Forecasting accuracy and estimation uncertainty using VAR models with short- and long-term economic restrictions: a Monte-Carlo study

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The Örst reduces parameter space by imposing long-term restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing short-term restrictions as discussed by the literature on serial-correlation common features (SCCF). Our simulations cover three important issues on model building, estimation, and forecasting. First, we examine the performance of standard and modiÖed information criteria in choosing lag length for cointegrated VARs with SCCF restrictions. Second, we provide a comparison of forecasting accuracy of Ötted VARs when only cointegration restrictions are imposed and when cointegration and SCCF restrictions are jointly imposed. Third, we propose a new estimation algorithm where short- and long-term restrictions interact to estimate the cointegrating and the cofeature spaces respectively. We have three basic results. First, ignoring SCCF restrictions has a high cost in terms of model selection, because standard information criteria chooses too frequently inconsistent models, with too small a lag length. Criteria selecting lag and rank simultaneously have a superior performance in this case. Second, this translates into a superior forecasting performance of the restricted VECM over the VECM, with important improvements in forecasting accuracy ñreaching more than 100% in extreme cases. Third, the new algorithm proposed here fares very well in terms of parameter estimation, even when we consider the estimation of long-term parameters, opening up the discussion of joint estimation of short- and long-term parameters in VAR models.

Identification and estimation of interventions using changes in inequality measures

This paper presents semiparametric estimators of changes in inequality measures of a dependent variable distribution taking into account the possible changes on the distributions of covariates. When we do not impose parametric assumptions on the conditional distribution of the dependent variable given covariates, this problem becomes equivalent to estimation of distributional impacts of interventions (treatment) when selection to the program is based on observable characteristics. The distributional impacts of a treatment will be calculated as differences in inequality measures of the potential outcomes of receiving and not receiving the treatment. These differences are called here Inequality Treatment Effects (ITE). The estimation procedure involves a first non-parametric step in which the probability of receiving treatment given covariates, the propensity-score, is estimated. Using the inverse probability weighting method to estimate parameters of the marginal distribution of potential outcomes, in the second step weighted sample versions of inequality measures are computed. Root-N consistency, asymptotic normality and semiparametric efficiency are shown for the semiparametric estimators proposed. A Monte Carlo exercise is performed to investigate the behavior in finite samples of the estimator derived in the paper. We also apply our method to the evaluation of a job training program.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties for a lack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties. In order to compute the fit of each model, we propose an iterative procedure to compute the maximum likelihood estimates of parameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank, relative to the commonly used procedure of selecting the lag-length only and then testing for cointegration.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties as well as the traditional ones. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank using our proposed procedure, relative to an unrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting the lag-length only and then testing for cointegration. Two empirical applications forecasting Brazilian inflation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. The gains in different measures of forecasting accuracy are substantial, especially for short horizons.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties as well as the traditional ones. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank using our proposed procedure, relative to an unrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting the lag-length only and then testing for cointegration. Two empirical applications forecasting Brazilian in ation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. The gains in di¤erent measures of forecasting accuracy are substantial, especially for short horizons.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. A Monte Carlo study explores the finite sample performance of this procedure and evaluates the forecasting accuracy of models selected by this procedure. Two empirical applications confirm the usefulness of the model selection procedure proposed here for forecasting.

Semiparametric estimation and inference using doubly robust moment conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.

Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Efficient semiparametric estimation of quantile treatment effects

This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when se1ection to treatment is based on observable characteristics. The paper also presents three estimation procedures forthese parameters, alI ofwhich have two steps: a nonparametric estimation and a computation ofthe difference between the solutions of two distinct minimization problems. Root-N consistency, asymptotic normality, and the achievement ofthe semiparametric efficiency bound is shown for one ofthe three estimators. In the final part ofthe paper, an empirical application to a job training program reveals the importance of heterogeneous treatment effects, showing that for this program the effects are concentrated in the upper quantiles ofthe earnings distribution.

Bounds on policy relevant parameters with discrete policy variation

When estimating policy parameters, also known as treatment effects, the assignment to treatment mechanism almost always causes endogeneity and thus bias many of these policy parameters estimates. Additionally, heterogeneity in program impacts is more likely to be the norm than the exception for most social programs. In situations where these issues are present, the Marginal Treatment Effect (MTE) parameter estimation makes use of an instrument to avoid assignment bias and simultaneously to account for heterogeneous effects throughout individuals. Although this parameter is point identified in the literature, the assumptions required for identification may be strong. Given that, we use weaker assumptions in order to partially identify the MTE, i.e. to stablish a methodology for MTE bounds estimation, implementing it computationally and showing results from Monte Carlo simulations. The partial identification we perfom requires the MTE to be a monotone function over the propensity score, which is a reasonable assumption on several economics' examples, and the simulation results shows it is possible to get informative even in restricted cases where point identification is lost. Additionally, in situations where estimated bounds are not informative and the traditional point identification is lost, we suggest a more generic method to point estimate MTE using the Moore-Penrose Pseudo-Invese Matrix, achieving better results than traditional methods.