Olaf Posch

Research

Working Papers

FTPL and the Maturity Structure of Government Debt in the New-Keynesian Model
with Max Ole Liemen

CESifo Working Paper Series No. 9840 (Version December 2023). Link

Web Appendix

Abstract

How do skyrocketing debt-to-GDP ratios and government expenditures affect inflation and how does this depend on the maturity structure of sovereign debt? In this paper, we revisit the fiscal theory of the price level (FTPL) within the New Keynesian (NK) model. We show in which cases the maturity of government debt matters for the transmission of policy shocks. The central task of this paper is to shed light on the theoretical predictions of the maturity structure on macro dynamics with an emphasis on (expected) inflation. In particular, we show how fiscal- and monetary policy shocks affect interest rate and inflation dynamics. We highlight our results by quantifying the economic effects of the US COVID-19-emergency fiscal package (CARES), and shed light on the surge of inflation in the FTPL-NK model. In contrast, the CARES Act shocks have only small inflationary effects in the corresponding NK model with active monetary policy.
Resurrecting the New Keynesian Model: (Un)conventional Policy and the Taylor Rule
CESifo Working Paper Series No. 6925 (2020). Link

Web Appendix

Abstract

This paper explores the ability of the New Keynesian (NK) model to explain the recent periods of quiet and stable inflation at near-zero nominal interest rates. We show that temporary and permanent shocks to the natural rate (and inflation) are sufficient for the ability of the simple NK model to explain the recent facts. Based on the identified shocks from a novel approach, we show that the model can replicate key macroeconomic variables in accordance with the term structure of interest rates. We find that the term structure helps to identify permanent shocks. Our analysis is restricted to an active role of monetary policy and the traditional regions of (local) determinacy. We also show that capturing highly nonlinear dynamics can be useful to generate a prolonged period of near-zero interest rates as a policy choice.
On the Estimation of the Volatility-Growth Link
with Andrey Launov and Klaus Wälde

CREATES Research Paper 2012-21 (2019). Link

Abstract

It is common practice to estimate the volatility-growth link by specifying a growth equation such that the variance of the error term appears as an explanatory variable. Hardly any of existing applications of this framework includes exogenous controls in the variance equation. We show that the absence of relevant explanatory variables in the variance equation is not innocuous, leading to an omitted variable problem with an biased and inconsistent estimate of the volatility-growth link. Our simulations suggest that this effect is large and should be addressed in the empirical work. Once the appropriate controls are included consistency is restored.
Delays in Public Goods
with Santanu Chatterjee and Dennis Wesselbaum

CESifo Working Paper Series No. 6341 (2017). Link

Abstract

In this paper, we analyze the consequences of delays and cost overruns typically associated with the provision of public infrastructure in the context of a growing economy. Our results indicate that uncertainty about the arrival of public capital can more than offset its positive spillovers for private-sector productivity. In a decentralized economy, unanticipated delays in the provision of public capital generate too much consumption and too little private investment relative to the first-best optimum. The characterization of the first-best optimum is also affected: facing delays in the arrival of public goods, a social planner allocates more resources to private investment and less to consumption relative to the first-best outcome in the canonical model (without delays). The presence of delays also lowers equilibrium growth, and leads to a diverging growth path relative to that implied by the canonical model. This suggests that delays in public capital provision may be a potential determinant of cross-country differences in income and economic growth.
Measuring Convergence using Dynamic Equilibrium Models: Evidence from Chinese Provinces
with Lei Pan and Michel van der Wel

CREATES Research Paper (2012). Link

Abstract

We propose a model to study economic convergence in the tradition of neoclassical growth theory. We employ a novel stochastic set-up of the Solow (1956) model with shocks to both capital and labor. Our novel approach identifies the speed of convergence directly from estimating the parameters which determine equilibrium dynamics. The inference on the structural parameters is done using a maximum-likelihood approach. We estimate our model using growth and population data for China’s provinces from 1980 to 2009. We report heterogeneity in the speed of convergence both across provinces and time. The Eastern provinces show a higher tendency of convergence, while there is no evidence of convergence for the Central and Western provinces. We find empirical evidence that the speed of convergence decreases over time for most provinces.
Solving the New Keynesian Model in Continuous Time
with Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez

Unpublished Manuscript, Federal Reserve Bank of Atlanta (2012).

Abstract

We show how to formulate and solve a New Keynesian model in continuous time. In our economy, monopolistic firms engage in infrequent price setting ́a la Calvo. We introduce shocks to preferences, to factor productivity, to monetary policy and to government expenditure, and show how the equilibrium system can be written in terms of 8 state variables. Our nonlinear and global numerical solution method allows us to compute equilibrium dynamics and impulse response functions in the time space, the collocation method based on Chebychev polynomials is used to compute the recursive-competitive equilibrium based on the continuous-time HJB equation in the policy function space. We illustrate advantages of continuous time by studying the effects on the zero lower bound of interest rates.

Publications

Estimation of Heterogeneous Agent Models: A Likelihood Approach
with Juan Carlos Parra-Alvarez and Mu-Chun Wang

Oxford Bulletin of Economics and Statistics 85 (2023): P. 304-330. Link

Web Appendix

Abstract

We study the statistical properties of heterogeneous agent models. Using a Bewley-Hugget- Aiyagari model we compute the density function of wealth and income and use it for likelihood inference. We study the finite sample properties of the maximum likelihood estimator (MLE) using Monte Carlo experiments on artificial cross-sections of wealth and income. We propose to use the Kullback-Leibler divergence to investigate identification problems that may affect inference. Our results suggest that the unrestricted MLE leads to considerable biases of some parameters. Calibrating weakly identified parameters allows to pin down the other unidentified parameter without compromising the estimation of the remaining parameters. We illustrate our approach by estimating the model for the U.S. economy using wealth and income data from the Survey of Consumer Finances.
Peso Problems in the Estimation of the C-CAPM
with Juan Carlos Parra-Alvarez and Andreas Schrimpf

Quantitative Economics 13 (2022): P. 259–313. Link

Web Appendix

Abstract

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: Breaking Certainty Equivalence in Linear Approximations
with Juan Carlos Parra-Alvarez and Hamza Polattimur

Journal of Economic Dynamics and Control 133 (2021): 104248. Link

Web Appendix

Abstract

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 study the extent to which a first- order approximated solution built by perturbation methods accounts for risk. 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 approximation in continuous time reduces pricing errors by 90 percent relative to the certainty equivalent linear solution.
Estimating Dynamic Equilibrium Models using Mixed Frequency Macro and Financial Data
with Bent Jesper Christensen and Michel van der Wel

Journal of Econometrics 194 (2016): P. 116–137. Link

Web Appendix

Abstract

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 U.S. macro and financial data.
Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty
with Timo Trimborn

Journal of Economic Dynamics and Control 37 (2013): P. 2606-2662. Link

Abstract

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: The Case of Taxation
Journal of Public Economics 95 (2011): P. 1589-1606. Link

Abstract

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 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
with Klaus Wälde

Journal of Economic Growth 16 (2011): P. 285-308. Link

Abstract

A model of growth with endogenous innovation and distortionary taxes is pre- sented. 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
Journal of Economic Dynamics and Control 35 (2011): P. 1557-1576. Link

Abstract

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 cur- vature 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
Journal of Econometrics 153 (2009): P. 196-210. Link

Abstract

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.

Research

Working Papers

FTPL and the Maturity Structure of Government Debt in the New-Keynesian Model
with Max Ole Liemen

CESifo Working Paper Series No. 9840 (Version December 2023).

Link

Web Appendix

Abstract

How do skyrocketing debt-to-GDP ratios and government expenditures affect inflation and how does this depend on the maturity structure of sovereign debt? In this paper, we revisit the fiscal theory of the price level (FTPL) within the New Keynesian (NK) model. We show in which cases the maturity of government debt matters for the transmission of policy shocks. The central task of this paper is to shed light on the theoretical predictions of the maturity structure on macro dynamics with an emphasis on (expected) inflation. In particular, we show how fiscal- and monetary policy shocks affect interest rate and inflation dynamics. We highlight our results by quantifying the economic effects of the US COVID-19-emergency fiscal package (CARES), and shed light on the surge of inflation in the FTPL-NK model. In contrast, the CARES Act shocks have only small inflationary effects in the corresponding NK model with active monetary policy.
Resurrecting the New Keynesian Model: (Un)conventional Policy and the Taylor Rule
CESifo Working Paper Series No. 6925 (2020).

Link

Web Appendix

Abstract

This paper explores the ability of the New Keynesian (NK) model to explain the recent periods of quiet and stable inflation at near-zero nominal interest rates. We show that temporary and permanent shocks to the natural rate (and inflation) are sufficient for the ability of the simple NK model to explain the recent facts. Based on the identified shocks from a novel approach, we show that the model can replicate key macroeconomic variables in accordance with the term structure of interest rates. We find that the term structure helps to identify permanent shocks. Our analysis is restricted to an active role of monetary policy and the traditional regions of (local) determinacy. We also show that capturing highly nonlinear dynamics can be useful to generate a prolonged period of near-zero interest rates as a policy choice.
On the Estimation of the Volatility-Growth Link
with Andrey Launov and Klaus Wälde

CREATES Research Paper 2012-21 (2019).

Link

Abstract

It is common practice to estimate the volatility-growth link by specifying a growth equation such that the variance of the error term appears as an explanatory variable. Hardly any of existing applications of this framework includes exogenous controls in the variance equation. We show that the absence of relevant explanatory variables in the variance equation is not innocuous, leading to an omitted variable problem with an biased and inconsistent estimate of the volatility-growth link. Our simulations suggest that this effect is large and should be addressed in the empirical work. Once the appropriate controls are included consistency is restored.
Delays in Public Goods
with Santanu Chatterjee and Dennis Wesselbaum

CESifo Working Paper Series No. 6341 (2017).

Link

Abstract

In this paper, we analyze the consequences of delays and cost overruns typically associated with the provision of public infrastructure in the context of a growing economy. Our results indicate that uncertainty about the arrival of public capital can more than offset its positive spillovers for private-sector productivity. In a decentralized economy, unanticipated delays in the provision of public capital generate too much consumption and too little private investment relative to the first-best optimum. The characterization of the first-best optimum is also affected: facing delays in the arrival of public goods, a social planner allocates more resources to private investment and less to consumption relative to the first-best outcome in the canonical model (without delays). The presence of delays also lowers equilibrium growth, and leads to a diverging growth path relative to that implied by the canonical model. This suggests that delays in public capital provision may be a potential determinant of cross-country differences in income and economic growth.
Measuring Convergence using Dynamic Equilibrium Models: Evidence from Chinese Provinces
with Lei Pan and Michel van der Wel

CREATES Research Paper (2012).

Link

Abstract

We propose a model to study economic convergence in the tradition of neoclassical growth theory. We employ a novel stochastic set-up of the Solow (1956) model with shocks to both capital and labor. Our novel approach identifies the speed of convergence directly from estimating the parameters which determine equilibrium dynamics. The inference on the structural parameters is done using a maximum-likelihood approach. We estimate our model using growth and population data for China’s provinces from 1980 to 2009. We report heterogeneity in the speed of convergence both across provinces and time. The Eastern provinces show a higher tendency of convergence, while there is no evidence of convergence for the Central and Western provinces. We find empirical evidence that the speed of convergence decreases over time for most provinces.
Solving the New Keynesian Model in Continuous Time
with Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez

Unpublished Manuscript, Federal Reserve Bank of Atlanta (2012).

Abstract

We show how to formulate and solve a New Keynesian model in continuous time. In our economy, monopolistic firms engage in infrequent price setting ́a la Calvo. We introduce shocks to preferences, to factor productivity, to monetary policy and to government expenditure, and show how the equilibrium system can be written in terms of 8 state variables. Our nonlinear and global numerical solution method allows us to compute equilibrium dynamics and impulse response functions in the time space, the collocation method based on Chebychev polynomials is used to compute the recursive-competitive equilibrium based on the continuous-time HJB equation in the policy function space. We illustrate advantages of continuous time by studying the effects on the zero lower bound of interest rates.

Publications

Estimation of Heterogeneous Agent Models: A Likelihood Approach
with Juan Carlos Parra-Alvarez and Mu-Chun Wang

Oxford Bulletin of Economics and Statistics 85 (2023): P. 304-330.

Link

Web Appendix

Abstract

We study the statistical properties of heterogeneous agent models. Using a Bewley-Hugget- Aiyagari model we compute the density function of wealth and income and use it for likelihood inference. We study the finite sample properties of the maximum likelihood estimator (MLE) using Monte Carlo experiments on artificial cross-sections of wealth and income. We propose to use the Kullback-Leibler divergence to investigate identification problems that may affect inference. Our results suggest that the unrestricted MLE leads to considerable biases of some parameters. Calibrating weakly identified parameters allows to pin down the other unidentified parameter without compromising the estimation of the remaining parameters. We illustrate our approach by estimating the model for the U.S. economy using wealth and income data from the Survey of Consumer Finances.
Peso Problems in the Estimation of the C-CAPM
with Juan Carlos Parra-Alvarez and Andreas Schrimpf

Quantitative Economics 13 (2022): P. 259–313.

Link

Web Appendix

Abstract

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: Breaking Certainty Equivalence in Linear Approximations
with Juan Carlos Parra-Alvarez and Hamza Polattimur

Journal of Economic Dynamics and Control 133 (2021): 104248.

Link

Web Appendix

Abstract

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 study the extent to which a first- order approximated solution built by perturbation methods accounts for risk. 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 approximation in continuous time reduces pricing errors by 90 percent relative to the certainty equivalent linear solution.
Estimating Dynamic Equilibrium Models using Mixed Frequency Macro and Financial Data
with Bent Jesper Christensen and Michel van der Wel

Journal of Econometrics 194 (2016): P. 116–137.

Link

Web Appendix

Abstract

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 U.S. macro and financial data.
Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty
with Timo Trimborn

Journal of Economic Dynamics and Control 37 (2013): P. 2606-2662.

Link

Abstract

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: The Case of Taxation
Journal of Public Economics 95 (2011): P. 1589-1606.

Link

Abstract

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 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
with Klaus Wälde

Journal of Economic Growth 16 (2011): P. 285-308.

Link

Abstract

A model of growth with endogenous innovation and distortionary taxes is pre- sented. 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
Journal of Economic Dynamics and Control 35 (2011): P. 1557-1576.

Link

Abstract

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 cur- vature 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
Journal of Econometrics 153 (2009): P. 196-210.

Link

Abstract

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.

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Model Data Protection Statement for Anwaltskanzlei Weiß & Partner

Olaf Posch

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