
on Econometrics 
By:  Jeremy T. Fox; Kyoo il Kim 
Abstract:  We explore a nonparametric mixtures estimator for recovering the joint distribution of random coefficients in economic models. The estimator is based on linear regression subject to linear inequality constraints and is computationally attractive compared to alternative, nonparametric estimators. We provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions. We verify the consistency conditions for discrete choice, continuous outcome and selection models. 
JEL:  C14 L0 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:17283&r=ecm 
By:  Tanaka, Katsuto 
Abstract:  We discuss some inference problems associated with the fractional OrnsteinUhlenbeck (fOU) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) for the drift parameter, and explore their distributional properties by paying attention to the influence of H and the sampling span M. We shall also derive the asymptotic distributions of the two estimators as M becomes large. We further deal with the ordinary least squares estimator (OLSE) and examine the asymptotic relative efficiency. It is shown that the MCE is asymptotically efficient, while the OLSE is inefficient. We also consider the unit root testing problem in the fOU process and compute the power of the tests based on the MLE and MCE. 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:hit:econdp:201107&r=ecm 
By:  Iglesias, Emma M.; Phillips, Garry D.A. (Cardiff Business School) 
Abstract:  We propose two simple bias reduction procedures that apply to estimators in a general static simultaneous equation model and which are valid under reatively weak distributional assumptions for the errors. Standard jackknife estimators, as applied to 2SLS, may not reduce the bias of the exogenous variable coefficient estimators since the estimator biases are not monotonically nonincreasing with sample size (a necessary condition for successful bias reduction) and they have moments only up to the order of overidentification. Our proposed approaches do not have either of these drawbacks. (1) In the first procedure, both endogenous and exogenous variable parameter estimators are unbiased to order T<sup>2</sup> and when implemented for kclass estimators for which k < 1, the higher order moments will exist. (2) An alternative second approach is based on taking linear combinations of kclass estimators for k < 1. In general, this yields estimators which are unbiased to order T<sup>1</sup> and which possess higher moments. We also prove theoretically how the combined kclass estimator produces a smaller mean squared error than 2SLS when the degree of overidentification of the system is larger than 8. Moreover, the combined kclass estimators remain unbiased to order T<sup>1</sup> even if there are redundant variables (including weak instruments) in any part of the simultaneous equation system, and we can allow for any number of endogenous variables. The performance of the two procedures is compared with 2SLS in a number of Monte Carlo experiments using a simple two equation model. Finally, an application shows the usefulness of our new estimator in practice versus competitor estimators. 
Keywords:  Combined <em>k</em>class estimators; Bias correction; Weak instruments; Endogenous and exogenous parameter estimators; Permanent Income Hypothesis 
JEL:  C12 C13 C30 C51 D12 D31 D91 E21 E40 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:cdf:wpaper:2011/19&r=ecm 
By:  Barbara Rossi; Atsushi Inoue 
Abstract:  This paper proposes new methodologies for evaluating outofsample forecasting performance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide range of window sizes. The authors show that the tests proposed in the literature may lack the power to detect predictive ability and might be subject to data snooping across different window sizes if used repeatedly. An empirical application shows the usefulness of the methodologies for evaluating exchange rate models' forecasting ability. 
Keywords:  Forecasting 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:fip:fedpwp:1131&r=ecm 
By:  Winston Wei Dou; David Pollard; Harrison H. Zhou 
Abstract:  This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinitedimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed by constrained maximum likelihood estimation with parameters whose dimension grows with sample size. A changeofmeasure argument, inspired by Le Cam's theory of asymptotic equivalence, is used to eliminate the bias caused by the nonlinearity of exponential family models. 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1108.3552&r=ecm 
By:  Fink, Günther; McConnell, Margaret; Vollmer, Sebastian 
Abstract:  Randomization has emerged as preferred empirical strategy for researchers in a variety of fields over the past years. While the advantages of RCTs in terms of identification are obvious, the statistical analysis of experimental data is not without challenges. In this paper we focus on multiple hypothesis testing as one statistical issue commonly encountered in economic research. In many cases, researchers are not only interested in the main treatment effect, but also want to investigate the degree to which the impact of a given treatment varies across specific geographic or sociodemographic groups of interest. In order to test for such heterogeneous treatment effects, researchers generally either use subsample analysis or interaction terms. While both approaches have been widely applied in the empirical literature, they are generally not valid statistically, and, as we demonstrate in this paper, lead to an almost linear increase in the likelihood of false discoveries. We show that the likelihood of finding one out of ten interaction terms statistically significant in standard OLS regressions is 42\%, and that two thirds of statistically significant interaction terms using PROGRESA data can be presumed to represent false discoveries. We demonstrate that applying correction procedures developed in the statistics literature can fully address this issue, and discuss the implications of multiple testing adjustments for power calculations and experimental design. While multiple testing corrections do require large sample sizes exante, the adjustments necessary to preserve power when corrections are applied appear relatively small. 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:han:dpaper:dp477&r=ecm 
By:  Phillips, Garry D.A. (Cardiff Business School); LiuEvans, Gareth 
Abstract:  In a seminal paper Nagar (1959) obtained first and second moment approximations for the kclass of estimators in a general static simultaneous equation model under the assumption that the structural disturbances were i.i.d and normally distributed. Later Mikhail (1972) obtained a higherorder bias approximation for 2SLS under the same assumptions as Nagar while Iglesias and Phillips (2010) obtained the higher order approximation for the general kclass of estimators. These approximations show that the higher order biases can be important especially in highly overidentified cases. In this paper we show that Mikhail.s higher order bias approximation for 2SLS continues to be valid under symmetric, but not necessarily normal, disturbances with an arbitrary degree of kurtosis but not when the disturbances are asymmetric. A modified approximation for the 2SLS bias is then obtained which includes the case of asymmetric disturbances. The results are then extended to the general kclass of estimators. 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:cdf:wpaper:2011/20&r=ecm 
By:  Toke, Ioane Muni; Pomponio, Fabrizio 
Abstract:  We model tradesthrough, i.e. transactions that reach at least the second level of limit orders in an order book. Using tickbytick data on Euronexttraded stocks, we show that a simple bivariate Hawkes process fits nicely our empirical observations of tradesthrough. We show that the crossinfluence of bid and ask tradesthrough is weak.  
Keywords:  Hawkes processes,limit order book,tradesthrough,highfrequency trading,microstructure 
JEL:  C32 C51 G14 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:zbw:ifwedp:201132&r=ecm 
By:  Glenn Boyle (University of Canterbury); Lulu Gu; W. Robert Reed (University of Canterbury) 
Abstract:  In an event study where at least some of the sample firms have their equity securities listed in more than one market, the question arises as to which is the most appropriate market (or markets) to use for the purpose of estimating average abnormal returns. When arbitrage activity across these markets is restricted in some way, estimating abnormal returns from just one of the listings potentially throws away valuable information. On the other hand, indiscriminate pooling is likely to result in the same information being counted more than once. We develop a Generalized Least Squares estimator that (i) uses all the information available from multiple listings, (ii) ‘downweights’ listing observations that provide little new information, and (iii) yields efficient abnormal return estimates. Finally, we apply this generalized approach to a unique sample of Chinese foreign mergers and acquisitions and compare that the results with conventional estimates of mean abnormal returns. 
Keywords:  event study; multiple listings; mergers and acquisitions; China 
JEL:  C12 G14 G15 G34 
Date:  2011–08–14 
URL:  http://d.repec.org/n?u=RePEc:cbt:econwp:11/30&r=ecm 
By:  Tanaka, Katsuto 
Abstract:  We discuss some computational problems associated with distributions of statistics arising from the fractional Brownian motion (fBm). In particular, we deal with (ratios of) its quadratic functionals. While it is easy in principle to deal with the standard Bm, the fBm is difficult to analyze because of its nonsemimartingale nature. Here we suggest how to derive and compute the distributions of such functionals by using a martingale approximation. For this purpose we employ the Fredholm theory concerning the integral equations, illustrating how to compute the characteristic function via the Fredholm determinant. We also apply the present methodology to compute the fractional unit root distribution, and demonstrate some interesting moment properties. 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:hit:econdp:201106&r=ecm 
By:  A. Saichev; D. Sornette 
Abstract:  We present a set of logprice integrated variance estimators, equal to the sum of openhighlowclose bridge estimators of spot variances within $n$ subsequent timestep intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the wellknown realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying logprice process is an It\^o stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies. 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1108.2611&r=ecm 
By:  Darrell Duffie; Yeneng Sun 
Abstract:  This paper provides a mathematical foundation for independent random matching of a large population, as widely used in the economics literature. We consider both static and dynamic systems with random mutation, partial matching arising from search, and type changes induced by matching. Under independence assumptions at each randomization step, we show that there is an almostsure constant crosssectional distribution of types in a large population, and moreover that the multiperiod crosssectional distribution of types is deterministic and evolves according to the transition matrices of the type process of a given agent. We also show the existence of a joint agentprobability space, and randomized mutation, partial matching and matchinduced typechanging functions that satisfy appropriate independence conditions, where the agent space is an extension of the classical Lebesgue unit interval. 
JEL:  C02 D83 
Date:  2011–08 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:17280&r=ecm 