Essays On Estimation Of Monetary Models Under Model Uncertainty

Chapter 1.-This chapter addresses model specification uncertainty using the Bayesian Generalized Method of Moments (GMM). Employing Canadian data, I estimate 64 hybrid New Keynesian models which differ in their lag specification, and use a modified GMM quadratic function to produce model posteriors. I compute optimal discretionary policies for each model and then derive a posterior-weighted policy and loss. My results show that i) policy should respond more to the output gap than inflation, ii) a more aggressive policy is prescribed for the period of stagflation in the 1970s and early 1980s and iii) a relatively light-touch policy is recommended during the Great Moderation, and produces better outcomes. This last result supports the hypothesis of 'good luck' over 'good policy'. Chapter 2.-In this chapter I develop an inverse control procedure to recover the under- lying preferences of a monetary authority engaged in discretionary policymaking. I adjoin the first-order condition (FOC) of the optimal interest rate rule-setting derived under discretion to the usual least squares moment conditions during the GMM procedure. Using Monte Carlo simulations, I show that the preferences on output gap stabilization and interest rate smoothing may be recovered. Robustness reveals that recovering the preference on the output gap is dependent upon policy actions having sufficient effect on the macroeconomy. Further testing indicates that the procedure functions for alternative starting values, may be adapted to different lag specifications of the underlying model, and is able to recover different sets of policy preferences. Chapter 3.-This chapter tests the hypothesis that the monetary authorities of Canada, the United States and the United Kingdom have exhibited similar preferences over stabilizing the output gap and smoothing the interest rate, by way of an inverse control algorithm (FOC- based GMM) for a discretionary policymaker. For the sample period covering 1968:1-2006:4, the FOC-based provides comparable structural estimates to a benchmark specification using an instrument-based GMM. The data suggest no role for output stabilization in any country, but a large and significant concern for interest rate smoothing is observed in Canada. Measures of fit reject optimality in the United States for baseline specification sample, but do not preclude it in any country when sample periods are restricted to the current man- dates. Policymakers' reaction functions are shown to be sensitive to the underlying policy preferences, though decreasingly so at high levels of interest rate smoothing. Robustness is seen with respect to starting values and fixed policy coefficients.

This dissertation consists of three essays on Bayesian inference in financial economics. The first essay explores the impact of discretization errors on the parametric estimation of continuous-time financial models. Euler and other discretization schemes cause discretization errors in solving stochastic differential equations. The empirical impact of these discretization errors on estimating two continuous-time financial models is investigated by using Monte Carlo experiments to compare the "exact" estimator and "Euler" estimator for the Euler scheme. The primary finding is that reducing the discretization interval to reduce the discretization error does not necessarily improve the performance of the estimators. This implies that discretization schemes may yield reliable results when the sampling interval is regularly small and shortening the discretization intervals or using data augmentation techniques may be redundant in practice. The second essay examines the identification problem in state-space models under the Bayesian framework. Underidentifiability causes no real difficulty in the Bayesian approach in that a legitimate posterior distribution might be achieved for unidentified parameters when appropriate priors are imposed. When estimating unidentified parameters, Markov chain Monte Carlo algorithms may yield misleading results even if the algorithms seem to converge successfully. In addition, the identification problem does really not matter when the prediction of state-space models instead of parameter estimation is concerned. The third essay extensively studies credit risk models using Bayesian inference. Bayesian inference is conducted and Markov chain Monte Carlo algorithms are developed for three popular credit risk models. Empirical results show that these three models in which the same PD (probability of default) can be estimated using different information may yield quite different results. Motivated by the empirical results about credit risk model uncertainty, I propose a "combined" Bayesian estimation method to incorporate information from different datasets and model structure for estimating the PD. This new approach provides an insight in dealing with two practical problems, model uncertainty and data insufficiency, in credit risk management.

The second innovative aspect of this book is its focus on policy preparation instead of well-covered topics as monetary policy strategy, tactics and implementation. Thirdly, a general, multi-model framework for preparing monetary policy is proposed, which is illustrated by case studies stressing the role of international economic linkages and of expectations. Written in a self-contained fashion, these case studies are of interest by themselves.".

This dissertation consists of three essays that delve into the intersection of econometrics and macroeconomics. The essays employ econometric tools to investigate various topics related to macroeconomic forecasting and policy-making. The first essay aims to help policy-makers conduct robust inference on parameters that may suffer identification issues from DSGE models, and perform reliable counterfactual analysis based on available macroeconomic indicators. The second essay from a non-structural perspective, explores how to optimally forecast these variables in real-time utilizing available macroeconomic variables under model uncertainty. The last essay looks at Survey of Professional Forecasters and studies how agents update their beliefs based on common and private signals during business cycles.The first chapter introduces a new algorithm to conduct robust Bayesian estimation and inference in dynamic stochastic general equilibrium models. The algorithm combines standard Bayesian methods with an equivalence characterization of model solutions. This algorithm allows researchers to perform the following analysis: First, find the complete range of posterior means of both the deep parameters and any parameters of interest robust to the choice of priors in a sense I make precise. Second, derive the robust Bayesian credible region for these parameters. I prove the validity of this algorithm and apply this method to the models in Cochrane (2011) and An and Schorfheide (2007) to achieve robust estimations for structural parameters and impulse responses. In addition, I conduct a sensitivity analysis of optimal monetary policy rules with respect to the choice of priors and provide bounds to the optimal Taylor rule parameters.In the second chapter, my coauthors Yongmiao Hong, Yuying Sun and I focus on real-time monitoring of economic activities, also known as nowcasting. Nowcasting can be particularly challenging in the era of Big Data because it requires the management of a substantial amount of time series data that exhibit different frequencies and release dates. In this paper, we propose a novel now-casting strategy that utilizes dynamic factor models, which we call leave-b-out forward validation model averaging with penalization (LboFVMA). We demonstrate that the selected weight converges asymptotically to an optimal and consistent estimator, even in cases where all candidate models are misspecified. Further-more, the proposed estimator is consistent and follows an asymptotic Gaussian distribution if the true model is included among the candidate models. Our simulation results demonstrate that the LboFVMA approach performs well, as it generates low mean square forecast errors. This highlights its effectiveness and accuracy in the field of nowcasting.In the third chapter, my coauthors Nathan Mislang, Kristoffer Nimark and I propose a method to empirically decompose a cross-section of observed belief revisions into components driven by private and common signals under weak assumptions. We define a common signal as the single signal that if observed by all agents can explain the maximum amount of belief revisions across agents. Private signals are defined to explain the residual belief revisions unaccounted for by the common signal. When applied to probability forecasts from the Survey of Professional Forecasters we find that private signals account for more of the observed belief revisions than common signals. There is a large cross-sectional heterogeneity in signal precision across forecasters, with about 1/2 of them observing private signals that are less precise than the common signal. Unconditionally, the precision of private and common signals are positively correlated, suggesting that private and common information are complements. Inflation volatility, perceived stock market volatility and a high risk of recession are all factors associated with increased informativeness and precision of both private and common signals. Disagreement between the private and common signals can partly explain increases in uncertainty about macro variables. We discuss the implications of our findings for theoretical models of information acquisition.

This edited collection concerns nonlinear economic relations that involve time. It is divided into four broad themes that all reflect the work and methodology of Professor Timo Teräsvirta, one of the leading scholars in the field of nonlinear time series econometrics. The themes are: Testing for linearity and functional form, specification testing and estimation of nonlinear time series models in the form of smooth transition models, model selection and econometric methodology, and finally applications within the area of financial econometrics. All these research fields include contributions that represent state of the art in econometrics such as testing for neglected nonlinearity in neural network models, time-varying GARCH and smooth transition models, STAR models and common factors in volatility modeling, semi-automatic general to specific model selection for nonlinear dynamic models, high-dimensional data analysis for parametric and semi-parametric regression models with dependent data, commodity price modeling, financial analysts earnings forecasts based on asymmetric loss function, local Gaussian correlation and dependence for asymmetric return dependence, and the use of bootstrap aggregation to improve forecast accuracy. Each chapter represents original scholarly work, and reflects the intellectual impact that Timo Teräsvirta has had and will continue to have, on the profession.

Using stochastic simulations and stability analysis, the paper compares how different monetary rules perform in a moderately nonlinear model with a time-varying nonaccelerating-inflation-rate-of-unemployment (NAIRU). Rules that perform well in linear models but implicitly embody backward-looking measures of real interest rates (such as conventional Taylor rules) or substantial interest rate smoothing perform very poorly in models with moderate nonlinearities, particularly when policymakers tend to make serially correlated errors in estimating the NAIRU. This challenges the practice of evaluating rules within linear models, in which the consequences of responding myopically to significant overheating are extremely unrealistic.

Recently there has been a great deal of interest in studying monetary policy under model uncertainty. We point out that different assumptions about the uncertainty may result in drastically different robust' policy recommendations. Therefore, we develop new methods to analyze uncertainty about the parameters of a model, the lag specification, the serial correlation of shocks, and the effects of real time data in one coherent structure. We consider both parametric and nonparametric specifications of this structure and use them to estimate the uncertainty in a small model of the US economy. We then use our estimates to compute robust Bayesian and minimax monetary policy rules, which are designed to perform well in the face of uncertainty. Our results suggest that the aggressiveness recently found in robust policy rules is likely to be caused by overemphasizing uncertainty about economic dynamics at low frequencies