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on Econometrics |
| By: | Aman Ullah (Department of Economics, University of California Riverside); Tao Wang (University of Victoria); Weixin Yao (University of California Riverside) |
| Abstract: | We in this paper propose a semiparametric partially linear varying coefficient (SPLVC) modal regression, in which the conditional mode function of the response variable given covariates admit a partially linear varying coefficient structure. In comparison to existing regressions, the newly developed SPLVC modal regression captures the most likely effect and provides superior prediction performance when the data distribution is skewed. The consistency and asymptotic properties of the resultant estimators for both parametric and nonparametric parts are rigorously established. We employ a kernel-based objective function to simplify the computation and a modified modal-expectation-maximization (MEM) algorithm to estimate the model numerically. Furthermore, taking the residual sums of modes as the loss function, we construct a goodness of fit testing statistic for hypotheses on the coefficient functions, whose limiting null distribution is shown to follow an asymptotically normal-distribution with a scale dependent on density functions. To achieve sparsity in the high-dimensional SPLVC modal regression, we develop a regularized estimation procedure by imposing a penalty on the coefficients in the parametric part to eliminate the irrelevant variables. Monte Carlo simulations and two real-data applications are conducted to examine the performance of the suggested estimation methods and hypothesis test. We also briefly explore the extension of the SPLVC modal regression to the case where some varying coefficient functions admit higher-order smoothness. |
| Keywords: | Goodness of fit test, MEM algorithm, Modal regression, Oracle property, Partially linear varying coefficient |
| JEL: | C01 C12 C14 C50 |
| Date: | 2022–06 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:202215&r= |
| By: | Phillip Heiler |
| Abstract: | In this paper we propose a method for nonparametric estimation and inference for heterogeneous bounds for causal effect parameters in general sample selection models where the initial treatment can affect whether a post-intervention outcome is observed or not. Treatment selection can be confounded by observable covariates while the outcome selection can be confounded by both observables and unobservables. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. It allows for conducting valid statistical inference on the unidentified conditional effect curves. We use a flexible semiparametric de-biased machine learning approach that can accommodate flexible functional forms and high-dimensional confounding variables between treatment, selection, and outcome processes. Easily verifiable high-level conditions for estimation and misspecification robust inference guarantees are provided as well. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.04329&r= |
| By: | Hao Dong (Southern Methodist University); Yuya Sasaki (Vanderbilt University) |
| Abstract: | This paper proposes a density-weighted average derivative estimator based on two noisy measures of a latent regressor. Both measures have classical errors with possibly asymmetric distributions. We show that the proposed estimator achieves the root-n rate of convergence, and derive its asymptotic normal distribution for statistical inference. Simulation studies demonstrate excellent small-sample performance supporting the root-n asymptotic normality. Based on the proposed estimator, we construct a formal test on the sub-unity of the marginal propensity to consume out of permanent income (MPCP) under a nonparametric consumption model and a permanent-transitory model of income dynamics with nonparametric distribution. Applying the test to four recent waves of U.S. Panel Study of Income Dynamics (PSID), we reject the null hypothesis of the unit MPCP in favor of a sub-unit MPCP, supporting the buffer-stock model of saving. |
| Keywords: | Average derivative, latent variables, income dynamics, consumption. |
| JEL: | C14 C23 D31 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:smu:ecowpa:2204&r= |
| By: | Etienne Wijler |
| Abstract: | In this paper, we develop a restricted eigenvalue condition for unit-root non-stationary data and derive its validity under the assumption of independent Gaussian innovations that may be contemporaneously correlated. The method of proof relies on matrix concentration inequalities and offers sufficient flexibility to enable extensions of our results to alternative time series settings. As an application of this result, we show the consistency of the lasso estimator on ultra high-dimensional cointegrated data in which the number of integrated regressors may grow exponentially in relation to the sample size. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.12990&r= |
| By: | Joshua C. C. Chan |
| Abstract: | Large Bayesian vector autoregressions with various forms of stochastic volatility have become increasingly popular in empirical macroeconomics. One main difficulty for practitioners is to choose the most suitable stochastic volatility specification for their particular application. We develop Bayesian model comparison methods -- based on marginal likelihood estimators that combine conditional Monte Carlo and adaptive importance sampling -- to choose among a variety of stochastic volatility specifications. The proposed methods can also be used to select an appropriate shrinkage prior on the VAR coefficients, which is a critical component for avoiding over-fitting in high-dimensional settings. Using US quarterly data of different dimensions, we find that both the Cholesky stochastic volatility and factor stochastic volatility outperform the common stochastic volatility specification. Their superior performance, however, can mostly be attributed to the more flexible priors that accommodate cross-variable shrinkage. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.13255&r= |
| By: | Qihui Chen |
| Abstract: | This paper develops a general framework for estimation of high-dimensional conditional factor models via nuclear norm regularization. We establish large sample properties of the estimators, and provide an efficient computing algorithm for finding the estimators as well as a cross validation procedure for choosing the regularization parameter. The general framework allows us to estimate a variety of conditional factor models in a unified way and quickly deliver new asymptotic results. We apply the method to analyze the cross section of individual US stock returns, and find that imposing homogeneity may improve the model's out-of-sample predictability. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.00391&r= |
| By: | Eskil Heinesen; Christian Hvid; Lars Kirkeb{\o}en; Edwin Leuven; Magne Mogstad |
| Abstract: | Abstract Instrumental variables (IV) estimation of treatment effects is challenging if there are multiple unordered treatments. This note revisits the identification argument of Kirkeboen et al. (2016) who showed how one may combine multiple instruments with information about individuals' ranking of treatment types to achieve identification while allowing for both observed and unobserved heterogeneity in treatment effects. First we show that the key assumptions underlying the identification argument of Kirkeboen et al. (2016) has testable implications. Second, we provide a new characterization of the bias based on principal strata, that may arise if these assumptions are violated. The strata are "next-best defiers", individuals who comply with the assigned treatment, but who otherwise choose a treatment other than the stated next-best alternative, and "irrelevance-defiers" who are shifted into other treatments than the assigned one. The bias is large only if there are both many defiers relative to compliers and there are large differences in the payoff between compliers and defiers. We show that the shares of next-best or irrelevance defiers can be bounded, but not point identified. We derive sharp bounds which are nontrivial and, thus, provides testable implications of the additional assumptions of Kirkeboen et al. (2016). These results have implications for the recent work of Nibbering et al. (2022), who propose an algorithm which aggregates fields into clusters based on estimated first-stage coefficients. The motivation for their approach is to avoid bias from irrelevance and next-best defiers. We show that this approach requires point identification of the shares of next-best and irrelevance defiers, and that it may produce biased estimates even if effects are constant across individuals. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.00417&r= |
| By: | Feiyu Jiang; Emmanuel Selorm Tsyawo |
| Abstract: | In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, their use is not common in empirical practice owing to (1) the non-pivotal nature of the test and (2) the high computational cost of available bootstrap schemes in large samples. Moreover, the local power of ICM tests is only substantial within a finite-dimensional space usually unbeknownst to the researcher. Based on a class of newly developed ICM metrics called the generalized martingale difference divergence (GMDD), this paper proposes a conditional moment and specification test that is consistent, asymptotically $\chi^2$ distributed under the null, and computationally efficient. The test also accounts for heteroskedasticity of unknown form and can be enhanced to augment power in the direction of given alternatives. Besides showing significant computational gains of the proposed test, Monte Carlo simulations demonstrate their good size control and power performance comparable to bootstrap-based ICM tests. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.13370&r= |
| By: | Michael Bates (Department of Economics, University of California Riverside); Jeffrey Wooldridge; Lelsie papke |
| Abstract: | We present simple procedures for estimating nonlinear panel data models in the presence of unobserved heterogeneity and possible endogeneity with respect to time-varying unobervables. We combine a correlated random effects approach with a control function approach while accounting for missing time periods for some units. We examine the performance of the approach in comparisons with standard estimators using Monte Carlo simulation. We apply the methods to estimating the effects of school spending on student pass rates on a standardized math exam. We find that a 10 percent increase in spending leads to an approximately two percentage point increase in math pass rates. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:ucr:wpaper:202214&r= |
| By: | Alyssa Carlson (Department of Economics, University of Missouri-Columbia) |
| Abstract: | Previously, identification of triangular random coefficient models required a restriction on the dimension of the first stage heterogeneity or independence assumptions across the different sources of the heterogeneity. This note proposes a new identification strategy that does not rely on either of these restrictions but rather assumes conditional means are conditional linear projections in order to construct “correction functions†to address endogeneity and gain identification of the average partial effect. This identification strategy allows for both continuous and discrete instruments. Finally, a simple simulation illustrates that the proposed identification strategy is valid in settings where no other existing methods can identify average partial effects. |
| Keywords: | Endogeneity, Control Function, Random Coefficient, Conditional Linear Projection |
| JEL: | C3 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:2207&r= |
| By: | Geert Mesters; Piotr Zwiernik |
| Abstract: | A seminal result in the ICA literature states that for AY=e, if the components of e are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows (Comon, 1994) In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on the moments or cumulants of e. We document minimal conditions for identifiability and propose efficient estimation methods based on the new identification results. In situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence. The proof strategy employed highlights new geometric and combinatorial tools that can be adopted to study identifiability via higher order restrictions in linear systems. |
| Keywords: | Independent components analysis, cumulants, moments, tensors, identification |
| JEL: | C20 C30 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1845&r= |
| By: | Grivas, Charisios |
| Abstract: | A data-driven version of a portmanteau test for detecting nonlinear types of statistical dependence is considered. An attractive feature of the proposed test is that it properly controls type I error without depending on the number of lags. In addition, the automatic test is found to have higher power in simulations when compared to the McLeod and Li test, for both raw data and residuals. |
| Keywords: | ARMA time series;Akaike's AIC;Schwarz's BIC; Portmanteau test; Data-driven test |
| JEL: | C01 |
| Date: | 2021–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:114312&r= |
| By: | Jonathan Berrisch; Sven Pappert; Florian Ziel; Antonia Arsova |
| Abstract: | We study the prices of European Emission Allowances (EUA), whereby we analyze their uncertainty and dependencies on related energy markets. We propose a probabilistic multivariate conditional time series model that exploits key characteristics of the data. The forecasting performance of the proposed model and various competing models is evaluated in an extensive rolling window forecasting study, covering almost two years out-of-sample. Thereby, we forecast 30-steps ahead. The accuracy of the multivariate probabilistic forecasts is assessed by the energy score. We discuss our findings focusing on volatility spillovers and time-varying correlations, also in view of the Russian invasion of Ukraine. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.14311&r= |
| By: | Barbaglia, Luca (European Commission); Frattarolo, Lorenzo (European Commission); Onorante, Luca (European Commission); Pericoli, Filippo Maria (European Monitoring Centre for Drugs and Drug Addiction); Ratto, Marco (European Commission); Tiozzo Pezzoli, Luca (European Commission) |
| Abstract: | During the COVID-19 pandemic, economists have struggled to obtain reliable economic predictions, with standard models becoming outdated and their forecasting performance deteriorating rapidly. This paper presents two novelties that could be adopted by forecasting institutions in unconventional times. The first innovation is the construction of an extensive data set for macroeconomic forecasting in Europe. We collect more than a thousand time series from conventional and unconventional sources, complementing traditional macroeconomic variables with timely big data indicators and assessing their added value at nowcasting. The second novelty consists of a methodology to merge an enormous amount of non-encompassing data with a large battery of classical and more sophisticated forecasting methods in a seamlessly dynamic Bayesian framework. Specifically, we introduce an innovative “selection prior†that is used not as a way to influence model outcomes, but as a selecting device among competing models. By applying this methodology to the COVID-19 crisis, we show which variables are good predictors for nowcasting Gross Domestic Product and draw lessons for dealing with possible future crises |
| Keywords: | Bayesian Model Averaging, Big Data, COVID-19 Pandemic, Nowcasting |
| JEL: | C11 C30 E3 E37 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:jrs:wpaper:202206&r= |