
on Econometrics 
By:  Patrick Kline; Andres Santos 
Abstract:  This paper develops practical methods for relaxing the missing at random assumption when estimating models of conditional quantiles with missing outcome data and discrete covariates. We restrict the degree of nonignorable selection governing the missingness process by imposing bounds on the KolmogorovSmirnov (KS) distance between the distribution of outcomes among missing observations and the overall (unselected) distribution. Two methods are developed for conducting inference in this environment. The first allows us to perform finite sample inference on the identified set and is well suited to tests of model specification. The second enables us to conduct inference on the parameters of potentially misspecified models. To illustrate our techniques, we revisit the results of Angrist, Chernozhukov, and FernandezVal (2006) regarding changes across Decennial Censuses in the quantile specific returns to schooling. 
JEL:  C01 C1 J3 
Date:  2010–02 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:15716&r=ecm 
By:  (Department of Statistical Sciences, University of Bologna); Anders Rahbek (Department of Economics, University of Copenhagen and CREATES); A.M.Robert Taylor (School of Economics and Granger Centre for Time Series Econometrics, University of Nottingham) 
Abstract:  Determining the cointegrating rank of a system of variables has become a fundamental aspect of applied research in macroeconomics and finance. It is wellknown that standard asymptotic likelihood ratio tests for cointegration rank of Johansen (1996) can be unreliable in small samples with empirical rejection frequencies often very much in excess of the nominal level. As a consequence, bootstrap versions of these tests have been developed. To be useful, however, sequential procedures for determining the cointegrating rank based on these bootstrap tests need to be consistent, in the sense that the probability of selecting a rank smaller than (equal to) the true cointegrating rank will converge to zero (one minus the marginal significance level), as the sample size diverges, for general I(1) processes. No such likelihoodbased procedure is currently known to be available. In this paper we fill this gap in the literature by proposing a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration rank estimation for general I(1) processes. Finite sample Monte Carlo simulations show the proposed procedure performs well in practice. 
Keywords:  Cointegration, trace test, sequential rank determination, i.i.d.bootstrap, wild bootstrap 
JEL:  C30 C32 
Date:  2010–02–01 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201007&r=ecm 
By:  Kuang, D; Nielsen, Bent; Nielsen, J. P. 
Abstract:  It has long been known that maximum likelihood estimation in a Poisson model reproduces the chainladder technique. We revisit this model. A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation. The maximum likelihood estimators for the canonical parameter are simple, interpretable and easy to derive. The boundary problem where all observations in one particular development year or on particular underwriting year is zero is also analysed. 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:ner:oxford:http://economics.ouls.ox.ac.uk/14469/&r=ecm 
By:  Zdzis{\l}aw Burda; Andrzej Jarosz; Maciej A. Nowak; Ma\l{}gorzata Snarska 
Abstract:  We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fixed. In this regime the underlying random matrices are asymptotically equivalent to Free Random Variables (FRV). We apply the FRV calculus to calculate the eigenvalue density of the sample covariance for several VARMAtype processes. We explicitly solve the VARMA(1,1) case and demonstrate a perfect agreement between the analytical result and the spectra obtained by Monte Carlo simulations. The proposed method is purely algebraic and can be easily generalized to q1>1 and q2>1. 
Date:  2010–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1002.0934&r=ecm 
By:  Søren Johansen (Department of Economics, University of Copenhagen and CREATES, University of Aarhus); Bent Nielsen (Department of Economics, University of Oxford) 
Abstract:  The Forward Search Algorithm is a statistical algorithm for obtaining robust estimators of regression coefficients in the presence of outliers. The algorithm selects a succession of subsets of observations from which the parameters are estimated. The present note shows how the theory of empirical processes can contribute to the understanding of how the subsets are chosen and how the sequence of estimators is changing. 
Keywords:  Empirical processes, Huber's skip, least trimmed squares estimator, onestep estimator, outlier robustness 
JEL:  C2 
Date:  2010–02–06 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201006&r=ecm 
By:  S. Bandyopadhyay; R. Baragona; U. Maulik 
Abstract:  Given a set of time series, it is of interest to discover subsets that share similar properties. For instance, this may be useful for identifying and estimating a single model that may fit conveniently several time series, instead of performing the usual identification and estimation steps for each one. On the other hand time series in the same cluster are related with respect to the measures assumed for cluster analysis and are suitable for building multivariate time series models. Though many approaches to clustering time series exist, in this view the most effective method seems to have to rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coe±cients, spectral measures or the eigenvectors of the covariance matrix. Some new indexes based on goodnessoffit criteria will be proposed in this paper for fuzzy clustering of multivariate time series. A general purpose fuzzy clustering algorithm may be used to estimate the proper cluster structure according to some internal criteria of cluster validity. Such indexes are known to measure actually definite often conflicting cluster properties, compactness or connectedness, for instance, or distribution, orientation, size and shape. It is argued that the multiobjective optimization supported by genetic algorithms is a most effective choice in such a di±cult context. In this paper we use the XieBeni index and the Cmeans functional as objective functions to evaluate the cluster validity in a multiobjective optimization framework. The concept of Pareto optimality in multiobjective genetic algorithms is used to evolve a set of potential solutions towards a set of optimal nondominated solutions. Genetic algorithms are well suited for implementing di±cult optimization problems where objective functions do not usually have good mathematical properties such as continuity, differentiability or convexity. In addition the genetic algorithms, as population based methods, may yield a complete Pareto front at each step of the iterative evolutionary procedure. The method is illustrated by means of a set of real data and an artificial multivariate time series data set. 
Keywords:  Fuzzy clustering, Internal criteria of cluster validity, Genetic algorithms, Multiobjective optimization, Time series, Pareto optimality 
Date:  2010–02–08 
URL:  http://d.repec.org/n?u=RePEc:com:wpaper:028&r=ecm 
By:  Martin M. Andreasen (Bank of England and CREATES) 
Abstract:  This paper improves the accuracy and speed of particle filtering for nonlinear DSGE models with potentially nonnormal shocks. This is done by introducing a new proposal distribution which i) incorporates information from new observables and ii) has a small optimization step that minimizes the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and this filter is therefore much more efficient than the standard particle filter. 
Keywords:  Likelihood inference, Nonlinear DSGE models, Nonnormal shocks, Particle filtering 
JEL:  C13 C15 E10 E32 
Date:  2010–01–27 
URL:  http://d.repec.org/n?u=RePEc:aah:create:201005&r=ecm 
By:  Wagner, Martin (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and Frisch Centre for Economic Research, Oslo, Norway) 
Abstract:  This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration and polynomial cointegration are defined. Based upon these definitions the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By means of detailing the cases most relevant for empirical applications, the I(1), MFI(1) and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly mentioned. 
Keywords:  State space models, unit roots, cointegration, polynomial cointegration, pseudo maximum likelihood estimation, subspace algorithms 
JEL:  C13 C32 
Date:  2010–02 
URL:  http://d.repec.org/n?u=RePEc:ihs:ihsesp:248&r=ecm 
By:  Giovanna Nicolini (Department of Economics, Business and Statistics); Luciana Dalla Valle (University of Milan) 
Abstract:  The present paper provides an overview of the main types of surveys carried out for customer satisfaction analyses. In order to carry out these surveys it is possible to plan a census or select a sample. The higher the accuracy of the survey, the more reliable the results of the analysis. For this very reason, researchers pay special attention to surveys with bias due to non sampling errors, in particular to selfselection errors. These phenomena are very frequent especially in web surveys. Some methods we consider are able to correct the selfselection bias. In literature these methods have been suggested and applied in other fields as well. Here we adapt and employ these techniques as far as customersatisfaction survey data are concerned. 
Keywords:  Selfselection errors, Propensity score matching, Twostep Heckman procedure, Hierarchical bayesian approach, Nonlinear Principal Component Analysis, 
Date:  2009–11–16 
URL:  http://d.repec.org/n?u=RePEc:bep:unimip:1094&r=ecm 
By:  Michiels F.; De Schepper A. 
Abstract:  A copula is a flexible modeling tool which contributes substantially to the study of dependencies among random variables. A broad copula class with many nice properties is the Archimedean copula class. Usually, one works with the classical bivariate models, e.g. as summarized in Nelsen (2006), which are oneparametric models. However, in many cases when practitioners want to model dependencies by means of copulas, it would be more rational to work with multiparametric models. Indeed, multiparametric models would allow to better harmonize empirical information with the model, as it would be possible to directly import more than one characteristic into the model, e.g. measures of concordance, tail dependence and so on. Various ways exist and have been explored to define multiparameter Archimedean models. This paper intends to elaborate on one particular method, namely the technique of transforms. More specifically, the contribution of this article is threefold: 1. Genest et al. (1998) sum up five feasible transformations applicable on the Archimedean generator '. In this note we present an overview of these transformations by generalizing tail dependence properties and limiting cases. 2. In an earlier paper, see Michiels et al. (2008), we showed that it can be advantageous to work with the function instead of with the generator function. We investigate here the effect of transforms on this function. 3. We introduce a new type of transform which is concordance invariant. As such, this type of transform has practical use as it allows to create comparable test spaces (see Michiels and De Schepper (2008)) from a particular copula family. The paper is organised as follows. In section two the most important copula properties are discussed, with the focus on the Archimedean class. Next, section three reviews generally known copula transforms and generator transforms. In section four the effect of the transforms on the level is being discussed, which allows the derivation of general tail dependence properties and limiting cases. We also introduce a concordance invariant transform and illustrate its use through simulations. Finally, section five concludes. 
Date:  2009–12 
URL:  http://d.repec.org/n?u=RePEc:ant:wpaper:2009012&r=ecm 
By:  Bennett T. McCallum 
Abstract:  Socalled “spurious regression” relationships between randomwalk (or strongly autoregressive) variables are generally accompanied by clear signs of severe autocorrelation in their residuals. A conscientious researcher would therefore not end an investigation with such a result, but would likely reestimate with an autocorrelation correction. Simulations show, for several typical cases, that the testrejection statistics for the reestimated relationships are very close to the true values, so do not yield results of the spurious type. 
JEL:  C22 C29 
Date:  2010–01 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:15690&r=ecm 
By:  Kurita, Takamitsu; Nielsen, Bent 
Abstract:  A family of cointegrated vector autoregressive models with adjusted shortrun dynamics is introduced. These models can describe evolving shortrun dynamics in a more flexible way than standard vector autoregressions, and yet likelihood analysis is based on reduced rank regression using conventional asymptotic tables. The family of dynamicsadjusted vector autoregressions consists of three models: a model subject to shortrun parameter changes, a model with partial shortrun dynamics and a model with shortrun explanatory variables. An empirical illustration using US gasoline prices is presented, together with some simulation experiments. 
JEL:  C51 C52 C31 
Date:  2009 
URL:  http://d.repec.org/n?u=RePEc:ner:oxford:http://economics.ouls.ox.ac.uk/14475/&r=ecm 
By:  Lopez, Claude; Papell, David 
Abstract:  We propose a new procedure to increase the power of panel unit root tests when used to study groupwise convergence. When testing for stationarity of the differential between a group of series and their crosssectional means, although each differential has nonzero mean, the group of differentials has a crosssectional average of zero for each time period by construction. We incorporate this constraint for estimation and generating finite sample critical values. Applying this new procedure to Euro Area inflation, we find strong evidence of convergence among the inflation rates soon after the implementation of the Maastricht treaty and a dramatic decrease in the persistence of the differential after the occurrence of the single currency. 
Keywords:  group wise convergence; inflation; euro 
JEL:  C32 E31 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:20585&r=ecm 
By:  Matthieu Bussière (Banque de France, 31 rue CroixdesPetitsChamps, 75001 Paris, France.); Michele Ca’ Zorzi (European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.); Alexander Chudík (European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.); Alistair Dieppe (European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.) 
Abstract:  This paper reviews three different concepts of equilibrium exchange rates that are widely used in policy analysis and constitute the backbone of the IMF CGER assessment: the Macroeconomic Balance, the External Sustainability and the reduced form approaches. We raise a number of econometric issues that were previously neglected, proposing some methodological advances to address them. The first issue relates to the presence of model uncertainty in deriving benchmarks for the current account, introducing Bayesian averaging techniques as a solution. The second issue reveals that, if one considers all the sets of plausible identification schemes, the uncertainty surrounding export and import exchange rate elasticities is large even at longer horizons. The third issue discusses the uncertainty associated to the estimation of a reduced form relationship for the real exchange rate, concluding that inference can be improved by panel estimation. The fourth and final issue addresses the presence of strong and weak cross section dependence in panel estimation, suggesting which panel estimators one could use in this case. Overall, the analysis puts forward a number of innovative solutions in dealing with the large uncertainties surrounding equilibrium exchange rate estimates. JEL Classification: F31, F32, F41. 
Keywords:  Equilibrium exchange rates, IMF CGER methodologies, current account, trade elasticities, global imbalances. 
Date:  2010–01 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20101151&r=ecm 
By:  Esmeralda A. Ramalho, (Departamento de Economia, Universidade de Evora and CEFAGEUE); Joaquim J.S. Ramalho (Departamento de Economia, Universidade de Evora and CEFAGEUE); Pedro D. Henriques (Departamento de Economia, Universidade de Evora and CEFAGEUE) 
Abstract:  TData envelopment analysis (DEA) is commonly used to measure the relative efficiency of decisionmaking units. Often, in a second stage, a regression model is estimated to relate DEA efficiency scores to exogenous factors. In this paper, we argue that the traditional linear or tobit approaches to secondstage DEA analysis do not constitute a reasonable datagenerating process for DEA scores. Under the assumption that DEA scores can be treated as descriptive measures of the relative performance of units in the sample, we show that using fractional regression models are the most natural way of modeling bounded, proportional response variables such as DEA scores. We also propose generalizations of these models and, given that DEA scores take frequently the value of unity, examine the use of twopart models in this framework. Several tests suitable for assessing the specification of each alternative model are also discussed. 
Keywords:  Secondstage DEA; Fractional data; Specification tests; One outcomes; Twopart models. 
JEL:  C12 C13 C25 C51 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:cfe:wpcefa:2010_01&r=ecm 
By:  Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT); Gary King (Institute for Quantitative Social Science, Harvard University); Giuseppe Porro (Department of Economics and Statistics, University of Trieste) 
Abstract:  We introduce a new ``Monotonic Imbalance Bounding'' (MIB) class of matching methods for causal inference that satisfies several important insample properties. MIB generalizes and extends in several new directions the only existing class, ``Equal Percent Bias Reducing'' (EPBR), which is designed to satisfy weaker properties and only in expectation. We also offer strategies to obtain specific members of the MIB class, and present a member of this class, called Coarsened Exact Matching, whose properties we analyze from this new perspective. 
Keywords:  causal inference, treatment effect, matching, 
Date:  2009–10–16 
URL:  http://d.repec.org/n?u=RePEc:bep:unimip:1089&r=ecm 
By:  Valdez, Emiliano A. 
Abstract:  This article examines the notion of distortion of copulas, a natural extension of distortion within the univariate framework. We study three approaches to this extension: (1) distortion of the margins alone while keeping the original copula structure, (2) distortion of the margins while simultaneously altering the copula structure, and (3) synchronized distortion of the copula and its margins. When applying distortion within the multivariate framework, it is important to preserve the properties of a copula function. For the first two approaches, this is a rather straightforward result, however for the third approach, the proof has been exquisitely constructed in Morillas (2005). These three approaches of multivariate distortion unify the different types of multivariate distortion that have scarcely scattered in the literature. Our contribution in this paper is to further consider this unifying framework: we give numerous examples to illustrate and we examine their properties particularly with some aspects of ordering multivariate risks. The extension of multivariate distortion can be practically implemented in risk management where there is a need to perform aggregation and attribution of portfolios of correlated risks. Furthermore, ancillary to the results discussed in this article, we are able to generalize the formula developed by Genest and Rivest (2001) for computing the distribution of the probability integral transformation of a random vector and extend it to the case within the distortion framework. 
Keywords:  Multivariate distortion; Ordering of risks; Probability integral transformation 
JEL:  C10 C46 
Date:  2009–12–23 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:20524&r=ecm 
By:  John A. List; Sally Sadoff; Mathis Wagner 
Abstract:  Experimental economics represents a strong growth industry. In the past several decades the method has expanded beyond intellectual curiosity, now meriting consideration alongside the other more traditional empirical approaches used in economics. Accompanying this growth is an influx of new experimenters who are in need of straightforward direction to make their designs more powerful. This study provides several simple rules of thumb that researchers can apply to improve the efficiency of their experimental designs. We buttress these points by including empirical examples from the literature. 
JEL:  C9 C91 C92 C93 
Date:  2010–01 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:15701&r=ecm 
By:  Arnouts H.; Goos P. 
Abstract:  The cost of experimentation can often be reduced by forgoing complete randomization. A wellknown design with restricted randomization is a splitplot design, which is commonly used in industry when some experimental factors are harder to change than others or when a twostage production process is studied. Splitplot designs are also often used in robust product design to develop products that are insensitive to environmental or noise factors. Another, lesser known, type of experimental design plan that can be used in such situations is the stripplot experimental design. Stripplot designs are economically attractive in situations where the factors are hard to change and the process under investigation consists of two distinct stages, and where it is possible to apply the second stage to groups of semifinished products from the first stage. They have a correlation structure similar to rowcolumn designs and can be seen as special cases of splitlot designs. In this paper,we show how optimal design of experiments allows for the creation of a broad range of stripplot designs. 
Date:  2009–06 
URL:  http://d.repec.org/n?u=RePEc:ant:wpaper:2009007&r=ecm 
By:  Patrick Bajari; Jane Cooley; Kyoo il Kim; Christopher Timmins 
Abstract:  We propose a new strategy for a pervasive problem in the hedonics literature—recovering hedonic prices in the presence of timevarying correlated unobservables. Our approach relies on an assumption about homebuyer rationality, under which prior sales prices can be used to control for timevarying unobservable attributes of the house or neighborhood. Using housing transactions data from California’s Bay Area between 1990 and 2006, we apply our estimator to recover marginal willingness to pay for reductions in three of the EPA’s “criteria” air pollutants. Our findings suggest that ignoring bias from timevarying correlated unobservables considerably understates the benefits of a pollution reduction policy. 
JEL:  C01 Q51 
Date:  2010–02 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:15724&r=ecm 
By:  Flavio Cunha; James Heckman; Susanne Schennach 
Abstract:  This paper formulates and estimates multistage production functions for childrens' cognitive and noncognitive skills. Skills are determined by parental environments and investments at different stages of childhood. We estimate the elasticity of substitution between investments in one period and stocks of skills in that period to assess the benefits of early investment in children compared to later remediation. We establish nonparametric identification of a general class of production technologies based on nonlinear factor models with endogenous inputs. A byproduct of our approach is a framework for evaluating childhood and schooling interventions that does not rely on arbitrarily scaled test scores as outputs and recognizes the differential effects of the same bundle of skills in different tasks. Using the estimated technology, we determine optimal targeting of interventions to children with different parental and personal birth endowments. Substitutability decreases in later stages of the life cycle in the production of cognitive skills. It increases slightly in later stages of the life cycle in the production of noncognitive skills. This finding has important implications for the design of policies that target the disadvantaged. For some configurations of disadvantage and for some outcomes, the return to investments in the later stages of childhood may exceed that to investments in the early stage. 
JEL:  C31 J13 
Date:  2010–01 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:15664&r=ecm 