
on Econometrics 
By:  Alexandre Belloni (Institute for Fiscal Studies); Victor Chernozhukov (Institute for Fiscal Studies and MIT); Kengo Kato (Institute for Fiscal Studies) 
Abstract:  We develop uniformly valid confidence regions for regression coefficients in a highdimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against nonregular estimation of the nuisance part of the median regression function by using Neyman’s orthogonalization. We establish that the resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally distributed uniformly with respect to the underlying sparse model and is semiparametrically efficient. We also generalize our method to a general nonsmooth Zestimation framework with the number of target parameters p1 being possibly much larger than the sample size n. We extend Huber’s results on asymptotic normality to this setting, demonstrating uniform asymptotic normality of the proposed estimators over p1dimensional rectangles, constructing simultaneous confidence bands on all of the p1 target parameters, and establishing asymptotic validity of the bands uniformly over underlying approximately sparse models. 
Keywords:  Instrument, postselection inference, sparsity, Neyman's Orthogonal Score test, uniformly valid inference, Zestimation 
Date:  2014–12 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:51/14&r=ecm 
By:  Fedotenkov, Igor 
Abstract:  This paper proposes a simple, fast and direct nonparametric test to verify if a sample is drawn from a distribution with a finite first moment. The method can also be applied to test for the existence of finite moments of another order by taking the sample to the corresponding power. The test is based on the difference in the asymptotic behaviour of the arithmetic mean between cases when the underlying probability function either has or does not have a finite first moment. Test consistency is proved; then, test performance is illustrated with MonteCarlo simulations and a practical application for the S&P500 index. 
Keywords:  Heavy tails, tail index, finite moment, test, consistency 
JEL:  C12 
Date:  2015–08–13 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:66089&r=ecm 
By:  Victor Chernozhukov (Institute for Fiscal Studies and MIT); Ivan FernandezVal (Institute for Fiscal Studies and University of Boston); Stefan Hoderlein (Institute for Fiscal Studies and Boston College); Whitney Newey (Institute for Fiscal Studies and MIT) 
Abstract:  This paper considers identiï¬cation and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity. The effects of interest are derivatives of the average and quantile structural functions of the model. We ï¬nd that these derivatives are identiï¬ed with two time periods for “stayers”, i.e. for individuals with the same regressor values in two time periods. We show that the identiï¬cation results carry over to models that allow location and scale time eï¬€ects. We propose nonparametric series methods and a weighted bootstrap scheme to estimate and make inference on the identiï¬ed eï¬€ects. The bootstrap proposed allows inference for functionvalued parameters such as quantile eï¬€ects uniformly over a region of quantile indices and/or regressor values. An empirical application to Engel curve estimation with panel data illustrates the results. 
Keywords:  Panel data, nonseparable model, average eï¬€ect, quantile eï¬€ect, Engel curve 
Date:  2014–12 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:54/14&r=ecm 
By:  Paul Larsen 
Abstract:  Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavytailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large samplesizes, a situation rarely encountered in operational risk. We study MLE in operational risk models for small samplesizes across a range of loss severity distributions. We apply these results to assess (1) the approximation of parameter confidence intervals by asymptotic normality, and (2) valueatrisk (VaR) stability as a function of samplesize. Finally, we discuss implications for operational risk modeling. 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1508.02824&r=ecm 
By:  Michael Vogt (Institute for Fiscal Studies); Oliver Linton (Institute for Fiscal Studies and cemmap and Cambridge) 
Abstract:  We investigate a nonparametric panel model with heterogeneous regression functions. In a variety of applications, it is natural to impose a group structure on the regression curves. Specifically, we may suppose that the observed individuals can be grouped into a number of classes whose members all share the same regression function. We develop a statistical procedure to estimate the unknown group structure from the observed data. Moreover, we derive the asymptotic properties of the procedure and investigate its finite sample performance by means of a simulation study and a realdata example. 
Keywords:  Classiï¬cation of regression curves, kmeans clustering, kernel estimation, nonparametric regression, panel data 
Date:  2015–02 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:06/15&r=ecm 
By:  Ivan Canay (Institute for Fiscal Studies); Vishal Kamat (Institute for Fiscal Studies and Northwestern University) 
Abstract:  This paper proposes an asymptotically valid permutation test for a testable implication of the identiï¬cation assumption in the regression discontinuity design (RDD). Here, by testable implication, we mean the requirement that the distribution of observed baseline covariates should not change discontinuously at the threshold of the socalled running variable. This contrasts to the common practice of testing the weaker implication of continuity of the means of the covariates at the threshold. When testing our null hypothesis using observations that are “close” to the threshold, the standard requirement for the ï¬nite sample validity of a permutation does not necessarily hold. We therefore propose an asymptotic framework where there is a ï¬xed number of closest observations to the threshold with the sample size going to inï¬nity, and propose a permutation test based on the socalled induced order statistics that controls the limiting rejection probability under the null hypothesis. In a simulation study, we ï¬nd that the new test controls size remarkably well in most designs. Finally, we use our test to evaluate the validity of the design in Lee (2008), a wellknown application of the RDD to study incumbency advantage. 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:27/15&r=ecm 
By:  Guillaume Chevillon (ESSEC Business School  Essec Business School) 
Abstract:  Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality. 
Date:  2013–11 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal00914830&r=ecm 
By:  Michael S. Delgado (Purdue University, United States); Raymond J.G.M. Florax (VU University Amsterdam, the Netherlands, and Purdue University, United States) 
Abstract:  We consider treatment effect estimation via a differenceindifference approach for data with local spatial interaction such that the outcome of observed units depends on their own treatment as well as on the treatment status of proximate neighbors. We show that under standard assumptions (common trend and ignorability) a straightforward spatially explicit version of the benchmark differenceindifferences regression is capable of identifying both direct and indirect treatment effects. We demonstrate the finite sample performance of our spatial estimator via Monte Carlo simulations. 
Keywords:  Differenceindifferences; Monte Carlo simulation; program evaluation; spatial autocorrelation; spatial interaction 
JEL:  C21 C53 
Date:  2015–07–30 
URL:  http://d.repec.org/n?u=RePEc:tin:wpaper:20150091&r=ecm 
By:  Jie Ding; Mohammad Noshad; Vahid Tarokh 
Abstract:  A new criterion is introduced for determining the order of an autoregressive model fit to time series data. The proposed technique is shown to give a consistent and asymptotically efficient order estimation. It has the benefits of the two wellknown model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the true order of the autoregression is relatively large compared with the sample size, the Akaike information criterion is known to be efficient, and the new criterion behaves in a similar manner. When the true order is finite and small compared with the sample size, the Bayesian information criterion is known to be consistent, and so is the new criterion. Thus the new criterion builds a bridge between the two classical criteria automatically. In practice, where the observed time series is given without any prior information about the autoregression, the proposed order selection criterion is more flexible and robust compared with classical approaches. Numerical results are presented demonstrating the robustness of the proposed technique when applied to various datasets. 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1508.02473&r=ecm 
By:  Joel Horowitz (Institute for Fiscal Studies and Northwestern University) 
Abstract:  Models with highdimensional covariates arise frequently in economics and other fields. Often, only a few covariates have important effects on the dependent variable. When this happens, the model is said to be sparse. In applications, however, it is not known which covariates are important and which are not. This paper reviews methods for discriminating between important and unimportant covariates with particular attention given to methods that discriminate correctly with probability approaching 1 as the sample size increases. Methods are available for a wide variety of linear, nonlinear, semiparametric, and nonparametric models. The performance of some of these methods in finite samples is illustrated through Monte Carlo simulations and an empirical example. 
Date:  2015–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:35/15&r=ecm 
By:  Le, Vo Phuong Mai (Cardiff Business School); Meenagh, David (Cardiff Business School); Minford, Patrick (Cardiff Business School); Wickens, Michael (Cardiff Business School); Xu, Yongdeng 
Abstract:  With Monte Carlo experiments on models in widespread use we examine the performance of indirect inference (II) tests of DSGE models in small samples. We compare these tests with ones based on direct inference (using the Likelihood Ratio, LR). We find that both tests have power so that a substantially false model will tend to be rejected by both; but that the power of the II test is substantially greater, both because the LR is applied after reestimation of the model error processes and because the II test uses the false model’s own restricted distribution for the auxiliary model’s coefficients. This greater power allows users to focus this test more narrowly on features of interest, trading off power against tractability. 
Keywords:  Bootstrap; DSGE; New Keynesian; New Classical; indirect inference; Wald statistic; likelihood ratio 
JEL:  C12 C32 C52 E1 
Date:  2015–07 
URL:  http://d.repec.org/n?u=RePEc:cdf:wpaper:2015/9&r=ecm 
By:  Yoichi Arai (National Graduate Institute for Policy Studies (GRIPS)); Hidehiko Ichimura (Faculty of Economics, The University of Tokyo) 
Abstract:  A new bandwidth selection rule that uses different bandwidths for the local linear regression estimators on the left and the right of the cutoffpoint is proposed for the sharp regression discontinuity estimator of the mean program impact at the cutoff point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection rule is shown to be smaller than other bandwidth selection rules proposed in the literature. An extensive simulation study shows that the proposed method's performances for the samples sizes 500, 2000, and 5000 closely match the theoretical predictions.  
Date:  2015–07 
URL:  http://d.repec.org/n?u=RePEc:tky:fseres:2015cf984&r=ecm 
By:  Russell Davidson (Institute for Fiscal Studies and McGIll) 
Abstract:  In an attempt to free bootstrap theory from the shackles of asymptotic considerations, this paper studies the possibility of justifying, or validating, the bootstrap, not by letting the sample size tend to infinity, but by considering the sequence of bootstrap P values obtained by iterating the bootstrap. The main idea of the paper is that, if this sequence converges to a random variable that follows the uniform U(0; 1) distribution, then the bootstrap is valid. The idea is studied by making the model under test discrete and finite, so that it is characterised by a finite threedimensional array of probabilities. This device, when available, renders bootstrap iteration to any desired order feasible. It is used for studying a unitroot test for a process driven by a stationary MA(1) process, where it is known that the unitroot test, even when bootstrapped, becomes quite unreliable when the MA(1) parameter is in the vicinity of 1. Iteration of the bootstrap P value to convergence achieves reliable inference except for a parameter value very close to 1. The paper then endeavours to see these specific results in a wider context, and tries to cast new light on where bootstrap theory may be going. 
Keywords:  Bootstrap, bootstrap iteration 
JEL:  C10 C12 C15 
Date:  2015–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:38/15&r=ecm 
By:  Amélie Charles (Audencia Recherche  Audencia); Olivier Darné (LEMNA  Laboratoire d'économie et de management de Nantes Atlantique  UN  Université de Nantes); Fabien Tripier (CEPII  Centre d'Etudes Prospectives et d'Informations Internationales  Centre d'analyse stratégique, CLERSE  Centre lillois d'études et de recherches sociologiques et économiques  CNRS  Université Lille 1  Sciences et technologies) 
Abstract:  The performance of unit root tests on simulated series is compared, using the businesscycle model of Chang et al. (2007) to generate data. Overall, Monte Carlo simulations show that the e¢ cient unit root tests of Ng and Perron (2001) are more powerful than the standard unit root tests. These e¢ cient tests are frequnetly able (i) to reject the unitroot hypothesis on simulated series, using the best speci…cation of the businesscycle model found by Chang et al. (2007), in which hours worked are stationary with adjustment costs, and (ii) to reduce the gap between the theoretical impulse response functions and those estimated with a Structural VAR model. The results of Monte Carlo simulations show that the humpshaped behaviour of data can explain the divergence between unit root tests. 
Date:  2015 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal01101618&r=ecm 
By:  Elena Di Bernardino (CEDRIC  Centre d'Etude et De Recherche en Informatique du Cnam  Conservatoire National des Arts et Métiers [CNAM]); Didier Rullière (SAF  Laboratoire de Sciences Actuarielle et Financière  UCBL  Université Claude Bernard Lyon 1) 
Abstract:  Calculating return periods and critical layers (i.e., multivariate quantile curves) in a multivariate environment is a di cult problem. A possible consistent theoretical framework for the calculation of the return period, in a multidimensional environment, is essentially based on the notion of copula and level sets of the multivariate probability distribution. In this paper we propose a fast and parametric methodology to estimate the multivariate critical layers of a distribution and its associated return periods. The model is based on transformations of the marginal distributions and transformations of the dependence structure within the class of Archimedean copulas. The model has a tunable number of parameters, and we show that it is possible to get a competitive estimation without any global optimum research. We also get parametric expressions for the critical layers and return periods. The methodology is illustrated on hydrological 5dimensional real data. On this real dataset we obtain a good quality of estimation and we compare the obtained results with some classical parametric competitors 
Date:  2015–01 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal00940089&r=ecm 
By:  Joshua C.C. Chan; Eric Eisenstat 
Abstract:  We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and deviance information criterion (DIC) for TVPVARs with stochastic volatility. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Specifically, integrated likelihood evaluation is achieved by integrating out the timevarying parameters analytically, while the logvolatilities are integrated out numerically via importance sampling. Using US and Australian data, we find overwhelming support for the TVPVAR with stochastic volatility compared to a conventional constant coefficients VAR with homoscedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility receives similar support as the more general model with timevarying parameters. 
Keywords:  Bayesian, state space, marginal likelihood, deviance information criterion, great moderation 
JEL:  C11 C52 E32 E52 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:een:camaaa:201532&r=ecm 
By:  Bet Helena Caeyers 
Abstract:  This paper formalises an unproven source of ordinary least squares estimation bias in standard linearinmeans peer effects models. I derive a formula for the magnitude of the bias and discuss its underlying parameters. I show the conditions under which the bias is aggravated in models adding cluster fixed effects and demonstate how it affects inference and interpertation of estimation results. Further, I reveal that twostage least squares (2SLS) estimation strategies eliminate the bias and provide illustrative simulations. The results may explain some counterintuitive findings in the social interaction literature, such as the observation of OLS estimates of endogenous peer effects that are larger than their 2SLS counterparts. 
Date:  2014–01–13 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:wps/201405&r=ecm 
By:  Elotma H (FSSM  Faculté des Sciences SEMLALIA  University Cadi Ayyad  UCA (Morocco)) 
Abstract:  Abstract. In the present paper we propose a new stochastic diffusion process with drift proportional to the Weibull density function defined as X $\epsilon$ = x, dX t = $\gamma$ t (1  t $\gamma$+1)  t $\gamma$ X t dt + $\sigma$X t dB t , t \textgreater{} 0, with parameters $\gamma$ \textgreater{} 0 and $\sigma$ \textgreater{} 0, where B is a standard Brownian motion and t = $\epsilon$ is a time proche to zero. First we interested to probabilistic solution of this process as the explicit expression of this process. By using the maximum likelihood method and by considering a discrete sampling of the sample of the new process we estimate the parameters $\gamma$ and $\sigma$. 
Date:  2015–02–25 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01081470&r=ecm 
By:  Toru Kitagawa (Institute for Fiscal Studies and cemmap and UCL) 
Abstract:  This paper develops a specification test for instrument validity in the heterogeneous treatment effect model with a binary treatment and a discrete instrument. The strongest testable implication for instrument validity is given by the condition for nonnegativity of point identifiable complier’s outcome densities. Our specification test infers this testable implication using a varianceweighted KolmogorovSmirnov test statistic. Implementation of the proposed test does not require smoothing parameters, even though the testable implications involve nonparametric densities. The test can be applied to both discrete and continuous outcome cases, and an extension of the test to settings with conditioning covariates is provided. 
Date:  2014–08 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:34/14&r=ecm 
By:  Andrew Chesher (Institute for Fiscal Studies and cemmap and UCL); Adam Rosen (Institute for Fiscal Studies and cemmap and UCL) 
Abstract:  An incomplete model of English auctions with symmetric independent private values, similar to the one studied in Haile and Tamer (2003), is shown to fall in the class of Generalized Instrumental Variable Models introduced in Chesher and Rosen (2014). A characterization of the sharp identified set for the distribution of valuations is thereby obtained and shown to refine the bounds available until now. 
Keywords:  English auctions; partial identification; sharp set identification; generalized instrumental variable models 
Date:  2015–06 
URL:  http://d.repec.org/n?u=RePEc:ifs:cemmap:30/15&r=ecm 
By:  Beaudry, Paul; Fève, Patrick; Guay, Alain; Portier, Franck 
Abstract:  When a structural model has a nonfundamental VAR representation, standard SVAR techniques cannot be used to properly identify the effects of structural shocks. This problem is known to potentially arise when one of the structural shocks represents news about the future. However, as we shall show, in many cases the nonfundamental representation of a time series may be very close to its fundamental representation implying that standard SVAR techniques may provide a very good approximation of the effects of structural shocks even when the nonfundamentalness is formally present. This leads to the question: When is nonfundamentalness a real problem? In this paper we derive and illustrate a diagnostic based on a R2 which provides a simple means of detecting whether nonfundamentalness is likely to be a quantitatively important problem in an applied settings. We use the identification of technological news shocks in US data as our running example. 
Keywords:  business cycles; news; nonfundamentalness; svar 
JEL:  E3 
Date:  2015–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:10763&r=ecm 
By:  Dlugosz, Stephan; Mammen, Enno; Wilke, Ralf A. 
Abstract:  We consider the semiparametric generalised linear regression model which has mainstream empirical models such as the (partially) linear mean regression, logistic and multinomial regression as special cases. As an extension to related literature we allow a misclassified covariate to be interacted with a nonparametric function of a continuous covariate. This model is tailormade to address known data quality issues of administrative labour market data. Using a sample of 20m observations from Germany we estimate the determinants of labour market transitions and illustrate the role of considerable misclassification in the educational status on estimated transition probabilities and marginal effects. 
Keywords:  semiparametric regression,measurement error,side information 
Date:  2015 
URL:  http://d.repec.org/n?u=RePEc:zbw:zewdip:15043&r=ecm 
By:  Brendon McConnell (Institute for Fiscal Studies); Marcos VeraHernandez (Institute for Fiscal Studies and University College London) 
Abstract:  Basic methods to compute the required sample size are well understood and supported by widely available software. However, the sophistication of the sample size methods commonly used has not kept pace with the complexity of the experimental designs most often employed in practice. In this paper, we compile available methods for sample size calculations for continuous and binary outcomes with and without covariates, for both clustered and nonclustered RCTs. Formulae for panel data and for unbalanced designs (where there are different numbers of treatment and control observations) are also provided. The paper includes three extensions: (1) methods to optimize the sample when costs constraints are binding; (2) simulation methods to compute the power of a complex design; and (3) methods to consider in the sample size calculation adjustments for multiple testing. The paper is provided together with spreadsheets and STATA code to implement the methods discussed. Click here to view accompanying sample size calculators for this paper. 
Keywords:  Power analysis; Sample size calculations; Randomised Control Trials; Cluster Randomised Control Trial; Covariates; Cost Minimisation; Multiple outcomes; Simulation 
JEL:  C8 C9 
Date:  2015–07 
URL:  http://d.repec.org/n?u=RePEc:ifs:ifsewp:15/17&r=ecm 
By:  Wei Wei (Aarhus University and CREATES); Denis Pelletier (North Carolina State University) 
Abstract:  Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate OrnsteinUlenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps. The algorithm provides smoothed estimates of the latent variables such as spot volatility, conditional duration, jump times, and jump sizes. We apply this model to IBM data and find that volatility and conditional duration are interdependent. We also find that jumps play an important role in return variation, but joint modeling of volatility and conditional duration reduces significantly the need for jumps. 
Keywords:  Durations, Stochastic Volatility, Price jumps, Highfrequency data, Bayesian inference 
JEL:  C1 C5 G1 
Date:  2015–08–06 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201534&r=ecm 
By:  Pasaogullari, Mehmet (Federal Reserve Bank of Cleveland) 
Abstract:  In this paper, I consider forecasting from a reducedform VAR under the zero lower bound (ZLB) for the shortterm nominal interest rate. I develop a method that a) computes the exact moments for the first n + 1 periods when n previous periods are tracked and b) approximates moments for the periods beyond n + 1 period using techniques for truncated normal distributions and approximations a la Kim (1994). I show that the algorithm produces satisfactory results for VAR systems with moderate to high persistence even when only one previous period is tracked. For very persistent VAR systems, however, tracking more periods is needed in order to obtain reliable approximations. I also show that the method is suitable for affine termstructure modeling, where the underlying state vector includes the shortterm interest rate as in Taylor rules with inertia. 
Keywords:  monetary policy; forecasting from VARs; zero lower bound; normal mixtures 
JEL:  C53 E42 E43 E47 
Date:  2015–08–05 
URL:  http://d.repec.org/n?u=RePEc:fip:fedcwp:1512&r=ecm 