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on Econometrics |
| By: | Takaki Sato |
| Abstract: | This study considers the generalized method of moment (GMM) estimation of spatial autoregressive (SAR) models with unknown cluster correlations among error terms. In the presence of cluster correlations within errors, nonlinear moment conditions suitable for independent errors lose their validity and GMM estimators obtained from the moment condition are inconsistent. In this paper, we propose the GMM estimator obtained from another nonlinear moment condition suitable for cluster dependent error terms and show its asymptotic properties. Because the asymptotic variance of the GMM estimator depends on the choice of the weight matrix for GMM estimation, we also discuss the optimal weight which minimizes the asymptotic variance, and introduce the feasible optimal GMM estimator based on the consistent estimator of the weight. Monte Carlo experiments indicate that the proposed GMM estimator has a small bias and root mean squared errors when error terms in SAR models have cluster correlation compared to two stage least squares estimators and GMM estimators for independent errors. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:toh:dssraa:131&r=ecm |
| By: | Wang, Wenjie |
| Abstract: | This note studies the validity of bootstrapping the test of overidentifying restrictions under many/many weak instruments and heteroskedasticity. We propose a wild bootstrap procedure and establish this bootstrap consistently estimates the null limiting distributions of a jackknife overidentification test statistic under this asymptotic framework, no matter studentized or not. Monte Carlo simulations show that the wild bootstrap provides more reliable inference than asymptotic critical values. In particular, the studentized wild bootstrap test has the best finite sample performance in terms of both size and power. |
| Keywords: | Wild Bootstrap, Overidentification Test, Many Instruments, Weak Instruments, Heteroskedasticity. |
| JEL: | C12 C15 C26 |
| Date: | 2022–10–26 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115168&r=ecm |
| By: | Anish Agarwal; Vasilis Syrgkanis |
| Abstract: | We propose a generalization of the synthetic control and synthetic interventions methodology to the dynamic treatment regime. We consider the estimation of unit-specific treatment effects from panel data collected via a dynamic treatment regime and in the presence of unobserved confounding. That is, each unit receives multiple treatments sequentially, based on an adaptive policy, which depends on a latent endogenously time-varying confounding state of the treated unit. Under a low-rank latent factor model assumption and a technical overlap assumption we propose an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be seen as an identification strategy for structural nested mean models under a low-rank latent factor assumption on the blip effects. Our method, which we term "synthetic blip effects", is a backwards induction process, where the blip effect of a treatment at each period and for a target unit is recursively expressed as linear combinations of blip effects of a carefully chosen group of other units that received the designated treatment. Our work avoids the combinatorial explosion in the number of units that would be required by a vanilla application of prior synthetic control and synthetic intervention methods in such dynamic treatment regime settings. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.11003&r=ecm |
| By: | Daisuke Kurisu; Yasumasa Matsuda |
| Abstract: | In this study, we develop a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region Rn ¼ Rd. We adopt a stochastic sampling design that can generate irregularly spaced sampling sites in a flexible manner and include both pure increasing and mixed increasing domain framework. We first introduce a nonparametric regression model for spatial data defined on Rd and then establish the asymptotic normality of LP estimators with general order p ? 1. We also propose methods for constructing confidence intervals and establish uniform convergence rates of LP estimators. Our dependence structure conditions on the underlying random field cover a wide class of random fields such as L Levy-driven continuous autoregressive moving average random fields. As an application of our main results, we also discuss a two-sample testing problem for mean functions and their partial derivatives. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:toh:dssraa:133&r=ecm |
| By: | Takaki Sato; Yuta Kuroda; Yasumasa Matsuda |
| Abstract: | This paper proposes a spatial extension of the mixed models of the analysis of variance(MANOVA) models, which are called mixed spatial ANOVA (MS-ANOVA) models. MS-ANOVA models have been used to evaluate spatial correlations between random effects in multilevel data which is a kind of cluster data in which observations belong to some kinds of nested clusters. Because the proposed model can be regarded as a Bayesian hierarchical models, we have introduced empirical Bayesian estimation methods in which hyper parameters are estimated by quasi-maximum likelihood estimation methods in the first step and posterior distributions for the parameters are evaluated with the estimated hyper-parameters in the second step. Moreover, we have justified the asymptotic properties of the first step estimators. The proposed models are applied to happiness survey data in Japan and empirical results show that social capital which can be interpreted as "the beliefs and norms by which a community values collective action and pursues activities worthy for the entire community" significantly increases people's happiness, even after controlling for a variety of individual characteristics and spatial correlations. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:toh:dssraa:132&r=ecm |
| By: | Daniel Buncic; Adrian Pagan |
| Abstract: | There exist many latent variables in macroeconometrics that are commonly referred to as "stars". Examples of such "stars" are the NAIRU, potential GDP, and the neutral real rate of interest. Because these "stars" are defined as latent variables, they are estimated using the Kalman filter and/or smoother from models that can be expressed in State Space Form. When there are more shocks than observables in the State Space Form representation of such models, issues arise related to the recoverability of these "stars" from the data. Recoverability is problematic in this setting even if the assumed model for the data is correct and all model parameters are known. In this paper, we examine recoverability in a range of popular models and show that many of these "stars" cannot be recovered. |
| Keywords: | Recoverability, excess shocks, latent variables, neutral rates, Kalman Filter |
| JEL: | E37 C51 C52 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2022-52&r=ecm |
| By: | Xiaowei Yang; Xinqiao Liu; Haoyu Wei |
| Abstract: | The Maximum Likelihood Estimator (MLE) serves an important role in statistics and machine learning. In this article, for i.i.d. variables, we obtain constant-specified and sharp concentration inequalities and oracle inequalities for the MLE only under exponential moment conditions. Furthermore, in a robust setting, the sub-Gaussian type oracle inequalities of the log-truncated maximum likelihood estimator are derived under the second-moment condition. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.09398&r=ecm |
| By: | Brendan K. Beare; Jackson D. Clarke |
| Abstract: | Given independent samples from two univariate distributions, one-sided Wilcoxon-Mann-Whitney statistics may be used to conduct rank-based tests of stochastic dominance. We broaden the scope of applicability of such tests by showing that the bootstrap may be used to conduct valid inference in a matched pairs sampling framework permitting dependence between the two samples. Further, we show that a modified bootstrap incorporating an implicit estimate of a contact set may be used to improve power. Numerical simulations indicate that our test using the modified bootstrap effectively controls the null rejection rates and can deliver more or less power than that of the Donald-Hsu test. In the course of establishing our results we obtain a weak approximation to the empirical ordinance dominance curve permitting its population density to diverge to infinity at zero or one at arbitrary rates. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.08892&r=ecm |
| By: | YAMAGUCHI Kazuo |
| Abstract: | This article introduces a new RCM method based on the inverse probability of treatment weighting for the analysis of two-level data of individuals and their social contexts when we expect unobserved contextual effects on the treatment and outcome. The method is an alternative to the use of fixed effects for social contexts in the estimation of propensity score when the fixed effects cannot be included in the estimation of propensity score due to small sample sizes for a non-negligible number of social contexts. The method is based on a novel ignorability assumption that may hold in many cases and permits the elimination of confounding unobserved contextual effects under such a situation. An application of the new method to the decomposition analysis of inequality by combining it with the DiNardo-Fortin-Lemieux method focuses on the decomposition of the gender income gap and gender gap in positional rank among white-collar regular employees in Japan when their employers are the social contexts. The application provides findings that are consistent with the hypotheses that women tend to remain employed in firms for which their relative income and relative opportunity of being promoted to supervisory positions compared with men are better than in other firms, and that the gender gap is consequently reduced among those who remain employed. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:eti:dpaper:22099&r=ecm |
| By: | Ilya Archakov; Peter Reinhard Hansen; Yiyao Luo |
| Abstract: | We propose a new method for generating random correlation matrices that makes it simple to control both location and dispersion. The method is based on a vector parameterization, gamma = g(C), which maps any distribution on R^d, d = n(n-1)/2 to a distribution on the space of non-singular nxn correlation matrices. Correlation matrices with certain properties, such as being well-conditioned, having block structures, and having strictly positive elements, are simple to generate. We compare the new method with existing methods. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.08147&r=ecm |
| By: | Anis Hoayek (LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes - Ecole Nationale Supérieure des Mines de St Etienne - CNRS - Centre National de la Recherche Scientifique - UCA - Université Clermont Auvergne - INP Clermont Auvergne - Institut national polytechnique Clermont Auvergne - UCA - Université Clermont Auvergne, FAYOL-ENSMSE - Institut Henri Fayol - Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris], FAYOL-ENSMSE - Département Génie mathématique et industriel - Ecole Nationale Supérieure des Mines de St Etienne - Institut Henri Fayol, Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris]); Didier Rullière (LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes - Ecole Nationale Supérieure des Mines de St Etienne - CNRS - Centre National de la Recherche Scientifique - UCA - Université Clermont Auvergne - INP Clermont Auvergne - Institut national polytechnique Clermont Auvergne - UCA - Université Clermont Auvergne, FAYOL-ENSMSE - Institut Henri Fayol - Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris], FAYOL-ENSMSE - Département Génie mathématique et industriel - Ecole Nationale Supérieure des Mines de St Etienne - Institut Henri Fayol, Mines Saint-Étienne MSE - École des Mines de Saint-Étienne - IMT - Institut Mines-Télécom [Paris]) |
| Abstract: | Unsupervised clustering algorithms are a very important source of information for how a dataset may be classified into subgroups of homogeneous sets. For these algorithms we present a full analysis of their quality by introducing a clustering confidentness metric. Based on this metric, a statistical test and a correction of cluster probabilities are introduced to improve the performance of the different algorithms. These results are illustrated by simulation analysis and by an application on a real world data set. |
| Date: | 2022–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-03812055&r=ecm |
| By: | Roland Meeks; Francesca Monti |
| Abstract: | Heterogeneous beliefs modify the New Keynesian Phillips curve by introducing a term in the cross-section distribution of expectations. We develop a novel functional data approach to estimation and inference in survey-based Phillips curves that accounts for variation in distributions of expectations, generalizing standard approaches. Our findings demonstrate the statistical and economic importance of heterogeneous beliefs for inflation dynamics, especially during periods of macroeconomic disruption.Our findings hold in similar form across two major economies. |
| Keywords: | Inflation dynamics, New Keynesian Phillips curve, Survey expectations, Functional principal Components, Functional regression |
| JEL: | C4 C55 D84 E31 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2022-51&r=ecm |
| By: | Christian Alemán; Christopher Busch; Alexander Ludwig; Raül Santaeulàlia-Llopis |
| Abstract: | We develop a method that identifies the effects of policy implemented nationwide—i.e. across all regions at the same time. Starting point is the insight that outcome paths can be tracked over stages using a reference path. The stage of a regional outcome path is defined as its location on the support of a reference path. It is formally the result of a normalization that maps the time-path of regional outcomes onto a reference path using pre-policy data only. Intuitively, our normalization seeks to reshape the structural parameters that determine the outcome path of non-reference regions into those of a reference region—a phenomenon that we show with an example for which we can derive exact identification. Since regions can differ by stage at any point in time, our normalization uncovers heterogeneity in the stage at the time of policy implementation—even in instances where the implementation occurs at the same time across regions. We use this stage variation at the time of policy implementation to identify the policy effects: a stageleading region delivers the counterfactual path inside an identification window in which nonleading regions are subject to policy whereas the leading region is not. Our identification assumption is that the normalization conducted using pre-policy data holds post policy, i.e. the normalization coefficients reshaping the regional pre-policy outcome paths into those of a reference region are unaffected by policy. We validate our method with Monte-Carlo experiments on model-generated data that detect bounds for a successful identification. We us our method to evaluate the effectiveness of public health stay-home policies (i.e. the national lockdown against Covid-19 in Spain), the effects of oral contraceptives (i.e. the 1960 FDA nationwide approval of oral contraceptives in the U.S.) on women’s fertility and college education and the effects of growth policy (e.g. German Reunification). We further show how our method can be applied to non-nationwide policy—i.e. untreated regions and staggered rollouts—and discuss the implications of spillovers across regions. |
| Keywords: | policy effects, identification, stages |
| JEL: | C01 H00 E01 E22 E25 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:1369&r=ecm |