
on Econometrics 
By:  Degui Li (University of York); Peter C.B. Phillips (Cowles Foundation, Yale University); Jiti Gao (Dept. of Econometrics and Business Statistics, Monash University) 
Abstract:  This paper studies nonlinear cointegrating models with timevarying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernelweighted signal matrix. To address these complications new \textsl{local} and \textsl{global rotation} techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain regularity conditions we derive asymptotic results that differ substantially from existing kernel regression asymptotics, leading to new limit theory under multiple convergence rates. For the practically important case of endogenous nonstationary regressors we propose a fullymodified kernel estimator whose limit distribution theory corresponds to the prototypical pure (i.e., exogenous covariate) cointegration case, thereby facilitating inference using a generalized Waldtype test statistic. These results substantially generalize econometric estimation and testing techniques in the cointegration literature to accommodate time variation and complications of comoving regressors. Finally an empirical illustration to aggregate US data on consumption, income, and interest rates is provided. 
Keywords:  Cointegration, FMkernel estimation, Generalized Wald test, Global rotation, Kernel degeneracy, Local rotation, Superconsistency, Timevarying coefficients 
JEL:  C22 C65 
Date:  2017–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2109&r=ecm 
By:  Alessandro Casini; Pierre Perron 
Abstract:  Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2017a) for inference in structural change models, we propose a Laplacebased (QuasiBayes) procedure for the construction of the estimate and confidence set for the date of a structural change. The procedure relies on a Laplacetype estimator defined by an integrationbased rather than an optimizationbased method. A transformation of the leastsquares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasiposterior. For a given choice of a loss function, the Laplacetype estimator is defined as the minimizer of the expected risk with the expectation taken under the Quasiposterior. Besides providing an alternative estimate that is more preciselower mean absolute error (MAE) and lower rootmean squared error (RMSE)than the usual leastsquares one, the Quasiposterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplacebased inferential procedure proposed is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional longspan methods, whether the break size is small or large. 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1804.00232&r=ecm 
By:  Wucherpfennig, Julian; Kachi, Aya (University of Basel); Bormann, NilsChristian; Hunziker, Philipp 
Abstract:  Binary outcome models are frequently used in Political Science. However, such models have proven particularly dicult in dealing with interdependent data structures, including spatial autocorrelation, temporal autocorrelation, as well as simultaneity arising from endogenous binary regressors. In each of these cases, the primary source of the estimation challenge is the fact that jointly determined error terms in the reducedform specication are analytically intractable due to a highdimensional integral. To deal with this problem, simulation approaches have been proposed, but these are computationally intensive and impractical for datasets with thousands of observations. As a way forward, in this paper we demonstrate how to reduce the computational burder signicantly by (i) introducing analytically tractable pseudo maximum likelihoodestimators for latent binary choice models that exhibit interdependence across space, time and/or outcomes, and by (ii) proposing an implementation strategy that increases computational eciency considerably. MonteCarlo experiments demonstrate that our estimators perform similarly to existing alternatives in terms of error, but require only a fraction of the computational cost. 
JEL:  C10 C33 
Date:  2018–03–30 
URL:  http://d.repec.org/n?u=RePEc:bsl:wpaper:2018/11&r=ecm 
By:  Hiroaki Kaido; Jiaxuan Li; Marc Rysman 
Abstract:  This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in nonstandard ways. In particular, a (firstorder) bias due to the simulation errors may remain in the estimated boundary of the confidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can significantly reduce the coverage probabilities of confidence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1804.03674&r=ecm 
By:  Christoph Breunig 
Abstract:  This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of observed regressors and additively separable unobservables. This paper proposes a novel estimator of the VRC density based on weighted sieve minimum distance. The main example of sieve bases are Hermite functions which yield a numerically stable estimation procedure. This paper shows inference results that go beyond what has been shown in ordinary RC models: Only estimation of the joint VRC density is affected by illposedness but not that of the varying random slope (VRS) density. We provide in each case the optimal rate of convergence and also establish pointwise limit theory of linear functionals, where a prominent example is the density of potential outcomes. In addition, a multiplier bootstrap procedure is proposed to construct uniform confidence bands. A Monte Carlo study examines finite sample properties of the estimator and shows that it performs well even when the regressors associated to RC are far from being heavy tailed. Finally, the methodology is applied to analyze heterogeneity in income elasticity of demand for housing. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1804.03110&r=ecm 
By:  Patrick Kline; Christopher R. Walters 
Abstract:  Structural econometric methods are often criticized for being sensitive to functional form assumptions. We study parametric estimators of the local average treatment effect (LATE) derived from a widely used class of latent threshold crossing models and show they yield LATE estimates algebraically equivalent to the instrumental variables (IV) estimator. Our leading example is Heckman's (1979) twostep ("Heckit") control function estimator which, with twosided noncompliance, can be used to compute estimates of a variety of causal parameters. Equivalence with IV is established for a semiparametric family of control function estimators and shown to hold at interior solutions for a class of maximum likelihood estimators. Our results suggest differences between structural and IV estimates often stem from disagreements about the target parameter rather than from functional form assumptions per se. In cases where equivalence fails, reporting structural estimates of LATE alongside IV provides a simple means of assessing the credibility of structural extrapolation exercises. 
Date:  2017–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1706.05982&r=ecm 
By:  Ke Zhu 
Abstract:  This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute deviations estimator (LADE) for the model. Second, we develop the random weighting (RW) method to estimate its asymptotic covariance matrix, leading to the implementation of the Wald test. Third, we construct a portmanteau test for model checking, and use the RW method to obtain its critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE) is proposed and proved to have the same efficiency as its infeasible counterpart. The importance of our entire methodology based on the feasible ALADE is illustrated by simulation results and the real data analysis on three U.S. economic data sets. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1804.02348&r=ecm 
By:  Qiying Wang (University of Sydney); Peter C.B. Phillips (Cowles Foundation, Yale University); Ioannis Kasparis (Dept. of Economics, University of Cyprus) 
Abstract:  This paper studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such regressions arise naturally in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent variable. The model considered allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable. Such a framework includes correctly specified systems as well as misspecified models in which the actual regressor serves as a proxy variable for the true regressor. The system is therefore intermediate between nonlinear nonparametric cointegrating regression (Wang and Phillips, 2009a, 2009b) and completely misspecified nonparametric regressions in which the relationship is entirely spurious (Phillips, 2009). The asymptotic results relate to recent work on dynamic misspecification in nonparametric nonstationary systems by Kasparis and Phillips (2012) and Duffy (2014). The limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. 
Keywords:  Cointegrating regression, Kernel regression, Latent variable, Local time, Misspecification, Nonlinear nonparametric nonstationary regression 
JEL:  C23 
Date:  2017–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2111&r=ecm 
By:  Anna Bykhovskaya (Department of Economics, Yale University); Peter C. B. Phillips (Cowles Foundation, Yale University) 
Abstract:  Limit theory for regressions involving local to unit roots (LURs) is now used extensively in time series econometric work, establishing power properties for unit root and cointegration tests, assisting the construction of uniform confidence intervals for autoregressive coefficients, and enabling the development of methods robust to departures from unit roots. The present paper shows how to generalize LUR asymptotics to cases where the localized departure from unity is a time varying function rather than a constant. Such a functional local unit root (FLUR) model has much greater generality and encompasses many cases of additional interest, including structural break formulations that admit subperiods of unit root, local stationary and local explosive behavior within a given sample. Point optimal FLUR tests are constructed in the paper to accommodate such cases. It is shown that against FLUR\ alternatives, conventional constant point optimal tests can have extremely low power, particularly when the departure from unity occurs early in the sample period. Simulation results are reported and some implications for empirical practice are examined. 
Keywords:  Functional local unit root, Local to unity, Uniform confidence interval, Unit root model 
JEL:  C22 C65 
Date:  2017–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2107&r=ecm 
By:  Ruiqi Liu; Anton Schick; Zuofeng Shang; Yonghui Zhang; Qiankun Zhou 
Abstract:  In this paper, we provide a simple approach to identify and estimate group structure in panel models by adapting the Mestimation method. We consider both linear and nonlinear panel models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown to researchers. The main result of the paper is that under certain assumptions, our approach is able to provide uniformly consistent group parameter estimator as long as the number of groups used in estimation is not smaller than the true number of groups. We also show that, with probability approaching one, our method can partition some true groups into further subgroups, but cannot mix individuals from different groups. When the true number of groups is used in estimation, all the individuals can be categorized correctly with probability approaching one, and we establish the limiting distribution for the estimates of the group parameters. In addition, we provide an information criterion to choose the number of group and established its consistency under some mild conditions. Monte Carlo simulations are conducted to examine the finite sample performance of our proposed method. Findings in the simulation confirm our theoretical results in the paper. Application to labor force participation also highlights the necessity to take into account of individual heterogeneity and group heterogeneity. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:lsu:lsuwpp:201803&r=ecm 
By:  Matias D. Cattaneo; Max H. Farrell; Yingjie Feng 
Abstract:  We present large sample results for partitioningbased least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, employing a carefully crafted coupling approach, we develop uniform distributional approximations for $t$statistic processes (indexed over the support of the conditioning variables). These results cover both undersmoothed and bias corrected inference, require seemingly minimal rate restrictions, and achieve fast approximation rates. Using the uniform approximations we construct valid confidence bands which share these same advantages. While our coupling approach exploits specific features of the estimators considered, the underlying ideas may be useful in other contexts more generally. Second, we obtain valid integrated mean square error approximations for partitioningbased estimators and develop feasible tuning parameter selection. We apply our general results to three popular partitionbased estimators: splines, wavelets, and piecewise polynomials (generalizing the regressogram). The supplemental appendix includes other general and examplespecific technical results that may be of independent interest. A companion \textsf{R} package is provided. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1804.04916&r=ecm 
By:  Anna Bykhovskaya (Department of Economics, Yale University); Peter C. B. Phillips (Cowles Foundation, Yale University) 
Abstract:  This paper studies functional local unit root models (FLURs) in which the autoregressive coefficient may vary with time in the vicinity of unity. We extend conventional local to unity (LUR) models by allowing the localizing coefficient to be a function which characterizes departures from unity that may occur within the sample in both stationary and explosive directions. Such models enhance the flexibility of the LUR framework by including break point, trending, and multidirectional departures from unit autoregressive coefficients. We study the behavior of this model as the localizing function diverges, thereby determining the impact on the time series and on inference from the time series as the limits of the domain of definition of the autoregressive coefficient are approached. This boundary limit theory enables us to characterize the asymptotic form of power functions for associated unit root tests against functional alternatives. Both sequential and simultaneous limits (as the sample size and localizing coefficient diverge) are developed. We find that asymptotics for the process, the autoregressive estimate, and its $t$ statistic have boundary limit behavior that differs from standard limit theory in both explosive and stationary cases. Some novel features of the boundary limit theory are the presence of a segmented limit process for the time series in the stationary direction and a degenerate process in the explosive direction. These features have material implications for autoregressive estimation and inference which are examined in the paper. 
Keywords:  Boundary asymptotics, Functional local unit root, Local to unity, Sequential limits, Simultaneous limits, Unit root model 
JEL:  C22 C65 
Date:  2017–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2108&r=ecm 
By:  Donald W.K. Andrews (Cowles Foundation, Yale University) 
Abstract:  This paper introduces identificationrobust subvector tests and confidence sets (CS’s) that have asymptotic size equal to their nominal size and are asymptotically efficient under strong identification. Hence, inference is as good asymptotically as standard methods under standard regularity conditions, but also is identification robust. The results do not require special structure on the models under consideration, or strong identification of the nuisance parameters, as many existing methods do. We provide general results under highlevel conditions that can be applied to moment condition, likelihood, and minimum distance models, among others. We verify these conditions under primitive conditions for moment condition models. In another paper, we do so for likelihood models. The results build on the approach of Chaudhuri and Zivot (2011), who introduce a C(a)type Lagrange multiplier test and employ it in a Bonferroni subvector test. Here we consider twostep tests and CS’s that employ a C(a)type test in the second step. The twostep tests are closely related to Bonferroni tests, but are not asymptotically conservative and achieve asymptotic efficiency under strong identification 
Keywords:  Asymptotics, Confidence set, Identificationrobust, Inference, Instrumental variables, Moment condition, Robust, Test 
JEL:  C10 C12 
Date:  2017–09 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2105&r=ecm 
By:  Doll, Monika; Klein, Ingo 
Abstract:  Sample size analysis is a key part of the planning phase of any research. So far, however, limited literature focusses on sample size analysis methods for twosample linear rank tests, although these methods have optimal properties at different distributions. This paper provides a new sample size analysis method for linear rank tests for location shift alternatives based on score generating functions. Results show a slightly anticonservative behavior, no severe risk of an occuring circular argument at small to moderate variances of the population's distribution, and good performance compared to alternate sample size analysis methods for the most wellknown linear rank test, the WilcoxonMannWhitney test. 
Keywords:  Sample Size Analysis,Linear Rank Test,Score Generating Function,Circular Argument 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:zbw:iwqwdp:052018&r=ecm 
By:  Sarah Abraham; Liyang Sun 
Abstract:  Event studies are frequently used to estimate average treatment effects on the treated (ATT). In estimating the ATT, researchers commonly use fixed effects models that implicitly assume constant treatment effects across cohorts. We show that this is not an innocuous assumption. In fixed effect models where the sole regressor is treatment status, the OLS coefficient is a nonconvex average of the heterogeneous cohortspecific ATTs. When regressors containing lags and leads of treatment are added, the OLS coefficient corresponding to a given lead or lag picks up spurious terms consisting of treatment effects from other periods. Therefore, estimates from these commonly used models are not causally interpretable. We propose alternative estimators that identify certain convex averages of the cohortspecific ATTs, hence allowing for causal interpretation even under heterogeneous treatment effects. To illustrate the empirical content of our results, we show that the fixed effects estimators and our proposed estimators differ substantially in an application to the economic consequences of hospitalization. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1804.05785&r=ecm 
By:  Hulya Eraslan (Rice University, Department of Economics); Xun Tang (Rice University, Department of Economics) 
Abstract:  We study the identification and estimation of large network games where each individual holds private information about its links and payoffs. Extending Galeotti, Goyal, Jackson, VegaRedondo and Yariv (2010), we build a tractable empirical model of network games where the individuals are heterogeneous with private link and payoff information, and characterize its unique, symmetric purestrategy Bayesian Nash equilibrium. We then show that the parameters in individual payoffs are identified under "large market" asymptotics, whereby the number of individuals increases to infinity in a fixed and small number of networks. We also propose a consistent twostep mestimator for individual payoffs. Our method is distributionfree in that it does not require parametrization of the distribution of shocks in individual payoffs. Monte Carlo simulation show that our estimator has good performance in moderatesized samples. 
Date:  2018–03 
URL:  http://d.repec.org/n?u=RePEc:koc:wpaper:1809&r=ecm 
By:  Joris de Wind (CPB Netherlands Bureau for Economic Policy Analysis) 
Abstract:  In this paper, I present a novel implementation of the exact nonlinear and nonGaussian Kalman smoother that can also deal with implicit functions in the measurement and/or state equations as well as equality constraints. Read the accompanying paper CPB Discussion Paper 360 . My approach has the additional advantage that it can be fully automated, on the basis of which I have developed a toolbox that can handle a wide class of discretetime state space models. The toolbox is documented in an accompanying paper, while the technical details are presented in the current one. 
JEL:  C21 C22 C25 J64 
Date:  2017–09 
URL:  http://d.repec.org/n?u=RePEc:cpb:discus:359&r=ecm 
By:  Cheng Hsiao; Qiankun Zhou 
Abstract:  We consider panel parametric, semiparametric and nonparametric methods of constructing counterfactuals. Through extensive simulations, no method is able to dominate other methods. In general, we fi?nd that if the observed data are stationary, the panel semi parametric method appears capable of generating counterfactuals close to the (true) data generating process in a wide array of situations. If the data are nonstationary, then the panel nonparametric method appears to dominate the parametric or semiparametric approaches. We also suggest a model averaging method as a robust method to generate counterfactuals. We compare the different estimates of the impact of California Tobacco Control Program on per capita cigarette consumption. 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:lsu:lsuwpp:201802&r=ecm 
By:  Haroon Mumtaz (Queen Mary University of London); 
Abstract:  This paper introduces a VAR with stochastic volatility in mean where the residuals of the volatility equations and the observation equations are allowed to be correlated. This implies that exogeneity of shocks to volatility is not assumed apriori and structural shocks can be identified expost by applying standard SVAR techniques. The paper provides a Gibbs algorithm to approximate the posterior distribution and demonstrates the proposed methods by estimating the impact of financial uncertainty shocks on the US economy. 
Keywords:  VAR, Stochastic volatility in mean, error covariance 
JEL:  C2 C11 E3 
Date:  2018–03–06 
URL:  http://d.repec.org/n?u=RePEc:qmw:qmwecw:855&r=ecm 
By:  Elmar Mertens; James M. Nason 
Abstract:  This paper studies the joint dynamics of realtime U.S. inflation and average inflation predictions of the Survey of Professional Forecasters (SPF) based on sample ranging from 1968Q4 to 2017Q2. The joint data generating process (DGP) comprises an unobserved components (UC) model of inflation and a sticky information (SI) prediction mechanism for the SPF predictions. We add drifting gap inflation persistence to a UC model in which stochastic volatility (SV) affects trend and gap inflation. Another innovation puts a timevarying frequency of inflation forecast updating into the SI prediction mechanism. The joint DGP is a nonlinear state space model (SSM). We estimate the SSM using Bayesian tools grounded in a RaoBlackwellized auxiliary particle filter, particle learning, and a particle smoother. The estimates show that (i) longer horizon average SPF inflation predictions inform estimates of trend inflation; (ii) gap inflation persistence is procyclical and SI inflation updating is frequent before the Volcker disinflation; and (iii) subsequently, gap inflation persistence turns countercyclical and SI inflation updating becomes infrequent. 
Keywords:  inflation; unobserved components;professional forecasts; sticky information; stochastic volatility; timevarying parameters; Bayesian; particle filter 
JEL:  E31 C11 C32 
Date:  2018–04 
URL:  http://d.repec.org/n?u=RePEc:bis:biswps:713&r=ecm 