Working Papers

The endogenous wage markup as a driver of the business cycle

Last update: May 2022

Abstract: We develop a model with an endogenous wage markup that can result in an endogenous business cycle (or limit cycle) under Rational Expectations. The endogenous wage markup captures the empirically established effect of aggregate labor market conditions on wages. When recent hours worked has been high (low) the endogenous wage markup shifts the labor supply curve up (down). This results in an intuitive driver of the business cycle, in which production increases more than labor costs during the recovery and early expansion phase, while late in the expansion labor costs increase more than output.

We implement this endogenous wage markup in a Real Business Cycle (RBC) model with a Cobb-Douglas production function. We show that the endogenous wage markup mechanism is a strong cyclical force, which can result in an attracting limit cycle for moderate increasing-returns-to-scale. These endogenous cycles can replicate basic business cycle properties in the absence of shocks.

Next, we bring a linearized version of the endogenous wage markup model to the data. The parameter estimates result in a model with a damped cycle, which is saddle path stable, but has complex eigenvalues. This damped cycle model has cyclical forces that result in a peak in the spectral density of hours worked at about 9 years, similar to what is observed in the data (Beaudry et al., 2020). The model without the endogenous wage markup fails to replicate this feature. This indicates that the endogenous wage markup can be an important driver of the business cycle.

Standardized projection algorithms to solve dynamic economic models

Download version: December 3, 2021

Abstract: We evaluate the performance of several projection algorithms with three Dynamic (Stochastic) General Equilibrium (DSGE) models. The algorithms are standardized and implemented in a projection method toolbox. We use cubic splines, complete Chebyshev polynomials, and Smolyak-Chebyshev polynomials as basis functions. For a small scale, and near-linear model complete Chebyshev polynomials with Galerkin’s method perform best. For more complex models or less linear models cubic splines perform better in terms of accuracy and speed than global polynomials.

The first DSGE model that we use to evaluate the algorithms is a standard RBC model, which is near-linear and has two state variables. For such a simple model a maximum error of 10−6 can be achieved in less than 0.05 seconds with all three basis functions. The second model is an RBC model with habits in consumption and investment adjustment costs, and has four state variables and two policy variables. For this model splines perform best and they achieve a maximum error of 10−5 in about 5 seconds. The third model is a highly non-linear limit cycle model, which is also best solved with a spline.

Optimal pensions when income and longevity are correlated, with Stefan Rohrbacher

Last update: September 2021

Abstract: We analyze optimal public pension schemes for the US economy when mortality and income are uncorrelated, and when they are correlated. We find that in both cases public pensions should fall with life-time income. With uncorrelated longevity the redistributive effects of public pension system are overstated, because the life-time poor (rich) are assumed to receive benefits longer (shorter) than they actually do. When income and longevity are correlated the optimal pension benefits fall sharper with earned life-time income to compensate the poor for their lower life expectancy.

Adaptive Beliefs in an RBC model

Download version: March 12, 2019

Abstract: This paper shows how extrapolative expectations can improve business cycle statistics in a Real Business Cycle model with preferences as in Jaimovich and Rebelo (2009, AER). The extrapolative expectations or `animal spirits' are applied to exogenous productivity shocks. Based on (recent) history of productivity shocks the agents perceives a permanent bias in the productivity shocks. The agent optimizes his behavior assuming he will maintain his beliefs indefinitely. This can induce a potentially large wealth effect and possibly result in a non-monotonic labor supply curve as a function of the productivity shock.

The standard deviation and serial correlation of the `animal spirits' are calibrated to match those values for consumer confidence series. When the standard deviation in consumer confidence is high, as the Consumer Confidence Index series, then labor supply is indeed non-monotonic, and results in the near perfect match of the standard deviation of output, consumption, hours worked and investment in the model with 'animal spirits'. When expectations are fitted to the lower standard deviation of Consumer Sentiment then the fit of the model with `animal spirits' is less good than the fit of the Rational Expectations model.

Optimal Age-Dependent Unemployment Insurance, with Jim Been

Download version: November 14, 2018

Abstract: We use a life-cycle model with job search and wealth accumulation to calculate optimal UI benefits, where we allow for an age-dependent replacement rate. We show that the optimal replacement rate is high for young people, but falls sharply with age. Varying the replacement rate over the life-cycle results in a welfare gain of about 5 to 15% of the Net Present Value of UI contributions compared to a system with an optimal constant replacement rate. The model is calibrated more extensively than is standard in the literature. The additional measures which are calibrated for are the elasticity of unemployment duration with respect to the level of unemployment benefits, the average consumption drop when agents become unemployed, and the unemployed duration with a linear trend in age. The additional parameters used in the calibration are the disutility of working, the adjustment costs to private wealth when the change in wealth is negative, and a linear trend in age of the parameter that determines the matching probability given search effort.