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on Econometrics |
| By: | Agnieszka Borowska (Vrije Universiteit Amsterdam); Lennart Hoogerheide (Vrije Universiteit Amsterdam); Siem Jan Koopman (Vrije Universiteit Amsterdam); Herman van Dijk (Erasmus University Rotterdam) |
| Abstract: | A novel approach to inference for a specific region of the predictive distribution is introduced. An important domain of application is accurate prediction of financial risk measures, where the area of interest is the left tail of the predictive density of logreturns. Our proposed approach originates from the Bayesian approach to parameter estimation and time series forecasting, however it is robust in the sense that it provides a more accurate estimation of the predictive density in the region of interest in case of misspecification. The first main contribution of the paper is the novel concept of the Partially Censored Posterior (PCP), where the set of model parameters is partitioned into two subsets: for the first subset of parameters we consider the standard marginal posterior, for the second subset of parameters (that are particularly related to the region of interest) we consider the conditional censored posterior. The censoring means that observations outside the region of interest are censored: for those observations only the probability of being outside the region of interest matters. This quasi-Bayesian approach yields more precise parameter estimation than a fully censored posterior for all parameters, and has more focus on the region of interest than a standard Bayesian approach. The second main contribution is that we introduce two novel methods for computationally efficient simulation: Conditional MitISEM, a Markov chain Monte Carlo method to simulate model parameters from the Partially Censored Posterior, and PCP-QERMit, an Importance Sampling method that is introduced to further decrease the numerical standard errors of the Value-at-Risk and Expected Shortfall estimators. The third main contribution is that we consider the effect of using a time-varying boundary of the region of interest, which may provide more information about the left tail of the distribution of the standardized innovations. Extensive simulation and empirical studies show the ability of the introduced method to outperform standard approaches. |
| Keywords: | Bayesian inference, censored likelihood, censored posterior, partially censored posterior, misspecification, density forecasting, Markov chain Monte Carlo, importance sampling, mixture of Student's t, Value-at-Risk, Expected Shortfall |
| JEL: | C11 C53 C58 |
| Date: | 2019–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20190057&r=all |
| By: | Sander Barendse (University of Oxford); Erik Kole (Erasmus University Rotterdam); Dick van Dijk (Erasmus University Rotterdam) |
| Abstract: | We investigate the effect of estimation error on backtests of (multi-period) expected shortfall (ES) forecasts. These backtests are based on first order conditions of a recently introduced family of jointly consistent loss functions for Value-at-Risk (VaR) and ES. We provide explicit expressions for the additional terms in the asymptotic covariance matrix that result from estimation error, and propose robust tests that account for it. Monte Carlo experiments show that the tests that ignore these terms suffer from size distortions, which are more pronounced for higher ratios of out-of-sample to in-sample observations. Robust versions of the backtests perform well, although this also depends on the choice of conditioning variables. In an application to VaR and ES forecasts for daily FTSE 100 index returns as generated by AR-GARCH, AR-GJR-GARCH, and AR-HEAVY models, we find that estimation error substantially impacts the outcome of the backtests. |
| Keywords: | expected shortfall, backtesting, risk management, tail risk, Value-at-Risk |
| JEL: | C12 C53 C58 G17 |
| Date: | 2019–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:2019058&r=all |
| By: | Beyhum, Jad |
| Abstract: | This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0. We apply an estimator penalizing the `1-norm of a random vector which is non-zero for outliers. We derive rates of convergence and asymptotic normality. Our estimator has the same asymptotic variance as the OLS estimator in the standard linear model. This enables to build tests and confidence sets in the usual and simple manner. The proposed procedure is also computationally advantageous as it amounts to solving a convex optimization program. Overall, the suggested approach constitutes a practical robust alternative to the ordinary least squares estimator. |
| Keywords: | robust regression; L1-norm penalization; unknown variance. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:123325&r=all |
| By: | Nandana Sengupta; Fallaw Sowell |
| Abstract: | This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and test samples. Conditional on the tuning parameter, the training sample creates a path from the IV estimator to a prior. The optimal tuning parameter is the value along this path that minimizes the IV objective function for the test sample. The empirically selected regularization tuning parameter becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution of the tuning parameter is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.09237&r=all |
| By: | Michael Zimmert; Michael Lechner |
| Abstract: | This paper considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties like consistency, asymptotic normality and rate double robustness. In particular, we derive the coupled convergence conditions between the nonparametric and the machine learning steps. We also show that estimating population average treatment effects by averaging the estimated heterogeneous effects is semi-parametrically efficient. The new estimator is an empirical example of the effects of mothers' smoking during pregnancy on the resulting birth weight. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.08779&r=all |
| By: | António Rua; Hossein Hassani; Emmanuel Sirimal Silva; Dimitrios Thomakos |
| Abstract: | The literature on mixed-frequency models is relatively recent and has found applications across economics and finance. The standard application in economics considers the use of (usually) monthly variables (e.g. industrial production) in predicting/fitting quarterly variables (e.g. real GDP). In this paper we propose a Multivariate Singular Spectrum Analysis (MSSA) based method for mixed frequency interpolation and forecasting, which can be used for any mixed frequency combination. The novelty of the proposed approach rests on the grounds of simplicity within the MSSA framework. We present our method using a combination of monthly and quarterly series and apply MSSA decomposition and reconstruction to obtain monthly estimates and forecasts for the quarterly series. Our empirical application shows that the suggested approach works well, as it offers forecasting improvements on a dataset of eleven developed countries over the last 50 years. The implications for mixed frequency modelling and forecasting, and useful extensions of this method, are also discussed. |
| JEL: | C1 C53 E1 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201913&r=all |
| By: | Victor Chernozhukov; Whitney Newey; Vira Semenova |
| Abstract: | This paper gives a consistent, asymptotically normal estimator of the expected value function when the state space is high-dimensional and the first-stage nuisance functions are estimated by modern machine learning tools. First, we show that value function is orthogonal to the conditional choice probability, therefore, this nuisance function needs to be estimated only at $n^{-1/4}$ rate. Second, we give a correction term for the transition density of the state variable. The resulting orthogonal moment is robust to misspecification of the transition density and does not require this nuisance function to be consistently estimated. Third, we generalize this result by considering the weighted expected value. In this case, the orthogonal moment is doubly robust in the transition density and additional second-stage nuisance functions entering the correction term. We complete the asymptotic theory by providing bounds on second-order asymptotic terms. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.09173&r=all |
| By: | Federico Crudu; Felipe Osorio |
| Abstract: | This paper develops a set of test statistics based on bilinear forms in the context of the extremum estimation framework. We show that the proposed statistic converges to a conventional chi-square limit. A Monte Carlo experiment suggests that the test statistic works well in ?nite samples |
| Keywords: | Extremum estimation, Gradient statistic, Bilinear form test, Nonlinear hypothesis. |
| JEL: | C12 C14 C69 |
| Date: | 2019–06 |
| URL: | http://d.repec.org/n?u=RePEc:usi:wpaper:804&r=all |
| By: | Paulo M.M. Rodrigues; Gabriel Zsurkis; João Nicolau |
| Abstract: | This paper introduces a simple and easy to implement procedure to test for changes in persistence. The time-varying parameter that characterizes persistence changes under the alternative hypothesis is approximated by a parsimonious cosine function. The new test procedure is the minimum of a t-statistic, computed from a test regression that considers a set of reasonable values for a frequency term that is used to evaluate the time varying properties of persistence. The asymptotic distributions of the new tests are derived and critical values are provided. An indepth Monte Carlo analysis shows that the new procedure has important power gains when compared to the local GLS de-trended Dickey-Fuller (DFGLS) type tests introduced by Elliott et al. (1996) under various data generating processes with persistence changes. Moreover, an empirical application to OECD countries’ inflation series shows that for most countries analysed persistence was high in the first half of the sample and subsequently decreased. These results are compatible with modern macroeconomic theories that point to changes in inflation behavior in the early 1980s and also with recent empirical evidence against the I(1)-I(0) dichotomy. |
| JEL: | C12 C22 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201909&r=all |
| By: | Joshua C. C. Chan |
| Abstract: | Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to make these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like the adaptive hierarchical priors, these new priors ensure that only ‘small’ coefficients are strongly shrunk to zero, while ‘large’ coefficients remain intact. At the same time, these new priors can also incorporate many useful features of the Minnesota priors, such as cross-variable shrinkage and shrinking coefficients on higher lags more aggressively. We introduce a fast posterior sampler to estimate BVARs with this family of priors - for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 minutes on a standard desktop. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors. |
| Keywords: | shrinkage prior, forecasting, stochastic volatility, structural VAR |
| JEL: | C11 C52 E37 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2019-61&r=all |
| By: | Andrii Babii; Rohit Kumar |
| Abstract: | In isotonic regression discontinuity designs, the average outcome and the treatment assignment probability are monotone in the running variable. We introduce novel nonparametric estimators for sharp and fuzzy designs based on the bandwidth-free isotonic regression. The large sample distributions of introduced estimators are driven by Brownian motions originating from zero and moving in opposite directions. Since these distributions are not pivotal, we also introduce a novel trimmed wild bootstrap procedure, which is free from nonparametric smoothing, typically needed in such settings, and show its consistency. We illustrate our approach on the well-known dataset of Lee (2008), estimating the incumbency effect in the U.S. House elections. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.05752&r=all |
| By: | Knüppel, Malte; Krüger, Fabian |
| Abstract: | The linear pool is the most popular method for combining density forecasts. We analyze the linear pool's implications concerning forecast uncertainty in a new theoretical framework that focuses on the mean and variance of each density forecast to be combined. Our results show that, if the variance predictions of the individual forecasts are unbiased, the well-known 'disagreement' component of the linear pool exacerbates the upward bias of the linear pool's variance prediction. Moreover, we find that disagreement has no predictive content for ex-post forecast uncertainty under conditions which can be empirically relevant. These findings suggest the removal of the disagreement component from the linear pool. The resulting centered linear pool outperforms the linear pool in simulations and in empirical applications to inflation and stock returns. |
| JEL: | C32 C53 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:282019&r=all |
| By: | Douglas L. Miller; Na’ama Shenhav; Michel Z. Grosz |
| Abstract: | Many papers use fixed effects (FE) to identify causal impacts of an intervention. In this paper we show that when the treatment status only varies within some groups, this design can induce non-random selection of groups into the identifying sample, which we term selection into identification (SI). We begin by illustrating SI in the context of several family fixed effects (FFE) applications with a binary treatment variable. We document that the FFE identifying sample differs from the overall sample along many dimensions, including having larger families. Further, when treatment effects are heterogeneous, the FFE estimate is biased relative to the average treatment effect (ATE). For the general FE model, we then develop a reweighting-on-observables estimator to recover the unbiased ATE from the FE estimate for policy-relevant populations. We apply these insights to examine the long-term effects of Head Start in the PSID and the CNLSY. Using our reweighting methods, we estimate that Head Start leads to a 2.6 percentage point (p.p.) increase (s.e. = 6.2 p.p.) in the likelihood of attending some college for white Head Start participants in the PSID. This ATE is 78% smaller than the traditional FFE estimate (12 p.p). Reweighting the CNLSY FE estimates to obtain the ATE produces similar attenuation in the estimated impacts of Head Start. |
| JEL: | C33 I28 I38 J13 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26174&r=all |
| By: | Bryan S. Graham |
| Abstract: | Dyadic data, where outcomes reflecting pairwise interaction among sampled units are of primary interest, arise frequently in social science research. Regression analyses with such data feature prominently in many research literatures (e.g., gravity models of trade). The dependence structure associated with dyadic data raises special estimation and, especially, inference issues. This chapter reviews currently available methods for (parametric) dyadic regression analysis and presents guidelines for empirical researchers. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.09029&r=all |
| By: | Anoek Castelein (Erasmus University Rotterdam); Dennis Fok (Erasmus University Rotterdam); Richard Paap (Erasmus University Rotterdam) |
| Abstract: | We develop a dynamic Bayesian model for clickthrough and conversion probabilities of paid search advertisements. These probabilities are subject to changes over time, due to e.g. changing consumer tastes or new product launches. Yet, there is little empirical research on these dynamics. Gaining insight into the dynamics is crucial for advertisers to develop effective search engine advertising (SEA) strategies. Our model deals with dynamic SEA environments for a large number of keywords: it allows for time-varying parameters, seasonality, data sparsity and position endogeneity. The model also discriminates between transitory and permanent dynamics. Especially for the latter case, dynamic SEA strategies are required for long-term profitability. We illustrate our model using a 2 year dataset of a Dutch laptop selling retailer. We find persistent time variation in clickthrough and conversion probabilities. The implications of our approach are threefold. First, advertisers can use it to obtain accurate daily estimates of clickthrough and conversion probabilities of individual ads to set bids and adjust text ads and landing pages. Second, advertisers can examine the extent of dynamics in their SEA environment, to determine how often their SEA strategy should be revised. Finally, advertisers can track ad performances to timely identify when keywords’ performances change. |
| Keywords: | Clickthrough, Conversion, Search engine advertising, Dynamic, Endogeneity, Time-varying parameters, Bayesian |
| JEL: | C32 C33 C11 |
| Date: | 2019–08–19 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20190056&r=all |
| By: | Goller, Daniel; Lechner, Michael; Moczall, Andreas; Wolff, Joachim |
| Abstract: | Matching-type estimators using the propensity score are the major workhorse in active labour market policy evaluation. This work investigates if machine learning algorithms for estimating the propensity score lead to more credible estimation of average treatment effects on the treated using a radius matching framework. Considering two popular methods, the results are ambiguous: We find that using LASSO based logit models to estimate the propensity score delivers more credible results than conventional methods in small and medium sized high dimensional datasets. However, the usage of Random Forests to estimate the propensity score may lead to a deterioration of the performance in situations with a low treatment share. The application reveals a positive effect of the training programme on days in employment for longterm unemployed. While the choice of the “first stage” is highly relevant for settings with low number of observations and few treated, machine learning and conventional estimation becomes more similar in larger samples and higher treatment shares. |
| Keywords: | Programme evaluation, active labour market policy, causal machine learning, treatment effects, radius matching, propensity score |
| JEL: | J68 C21 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:usg:econwp:2019:10&r=all |
| By: | Katherine Baicker; Theodore Svoronos |
| Abstract: | Given the complex relationships between patients’ demographics, underlying health needs, and outcomes, establishing the causal effects of health policy and delivery interventions on health outcomes is often empirically challenging. The single interrupted time series (SITS) design has become a popular evaluation method in contexts where a randomized controlled trial is not feasible. In this paper, we formalize the structure and assumptions underlying the single ITS design and show that it is significantly more vulnerable to confounding than is often acknowledged and, as a result, can produce misleading results. We illustrate this empirically using the Oregon Health Insurance Experiment, showing that an evaluation using a single interrupted time series design instead of the randomized controlled trial would have produced large and statistically significant results of the wrong sign. We discuss the pitfalls of the SITS design, and suggest circumstances in which it is and is not likely to be reliable. |
| JEL: | C1 I1 I13 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:26080&r=all |
| By: | Kamat, Vishal |
| Abstract: | In a common experimental format, individuals are randomly assigned to either a treatment group with access to a program or a control group without access. In such experiments, analyzing the average effects of the treatment of program access may be hindered by the problem that some control individuals do not comply with their assigned status and receive program access from outside the experiment. Available tools to account for such a problem typically require the researcher to observe the receipt of program access for every individual. However, in many experiments, this is not the case as data is not collected on where any individual received access. In this paper, I develop a framework to show how data on only each individual's treatment assignment status, program participation decision and outcome can be exploited to learn about the average effects of program access. I propose a nonparametric selection model with latent choice sets to relate where access was received to the treatment assignment status, participation decision and outcome, and a linear programming procedure to compute the identified set for parameters evaluating the average effects of program access in this model. I illustrate the framework by analyzing the average effects of Head Start preschool access using the Head Start Impact Study. I nd that the provision of Head Start access induces parents to enroll their child into Head Start and also positively impacts test scores, and that these effects heterogeneously depend on the availability of access to an alternative preschool. |
| Keywords: | Program evaluation, latent choice sets, unobserved treatment, program access, multiple treatments, average treatment effect, noncompliance, discrete choice, partial identification, social experiments, head start impact study. |
| JEL: | C31 C14 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:123308&r=all |