Risk Premia in General Equilibrium

This paper shows that non-linearities imposed by a neoclassical production function alone can generate time-varying and asymmetric risk premia over the business cycle. These (empirical) key features become relevant, and asset market implications improve substantially when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to endowment economies, the curvature of the policy functions affects the risk premium through controlling the individual’s effective risk aversion.risk premium, continuous-time DSGE

Natural Volatility, Welfare and Taxation

Cyclical components are analytically computed in a theoretical model of stochastic endogenous fluctuations and growth. Volatility is shown to depend on the speed of convergence of the cyclical component, the expected length of a cycle and on the altitude of the slump. Taxes affect these channels and can therefore explain cross-country differences and breaks over time in volatility. With exogenous sources of fluctuations, a special case of our model, decentralized factor allocation is efficient. With endogenous fluctuations and growth, decentralized factor allocation is inefficient and (time-invariant) taxes can (de-) stabilize the economy. No unambiguous link exists between volatility and welfare.endogenous fluctuations and growth, welfare analysis, taxation, stochasticcontinuous time model, poisson uncertainty

On the non-causal link between volatility and growth

A model highlighting the endogeneity of both volatility and growth is presented. Volatility and growth are therefore correlated but there is no causal link from volatility to growth. This joint endogeneity is illustrated by working out the effects through which economies with different tax levels differ both in their volatility and growth. Using a continuous-time DSGE model with plausible parametric restrictions, we obtain closedform measures of macro volatility based on cyclical components and output growth rates. Given our results, empirical volatility-growth analysis should include controls in the conditional variance equation. Otherwise an omitted variable bias is likely.Tax effects, Volatility measures, Poisson uncertainty, Endogenous cycles and growth, Continuous-time DSGE models

Natural volatility, welfare and taxation

Cyclical components are analytically computed in a theoretical model of stochastic endogenous fluctuations and growth. Volatility is shown to depend on the speed of convergence of the cyclical component, the expected length of a cycle and on the attitude of the slump. Taxes affect these channels and can therefore explain cross-country differences and breaks over time in volatility. With exogenous sources of fluctuations, a special case of our model, decentralized factor allocation is efficient. With endogenous fluctuations and growth decentralized factor allocation is inefficient and (time invariant) taxes can (de-) stabilize the economy. No unambiguous link exists between volatility and welfare.Endogenous fluctuations and growth; welfare analysis; taxation; stochastic continuous time model; Poisson uncertainty

On the Non-Causal Link between Volatility and Growth

A model highlighting the endogeneity of both volatility and growth is presented. Volatility and growth are therefore correlated but there is no causal link from volatility to growth. This joint endogeneity is illustrated by working out the eects through which economies with dierent tax levels dier both in their volatility and growth. Using a continuous-time dynamic stochastic general equilibrium (DSGE) model with plausible parametric restrictions, we obtain closed-form measures of macro volatility based on cyclical components and output growth rates. Given our results, empirical volatility-growth analysis should include controls in the conditional variance equation. Otherwise an omitted variable bias is likely.Tax effects, Volatility measures, Poisson uncertainty, Endogenous cycles and growth, Continuous-time DSGE models

Natural volatility, welfare and taxation

Cyclical components are analytically computed in a theoretical model of stochastic endogenous fluctuations and growth. Volatility is shown to depend on the speed of convergence of the cyclical component, the expected length of a cycle and on the altitude of the slump. Taxes affect these channels and can therefore explain cross-country differences and breaks over time in volatility. With exogenous sources of fluctuations, a special case of our model, decentralized factor allocation is efficient. With endogenous fluctuations and growth, decentralized factor allocation is inefficient and (time-invariant) taxes can (de-) stabilize the economy. No unambiguous link exists between volatility and welfare.Endogenous fluctuations and growth, welfare analysis, taxation, stochastic continuous time model, Poisson uncertainty

Natural volatility, welfare and taxation

Cyclical components are analytically computed in a theoretical model of stochastic endogenous fluctuations and growth. Volatility is shown to depend on the speed of convergence of the cyclical component, the expected length of a cycle and on the altitude of the slump. Taxes affect these channels and can therefore explain cross-country differences and breaks over time in volatility. With exogenous sources of fluctuations, a special case of our model, decentralized factor allocation is efficient. With endogenous fluctuations and growth, decentralized factor allocation is inefficient and (time-invariant) taxes can (de-) stabilize the economy. No unambiguous link exists between volatility and welfare. --Endogenous fluctuations and growth,welfare analysis,taxation,stochastic continuous time model,Poisson uncertainty

Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.continuous-time DSGE, Poisson uncertainty, waveform relaxation

Structural estimation of jump-diffusion processes in macroeconomics

This paper shows how to solve and estimate a continuous-time dynamic stochastic general equilibrium (DSGE) model with jumps. It also shows that a continuous-time formulation can make it simpler (relative to its discrete-time version) to compute and estimate the deep parameters using the likelihood function when non-linearities and/or non-normalities are considered. We illustrate our approach by solving and estimating the stochastic AK and the neoclassical growth models. Our Monte Carlo experiments demonstrate that non-normalities can be detected for this class of models. Moreover, we provide strong empirical evidence for jumps in aggregate US data

Explaining Output Volatility: The Case of Taxation

This paper presents empirical evidence against the popular perception that macro volatility is exogenous. We obtain tax effects on macro aggregates in the stochastic neoclassical model. Taxes are shown to affect the second moment of output growth rates without affecting the first moment. Exploiting heterogeneity patterns in a panel of OECD countries, we estimate tax effects on macro volatility, explicitly modeling the unobserved variance process. We find a strong empirical link between taxes and output volatility. Accounting for non-stationarity of taxes and output volatility, we find empirical evidence of a cointegrating relationship.macroeconomic volatility, tax effects, continuous-time DSGE models