Fabrice Collard

Accuracy of stochastic perturbation methods: The case of asset pricing models

This paper investigates the accuracy of a perturbation method in approximating the solution to stochastic equilibrium models under rational expectations. As a benchmark model, we use a version of asset pricing models proposed by Burnside [1988] which admits a closed-form solution while not making the assumptions of certainty equivalence. We then check the accuracy of perturbation methods -extended to a stochastic environment- against the closed form solution. Second an especially fourth order expansions are then found to be more efficient than standard linear approximation, as they are able to account for higher order moments of the distribution.

Fiscal Multipliers in Recessions

The Great Recession, and the fiscal response to it, has revived interest in the size of fiscal multipliers. Standard business cycle models have difficulties generating multipliers greater than one. And they also cannot produce any significant state-dependence in the size of the multipliers over the business cycle. In this paper we employ a variant of the Curdia-Woodford model of costly financial intermediation and show that fiscal multipliers can be strongly state dependent in a countercyclical manner. In particular, a fiscal expansion during a recession may lead to multiplier values exceeding two, while a similar expansion during an economic boom would produce multipliers falling short of unity. This pattern obtains if the spread (the financial friction) is more sensitive to fiscal policy during recessions than during expansions, a feature that is present in the data. Our results are consistent with recent empirical work documenting the state contingency of multipliers.

Optimal Monetary and Prudential Policies

The recent financial crisis has highlighted the interconnectedness between macroeconomic and financial stability and has raised the question of whether and how to combine the corresponding main policy instruments (interest rate and bank-capital requirements). This paper offers a characterization of the jointly optimal setting of monetary and prudential policies and discusses its implications for the business cycle. The source of financial fragility is the socially excessive risk-taking by banks due to limited liability and deposit insurance. We characterize the conditions under which locally optimal (Ramsey) policy dedicates the prudential instrument to preventing inefficient risk-taking by banks; and the monetary instrument to dealing with the business cycle, with the two instruments co-varying negatively. Our analysis thus identifies circumstances that can validate the prevailing view among central bankers that standard interest-rate policy cannot serve as the first line of defense against financial instability. In addition, we also provide conditions under which the two instruments might optimally co-move positively and countercyclically.

Exchange Rate Systems and Macroeconomic Stability

We examine macroeconomic stability and the properties of the international transmission of business cycles under three exchange rate systems: a flexible, a unilateral peg and a single currency. The subjects of study are Germany and France. EMU increases output and decreases inflation variability in Germany but it has the opposite effect in France. It induces a strong negative international transmission of country specific supply shocks and amplifies the role of German supply shocks. These two facts may complicate ECB policy-making.

Asymmetries in Monetary Policy Reaction Function: Evidence for U.S. French and German Central Banks

This paper proposes an empirical exploration of the possible asymmetric nature of the preferences of central bankers, with respect to inflation and output targets. The idea underlying this work lies in the widespread belief that central bankers interventions - through changes in a short-term interest rate - are influenced by the state of the current and/or expected state of the business cycle. The GMM estimates of a threshold model support the asymmetric representation of the monetary policy reaction function for recent U.S, French and German data.

Spectral and persistence properties of cyclical growth

Abstract This article investigates the cyclical properties of an endogenous growth model. An explicit solution is derived which permits the full characterization of the cyclical as well as the long-run properties of the model. Using spectral, autocorrelation and impulse response functions, we show that introducing endogenous growth overcomes some of the main shortcomings of RBC models. In particular, the model can generate positive autocorrelation of output growth when endogenous growth dominates the dynamics. Moreover, the model exhibits the hump-shaped pattern of impulse response functions of the trend-reverting component of output.

A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model

We propose to apply to the simulation of general nonlinearrational-expectation models a method where the expectation functions areapproximated through a higher-order Taylor expansion. This method has beenadvocated by Judd (1998) and others for the simulation of stochasticoptimal-control problems and we extend its application to more general cases.The coefficients for the first-order approximation of the expectation functionare obtained using a generalized eigenvalue decomposition as it is usual forthe simulation of linear rational-expectation models. Coefficients forhigher-order terms in the Taylor expansion are then obtained by solving asuccession of linear systems. In addition, we provide a method to reduce abias in the computation of the stochastic equilibrium of such models. Theseprocedures are made available in DYNARE, a MATLAB and GAUSS based simulationprogram.This method is then applied to the simulation of a macroeconomic modelembodying a nonlinear Phillips curve. We show that in this case a quadraticapproximation is sufficient, but different in important ways from thesimulation of a linearized version of the model.

Technology Shocks and Employment

Recent empirical work has suggested that in response to a positive technology shock employment shows a persistent decline. We show that the standard, open economy, flexible price model can generate a negative response of employment to a positive technology shock and can also match the negative conditional correlation between productivity and employment quite well if trade elasticities are low. While the model also has good overall properties, it fails to generate sufficient procyclicality in employment. This finding indicates that the RBC model faces a tension between accounting for the negative response of employment to technology shocks and simultaneously maintaining that technology shocks are the major source of business cycle fluctuations.

The short-run Dynamics of Optimal Growth Model with Delays.

Differential equations with advanced and delayed time arguments may arise in the optimality conditions of simple growth models with delays. Models with investment gestation lags (time-to-build), consumption gestation lags (habit formation) or learning by using lie in this category. In this paper, we propose a shooting method to deal with leads and lags in the Euler system associated to dynamic general equilibrium models in continuous time. We introduce the discussion describing the dynamics that emerge under various assumptions on learning by using and gestation lags. Then, we implement the numerical method we propose to solve for the short run dynamics of a neoclassical growth model with a simple time-to-build lag.

The Dynamic Effects of Disinflation Policies

This paper investigates the effects of disinflation policies on key macroeconomic variables. Using postwar US data and episode techniques, we identify disinflation shocks as shocks that drive the inflation rate to a lower level in the long-run. We find that in the immediate aftermath of a disinflation policy, the economy enters in a persistent recession. The inflation rate increases above its long-run level and exhibits a positive hump-shaped response. A similar pattern is found for the nominal interest rate, which responds even more strongly in the short-run. We then show that the standard new Keynesian model fails to account for macroeconomic dynamics in disinflationary times. On the contrary a deep habit version of the model successfully accounts for the effects of disinflation policies.