|
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 Ornstein-Uhlenbeck (fO-U) 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 fO-U 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:2011-07&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 non-increasing 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 k-class estimators for which k < 1, the higher order moments will exist. (2) An alternative second approach is based on taking linear combinations of k-class 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 k-class estimator produces a smaller mean squared error than 2SLS when the degree of overidentification of the system is larger than 8. Moreover, the combined k-class 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 out-of-sample 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:11-31&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 infinite-dimensional 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 change-of-measure argument, inspired by Le Cam's theory of asymptotic equivalence, is used to eliminate the bias caused by the non-linearity 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 socio-demographic 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 ex-ante, 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:dp-477&r=ecm |
| By: | Phillips, Garry D.A. (Cardiff Business School); Liu-Evans, Gareth |
| Abstract: | In a seminal paper Nagar (1959) obtained first and second moment approximations for the k-class 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 higher-order bias approximation for 2SLS under the same assumptions as Nagar while Iglesias and Phillips (2010) obtained the higher order approximation for the general k-class 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 k-class 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 trades-through, i.e. transactions that reach at least the second level of limit orders in an order book. Using tick-by-tick data on Euronext-traded stocks, we show that a simple bivariate Hawkes process fits nicely our empirical observations of trades-through. We show that the cross-influence of bid and ask trades-through is weak. -- |
| Keywords: | Hawkes processes,limit order book,trades-through,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 non-semimartingale 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:2011-06&r=ecm |
| By: | A. Saichev; D. Sornette |
| Abstract: | We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step 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 well-known 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 log-price 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 almost-sure constant cross-sectional distribution of types in a large population, and moreover that the multi-period cross-sectional 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 agent-probability space, and randomized mutation, partial matching and match-induced type-changing 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 |