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on Econometrics |
| By: | Timothy B. Armstrong; Martin Weidner; Andrei Zeleneev |
| Abstract: | We consider estimation and inference for a regression coefficient in a panel setting with time and individual specific effects which follow a factor structure. Previous approaches to this model require a "strong factor" assumption, which allows the factors to be consistently estimated, thereby removing omitted variable bias due to the unobserved factors. We propose confidence intervals (CIs) that are robust to failure of this assumption, along with estimators that achieve better rates of convergence than previous methods when factors may be weak. Our approach applies the theory of minimax linear estimation to form a debiased estimate using a nuclear norm bound on the error of an initial estimate of the individual effects. In Monte Carlo experiments, we find a substantial improvement over conventional approaches when factors are weak, with little cost to estimation error when factors are strong. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.06639&r= |
| By: | Lukas Hoesch; Adam Lee; Geert Mesters |
| Abstract: | All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non-Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a robust semi-parametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non-Gaussianity when it is present, but yields correct size / coverage regardless of the distance to the Gaussian distribution. Empirically we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012) we find that non-Gaussianity can robustly identify reasonable confidence sets, whereas for the labour supply-demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to asses estimation uncertainty when using non-Gaussianity for identification. |
| Keywords: | weak identification, semi-parametric inference, hypothesis testing, impulse responses, independent component analysis |
| JEL: | C32 C39 C51 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1847&r= |
| By: | Yu Hao; Hiroyuki Kasahara |
| Abstract: | This paper develops the likelihood ratio-based test of the null hypothesis of a M0-component model against an alternative of (M0 + 1)-component model in the normal mixture panel regression by extending the Expectation-Maximization (EM) test of Chen and Li (2009a) and Kasahara and Shimotsu (2015) to the case of panel data. We show that, unlike the cross-sectional normal mixture, the first-order derivative of the density function for the variance parameter in the panel normal mixture is linearly independent of its second-order derivatives for the mean parameter. On the other hand, like the cross-sectional normal mixture, the likelihood ratio test statistic of the panel normal mixture is unbounded. We consider the Penalized Maximum Likelihood Estimator to deal with the unboundedness, where we obtain the data-driven penalty function via computational experiments. We derive the asymptotic distribution of the Penalized Likelihood Ratio Test (PLRT) and EM test statistics by expanding the log-likelihood function up to five times for the reparameterized parameters. The simulation experiment indicates good finite sample performance of the proposed EM test. We apply our EM test to estimate the number of production technology types for the finite mixture Cobb-Douglas production function model studied by Kasahara et al. (2022) used the panel data of the Japanese and Chilean manufacturing firms. We find the evidence of heterogeneity in elasticities of output for intermediate goods, suggesting that production function is heterogeneous across firms beyond their Hicks-neutral productivity terms. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.02824&r= |
| By: | Xu, Haotian (Université catholique de Louvain, LIDAM/ISBA, Belgium); Wang, Daren; Zhao, Zifeng; Yu, Yi |
| Abstract: | This paper concerns about the limiting distributions of change point estimators, in a high- dimensional linear regression time series context, where a regression object (yt, Xt) ∈ R × Rp is observed at every time point t ∈ {1, . . . , n}. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in l2-norm. We provide limiting distributions of the change point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change point localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package changepoints (Xu et al., 2021). |
| Keywords: | High-dimensional linear regression ; Change point inference ; Functional dependence ; Long-run variance ; Confidence interval |
| Date: | 2022–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2022027&r= |
| By: | Lambert, Philippe (Université catholique de Louvain, LIDAM/ISBA, Belgium); Gressani, Oswaldo (Université catholique de Louvain, LIDAM/ISBA, Belgium) |
| Abstract: | Laplacian-P-splines (LPS) associate the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. Gaussian Markov field priors imposed on penalized latent variables and the Bernstein-von Mises theorem typically ensure a razor-sharp accuracy of the Laplace approximation to the posterior distribution of these variables. This accuracy can be seriously compromised for some unpenalized parameters, especially when the information synthesized by the prior and the likelihood is sparse. We propose a refined version of the LPS methodology by splitting the latent space in two subsets. The first set involves latent variables for which the joint posterior distribution is approached from a non-Gaussian perspective with an approximation scheme that is particularly well tailored to capture asymmetric patterns, while the posterior distribution for parameters in the complementary latent set undergoes a traditional treatment with Laplace approximations. As such, the dichotomization of the latent space provides the necessary structure for a separate treatment of model parameters, yielding improved estimation accuracy as compared to a setting where posterior quantities are uniformly handled with Laplace. In addition, the proposed enriched version of LPS remains entirely sampling-free, so that it operates at a computing speed that is far from reach to any existing Markov chain Monte Carlo approach. The methodology is illustrated on the additive proportional odds model with an application on ordinal survey data. |
| Keywords: | Additive model ; P-splines ; Laplace approximation ; Skewness |
| Date: | 2022–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2022030&r= |
| By: | JoonHwan Cho; Yao Luo; Ruli Xiao |
| Abstract: | Economic data are often truncated by ranking and contaminated by measurement errors. We study the identification of the distributions of a latent variable of interest and its measurement errors using a subvector of order statistics of repeated measurements. Kotlarski's lemma is inapplicable due to dependence in the order statistics of measurement errors. Exploiting the ratio of characteristic functions of order statistics, we show observing two order statistics are sufficient to identify the underlying distributions nonparametrically. We adapt an existing simulated sieve estimator to our setting and illustrate its performance in finite samples. |
| Keywords: | Measurement Error, Order Statistics, Nonparametric Identification, Spacing, Cross-Sum |
| JEL: | C14 D44 J31 |
| Date: | 2022–10–18 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-739&r= |
| By: | H. Peter Boswijk; Roger J. A. Laeven; Evgenii Vladimirov |
| Abstract: | We develop a novel filtering and estimation procedure for parametric option pricing models driven by general affine jump-diffusions. Our procedure is based on the comparison between an option-implied, model-free representation of the conditional log-characteristic function and the model-implied conditional log-characteristic function, which is functionally affine in the model's state vector. We formally derive an associated linear state space representation and establish the asymptotic properties of the corresponding measurement errors. The state space representation allows us to use a suitably modified Kalman filtering technique to learn about the latent state vector and a quasi-maximum likelihood estimator of the model parameters, which brings important computational advantages. We analyze the finite-sample behavior of our procedure in Monte Carlo simulations. The applicability of our procedure is illustrated in two case studies that analyze S&P 500 option prices and the impact of exogenous state variables capturing Covid-19 reproduction and economic policy uncertainty. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.06217&r= |
| By: | Ramis Khabibullin; Sergei Seleznev |
| Abstract: | This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at the first stage, and then a flexible model is trained to predict the variables of interest. In contrast to those proposed earlier, the procedure described in this paper makes it possible to train estimators for hidden states by concentrating only on certain characteristics of the marginal posterior distributions and introducing inductive bias. Illustrations using the examples of the stochastic volatility model, nonlinear dynamic stochastic general equilibrium model, and seasonal adjustment procedure with breaks in seasonality show that the algorithm has sufficient accuracy for practical use. Moreover, after pretraining, which takes several hours, finding the posterior distribution for any dataset takes from hundredths to tenths of a second. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.07154&r= |
| By: | Yao Luo; Peijun Sang; Ruli Xiao |
| Abstract: | We establish nonparametric identification of auction models with continuous and nonseparable unobserved heterogeneity using three consecutive order statistics of bids. We then propose sieve maximum likelihood estimators for the joint distribution of unobserved heterogeneity and the private value, as well as their conditional and marginal distributions. Lastly, we apply our methodology to a novel dataset from judicial auctions in China. Our estimates suggest substantial gains from accounting for unobserved heterogeneity when setting reserve prices. We propose a simple scheme that achieves nearly optimal revenue by using the appraisal value as the reserve price. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.03547&r= |
| By: | Alejandro Sanchez-Becerra |
| Abstract: | I establish primitive conditions for unconfoundedness in a coherent model that features heterogeneous treatment effects, spillovers, selection-on-observables, and network formation. I identify average partial effects under minimal exchangeability conditions. If social interactions are also anonymous, I derive a three-dimensional network propensity score, characterize its support conditions, relate it to recent work on network pseudo-metrics, and study extensions. I propose a two-step semiparametric estimator for a random coefficients model which is consistent and asymptotically normal as the number and size of the networks grows. I apply my estimator to a political participation intervention Uganda and a microfinance application in India. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.14391&r= |
| By: | Raghavendra Addanki; David Arbour; Tung Mai; Cameron Musco; Anup Rao |
| Abstract: | Treatment effect estimation is a fundamental problem in causal inference. We focus on designing efficient randomized controlled trials, to accurately estimate the effect of some treatment on a population of $n$ individuals. In particular, we study sample-constrained treatment effect estimation, where we must select a subset of $s \ll n$ individuals from the population to experiment on. This subset must be further partitioned into treatment and control groups. Algorithms for partitioning the entire population into treatment and control groups, or for choosing a single representative subset, have been well-studied. The key challenge in our setting is jointly choosing a representative subset and a partition for that set. We focus on both individual and average treatment effect estimation, under a linear effects model. We give provably efficient experimental designs and corresponding estimators, by identifying connections to discrepancy minimization and leverage-score-based sampling used in randomized numerical linear algebra. Our theoretical results obtain a smooth transition to known guarantees when $s$ equals the population size. We also empirically demonstrate the performance of our algorithms. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.06594&r= |
| By: | Jochmans, Koen; Higgins, Ayden |
| Abstract: | We present a constructive proof of (nonparametric) identication of the parameters of a bivariate Markov chain when only one of the two random variables is observable. This setup generalizes the hidden Markov model in various useful directions, allowing for state dependence in the observables and allowing the transition kernel of the hidden Markov chain to depend on past observables. We give conditions under which the transition kernel and the distribution of the initial condition are both identied (up to a permutation of the latent states) from the joint distribution of four (or more) time-series observations. |
| Keywords: | Dynamic discrete choice; finite mixture; Markov process; regime switching;; state dependence |
| JEL: | C14 C23 |
| Date: | 2022–10–04 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:127401&r= |
| By: | Das, Tirthatanmoy (Indian Institute of Management Bangalore); Polachek, Solomon (Binghamton University, New York) |
| Abstract: | Some interventions or population attributes negate the effects of a treatment. This paper shows that incorporating these, what we call antidotal variables (AV), into a causal treatment effects analysis can with one cross-sectional regression identify the true causal effect, in addition to possible biases from selectivity and SUTVA violations. Whereas we apply the AV technique to analyze the California Paid Family Leave program, it has applications beyond this example. |
| Keywords: | antidotal variables, causality, CPFL |
| JEL: | C18 C36 I38 J18 J38 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15558&r= |
| By: | Jun Lu; Joerg Osterrieder |
| Abstract: | In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of features that are representative of the entire set of features, and the selected features also have higher priority than others. This approach is commonly used for low-rank approximation, feature selection, and extracting hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Gibbs sampling for Bayesian inference is applied to carry out the optimization. We evaluate the proposed models on real-world datasets, including ten Chinese A-share stocks, and demonstrate that the proposed Bayesian ID algorithm with intervention (IID) produces comparable reconstructive errors to existing Bayesian ID algorithms while selecting features with higher scores or priority. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.14532&r= |
| By: | Fengler, Matthias; Polivka, Jeannine |
| Abstract: | In this paper, we make three contributions to the volatility impulse response function (VIRF) developed by Hafner and Herwartz (2006), the most widely applied impulse response function in the context of multivariate volatility models. First, we derive its law for multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models of the BEKK type. Second, we present a structural embedding of the VIRF by relying on recent developments concerning identification of MGARCH models. This broadens the use cases of the VIRF, which has previously been limited to historical analyses, by allowing for counterfactual and out-of-sample scenario analyses of volatility responses. Third, we show how to endow the VIRF with a causal interpretation. We illustrate the merits of a structural VIRF analysis by investigating the impacts of historical shock events as well as the consequences of well-defined future shock scenarios on the U.S. equity, government bond and foreign exchange markets. Our findings suggest that it is vital to be able to assess the statistical significance of volatility impulse responses. |
| Keywords: | causality in volatility, multivariate GARCH models, proxy identification, structural identification, volatility impulse response functions |
| JEL: | C32 C58 G17 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2022:11&r= |
| By: | Weihuan Huang; Nifei Lin; L. Jeff Hong |
| Abstract: | ${\rm CoVaR}$ is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo simulation-based batching estimator of CoVaR and study its consistency and asymptotic normality. We show that the optimal rate of convergence of the batching estimator is $n^{-1/3}$, where $n$ is the sample size. We then develop an importance-sampling inspired estimator under the delta-gamma approximations to the portfolio losses, and we show that the rate of convergence of the estimator is $n^{-1/2}$. Numerical experiments support our theoretical findings and show that both estimators work well. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.06148&r= |
| By: | Kneip, Alois (Universität Bonn); Simar, Léopold (Université catholique de Louvain, LIDAM/ISBA, Belgium); Wilson, Paul W. (Clemson University) |
| Abstract: | Nonparametric envelopment estimators are often used to estimate the attainable sets and its efficient boundary and to assess efficiency and changes in productivity. Kneip et al. (2015, 2016) provide asymptotic theory enabling inference about expected efficiency and testing constant versus variable returns to scale using these estimators, and Kneip et al. (2021) provide asymptotic results that can be used to make inference about expected changes in productivity measured by Malmquist indices. All of these results require convexity of the attainable set, but in a number of situations this assumption is questionable. Kneip et al. (2016) also provide a test of convexity versus non-convexity of a production set, and convexity is rejected in several recent studies. This paper extends the results mentioned above to allow for possibly nonconvex technologies. Properties of a nonparametric envelopment estimator of distance to the boundary of the cone spanned by a possibly non-convex attainable set are derived. These new results are then extended to make inference about geometric means of Malmquist indices and to test constant versus non-constant returns to scale when the production set is not convex. |
| Keywords: | Non-convex production sets ; FDH ; hypothesis test ; returns to scale ; Malmquist index ; productivity change |
| JEL: | C12 C14 C18 |
| Date: | 2022–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2022024&r= |
| By: | Canepa, Alessandra (University of Turin) |
| Abstract: | In this article, we employ a time-varying GARCH-type speci?cation to model in?ation and in- vestigate the behaviour of its persistence. Speci?cally, by modelling the in?ation series as AR(1)- APARCH(1,1)-in-mean-level process with breaks, we show that persistence is transmitted from the conditional variance to the conditional mean. Hence, by studying the conditional mean/variance independently, one will obtain a biased estimate of the true degree of persistence. Accordingly, we propose a new measure of time-varying persistence, which not only distinguishes between changes in the dynamics of in?ation and its volatility but also allows for feedback between the two variables. Analysing the in?ation series for a number of countries, we ?nd evidence that in?ation uncertainty plays an important role in shaping expectations, and a higher level of uncertainty increases in?ation persistence. We also consider a number of unit root tests and present the results of a Monte Carlo experiment to investigate the size and power properties of these tests in the presence of breaks in the mean and the variance equation of an AR(1)-APARCH(1,1)-in-mean-level data generating process. The Monte Carlo experiment reveals that if the model is misspeci?ed, then commonly used unit root tests will misclassify in?ation as a nonstationary, rather than a stationary process. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:uto:dipeco:202211&r= |
| By: | Leluc, Rémi; Portier, François; Segers, Johan (Université catholique de Louvain, LIDAM/ISBA, Belgium); Zhuman, Aigerim (Université catholique de Louvain, LIDAM/ISBA, Belgium) |
| Abstract: | Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of the particles to evolve during the algorithm, as is the case in sequential simulation methods. Within the standard adaptive importance sampling framework, a simple weighted least squares approach is proposed to improve the procedure with control variates. The procedure takes the form of a quadrature rule with adapted quadrature weights to reflect the information brought in by the control variates. The quadrature points and weights do not depend on the integrand, a computational advantage in case of multiple integrands. Moreover, the target density needs to be known only up to a multiplicative constant. Our main result is a non-asymptotic bound on the prob- abilistic error of the procedure. The bound proves that for improving the estimate’s accuracy, the benefits from adaptive importance sampling and control variates can be combined. The good behavior of the method is illustrated empirically on synthetic examples and real-world data for Bayesian linear regression. |
| Date: | 2022–05–24 |
| URL: | http://d.repec.org/n?u=RePEc:aiz:louvad:2022018&r= |
| By: | Xenxo Vidal-Llana (Universitat de Barcelona. Gran Via de les Corts Catalanes 585. 08007 Barcelona, Spain.); Carlos Salort Sánchez (Universitat de Barcelona. Gran Via de les Corts Catalanes 585. 08007 Barcelona, Spain.); Vincenzo Coia (University of British Columbia. West Mall 2329. Vancouver, BC Canada.); Montserrat Guillen (Gran Via de les Corts Catalanes 585. 08007 Barcelona, Spain.) |
| Abstract: | When datasets present long conditional tails on their response variables, algorithms based on Quantile Regression have been widely used to assess extreme quantile behaviors. Value at Risk (VaR) and Conditional Tail Expectation (CTE) allow the evaluation of extreme events to be easily interpretable. The state-of-the-art methodologies to estimate VaR and CTE controlled by covariates are mainly based on linear quantile regression, and usually do not have in consideration non-crossing conditions across VaRs and their associated CTEs. We implement a non-crossing neural network that estimates both statistics simultaneously, for several quantile levels and ensuring a list of non-crossing conditions. We illustrate our method with a household energy consumption dataset from 2015 for quantile levels 0.9, 0.925, 0.95, 0.975 and 0.99, and show its improvements against a Monotone Composite Quantile Regression Neural Network approximation. |
| Keywords: | Risk evaluation, Deep learning, Extreme quantiles. JEL classification: C31, C45, C52. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:ira:wpaper:202215&r= |