression can be applied to a case-control 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; Case-Control 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 non-experimental 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 survey-based outcomes, we develop a reweighting estimator which takes account of both non-participation and non-response. |
| 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 |