Quantifying the Welfare Gains from History Dependent Income Taxation

August 4, 2017

By Marek Kapicka


I quantify the welfare gains from introducing history dependent income tax in an incomplete markets framework where individuals face uninsurable random walk idiosyncratic shocks. I assume that the income tax paid is a function of a geometrical weighted average of past incomes, and solve for the optimal weights. I find that the optimal weights on past incomes decline geometrically at a rate equal to the discount rate. The welfare gains from history dependence are large, about 1.77 percent of consumption. I decompose the total effect into an efficiency effect that increases labor supply, and an insurance effect that reduces volatility of consumption and find that, quantitatively, the insurance effect dominates the efficiency effect. The optimal tax increases consumption insurance by trading higher tax progressivity with repect to past incomes for a reduced tax progressivity with respect to the current income.

Interesting result. It clearly makes sense that taxes should not only depend on income in the current snapshot in time. The paper shows that even a rigid formula on past taxes easily enhances welfare. Imagine if the formula were more flexible than a weighted average.

Velocity in the Long Run: Money and Structural Transformation

July 24, 2017

By Antonio Mele and Radek Stefanski


Monetary velocity declines as economies grow. We argue that this is due to the process of structural transformation – the shift of workers from agricultural to non-agricultural production associated with rising income. A calibrated, two-sector model of structural transformation with monetary and non-monetary trade accurately generates the long run monetary velocity of the US between 1869 and 2013 as well as the velocity of a panel of 92 countries between 1980 and 2010. Three lessons arise from our analysis: 1) Developments in agriculture, rather than non-agriculture, are key in driving monetary velocity; 2) Inflationary policies are disproportionately more costly in richer than in poorer countries; and 3) Nominal prices and inflation rates are not “always and everywhere a monetary phenomenon”: the composition of output influences money demand and hence the secular trends of price levels.

It is rather well-known that the velocity of money has dramatically declined since the last recession, and the reasons are rather well understood and are largely of temporary nature. This paper made me aware of a larger trend in the decline of velocity, which could explain that velocity should not be getting back to pre-recession levels. How this is explained in the paper, though, is not too convincing for a modern economy: the agricultural sector is non-monetary, and as its importance in the economy shrinks, money velocity declines. Agriculture has been small already for some time in developed economies, and a further decline is not going to noticeably matter, and the sector is largely monetized by now.

A note on automation, stagnation, and the implications of a robot tax

July 18, 2017

Emanuel Gasteiger and Klaus Prettner


We analyze the long-run growth effects of automation in the canonical overlapping generations framework. While automation implies constant returns to capital within this model class (even in the absence of technological progress), we show that it does not have the potential to lead to positive long-growth. The reason is that automation suppresses wages, which are the only source of investment because of the demographic structure of the overlapping generations model. This result stands in sharp contrast to the effects of automation in the representative agent setting, where positive long-run growth is feasible because agents can invest out of their wage income and out of their asset income. We also analyze the effects of a robot tax that has featured prominently in the policy debate on automation and show that it could raise the capital stock and per capita output at the steady state. However, the robot tax cannot induce a takeoff toward positive long-run growth.

That paper left me puzzling. I think a lot of the results hinge on the particular production function that has been applied here: infinite elasticity of substitution between robots and humans, unit elasticity of substitution between them and “traditional” capital. I do not think reality is that extreme.

Robustness, Low Risk-Free Rates, and Consumption Volatility in General Equilibrium

July 12, 2017

By Yulei Luo, Jun Nie and Eric Young


This paper develops a tractable continuous-time recursive utility (RU) version of the Huggett (1993) model to explore how the preference for robustness (RB) interacts with intertemporal substitution and risk aversion and then affects the interest rate, the dynamics of consumption and income, and the welfare costs of model uncertainty in general equilibrium. We show that RB reduces the equilibrium interest rate and the relative volatility of consumption growth to income growth when the income process is stationary, but our benchmark model cannot match the observed relative volatility. An extension to an RU-RB model with a risky asset is successful at matching this ratio. The model implies that the welfare costs of uncertainty are very large.

I was not aware of a continuous-time version of the Huggett model, and it looks like a pretty powerful tool. It may be useful in addressing questions that are too difficult for the discrete-time version, like in this paper.

Monetary Policy According to HANK

July 10, 2017

By Greg Kaplan, Benjamin Moll and Giovanni L. Violante


We revisit the transmission mechanism of monetary policy for household consumption in a Heterogeneous Agent New Keynesian (HANK) model. The model yields empirically realistic distributions of wealth and marginal propensities to consume because of two features: uninsurable income shocks and multiple assets with different degrees of liquidity and different returns. In this environment, the indirect effects of an unexpected cut in interest rates, which operate through a general equilibrium increase in labor demand, far outweigh direct effects such as intertemporal substitution. This finding is in stark contrast to small- and medium-scale Representative Agent New Keynesian (RANK) economies, where the substitution channel drives virtually all of the transmission from interest rates to consumption. Failure of Ricardian equivalence implies that, in HANK models, the fiscal reaction to the monetary expansion is a key determinant of the overall size of the macroeconomic response.

This is an exciting paper that merits highlighting even it has been circulating for a few years. Beyond the interesting results, this paper shows how much we have progressed in modeling. Only a few years ago, the justification of using representative agents was that heterogeneous agents do not really matter for aggregates. And indeed, this was true at the time. But since, both RANK and HANK models have evolved, and now they are able to answer questions where heterogeneity matters. And this paper is the best example of this.

Reorganization or Liquidation: Bankruptcy Choice and Firm Dynamics

July 7, 2017

By Dean Corbae and Pablo D’Erasmo


In this paper, we ask how bankruptcy law affects the financial decisions of corporations and its implications for firm dynamics. According to current U.S. law, firms have two bankruptcy options: Chapter 7 liquidation and Chapter 11 reorganization. Using Compustat data, we first document capital structure and investment decisions of non-bankrupt, Chapter 11, and Chapter 7 firms. Using those data moments, we then estimate parameters of a firm dynamics model with endogenous entry and exit to include both bankruptcy options in a general equilibrium environment. Finally, we evaluate a bankruptcy policy change recommended by the American Bankruptcy Institute that amounts to a “fresh start” for bankrupt firms. We find that changes to the law can have sizable consequences for borrowing costs and capital structure, which via selection affects productivity (allocative efficiency rises by 2:58%) and welfare (rises by 0:54%).

The US has a rather unique bankruptcy system that has serve it very well. For individuals, the fresh start option has been instrumental in encouraging entrepreneurship. For firms, Chapter 7 and 11 have helped many to avoid a shut down and then to flourish again. This paper shows that there is still scope to improve bankruptcy law in simple and significant ways.

Medium and long term implications of financial integration without financial development

June 29, 2017

By Flavia Corneli


We show that, in a two-country model where the two economies differ in their level of financial market development and initial capital endowment, financial integration has sizeable transitory as well as permanent effects. We confirm that, consistent with the Lucas paradox, financial integration in the medium term can reduce capital accumulation and increase savings in the financially less developed country, characterized by domestic capital market distortions, due to a higher risk premium in production activities. In the long run, however, integration produces higher levels of capital than in the autarky steady state. The opposite happens to the financially advanced economy, where integration initially boosts consumption and leads to a lower saving rate, and in the long run causes a reduction in capital compared with the autarky steady state. Two forces drive these results: precautionary saving and the propensity to move resources from risky capital to safe assets until the risk-adjusted return on capital equalizes the risk-free interest rate; assuming a constant relative risk aversion (CRRA) utility function, these forces are both decreasing in wealth.

The path to development is not uniform. This paper shows nicely the starting point matters, depending on the level of financial development and financial integration. This can also explain some of the shorter term difficulties that some economies suffered along their path.