arXiv subjects

D. S. Poskitt

Publications and source records attributed to D. S. Poskitt.

8 recordsLinked to original sources

arXiv2024

Partial Identification of Distributional Treatment Effects in Panel Data using Copula Equality Assumptions

This paper aims to partially identify the distributional treatment effects (DTEs) that depend on the unknown joint distribution of treated and untreated potential outcomes. We construct the DTE bounds using panel data and allow individuals to switch between the treated and untreated states more than once over time. Individuals are grouped based on their past treatment history, and DTEs are allowed to be heterogeneous across different groups. We provide two alternative group-wise copula equality assumptions to bound the unknown joint and the DTEs, both of which leverage information from the past observations. Testability of these two assumptions are also discussed, and test results are presented. We apply this method to study the treatment effect heterogeneity of exercising on the adults' body weight. These results demonstrate that our method improves the identification power of the DTE bounds compared to the existing methods.

econ.EM↗

arXiv2024

Partially Identified Heterogeneous Treatment Effect with Selection: An Application to Gender Gaps

This paper addresses the sample selection model within the context of the gender gap problem, where even random treatment assignment is affected by selection bias. By offering a robust alternative free from distributional or specification assumptions, we bound the treatment effect under the sample selection model with an exclusion restriction, an assumption whose validity is tested in the literature. This exclusion restriction allows for further segmentation of the population into distinct types based on observed and unobserved characteristics. For each type, we derive the proportions and bound the gender gap accordingly. Notably, trends in type proportions and gender gap bounds reveal an increasing proportion of always-working individuals over time, alongside variations in bounds, including a general decline across time and consistently higher bounds for those in high-potential wage groups. Further analysis, considering additional assumptions, highlights persistent gender gaps for some types, while other types exhibit differing or inconclusive trends. This underscores the necessity of separating individuals by type to understand the heterogeneous nature of the gender gap.

econ.EM↗

arXiv2022

Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects

This paper examines the identification power of instrumental variables (IVs) for average treatment effect (ATE) in partially identified models. We decompose the ATE identification gains into components of contributions driven by IV relevancy, IV strength, direction and degree of treatment endogeneity, and matching via exogenous covariates. Our decomposition is demonstrated with graphical illustrations, simulation studies and an empirical example of childbearing and women's labour supply. Our analysis offers insights for understanding the complex role of IVs in ATE identification and for selecting IVs in practical policy designs. Simulations also suggest potential uses of our analysis for detecting irrelevant instruments.

econ.EM↗

arXiv2022

The Impact of Sampling Variability on Estimated Combinations of Distributional Forecasts

We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according to criterion functions based on proper scoring rules, which are chosen to reward the form of forecast accuracy that matters for the problem at hand, and forecast performance is measured using the out-of-sample expectation of said scoring rule. Our results provide novel insights into the behavior of estimated forecast combinations. Firstly, we show that, asymptotically, the sampling variability in the performance of standard forecast combinations is determined solely by estimation of the constituent models, with estimation of the combination weights contributing no sampling variability whatsoever, at first order. Secondly, we show that, if computationally feasible, forecast combinations produced in a single step -- in which the constituent model and combination function parameters are estimated jointly -- have superior predictive accuracy and lower sampling variability than standard forecast combinations -- where constituent model and combination function parameters are estimated in two steps. These theoretical insights are demonstrated numerically, both in simulation settings and in an extensive empirical illustration using a time series of S&P500 returns.

stat.ME↗

arXiv2018

Issues in the Estimation of Mis-Specified Models of Fractionally Integrated Processes

We provide a comprehensive set of new results on the impact of mis-specifying the short run dynamics in fractionally integrated processes. We show that four alternative parametric estimators - frequency domain maximum likelihood, Whittle, time domain maximum likelihood and conditional sum of squares - converge to the same pseudo-true value under common mis-specification, and that they possess a common asymptotic distribution. The results are derived assuming a completely general parametric specification for the short run dynamics of the estimated (mis-specified) fractional model, and with long memory, short memory and antipersistence in both the model and the true data generating process accommodated. As well as providing new theoretical insights, we undertake an extensive set of numerical explorations, beginning with the numerical evaluation, and implementation, of the (common) asymptotic distribution that holds under the most extreme form of mis-specification. Simulation experiments are then conducted to assess the relative finite sample performance of all four mis-specified estimators, initially under the assumption of a known mean, as accords with the theoretical derivations. The importance of the known mean assumption is illustrated via the production of an alternative set of bias and mean squared error results, in which the estimators are applied to demeaned data. The paper concludes with a discussion of open problems.

math.ST↗

arXiv2017

Construction and Visualization of Optimal Confidence Sets for Frequentist Distributional Forecasts

The focus of this paper is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use animated graphics to visualize the impact of parameter uncertainty on the location, dispersion and shape of the distribution. The confidence sets are derived via the inversion of a Wald test and are asymptotically uniformly most accurate and, hence, optimal in this sense. A wide range of linear and non-linear time series models - encompassing long memory, state space and mixture specifications - is used to demonstrate the procedure, based on artificially generated data. An empirical example in which distributional forecasts of both financial returns and its stochastic volatility are produced is then used to illustrate the practical importance of accommodating sampling variation in the manner proposed.

stat.ME↗

arXiv2014

Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap

This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate of the long memory parameter. Theoretical justification for using the bootstrap techniques to bias adjust log-periodogram and semi-parametric local Whittle estimators of the memory parameter is provided. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias correction techniques is also presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which analytical adjustments have already been used. The empirical coverage of confidence intervals based on the bias-adjusted estimators is very close to the nominal, for a reasonably large sample size, more so than for the comparable analytically adjusted estimators. The precision of inferences (as measured by interval length) is also greater when the bootstrap is used to bias correct rather than analytical adjustments.

stat.ME↗

arXiv2013

Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used to produce the bootstrap draws are captured by an autoregressive approximation. Application of the sieve method to data pre-filtered by a semi-parametric estimate of the long memory parameter is also explored. Higher-order improvements yielded by both forms of re-sampling are demonstrated using Edgeworth expansions for a broad class of statistics that includes first- and second-order moments, the discrete Fourier transform and regression coefficients. The methods are then applied to the problem of estimating the sampling distributions of the sample mean and of selected sample autocorrelation coefficients, in experimental settings. In the case of the sample mean, the pre-filtered version of the bootstrap is shown to avoid the distinct underestimation of the sampling variance of the mean which the raw sieve method demonstrates in finite samples, higher order accuracy of the latter notwithstanding. Pre-filtering also produces gains in terms of the accuracy with which the sampling distributions of the sample autocorrelations are reproduced, most notably in the part of the parameter space in which asymptotic normality does not obtain. Most importantly, the sieve bootstrap is shown to reproduce the (empirically infeasible) Edgeworth expansion of the sampling distribution of the autocorrelation coefficients, in the part of the parameter space in which the expansion is valid.

stat.ME↗