|
on Econometrics |
| By: | Byunghoon Kang |
| Abstract: | Nonparametric series estimation often involves specification search over the different number of series terms due to the unknown smoothness of underlying function. This paper considers pointwise inference in the nonparametric series regression for the conditional mean and introduces test based on the supremum of t-statistics over different series terms. I show that proposed test has correct asymptotic size and it can be used to construct confidence intervals that have correct asymptotic coverage probability uniform in the number of series terms. With possibly large bias in this setup, I also consider infimum of the t-statistics which is shown to reduce size distortions in such case. Asymptotic distribution of the test statistics, asymptotic size, and local power results are derived. I investigate the performance of the proposed tests and CIs in various simulation setups as well as an illustrative example, nonparametric estimation of wage elasticity of the expected labor supply from Blomquist and Newey (2002). I also extend our inference methods to the partially linear model setup. |
| Keywords: | Nonparametric series regression, Pointwise confidence interval, Smoothing parameter choice, Specification search, Undersmoothing |
| JEL: | C14 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:240829404&r=ecm |
| By: | Alexander Mayer |
| Abstract: | This paper develops techniques of estimation and inference in a prototypical macroeconomic adaptive learning model with slowly decreasing gains. A sequential three-step procedure based on a ‘super-consistent’ estimator of the rational expectations equilibrium parameter is proposed. It is shown that this procedure is asymptotically equivalent to first estimating the structural parameters jointly via ordinary least-squares (OLS) and then using the so-obtained estimates to form a plug-in estimator of the rational expectations equilibrium parameter. In spite of failing Grenander’s conditions for well-behaved data, a limiting normal distribution of the estimators centered at the true parameters is derived. Although this distribution is singular, it can nevertheless be used to draw inferences about joint restrictions by applying results from Andrews (1987) to show that Wald-type statistics remain valid when equipped with a pseudo-inverse. Monte-Carlo evidence confirms the accuracy of the asymptotic theory for the finite sample behaviour of estimators and test statistics discussed here. |
| Keywords: | adaptive learning, rational expectations, singular limiting-distribution, non-stationary regression, generalized Wald statistic, degenerate variances |
| JEL: | C12 C22 C51 D83 |
| Date: | 2018–07–05 |
| URL: | http://d.repec.org/n?u=RePEc:whu:wpaper:18-03&r=ecm |
| By: | Alexandre Belloni; Federico Bugni; Victor Chernozhukov |
| Abstract: | This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential rates. Our main motivating application is subvector inference, i.e., inference on a single component of the partially identified parameter vector associated with a treatment effect or a policy variable of interest. Our inference method compares a MinMax test statistic (minimum over parameters satisfying $H_0$ and maximum over moment inequalities) against critical values that are based on bootstrap approximations or analytical bounds. We show that this method controls asymptotic size uniformly over a large class of data generating processes despite the partially identified many moment inequality setting. The finite sample analysis allows us to obtain explicit rates of convergence on the size control. Our results are based on combining non-asymptotic approximations and new high-dimensional central limit theorems for the MinMax of the components of random matrices. Unlike the previous literature on functional inference in partially identified models, our results do not rely on weak convergence results based on Donsker's class assumptions and, in fact, our test statistic may not even converge in distribution. Our bootstrap approximation requires the choice of a tuning parameter sequence that can avoid the excessive concentration of our test statistic. To this end, we propose an asymptotically valid data-driven method to select this tuning parameter sequence. This method generalizes the selection of tuning parameter sequences to problems outside the Donsker's class assumptions and may also be of independent interest. Our procedures based on self-normalized moderate deviation bounds are relatively more conservative but easier to implement. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.11466&r=ecm |
| By: | Riccardo D'Adamo |
| Abstract: | The linear regression model is widely used in empirical economics to estimate the structural/treatment effect of some variable on an outcome of interest. Researchers often include a large set of regressors in order to control for observed and unobserved confounders. In this paper, we develop inference methods for linear regression models with many controls and clustering. We show that inference based on the usual cluster-robust standard errors by White (1984) is invalid in general when the number of controls is a non-vanishing fraction of the sample size. We then propose a new clustered standard errors formula that is robust to the inclusion of many controls and allows to carry out valid inference in a variety of high-dimensional linear regression models, including multi-way fixed effects panel data models and the semiparametric partially linear model. Monte Carlo evidence supports our theoretical results and shows that our proposed variance estimator performs well in finite samples. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.07314&r=ecm |
| By: | Bartalotti, Otávio (Iowa State University) |
| Abstract: | In regression discontinuity design (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the "fixed-bandwidth" alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators as locally parametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel, bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested. |
| Keywords: | average treatment effect, locally parametric inference, local polynomial estimators, fixed bandwidth, heteroskedasticity robust standard errors, bias correction |
| JEL: | C12 C21 |
| Date: | 2018–05 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp11560&r=ecm |
| By: | Miruna Oprescu; Vasilis Syrgkanis; Zhiwei Steven Wu |
| Abstract: | We study the problem of estimating heterogeneous treatment effects from observational data, where the treatment policy on the collected data was determined by potentially many confounding observable variables. We propose orthogonal random forest1, an algorithm that combines orthogonalization, a technique that effectively removes the confounding effect in two-stage estimation, with generalized random forests [Athey et al., 2017], a flexible method for estimating treatment effect heterogeneity. We prove a consistency rate result of our estimator in the partially linear regression model, and en route we provide a consistency analysis for a general framework of performing generalized method of moments (GMM) estimation. We also provide a comprehensive empirical evaluation of our algorithms, and show that they consistently outperform baseline approaches. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.03467&r=ecm |
| By: | D. Kuang; B. Nielsen |
| Abstract: | We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder based bootstrap. We embed the log normal chain-ladder model in a class of infinitely divisible distributions called the generalized log normal chain-ladder model. The asymptotic theory uses small $\sigma$ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.05939&r=ecm |
| By: | Joshua C.C. Chan; Eric Eisenstat |
| Abstract: | Empirical questions such as whether the Phillips curve or the Okun’s law is stable can often be framed as a model comparison—e.g., comparing a vector autoregression (VAR) in which the coefficients in one equation are constant versus one that has time-varying parameters. We develop Bayesian model comparison methods to compare a class of time-varying parameter VARs we call hybrid TVP-VARs—VARs with time-varying parameters in some equations but constant coefficients in others. Using US data, we find evidence that the VAR coefficients in some, but not all, equations are time varying. Our finding highlights the empirical relevance of these hybrid TVP-VARs. |
| Keywords: | state space, marginal likelihood, Bayesian model comparison |
| JEL: | C11 C52 E32 E52 |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2018-31&r=ecm |
| By: | Rajbir-Singh Nirwan; Nils Bertschinger |
| Abstract: | Estimating covariances between financial assets plays an important role in risk management and optimal portfolio allocation. In practice, when the sample size is small compared to the number of variables, i.e. when considering a wide universe of assets over just a few years, this poses considerable challenges and the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.03294&r=ecm |
| By: | Iskrev, Nikolay |
| Abstract: | Standard economic intuition suggests that asset prices are more sensitive to news than other economic aggregates. This has led many researchers to conclude that asset price data would be very useful for the estimation of business cycle models containing news shocks. This paper shows how to formally evaluate the information content of observed variables with respect to unobserved shocks in structural macroeconomic models. The proposed methodology is applied to two different real business cycle models with news shocks. The contribution of asset prices is found to be relatively small. The methodology is general and can be used to measure the informational importance of observables with respect to latent variables in DSGE models. Thus, it provides a framework for systematic treatment of such issues, which are usually discussed in an informal manner in the literature. JEL Classification: C32, C51, C52, E32 |
| Keywords: | asset prices, DSGE models, identification, information, news shocks |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20182161&r=ecm |
| By: | Florian Gunsilius |
| Abstract: | In this article we introduce a general nonparametric point-identification result for nonseparable triangular models with a multivariate first- and second stage. Based on this we prove point-identification of Hedonic models with multivariate heterogeneity and endogenous observable characteristics, extending and complementing identification results from the literature which all require exogeneity. As an additional application of our theoretical result, we show that the BLP model (Berry et al. 1995) can also be identified without index restrictions. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.09680&r=ecm |
| By: | Florian Gunsilius |
| Abstract: | In this note we prove Pearl's conjecture, showing that the exclusion restriction of an instrument cannot be tested without structural assumptions in general instrumental variable models with a continuously distributed endogenous variable. This stands in contrast to models with a discretely distributed endogenous variable, where tests have been devised in the literature, and shows that there is a fundamental difference between the continuous and the discrete case. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.09517&r=ecm |
| By: | Marie-Hélène Felt |
| Abstract: | This paper proposes a new bootstrap procedure for mean squared errors of robust small-area estimators. We formally prove the asymptotic validity of the proposed bootstrap method and examine its finite sample performance through Monte Carlo simulations. The results show that our procedure performs well and outperforms existing ones. We also apply our procedure to the estimation of the total volume and value of cash, debit card and credit card transactions in Canada as well as in its provinces and subgroups of households. In particular, we find that there is a significant average annual decline rate of 3.1 percent in the volume of cash transactions, and that this decline is relatively higher among high-income households living in heavily populated provinces. Our bootstrap estimator also provides indicators of quality useful in selecting the best small-area predictors from among several alternatives in practice. |
| Keywords: | Bank notes, Digital Currencies, Econometric and statistical methods |
| JEL: | C C14 D14 E41 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:18-29&r=ecm |
| By: | Bingling Wang (Department of Biostatistics, University of California, Los Angeles); Sudipto Banerjee (Department of Biostatistics, University of California, Los Angeles); Rangan Gupta (Department of Economics, University of Pretoria, Pretoria, South Africa) |
| Abstract: | Spatial process models are increasingly getting attention as data have become available at geocoded locations. In this paper, we build a hierarchical framework with multivariate spatial processes. The hierarchical models are implemented through Markov chain Monte Carlo methods. And Bayesian inference is carried out for parameter estimation and interpretation. The proposed models are illustrated using housing data collected in the Walmer district of Port Elizabeth, South Africa. Our interest is to evaluate the spatial dependencies of dependent outcomes and associations with other independent variables. Comparison across different models confirm that the selling price of a house in our data set is relatively better modeled by incorporating spatial processes. |
| Keywords: | Bayesian inference, Hierarchical models, Multivariate spatial models, Point-referenced data, Spatial processes |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201837&r=ecm |
| By: | Bo Zhang; Joshua C.C. Chan; Jamie L. Cross |
| Abstract: | We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence which renders standard Kalman filter techniques not directly applicable. To overcome this hurdle we develop an efficient posterior simulator that builds on recently developed precision based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy and the US. |
| Keywords: | autoregressive moving average errors, stochastic volatility, inflation forecast, state space models, unobserved components model |
| JEL: | C11 C52 C53 E37 |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2018-32&r=ecm |
| By: | Gerard Van Den Berg (Institute for Fiscal Studies and University of Mannheim); Antoine Bozio (Institute for Fiscal Studies and Institut des Politiques Publiques, Paris School of Economics); Monica Costa Dias (Institute for Fiscal Studies and Institute for Fiscal Studies) |
| Abstract: | Causal effects of a policy change on the hazard rates of a duration outcome variable are not identifi ed from a comparison of spells before and after the policy change when there is unobserved heterogeneity in the effects and no model structure is imposed. We develop a discontinuity approach that overcomes this by considering spells that include the moment of the policy change and by exploiting variation in the moment at which different cohorts are exposed to the policy change. We prove identi cation of average treatment effects on hazard rates without model structure. We estimate these effects by kernel hazard regression. We use the introduction of the NDYP program for young unemployed individuals in the UK to estimate average program participation effects on the exit rate to work as well as anticipation effects. |
| Keywords: | policy evaluation, hazard rate, identi fication, causality, regression discontinuity, selectivity, kernel hazard estimation, local linear regression, average treatment effect, job search assistance, youth unemployment |
| Date: | 2018–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:ifsewp:18/10&r=ecm |
| By: | Zhan Gao; Zhentao Shi |
| Abstract: | Economists specify high-dimensional models to address heterogeneity in empirical studies with complex big data. Estimation of these models calls for optimization techniques to handle a large number of parameters. Convex problems can be effectively executed in modern statistical programming languages. We complement Koenker and Mizera (2014)'s work on numerical implementation of convex optimization, with focus on high-dimensional econometric estimators. In particular, we replicate the simulation exercises in Su, Shi, and Phillips (2016) and Shi (2016) to show the robust performance of convex optimization cross platforms. Combining R and the convex solver MOSEK achieves faster speed and equivalent accuracy as in the original papers. The convenience and reliability of convex optimization in R make it easy to turn new ideas into prototypes. |
| Date: | 2018–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1806.10423&r=ecm |
| By: | Rafal Rak; Dariusz Grech |
| Abstract: | We analyze quantitatively the effect of spurious multifractality induced by the presence of fat-tailed symmetric and asymmetric probability distributions of fluctuations in time series. In the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from Levy regime up to those with finite variance. We use nonextensive Tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power-law decay for tails of probability distribution. The semi-analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of Tsallis parameter $\tilde{q}$ and the scaling exponent $\beta$ of the asymptotic decay of cumulated probability density function (CDF).The results are presented in Hurst and H\"{o}lder languages - more often used in study of multifractal phenomena. According to the provided semi-analytical relations, it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations, spurious multifractality generated by fat-tailed shape of distributions - eventually with their asymmetry, and the correction due to linear autocorrelations in analyzed time series of finite length. In particular, the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects. Examples from stock market data are presented to support these findings. |
| Date: | 2018–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1805.11909&r=ecm |
| By: | Orozco, Valérie; Bontemps, Christophe; Maigné, Elise; Piguet, V.; Hofstetter, A.; Lacroix, Anne; Levert, F.; Rousselle, J.M |
| Abstract: | Empirical economics and econometrics (EEE) research now relies primarily on the application of code to datasets. Handling the workflow linking datasets, programs, results and finally manuscript(s) is essential if one wish to reproduce results, which is now increasingly required by journals and institutions. We underline here the importance of “reproducible research” in EEE and suggest three simple principles to follow. We illustrate these principles with good habits and tools, with particular focus on their implementation in most popular software and languages in applied economics. |
| Keywords: | Reproducibility; workflow; replication; literate programming; software |
| Date: | 2018–07 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:32757&r=ecm |
| By: | Tallman, Ellis W. (Federal Reserve Bank of Cleveland); Zaman, Saeed (Federal Reserve Bank of Cleveland) |
| Abstract: | This paper constructs hybrid forecasts that combine both short- and long-term conditioning information from external surveys with forecasts from a standard fixed-coefficient vector autoregression (VAR) model. Specifically, we use relative entropy to tilt one-step ahead and long-horizon VAR forecasts to match the nowcast and long-horizon forecast from the Survey of Professional Forecasters. The results indicate meaningful gains in multi-horizon forecast accuracy relative to model forecasts that do not incorporate long-term survey conditions. The accuracy gains are achieved for a range of variables, including those that are not directly tilted but are affected through spillover effects from tilted variables. The forecast accuracy gains for inflation are substantial, statistically significant, and are competitive with the forecast accuracy from both time-varying VARs and univariate benchmarks. We view our proposal as an indirect approach to accommodating structural change and moving end points. |
| Keywords: | Bayesian analysis; relative entropy; survey forecasts; nowcasts; density forecasts; real-time data; |
| JEL: | C11 C32 C53 E17 |
| Date: | 2018–06–22 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwp:1809&r=ecm |