Despite accelerating debt levels, the real yield on U.S. Treasuries remains low due to investors' desire for their extreme safety and liquidity services. The convenience premium on Treasuries allows fiscal policy to pursue profligate budget plans without imposing inflationary threats on a low-interest-rate monetary policy. Exploring these economic relations in a change-point vector autoregression model, I estimate the time-varying properties of U.S. inflation and its stance of fiscal policy that characterize long-term debt cycles. An archetypal debt cycle consists of alternating phases of persistent deficits and surpluses in tandem with alternating patterns of inflation and fiscal stance. In line with these key properties found in the data, I present a simple analytical model based on the fiscal theory of the price level where the household has a preference for holding government bonds. Determinacy admits a standard passive monetary policy coupled with a broad range of active fiscal policy. When the real interest rate falls below the economy's growth rate, permanent fiscal deficits can be sustained in the long run. The model explains why fiscal inflation has largely remained benign over the past two decades.

We present a dynamic incomplete information model where monetary and fiscal policy instruments serve as endogenous signals for the private sector. We highlight a novel information channel of policy interactions, and show the general equilibrium (GE) information feedback between policies largely shapes the economy's response to policy shocks. We document a non-monotone signaling effect of policies with respect to the policy rule parameters. Our analysis shows the GE information feedback is quantitatively significant, and the model provides a unified explanation of the various policy impacts on inflation, the dynamics of survey expectations, and the missing inflation after the Great Recession.

We examine monetary policy shifts by taking a new approach to regime switching in a small scale monetary DSGE model with threshold-type switching in the monetary policy rule. The policy response to inflation is allowed to switch endogenously between two regimes, hawkish and dovish, depending on whether a latent regime factor crosses a threshold level. Endogeneity stems from the historical impacts of structural shocks driving the economy on the regime factor. By estimating our DSGE model using the U.S. data, we quantify the endogenous feedback from each structural shock to the regime factor to understand the sources of the observed policy shifts. This new channel sheds new light on the interaction between policy changes and measured economic behavior.

Is inflation â€˜always and everywhere a monetary phenomenonâ€™ or is it fundamentally a fiscal phenomenon? The answer hinges crucially on the underlying monetaryâ€“fiscal policy regime. Scant attention has been directed to the role of credit market frictions in discerning the policy regime, despite its growing importance in empirical macroeconomics. We augment a standard monetary model to incorporate fiscal details and credit market imperfections. These ingredients allow for both interpretations of the inflation process in a financially constrained environment. We find that introducing financial frictions to the model and adding financial variables to the dataset generate important identifying restrictions on the observed pattern between inflation and measures of financial and fiscal stress, to the extent that it overturns existing findings about which monetaryâ€“fiscal policy regime produced the U.S. data. To confront policy regime uncertainty, we propose the use of dynamic prediction pools and find strong cyclical patterns in the estimated historical regime weights.

We propose an approach to solving and analyzing linear rational expectations models with general information frictions. Our approach is built upon policy function iterations in the frequency domain. We develop the theoretical framework of this approach using rational approximation, analytic continuation, and discrete Fourier transform. Conditional expectations, which are difficult to evaluate in the time domain, can be calculated efficiently in the frequency domain. We provide the numerical implementation accompanied by a flexible object-oriented toolbox. We demonstrate the efficiency and accuracy of our method by studying four models in macroeconomics and finance that feature asymmetric information sets, endogenous signals, and higher-order expectations.

This article is concerned with frequency-domain analysis of dynamic linear models under the hypothesis of rational expectations. We develop a unified framework for conveniently solving and estimating these models. Unlike existing strategies, our starting point is to obtain the model solution entirely in the frequency domain. This solution method is applicable to a wide class of models and allows for straightforward construction of the spectral density for performing likelihood-based inference. To cope with potential model uncertainty, we also generalize the well-known spectral decomposition of the Gaussian likelihood function to a composite version implied by several competing models. Taken together, these techniques yield fresh insights into the model's theoretical and empirical implications beyond what conventional time-domain approaches can offer. We illustrate the proposed framework using a prototypical new Keynesian model with fiscal details and two distinct monetary-fiscal policy regimes. The model is simple enough to deliver an analytical solution that makes the policy effects transparent under each regime, yet still able to shed light on the empirical interactions between U.S. monetary and fiscal policies along different frequencies.

This article illustrates a widely applicable frequency-domain methodology to solving multivariate linear rational expectations models. As an example, we solve a prototypical new Keynesian model under the assumption that primary surpluses evolve independently of government liabilities, a regime in which the fiscal theory of the price level is valid. The resulting analytical solution is useful in characterizing the cross-equation restrictions and illustrating the complex interaction between the fiscal theory and price rigidity. We also highlight some useful by-products of such method which are not easily obtainable for more sophisticated models using time-domain methods.

An analytic function method is applied to illustrate Geweke's (2010) three econometric interpretations for a generic rational expectations (RE) model. This delivers an explicit characterization of the model's cross-equation restrictions imposed by the RE hypothesis under each interpretation. It is shown that the degree of identification on the deep parameters is positively related to the strength of the underlying econometric interpretation, and observationally equivalent models may arise once the cross-equation restrictions are interpreted in a minimal sense. This offers important insights into the econometric modeling and evaluation of dynamic economic models.

We generalize the linear rational expectations solution method of Whiteman (1983) to the multivariate case. This facilitates the use of a generic exogenous driving process that must only satisfy covariance stationarity. Multivariate cross-equation restrictions linking the Wold representation of the exogenous process to the endogenous variables of the rational expectations model are obtained. We argue that this approach offers important insights into rational expectations models. We give two examples in the paperâ€”an asset pricing model with incomplete information and a monetary model with observationally equivalent monetary-fiscal policy interactions. We relate our solution methodology to other popular approaches to solving multivariate linear rational expectations models, and provide user-friendly code that executes our approach.

Presently there is growing interest in dynamic stochastic general equilibrium (DSGE) models that have more parameters, endogenous variables, exogenous shocks, and observables than the Smets and Wouters (2007) model, and substantial additional complexities from non-Gaussian distributions and the incorporation of time-varying volatility. The popular DYNARE software package, which has proved useful for small and medium-scale models is, however, not capable of handling such models, thus inhibiting the formulation and estimation of more realistic DSGE models. A primary goal of this paper is to introduce a user-friendly MATLAB software program designed to reliably estimate high-dimensional DSGE models. It simulates the posterior distribution by the tailored random block Metropolis-Hastings (TaRB-MH) algorithm of Chib and Ramamurthy (2010), calculates the marginal likelihood by the method of Chib (1995) and Chib and Jeliazkov (2001), and includes various post-estimation tools that are important for policy analysis, for example, functions for generating point and density forecasts. Another goal is to provide pointers on the prior, estimation, and comparison of these DSGE models. An extended version of the new Keynesian model of Leeper, Traum and Walker (2017) that has 51 parameters, 21 endogenous variables, 8 exogenous shocks, 8 observables, and 1,494 non-Gaussian and nonlinear latent variables is considered in detail.

WP

Bayesian Estimation of Macro-Finance DSGE Models with Stochastic Volatility

Rapach, David E.,
and Tan, Fei

revised and resubmitted at
Journal of Applied Econometrics,
2020

We develop a Bayesian Markov chain Monte Carlo algorithm for estimating risk premia in dynamic stochastic general equilibrium (DSGE) models with stochastic volatility. Our approach is fully Bayesian and employs an affine solution strategy that makes estimation of large-scale DSGE models computationally feasible. We use our algorithm to estimate the US equity risk premium in a DSGE model that includes time-preference, technology, investment, and volatility shocks. Time-preference and technology shocks are primarily responsible for the sizable equity risk premium in the estimated DSGE model. The estimated historical stochastic volatility and equity risk premium series display pronounced countercyclical fluctuations.

Humans benefit from extensive cooperation; however, the existence of free-riders may cause cooperation to collapse. This is called the social dilemma. It has been shown that punishing free-riders is an effective way of resolving this problem. Because punishment is costly, this gives rise to the second-order social dilemma. Without exception, existing solutions rely on some stringent assumptions. This paper proposes, under very mild conditions, a simple model of a public goods game featuring increasing returns to scale. We find that punishers stand out and even dominate the population provided that the degree of increasing returns to scale is large enough; consequently, the second-order social dilemma dissipates. Historical evidence shows that people are more willing to cooperate with others and punish defectors when they suffer from either internal or external menaces. During the prehistoric age, the abundance of contributors was decisive in joint endeavours such as fighting floods, defending territory, and hunting. These situations serve as favourable examples of public goods games in which the degrees of increasing returns to scale are undoubtedly very large. Our findings show that natural selection has endowed human kind with a tendency to pursue justice and punish defection that deviates from social norms.

An important way to maintain human cooperation is punishing defection. However, since punishment is costly, how can it arise and evolve given that individuals who contribute but do not punish fare better than the punishers? This leads to a violation of causality, since the evolution of punishment is prior to the one of cooperation behaviour in evolutionary dynamics. Our public goods game computer simulations based on generalized Moran Process, show that, if there exists a 'behaviour-based sympathy' that compensates those who punish at a personal cost, the way for the emergence and establishment of punishing behaviour is paved. In this way, the causality violation dissipates. Among humans sympathy can be expressed in many ways such as care, praise, solace, ethical support, admiration, and sometimes even adoration; in our computer simulations, we use a small amount of transfer payment to express 'behaviour-based sympathy'. Our conclusions indicate that, there exists co-evolution of sympathy, punishment and cooperation. According to classical philosophy literature, sympathy is a key factor in morality and justice is embodied by punishment; in modern societies, both the moral norms and the judicial system, the representations of sympathy and punishment, play an essential role in stable social cooperation.