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on Econometrics |
| By: | Powell, David |
| Abstract: | This paper introduces a method which permits valid inference given a finite number of heterogeneous, correlated clusters. It is common in empirical analysis to use inference methods which assume that each unit is independent. Panel data permit this assumption to be relaxed as it is possible to estimate the correlations across clusters and isolate the independent variation in each cluster for proper inference. Clusters may be correlated for many reasons such as geographic proximity, similar institutions, comparable industry compositions, etc. Moreover, with panel data, it is typical to include time fixed effects, which mechanically induce correlations across clusters. The introduced inference procedure uses a Wald statistic and simulates the distribution of this statistic in a manner that is valid even for a small number of clusters. To account for correlations across clusters, the relationship between each cluster is estimated and only the independent component of each cluster is used. The method is simple to use and only requires one estimation of the model. It can be employed for linear and nonlinear estimators. I present several sets of simulations and show that the inference procedure consistently rejects at the appropriate rate, even in the presence of highly-correlated clusters in which traditional inference methods severely overreject. |
| Keywords: | finite inference, correlated clusters, fixed effects, panel data, Wald statistic |
| JEL: | C12 C15 C21 C22 C23 |
| Date: | 2015–12 |
| URL: | http://d.repec.org/n?u=RePEc:ran:wpaper:1137&r=ecm |
| By: | Daniele Di Gennaro (Sapienza, University of Rome); Guido Pellegrini (Sapienza, University of Rome) |
| Abstract: | During the last decades SUTVA has represented the "gold standard" for the identification and evaluation of causal effects. However, the presence of interferences in causal analysis requires a substantial review of the SUTVA hypothesis. This paper proposes a framework for causal inference in presence of spatial interactions within a new spatial hierarchical Difference-in-Differences model (SH-DID). The novel approach decomposes the ATE (Average Treatment Effect), allowing the identification of direct (ADTE) and indirect treatment effects. In addition, our approach permits the identification of different indirect causal impact both on treated (AITET) and on controls (AITENT). The performance of the SH-DID are evaluated by a Montecarlo Simulation. The results confirm how omitting the presence of interferences produces biased parameters of direct and indirect effects, even though the estimates of the ATE in the traditional model are correct. Conversely, the SH-DID provides unbiased estimates of both total, direct and indirect effects. In addition, this model is the more efficient compared both to the traditional and a Spatial modified Difference-in-Differences estimator. |
| Keywords: | Causal Inference, Spatial Interferences, Hierarchical Model, Montecarlo Simulation. |
| JEL: | C15 C21 C19 C33 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:rcr:wpaper:04_16&r=ecm |
| By: | Jack Fosten (University of East Anglia) |
| Abstract: | This paper provides an extension of Diebold-Mariano-West (DMW) forecast accuracy tests to allow for factor-augmented models to be compared with non-nested benchmarks. The out-of- sample approach to forecast evaluation requires that both the factors and the forecasting model parameters are estimated in a rolling fashion, which poses several new challenges which we address in this paper. Firstly, we show the convergence rates of factors estimated in different rolling windows, and then give conditions under which the asymptotic distribution of the DMW test statistic is not affected by factor estimation error. Secondly, we draw attention to the issue of "sign-changing" across rolling windows of factor estimates and factor-augmented model coefficients, caused by the lack of sign identification when using Principal Components Analysis to estimate the factors. We show that arbitrary sign-changing does not affect the distribution of the DMW test statistic, but it does prohibit the construction of valid bootstrap critical values using existing procedures. We solve this problem by proposing a novel new normalization for rolling factor estimates, which has the effect of matching the sign of factors estimated in different rolling windows. We establish the first-order validity of a simple-to-implement block bootstrap procedure and illustrate its properties using Monte Carlo simulations and an empirical application to forecasting U.S. CPI inflation. |
| Keywords: | boostrap, diffusion index, factor model, predictive ability |
| JEL: | C12 C22 C38 C53 |
| Date: | 2016–01–28 |
| URL: | http://d.repec.org/n?u=RePEc:uea:ueaeco:2016_05&r=ecm |
| By: | David Pacini; Frank Windmeijer |
| Abstract: | The Two-Sample Two-Stage Least Squares (TS2SLS) data combination estimator is a popular estimator for the parameters in linear models when not all variables are observed jointly in one single data set. Although the limiting normal distribution has been established, the asymptotic variance formula has only been stated explicitly in the literature for the case of conditional homoskedasticity. By using the fact that the TS2SLS estimator is a function of reduced form and first-stage OLS estimators, we derive the variance of the limiting normal distribution under conditional heteroskedasticity. A robust variance estimator is obtained, which generalises to cases with more general patterns of variable (non-)availability. Stata code and some Monte Carlo results are provided in an Appendix. Stata code for a nonlinear GMM estimator that is identical to the TS2SLS estimator in just identified models and asymptotically equivalent to the TS2SLS estimator in overidentified models is also provided there. |
| Keywords: | Linear Model, Data Combination, Instrumental Variables, Robust Inference, Nonlinear GMM. |
| JEL: | C12 C13 C26 |
| Date: | 2016–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:bri:uobdis:16/676&r=ecm |
| By: | Kolesár, Michal (Princeton University); Rothe, Christoph (Columbia University) |
| Abstract: | We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable. We derive theoretical results and present simulation and empirical evidence showing that these CIs have poor coverage properties and therefore recommend that they not be used in practice. We also suggest alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function. |
| Keywords: | regression discontinuity design, discrete running variable, clustered standard errors |
| JEL: | C13 C14 C21 C25 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp9990&r=ecm |
| By: | Jack Fosten (University of East Anglia) |
| Abstract: | This paper provides consistent information criteria for the selection of forecasting models which use a subset of both the idiosyncratic and common factor components of a big dataset. This hybrid model approach has been explored by recent empirical studies to relax the strictness of pure factor-augmented model approximations, but no formal model selection procedures have been developed. The main difference to previous factor-augmented model selection procedures is that we must account for estimation error in the idiosyncratic component as well as the factors. Our first contribution shows that this combined estimation error vanishes at a slower rate than in the case of pure factor-augmented models in circumstances in which N is of larger order than sqrt(T), where N and T are the cross-section and time series dimensions respectively. Under these circumstances we show that existing factor-augmented model selection criteria are inconsistent, and the standard BIC is inconsistent regardless of the relationship between N and T. Our main contribution solves this issue by proposing new information criteria which account for the additional source of estimation error, whose properties are explored through a Monte Carlo simulation study. We conclude with an empirical application to long-horizon exchange rate forecasting using a recently proposed model with country-specific idiosyncratic components from a panel of global exchange rates. |
| Keywords: | forecasting, factor model, model selection, information criteria, idiosyncratic |
| JEL: | C13 C22 C38 C52 C53 |
| Date: | 2016–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:uea:ueaeco:2016_07&r=ecm |
| By: | Antonio Ciccone; Elias Papaioannou |
| Abstract: | Empirical cross-industry cross-country models are applied widely in economics, for example to investigate the determinants of economic growth or international trade. Estimation generally relies on US proxies for unobservable technological industry characteristics, for example industries' dependence on external finance or relationship-specific inputs. We examine the properties of the estimator and find that estimates can be biased towards zero (attenuated) or away from zero (amplified), depending on how technological similarity with the US covaries with other country characteristics. We also develop an alternative estimator that yields a lower bound on the true effect in cross-industry cross-country models of comparative advantage. |
| JEL: | F10 G30 O40 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:22368&r=ecm |
| By: | Straub, Ludwig; Ulbricht, Robert |
| Abstract: | Many important statistics in macroeconomics and finance -- such as cross-sectional dispersions, risk, volatility, or uncertainty -- are second moments. In this paper, we explore a mechanism by which second moments naturally and endogenously fluctuate over time as nonlinear transformations of fundamentals. Specifically, we provide general results that characterize second moments of transformed random variables when the underlying fundamentals are subject to distributional shifts that affect their means, but not their variances. We illustrate the usefulness of our results with a series of applications to (1) the cyclicality of the cross-sectional dispersions of macroeconomic variables, (2) the dispersion of MRPKs, (3) security pricing, and (4) endogenous uncertainty in Bayesian inference problems. |
| Keywords: | Cross-sectional dispersion, endogenous uncertainty, monotone likelihood ratio property, nonlinear transformations, risk, second moments, volatility. |
| JEL: | C19 D83 E32 G13 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:30521&r=ecm |
| By: | Chris McDonald; Craig Thamotheram; Shaun P. Vahey; Elizabeth C. Wakerly (Reserve Bank of New Zealand) |
| Abstract: | We consider the fundamental issue of what makes a 'good' probability forecast for a central bank operating within an inflation targeting framework. We provide two examples in which the candidate forecasts comfortably outperform those from benchmark specifications by conventional statistical metrics such as root mean squared prediction errors and average logarithmic scores. Our assessment of economic significance uses an explicit loss function that relates economic value to a forecast communication problem for an inflation targeting central bank. We analyse the Bank of England's forecasts for inflation during the period in which the central bank operated within a strict inflation targeting framework in our first example. In our second example, we consider forecasts for inflation in New Zealand generated from vector autoregressions, when the central bank operated within a flexible inflation targeting framework. In both cases, the economic significance of the performance differential exhibits sensitivity to the parameters of the loss function and, for some values, the differentials are economically negligible. |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:nzb:nzbdps:2016/10&r=ecm |
| By: | Baird, Matthew D. |
| Abstract: | Little attention has been given to the effect of higher order kernels for bandwidth selection for multidimensional derivatives of densities. This paper investigates the extension of cross validation methods to higher dimensions for the derivative of an unconditional joint density. I present and derive different cross validation criteria for arbitrary kernel order and density dimension, and show consistency of the estimator. Doing a Monte Carlo simulation study for various orders of kernels in the Gaussian family and additionally comparing a weighted integrated square error criterion, I find that higher order kernels become increasingly important as the dimension of the distribution increases. I find that standard cross validation selectors generally outperform the weighted integrated square error cross validation criteria. Using the infinite order Dirichlet kernel tends to have the best results. |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:ran:wpaper:1060&r=ecm |
| By: | Michal Franta |
| Abstract: | Iterated multi-step forecasts are usually constructed assuming the same model in each forecasting iteration. In this paper, the model coefficients are allowed to change across forecasting iterations according to the in-sample prediction performance at a particular forecasting horizon. The technique can thus be viewed as a combination of iterated and direct forecasting. The superior point and density forecasting performance of this approach is demonstrated on a standard medium-scale vector autoregression employing variables used in the Smets and Wouters (2007) model of the US economy. The estimation of the model and forecasting are carried out in a Bayesian way on data covering the period 1959Q1-2016Q1. |
| Keywords: | Bayesian estimation, direct forecasting, iterated forecasting, multi-step forecasts, VAR |
| JEL: | C11 C32 C53 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:cnb:wpaper:2016/05&r=ecm |
| By: | Geert Dhaene; Jianbin Wu |
| Abstract: | We introduce and evaluate mixed-frequency multivariate GARCH models for forecasting low-frequency (weekly or monthly) multivariate volatility based on high-frequency intra-day returns (at five-minute intervals) and on the overnight returns. The low-frequency conditional volatility matrix is modelled as a weighted sum of an intra-day and an overnight component, driven by the intra-day and the overnight returns, respectively. The components are specified as multivariate GARCH (1,1) models of the BEKK type, adapted to the mixed-frequency data setting. For the intra-day component, the squared high-frequency returns enter the GARCH model through a parametrically specified mixed-data sampling (MIDAS) weight function or through the sum of the intra-day realized volatilities. For the overnight component, the squared overnight returns enter the model with equal weights. Alternatively, the low-frequency conditional volatility matrix may be modelled as a single-component BEKK-GARCH model where the overnight returns and the high-frequency returns enter through the weekly realized volatility (defined as the unweighted sum of squares of overnight and high-frequency returns), or where the overnight returns are simply ignored. All model variants may further be extended by allowing for a non-parametrically estimated slowly-varying long-run volatility matrix. The proposed models are evaluated using five-minute and overnight return data on four DJIA stocks (AXP, GE, HD, and IBM) from January 1988 to November 2014. The focus is on forecasting weekly volatilities (defined as the low frequency). The mixed-frequency GARCH models are found to systematically dominate the low-frequency GARCH model in terms of in-sample fit and out-of-sample forecasting accuracy. They also exhibit much lower low-frequency volatility persistence than the low-frequency GARCH model. Among the mixed-frequency models, the low-frequency persistence estimates decrease as the data frequency increases from daily to five-minute frequency, and as overnight returns are included. That is, ignoring the available high-frequency information leads to spuriously high volatility persistence. Among the other findings are that the single-component model variants perform worse than the two-component variants; that the overnight volatility component exhibits more persistence than the intra-day component; and that MIDAS weighting performs better than not weighting at all (i.e., than realized volatility). |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:ete:ceswps:544330&r=ecm |
| By: | ALTINAY, Galip |
| Abstract: | In this paper, a simple class of measures for detecting skewness in samples is introduced. The new class of measures is based on a new definition of skewness that takes midrange into consideration. The proposed coefficients of skewness can be computed easily with only three of the summary statistics, i.e., the minimum value, the maximum value and the median (or the mode, or the mean). Another advantage of the new statistics is that they are bounded by -1 and +1, hence, the coefficients of skewness can be interpreted easily. The powers of the proposed statistics to detect skewness are investigated by a limited Monte Carlo simulation in order to have an idea. The preliminary results indicate that the performances of the new statistics look generally good in a limited simulation. However, a more comprehensive investigation is needed. |
| Keywords: | Symmetry, Measure of Skewness, Monte Carlo Study, Midrange, Critical Values. |
| JEL: | C0 C40 |
| Date: | 2016–07–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:72353&r=ecm |
| By: | Gargano, Antonio; Timmermann, Allan G |
| Abstract: | We compare different approaches to accounting for parameter instability in the context of macroeconomic forecasting models that assume either small, frequent changes versus models whose parameters exhibit large, rare changes. An empirical out-of-sample forecasting exercise for U.S. GDP growth and inflation suggests that models that allow for parameter instability generate more accurate density forecasts than constant-parameter models although they fail to produce better point forecasts. Model combinations deliver similar gains in predictive performance although they fail to improve on the predictive accuracy of the single best model which is a specification that allows for time-varying parameters and stochastic volatility. |
| Keywords: | GDP growth; inflation; regime switching; stochastic volatility; time-varying parameters |
| JEL: | C22 C53 |
| Date: | 2016–06 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:11355&r=ecm |