Optimal Tax Progressivity: An Analytical Framework

February 28, 2014

By Jonathan Heathcote, Kjetil Storesletten and Gianluca Violante


What shapes the optimal degree of progressivity of the tax and transfer system? On the one hand, a progressive tax system can counteract inequality in initial conditions and substitute for imperfect private insurance against idiosyncratic earnings risk. At the same time, progressivity reduces incentives to work and to invest in skills, and aggravates the externality associated with valued public expenditures. We develop a tractable equilibrium model that features all of these trade-offs. The analytical expressions we derive for social welfare deliver a transparent understanding of how preferences, technology, and market structure parameters influence the optimal degree of progressivity. A calibration for the U.S. economy indicates that endogenous skill investment, flexible labor supply, and the externality linked to valued government purchases play quantitatively similar roles in limiting desired progressivity.

This is an interesting paper for several reasons. First, it finds that progressivity is optimal without having any preference for equality. The welfare criterion is the expected utility of an agent born into this model economy, and this agent is purely selfish. Second, the paper nicely shows how various model features contribute to the progressivity. And third, but little exploited in the paper, it shows how some intrinsic features (outside of preferences) of an economy can lead to different degrees of progressivity.

Public Investment, Time to Build, and the Zero Lower Bound

February 10, 2014

By Hafedh Bouakez, Michel Guillard and Jordan Roulleau-Pasdeloup


Public investment represents a non-negligible fraction of total public expenditures. Yet, theoretical studies of the effects of public spending when the economy is stuck in a liquidity trap invariably assume that government expenditures are entirely wasteful. In this paper, we consider a new-Keynesian economy in which a fraction of government spending increases the stock of public capital-which is an external input in the production technology-subject to a time-to-build constraint. In this environment, an increase in public spending has two conflicting effects on current and expected inflation: a positive effect due to higher aggregate demand and a negative effect reflecting future declines in real marginal cost. We solve the model analytically both in normal times and when the zero lower bound (ZLB) on nominal interest rates binds. We show that under relatively short time-to-build delays, the spending multiplier at the ZLB decreases with the fraction of public investment in a stimulus plan. Conversely, when several quarters are required to build new public capital, this relationship is reversed. In the limiting case where a fiscal stimulus is entirely allocated to investment in public infrastructure, the spending multiplier at the ZLB is 4 to 5 times larger than in normal times when the time to build is 12 quarters.

It surprises Europeans that the US has not taken advantage of a deep recession and very low interest rates to renew its crumbling infrastructure. After all, this seems like a greate opportunity for some intertemporl substitution of government expenses. The key is likely in the American distate for public deficits. Yet, given that the stimulus money was decided anyway, why not focus on public infrastrucutre? This paper shows that the returns could have been very large. Unfortunately, I am not quite convinced of the results. Indeed, using a log-linearization in the context of a highly non-linear situation like the ZLB can yield misleading results. In addition, the log-linearization is taken around the deterministic steady-state, which is quite far from the ZLB under stochastics and the approximation error could be large even if there were no linearity issue.

News shocks and business cycles: bridging the gap from different methodologies

February 2, 2014

By Christoph Görtz and John Tsoukalas


An important disconnect in the news driven view of the business cycle formalized by Beaudry and Portier (2004), is the lack of agreement between different—VAR and DSGE—methodologies over the empirical plausibility of this view. We argue that this disconnect can be largely resolved once we augment a standard DSGE model with a financial channel that provides amplification to news shocks. Both methodologies suggest news shocks to the future growth prospects of the economy to be significant drivers of U.S. business cycles in the post-Greenspan era (1990-2011), explaining as much as 50% of the forecast error variance in hours worked in cyclical frequencies.

News shocks are interesting because they are forward-looking, compared to the other shocks in the literature that focus on current conditions. In retrospect, it is thus natural that forward-looking features of the economy, like the financial sector, need to be included in a model to properly account for news shocks. This is what this paper does.