Granger Causality, Exogeneity, Cointegration, and Economic Policy Analysis

Policy analysis has long been a main interest of Clive Granger's. Here, we present a framework for economic policy analysis that provides a novel integration of several fundamental concepts at the heart of Granger's contributions to time-series analysis. We work with a dynamic structural system analyzed by White and Lu (2010) with well-defined causal meaning; under suitable conditional exogeneity restrictions, Granger causality coincides with this structural notion. The system contains target and control subsystems, with possibly integrated or cointegrated behavior. We ensure the invariance of the target subsystem to policy interventions using an explicitly causal partial equilibrium recursivity condition. Policy effectiveness is ensured by another explicit causality condition. These properties only involve the data generating process; models play a subsidiary role. Our framework thus complements that of Ericsson, Hendry, and Mizon (1998) (EHM) by providing conditions for policy analysis alternative to weak, strong, and super-exogeneity. This makes possible policy analysis for systems that may fail EHM's conditions. It also facilitates analysis of the cointegrating properties of systems subject to policymaker control. We discuss a variety of practical procedures useful for analyzing such systems and illustrate with an application to a simple model of the U.S. macroeconomy.

Forecasting Time Series Subject to Multiple Structural Breaks

This paper provides a novel approach to forecasting time series subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks over the forecast horizon, taking account of the size and duration of past breaks (if any) by means of a hierarchical hidden Markov chain model. Predictions are formed by integrating over the hyper parameters from the meta distributions that characterize the stochastic break point process. In an application to US Treasury bill rates, we find that the method leads to better out-of-sample forecasts than alternative methods that ignore breaks, particularly at long horizons.structural breaks, forecasting, hierarchical hidden Markov chain model, Bayesian model averaging.

Learning, Structural Instability and Present Value Calculations

Present value calculations require predictions of cash flows both at near and distant future points in time. Such predictions are generally surrounded by considerable uncertainty and may critically depend on assumptions about parameter values as well as the form and stability of the data generating process underlying the cash flows. This paper presents new theoretical results for the existence of the infinite sum of discounted expected future values under uncertainty about the parameters characterizing the growth rate of the cash flow process. Furthermore, we explore the consequences for present values of relaxing the stability assumption in a way that allows for past and future breaks to the underlying cash flow process. We find that such breaks can lead to considerable changes in present values

Learning, Structural Instability and Present Value Calculations

Present value calculations require predictions of cash flows both at near and distant future points in time. Such predictions are generally surrounded by considerable uncertainty and may critically depend on assumptions about parameter values as well as the form and stability of the data generating process underlying the cash flows. This paper presents new theoretical results for the existence of the infinite sum of discounted expected future values under uncertainty about the parameters characterizing the growth rate of the cash flow process. Furthermore, we explore the consequences for present values of relaxing the stability assumption in a way that allows for past and future breaks to the underlying cash flow process. We find that such breaks can lead to considerable changes in present values.present value, stock prices, structural breaks, Bayesian learning

Learning, structural instability and present value calculations

Present value calculations require predictions of cash flows both at near and distant future points in time. Such predictions are generally surrounded by considerable uncertainty and may critically depend on assumptions about parameter values as well as the form and stability of the data generating process underlying the cash flows. This paper presents new theoretical results for the existence of the infinite sum of discounted expected future values under uncertainty about the parameters characterizing the growth rate of the cash flow process. Furthermore, we explore the consequences for present values of relaxing the stability assumption in a way that allows for past and future breaks to the underlying cash flow process. We find that such breaks can lead to considerable changes in present values.present value, stock prices, structural breaks, Bayesian learning

Learning, structural instability and present value calculations

Present value calculations require predictions of cash flows both at near and distant future points in time. Such predictions are generally surrounded by considerable uncertainty and may critically depend on assumptions about parameter values as well as the form and stability of the data generating process underlying the cash flows. This paper presents new theoretical results for the existence of the infinite sum of discounted expected future values under uncertainty about the parameters characterizing the growth rate of the cash flow process. Furthermore, we explore the consequences for present values of relaxing the stability assumption in a way that allows for past and future breaks to the underlying cash flow process. We find that such breaks can lead to considerable changes in present values. --present value,stock prices,structural breaks,Bayesian learning

Optimal Portfolio Choice under Decision-Based Model Combinations

We extend the density combination approach of Billio et al. (2013) to feature combination weights that depend on the past forecasting performance of the individual models entering the combination through a utility-based objective function. We apply our model combination scheme to forecast stock returns, both at the aggregate level and by industry, and investigate its forecasting performance relative to a host of existing combination methods. Overall, we find that our combination scheme produces markedly more accurate predictions than the existing alternatives, both in terms of statistical and economic measures of out-of-sample predictability. We also investigate the performance of our model combination scheme in the presence of model instabilities, by considering individual predictive regressions that feature time-varying regression coefficients and stochastic volatility. We find that the gains from using our combination scheme increase significantly when we allow for instabilities in the individual models entering the combination

Return Predictability under Equilibrium Constraints on the Equity Premium

This paper proposes a new approach for incorporating theoretical constraints on return forecasting models such as non-negativity of the conditional equity premium and sign restrictions on the coefficients linking state variables to the equity premium. Our approach makes use of Bayesian methods that update the estimated parameters at each point in time in a way that optimally exploits information in these constraints. Using a variety of predictor variables from the literature on predictability of stock returns, we find that theoretical constraints have an important effect on the coefficient estimates and can significantly reduce biases and estimation errors in these. In out-of-sample forecasting experiments we find that models that exploit the theoretical restrictions produce better forecasts than unconstrained models.Return Predictability, Constraints, Out-of-Sample Forecasts

Conditional Forecasts in Large Bayesian VARs with Multiple Equality and Inequality Constraints

Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing algorithms used to generate conditional forecasts tend to be very computationally intensive, especially when working with large Vector Autoregressions or when multiple linear equality and inequality constraints are imposed at once. We introduce a novel precision-based sampler that is fast, scales well, and yields conditional forecasts from linear equality and inequality constraints. We show in a simulation study that the proposed method produces forecasts that are identical to those from the existing algorithms but in a fraction of the time. We then illustrate the performance of our method in a large Bayesian Vector Autoregression where we simultaneously impose a mix of linear equality and inequality constraints on the future trajectories of key US macroeconomic indicators over the 2020--2022 period

Bayesian compressed vector autoregressions

Macroeconomists are increasingly working with large Vector Autoregressions (VARs) where the number of parameters vastly exceeds the number of observations. Existing approaches either involve prior shrinkage or the use of factor methods. In this paper, we develop an alternative based on ideas from the compressed regression literature. It involves randomly compressing the explanatory variables prior to analysis. A huge dimensional problem is thus turned into a much smaller, more computationally tractable one. Bayesian model averaging can be done over various compressions, attaching greater weight to compressions which forecast well. In a macroeconomic application involving up to 129 variables, we find compressed VAR methods to forecast as well or better than either factor methods or large VAR methods involving prior shrinkage