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on Econometrics |
| By: | David Kaplan (Department of Economics, University of Missouri-Columbia) |
| Abstract: | Estimation of a sample quantile's variance requires estimation of the probability density at the quantile. The common quantile spacing method involves smoothing parameter m. When m, n → ∞ , the corresponding Studentized test statistic asymptotically follows a standard normal distribution. Holding m fixed asymptotically yields a nonstandard distribution dependent on m that contains the Edgeworth expansion term capturing the variance of the quantile spacing. Consequently, the fixed-m distribution is more accurate than the standard normal under both asymptotic frameworks. For the fixed-m test, I propose an m to maximize power subject to size control, as calculated via Edgeworth expansion. Compared with similar methods, the new method controls size better and maintains good or better power in simulations. Results for two-sample quantile treatment effect inference are given in parallel. |
| Keywords: | Edgeworth expansion, fixed-smoothing asymptotics, inference, quantile, studentize, testing-optimal |
| JEL: | C01 C12 C21 |
| Date: | 2013–07–05 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1313&r=ecm |
| By: | David Kaplan (Department of Economics, University of Missouri-Columbia); Matt Goldman |
| Abstract: | We propose new methods of inference on distributions based on the nite-sample joint (ordered) Dirichlet distribution of uniform order statistics. The commonly-used Kolmogorov-Smirnov test is known to have low sensitivity to deviations in the tails. Weighting by the inverse pointwise asymptotic standard deviation is known to suffer the opposite problem: sensitivity in the middle of the distribution is much lower than in the tails. Our Dirichlet-based method finally succeeds in having equal pointwise type I error across the entire distribution, even in finite samples, while maintaining exact overall type I error. Our method may alternatively be interpreted as a family of tests (one at each order statistic) that controls the familywise error rate, or as constructing a uniform confidence band for the unknown distribution function. We also propose two-sample tests, which also have exact finite-sample size, for equality or first-order stochastic dominance, based on uniform confidence bands for the two distribution functions. Simulations and empirical examples demonstrate our new methods. Fully operational code is provided.Classification-JEL: C01, C12, C21 |
| Keywords: | fractional order statistics, nonparametric statistics, quantile inference, quantile treatment effect |
| Date: | 2013–10–31 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1319&r=ecm |
| By: | David Kaplan (Department of Economics, University of Missouri-Columbia); Matt Goldman |
| Abstract: | The literature has two types of fractional order statistics: an `ideal' (unobserved) type based on a beta distribution, and an observable type linearly interpolated between consecutive order statistics. We show convergence in distribution of the two types at an O(n-1) rate, which we also show holds for joint vectors and linear combinations of fractional order statistics. This connection justifies use of the linearly interpolated type in practice when sampling theory is based on the `ideal' type. For example, the coverage probability error (CPE) has the same O(n-1) magnitude for one- sample nonparametric joint confidence intervals over multiple quantiles. For a single quantile, our new analytic calibration reduces the CPE to nearly O(n-3/2), and our new inference method on linear combinations of quantiles has O(n-2/3) CPE. With additional theoretical work, we propose a new method for two-sample quantile treatment effect inference, which has two-sided CPE of order O(n-2/3), or O(n-1) under exchangeability, and one-sided CPE of order O(n-1/2). In an application of our method to data from a recent paper on "gift exchange," we reveal interesting heterogeneity in the treatment effect of "gift wages." In simulations, our quantile treatment effect hypothesis test compares favorably with existing methods in both size and power properties. Along the way, we provide highorder approximations of the PDF and PDF derivative of a Dirichlet distribution in terms of the normal. |
| Keywords: | fractional order statistics, nonparametric statistics, quantile inference, quantile treatment effect |
| JEL: | C01 C12 C21 |
| Date: | 2013–09–05 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1315&r=ecm |
| By: | Heng Chen |
| Abstract: | Estimation of the quantile model, especially with a large data set, can be computationally burdensome. This paper proposes using the Gaussian approximation, also known as quantile coupling, to estimate a quantile model. The intuition of quantile coupling is to divide the original observations into bins with an equal number of observations, and then compute order statistics within these bins. The quantile coupling allows one to apply the standard Gaussian-based estimation and inference to the transformed data set. The resulting estimator is asymptotically normal with a parametric convergence rate. A key advantage of this method is that it is faster than the conventional check function approach, when handling a sizable data set. |
| Keywords: | Econometric and statistical methods |
| JEL: | C13 C14 C21 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:14-24&r=ecm |
| By: | David Kaplan (Department of Economics, University of Missouri-Columbia) |
| Abstract: | The literature has two types of fractional order statistics: an `ideal' (unobserved) type based on a beta distribution, and an observable type linearly interpolated between consecutive order statistics. From the nonparametric perspective of local smoothing, we examine inference on conditional quantiles, as well as linear combinations of conditional quantiles and conditional quantile treatment effects. This paper develops a framework for translating the powerful, high-order accurate IDEAL results (Goldman and Kaplan, 2012) from their original unconditional context into a conditional context, via a uniform kernel. Under mild smoothness assumptions, our new conditional IDEAL method's two-sided pointwise coverage probability error is O(n-2/(2+d)), where d is the dimension of the conditioning vector and n is the total sample size. For d ≤ 2, this is better than the conventional inference based on asymptotic normality or a standard bootstrap. It is also better for other d depending on smoothness assumptions. For example, conditional IDEAL is more accurate for d = 3 unless 11 or more derivatives of the unknown function exist and a corresponding local polynomial of degree 11 is used (which has 364 terms since interactions are required). Even as d → ∞, conditional IDEAL is more accurate unless the number of derivatives is at least four, and the number of terms in the corresponding local polynomial goes to infinity as d → ∞. The tradeoff between the effective (local) sample size and bias determines the optimal bandwidth rate, and we propose a feasible plug-in bandwidth. Simulations show that IDEAL is more accurate than popular current methods, significantly reducing size distortion in some cases while substantially increasing power (while still controlling size) in others. Computationally, our new method runs much more quickly than existing methods for medium and large datasets (roughly n ≥ 1000). We also examine health outcomes in Indonesia for an empirical example. |
| Keywords: | fractional order statistics, nonparametric statistics, quantile inference, quantile treatment effect |
| JEL: | C01 C12 C21 |
| Date: | 2013–09–05 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1316&r=ecm |
| By: | David Kaplan (Department of Economics, University of Missouri-Columbia); Yixiao Sun |
| Abstract: | The moment conditions or estimating equations for instrumental variables quantile regression involves the discontinuous indicator function. We instead use smoothed estimating equations, with bandwidth h. This is known to allow higher-order expansions that justify bootstrap refinements for inference. Computation of the estimator also becomes simpler and more reliable, especially with (more) endogenous regressors. We show that the mean squared error of the vector of estimating equations is minimized for some h > 0, which also reduces the mean squared error of the parameter estimators. The same h also minimizes higher-order type I error for a χ2 test, leading to improved size-adjusted power. Our plug-in bandwidth consistently reproduces all of these properties in simulations. |
| Keywords: | bandwidth choice, higher-order properties, instrumental variables, quantile regression, smoothing |
| JEL: | C01 C12 C13 C21 C26 |
| Date: | 2013–09–05 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1314&r=ecm |
| By: | Markku Lanne (University of Helsinki and CREATES); Henri Nyberg (University of Helsinki) |
| Abstract: | We propose a new generalized forecast error variance decomposition with the property that the proportions of the impact accounted for by innovations in each variable sum to unity. Our decomposition is based on the well-established concept of the generalized impulse response function. The use of the new decomposition is illustrated with an empirical application to U.S. output growth and interest rate spread data. |
| Keywords: | Forecast error variance decomposition, generalized impulse response function, output growth, term spread |
| JEL: | C13 C32 C53 |
| Date: | 2014–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2014-17&r=ecm |
| By: | Harald Oberhofer; Michael Pfaffermayr (WIFO) |
| Abstract: | This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996) and thus, allows to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion. Monte Carlo studies reveal that, for both models, the proposed tests are equipped with sufficient power and are properly sized. Finally, we demonstrate the usefulness of the proposed two-part models for data on the 401(k) pension plan participation rates used in Papke and Wooldridge (1996). |
| Keywords: | Fractional response models for ratios of integers, one-part versus two-part models, Wald test, LM test, LR test |
| Date: | 2014–06–17 |
| URL: | http://d.repec.org/n?u=RePEc:wfo:wpaper:y:2014:i:472&r=ecm |
| By: | Peter Ganong; Simon Jäger |
| Abstract: | The Regression Kink (RK) design is an increasingly popular empirical method, with more than 20 studies circulated using RK in the last 5 years since the initial circulation of Card, Lee, Pei and Weber (2012). We document empirically that these estimates, which typically use local linear regression, are highly sensitive to curvature in the underlying relationship between the outcome and the assignment variable. As an alternative inference procedure, motivated by randomization inference, we propose that researchers construct a distribution of placebo estimates in regions without a policy kink. We apply our procedure to three empirical RK applications – two administrative UI datasets with true policy kinks and the 1980 Census, which has no policy kinks – and we find that statistical significance based on conventional p-values may be spurious. In contrast, our permutation test reinforces the asymptotic inference results of a recent Regression Discontinuity study and a Difference-in-Difference study. Finally, we propose estimating RK models with a modified cubic splines framework and test the performance of different estimators in a simulation exercise. Cubic specifications – in particular recently proposed robust estimators (Calonico, Cattaneo and Titiunik 2014) – yield short interval lengths with good coverage rates. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:qsh:wpaper:174531&r=ecm |
| By: | Ishanu Chattopadhyay |
| Abstract: | While correlation measures are used to discern statistical relationships between observed variables in almost all branches of data-driven scientific inquiry, what we are really interested in is the existence of causal dependence. Designing an efficient causality test, that may be carried out in the absence of restrictive pre-suppositions on the underlying dynamical structure of the data at hand, is non-trivial. Nevertheless, ability to computationally infer statistical prima facie evidence of causal dependence may yield a far more discriminative tool for data analysis compared to the calculation of simple correlations. In the present work, we present a new non-parametric test of Granger causality for quantized or symbolic data streams generated by ergodic stationary sources. In contrast to state-of-art binary tests, our approach makes precise and computes the degree of causal dependence between data streams, without making any restrictive assumptions, linearity or otherwise. Additionally, without any a priori imposition of specific dynamical structure, we infer explicit generative models of causal cross-dependence, which may be then used for prediction. These explicit models are represented as generalized probabilistic automata, referred to crossed automata, and are shown to be sufficient to capture a fairly general class of causal dependence. The proposed algorithms are computationally efficient in the PAC sense; $i.e.$, we find good models of cross-dependence with high probability, with polynomial run-times and sample complexities. The theoretical results are applied to weekly search-frequency data from Google Trends API for a chosen set of socially "charged" keywords. The causality network inferred from this dataset reveals, quite expectedly, the causal importance of certain keywords. It is also illustrated that correlation analysis fails to gather such insight. |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1406.6651&r=ecm |
| By: | Juan Carlos Martínez-Ovando; Sergio I. Olivares-Guzmán; Adriana Roldán-Rodríguez |
| Abstract: | In this paper, we develop a new model-based method to inference on totals and averages of nite populations segmented in planned domains or strata. Within each stratum, we decompose the total as the sum of its sampled and unsampled parts, making inference on the unsampled part using Bayesian nonparametric methods. Additionally, we extend this method to make inference on totals of unplanned domains simultaneously modelling, within each stratum, the underlying uncertainty about the composition of the population and the totals across unplanned domains. Making inference on population averages is straightforward in both frameworks. To illustrate these methods, we develop a simulation exercise and evaluate the uncertainty surrounding the gender wage gap in Mexico. |
| Keywords: | Survey methods, robustness, species-sampling models |
| JEL: | C11 C14 C42 C81 C88 J31 |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:bdm:wpaper:2014-04&r=ecm |
| By: | Barbara Rossi; Tatevik Sekhposyan |
| Abstract: | This paper proposes a framework to implement regression-based tests of predictive ability in unstable environments, including, in particular, forecast unbiasedness and efficiency tests, commonly referred to as tests of forecast rationality. Our framework is general: it can be applied to model-based forecasts obtained either with recursive or rolling window estimation schemes, as well as to forecasts that are model-free. The proposed tests provide more evidence against forecast rationality than previously found in the Federal Reserve's Greenbook forecasts as well as survey-based private forecasts. It confirms, however, that the Federal Reserve has additional information about current and future states of the economy relative to market participants. |
| Keywords: | Forecasting, forecast rationality, regression-based tests of forecasting ability, Greenbook forecasts, survey forecasts, real-time data |
| JEL: | C22 C52 C53 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1426&r=ecm |
| By: | Dirk Tasche |
| Abstract: | How to forecast next year's portfolio-wide credit default rate based on last year's default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year's portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fix. From this observation we can conclude that the standard default rate forecast based on last year's conditional default rates will always be located between last year's portfolio-wide default rate and the ML forecast for next year. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem. |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1406.6038&r=ecm |
| By: | Malikov, Emir; Kumbhakar, Subal C. |
| Abstract: | This paper considers a generalized panel data model of polychotomous and/or sequential switching which can also accommodate the dependence between unobserved effects and covariates in the model. We showcase our model using an empirical illustration in which we estimate scope economies for the publicly owned electric utilities in the U.S. during the period from 2001 to 2003. |
| Keywords: | Correlated Effects, Multinomial Logit, Nested Logit, Panel Data, Polychotomous, Selection |
| JEL: | C33 C34 |
| Date: | 2014–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:56770&r=ecm |
| By: | Casasnovas, Valero L.; Aldanondo, Ana M. |
| Abstract: | We extend the Tauer (2001) and Färe et al. (2004) analyses of aggregation bias in technical efficiency measurement to multiple criteria decision analysis. We show input aggregation conditions consistent with multiple criteria evaluation of overall efficiency in conjunction with variation in aggregation bias. |
| Keywords: | Data Envelopment Analysis, Input aggregation, multiple objectives |
| JEL: | C61 D20 |
| Date: | 2014–06–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:56778&r=ecm |
| By: | Karapanagiotidis, Paul |
| Abstract: | A review of the general state-space modeling framework. The discussion focuses heavily on the three prediction problems of forecasting, filtering, and smoothing within the state- space context. Numerous examples are provided detailing special cases of the state-space model and its use in solving a number of modeling issues. Independent sections are also devoted to both the topics of Factor models and Harvey’s Unobserved Components framework. |
| Keywords: | state-space models, signal extraction, unobserved components |
| JEL: | C10 C32 C51 C53 C58 |
| Date: | 2014–06–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:56807&r=ecm |