Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) Model

I introduce the notion of continuous invertibility on a compact set for volatility models driven by a stochastic recurrence equation. I prove strong consistency of the quasi‐maximum likelihood estimator (QMLE) when the quasi‐likelihood criterion is maximized on a continuously invertible domain. This approach yields, for the first time, the asymptotic normality of the QMLE for the exponential general autoregressive conditional heteroskedastic (EGARCH(1,1)) model under explicit but non‐verifiable conditions. In practice, I propose to stabilize the QMLE by constraining the optimization procedure to an empirical continuously invertible domain. The new method, called stable QMLE, is asymptotically normal when the observations follow an invertible EGARCH(1,1) model.     

Does the Representation of Household Behavior Matter for Welfare Analysis of Tax-benefit Policies? An Introduction

A widely shared intuition holds that individual control over money matters for the decision process within the household and the subsequent distribution of resources and welfare. As a consequence, there are good reasons to depart from the unitary model of the household and to explore the possibilities offered by models of the family accounting for several decision makers in the household and for the potential impact of tax reforms on the balance of power. This paper summarizes both the methodological and empirical findings presented in the next three papers of this special issue of the Review of the Economics of the Household. This series of contributions primarily entails a concrete comparison of the policy implications of the choice between the unitary and a particular multi-person representation: the collective representation. On the one hand, it suggests a methodology to implement the collective model of labor supply in a realistic context where participation is modeled together with working hours, and where the full tax-benefit system is accounted for. On the other hand, the empirical part relies on comprehensive simulations of tax reforms in Belgium, France, Germany, Italy, Spain, and the United Kingdom, and allows to quantify the distortions that may affect policy recommendations based on the unitary model.

Simple Bounds on the Value of a Reputation

We introduce entropy techniques to study the classical reputation model in which a long‐run player faces a series of short‐run players. The long‐run player's actions are possibly imperfectly observed. We derive explicit lower and upper bounds on the equilibrium payoffs to the long‐run player.     

DISTANCE TO RETIREMENT AND OLDER WORKERS‘ EMPLOYMENT: THE CASE FOR DELAYING THE RETIREMENT AGE

This paper presents empirical evidence and a theoretical foundation in favor of the view that the retirement age decision affects older workers' employment prior to retirement. To the extent that there are search frictions on the labor market, the return on jobs is determined by their expected duration: The time to retirement is then key to understanding older workers' employment. Countries with a retirement age of 60 are indeed characterized by lower employment rates for workers aged 55–59. Based on the French Labor Force Survey, we show that the likelihood of employment is significantly affected by the distance to retirement, in addition to age and other relevant variables. We then extend McCall's job search model by explicitly integrating life‐cycle features with the retirement decision. Using simulations, we show that the distance effect in interaction with the generosity of unemployment benefits and the depressed demand for older workers explains the low rate of employment just before the eligibility age for the Social Security pension. Finally, we show that implementing actuarially fair schemes not only extends the retirement age, but also encourages a more intensive job search by older unemployed workers. (JEL: J22, J26, H55)