Publications - Olaf Posch

Estimation of Heterogeneous Agent Models

Parra-Alvarez, J. C., Posch, O., Wang, M. C. — Sat, 01 Apr 2023 10:56:56 +0200

Using a Bewley-Hugget-Aiyagari model we show how to use the Fokker-Planck equation for likelihood inference in heterogeneous agent (HA) models. We study the finite sample properties of the maximum likelihood estimator (MLE) in Monte Carlo experiments using cross-sectional data on wealth and income. We use the Kullback–Leibler divergence to investigate identification problems that may affect inference. Unrestricted MLE leads to considerable biases of some parameters. Calibrating weakly identified parameters is shown to be useful to pin down the remaining structural parameters. We illustrate our approach by estimating the model for the US economy using the Survey of Consumer Finances.

Peso problems in the estimation of the C-CAPM

Parra-Alvarez, J. C., Posch, O., Schrimpf, A. — Sat, 01 Jan 2022 10:56:56 +0100

This paper shows that the consumption-based capital asset pricing model (C-CAPM) with low-probability disaster risk rationalizes pricing errors. We find that implausible estimates of risk aversion and time preference are not puzzling if market participants expect a future catastrophic change in fundamentals, which just happens not to occur in the sample (a “peso problem”). A bias in structural parameter estimates emerges as a result of pricing errors in quiet times. While the bias essentially removes the pricing error in the simple models when risk-free rates are constant, time-variation may also generate large and persistent estimated pricing errors in simulated data. We also show analytically how the problem of biased estimates can be avoided in empirical research by resolving the misspecification in moment conditions.

Risk matters

Parra-Alvarez, J. C., Polattimur, H., Posch, O. — Wed, 01 Dec 2021 10:56:56 +0100

In this paper we use the property that certainty equivalence, as implied by a first-order approximation to the solution of stochastic discrete-time models, breaks in its equivalent continuous-time version. We derive a risk-sensitive first-order perturbation solution for a general class of rational expectations models. We show that risk matters economically in a real business cycle (RBC) model with habit formation and capital adjustment costs, and that neglecting risk leads to substantial pricing errors. A first-order perturbation provides a sensible approximation to the effects of risk in continuous-time models. It reduces pricing errors by around 90% relative to the certainty equivalent linear approximation.

Estimating dynamic equilibrium models using mixed frequency macro and financial data

Christensen, B. J., Posch, O., Van Der Wel, M. — Thu, 01 Sep 2016 10:56:56 +0200

We provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency, along with macro series at standard lower frequency. Our formulation of the macro-finance model in continuous time conveniently accounts for the difference in observation frequency. We suggest the use of martingale estimating functions (MEF) to infer the structural parameters of the model directly through a nonlinear scheme. This method is compared to regression-based methods and the generalized method of moments (GMM). We illustrate our approaches by estimating various versions of the AK-Vasicek model with mean-reverting interest rates. We provide asymptotic theory and Monte Carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of US macro and financial data.

Numerical solution of dynamic equilibrium models under Poisson uncertainty

Posch, O., Trimborn, T. — Tue, 01 Jan 2013 10:56:56 +0100

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.

Explaining output volatility

Posch, O. — Sat, 01 Jan 2011 10:56:56 +0100

This paper presents strong empirical evidence that the observed heterogeneity of output volatility across countries and over time is partly endogenous. In particular, based on a closed-form solution we obtain a (long-run) equilibrium relationship between taxes and output volatility in the stochastic neoclassical growth model by showing that asymptotically the variance of output growth rates is affected by the level of taxes, without affecting the mean. We estimate the tax semi-elasticities on output volatility and provide convincing empirical evidence that taxes are important to understand differences in output volatility among OECD countries.

On the link between volatility and growth

Posch, O., Wälde, K. — Sat, 01 Jan 2011 10:56:56 +0100

A model of growth with endogenous innovation and distortionary taxes is presented. Since innovation is the only source of volatility, any variable that influences innovation directly affects volatility and growth. This joint endogeneity is illustrated by working out the effects through which economies with different tax levels differ in their volatility and growth process. We obtain analytical measures of macro volatility based on cyclical output and on output growth rates for plausible parametric restrictions. This analysis implies that controls for taxes should be included in the standard growth-volatility regressions. Our estimates show that the conventional Ramey-Ramey coefficient is affected sizeably. In addition, tax levels do indeed appear to affect volatility in our empirical application.

Risk premia in general equilibrium

Posch, O. — Sat, 01 Jan 2011 10:56:56 +0100

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant 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 an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.

Structural estimation of jump-diffusion processes in macroeconomics

Posch, O. — Thu, 01 Jan 2009 10:56:56 +0100

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.