Bootstrapping in Macroeconometrics

Unlike traditional first order asymptotic approximations, the bootstrap is a simulation method to solve inferential issues in statistics and econometrics conditional on the available sample information (e.g. constructing confidence intervals, generating critical values for test statistics). Even though econometric theory yet provides sophisticated central limit theory covering various data characteristics, bootstrap approaches are of particular appeal if establishing asymptotic pivotalness of (econometric) diagnostics is infeasible or requires rather complex assessments of estimation uncertainty. Moreover, empirical macroeconomic analysis is typically constrained by short- to medium-sized time windows of sample information, and convergence of macroeconometric model estimates toward their asymptotic limits is often slow. Consistent bootstrap schemes have the potential to improve empirical significance levels in macroeconometric analysis and, moreover, could avoid explicit assessments of estimation uncertainty. In addition, as time-varying (co)variance structures and unmodeled serial correlation patterns are frequently diagnosed in macroeconometric analysis, more advanced bootstrap techniques (e.g., wild bootstrap, moving-block bootstrap) have been developed to account for nonpivotalness as a results of such data characteristics.

Beyond Socially Responsible Investing: Effects of Mission-Driven Portfolio Selection

In their pursuit of value creation, charitable foundations are mission- rather than profit-driven. Therefore, foundations are also mission-driven investors. We explore the effects of mission-driven portfolio selection based on three model foundations, representing common fields of activity in Switzerland. Employing a moving block bootstrap approach, we simulate time series. Based on these model foundations and under the integration of qualitative company rating data, such as environmental, social, and governance-related characteristics (ESG), we find both negative and no significant financial effects of portfolio screening. However, screening portfolios substantially increases mission-driven portfolio quality. Additionally, screening reduces reputational risks and even leptokurtic return characteristics under special consideration of governance issues. After a joint analysis of financial and qualitative factors for portfolios with equity shares of 25% and 50%, we did find strong enough evidence to encourage foundations to implement negative and positive screening criteria. Additionally, we argue that without the integration of mission-based qualitative criteria, for instance, the involvement in business activities contradicting the foundation’s mission, an adequate evaluation of investment opportunities’ desirability is not feasible.

QUANTILOGRAMS UNDER STRONG DEPENDENCE

We develop the limit theory of the quantilogram and cross-quantilogram under long memory. We establish the sub-root-n central limit theorems for quantilograms that depend on nuisance parameters. We propose a moving block bootstrap (MBB) procedure for inference and establish its consistency, thereby enabling a consistent confidence interval construction for the quantilograms. The newly developed reduction principles for the quantilograms serve as the main technical devices used to derive the asymptotics and establish the validity of MBB. We report some simulation evidence that our methods work satisfactorily. We apply our method to quantile predictive relations between financial returns and long-memory predictors.

The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States: Comment

Mertens and Ravn (2013) estimate impulse response functions (IRFs) from income tax changes in a structural vector autoregression (SVAR) by using narrative accounts of tax liability changes as proxy variables. To produce confidence intervals for their IRFs, they use a residual-based wild bootstrap, which has subsequently become popular in the proxy SVAR literature. We argue that their wild bootstrap is not valid, producing confidence intervals that are much too small. Using a residual-based moving block bootstrap that is proven to be asymptotically valid, we reestimate confidence intervals for Mertens and Ravn’s (2013) IRFs and find no statistically significant effects of tax changes on output, labor, and investment. (JEL E23, E62, H24, H25, H31, H32)

Bootstrap generated confidence interval for time averaged measure

In the simulation output analysis, there are some measures that should be calculated by time average concept such as the mean queue length. Especially, the confidence interval of those measures might be required for statistical analysis. In this situation, the traditional method that utilizes the central limit theorem (CLT) is inapplicable if the output data set has autocorrelation structure. The bootstrap is one of the most suitable methods which can reflect the autocorrelated phenomena in statistical analysis. Therefore, the confidence interval for a time averaged measure having autocorrelation structure can also be calculated by the bootstrap methods. This study introduces the method that constructs these confidence intervals applying the bootstraps. The bootstraps proposed are the threshold bootstrap (TB), the moving block bootstrap (MBB) and stationary bootstrap (SB). Finally, some numerical examples will be provided for verification.

Neural Networks and Bootstrap Methods for Regression Models with Dependent Errors

This chapter introduces the use of the bootstrap in a nonlinear, nonparametric regression framework with dependent errors. The aim is to construct approximate confidence intervals for the regression function which is estimated by using a single hidden layer feedforward neural network. In this framework, the use of a standard residual bootstrap scheme is not appropriate and it may lead to results that are not consistent. As an alternative solution, we investigate the AR-Sieve bootstrap and the Moving Block bootstrap, which are used to generate bootstrap replicates with a proper dependence structure. Both approaches are nonparametric bootstrap schemes, a consistent choice when dealing with neural network models which are often used as an accurate nonparametric estimation and prediction tool. In this context, both procedures may lead to satisfactory results but the AR sieve bootstrap seems to outperform the moving block bootstrap delivering confidence intervals with coverages closer to the nominal levels.