## Optimal Taxation with Incomplete Markets

with Anmol Bhandari, David Evans, and Mikhail Golosov

November 2013

This paper characterizes tax and debt dynamics in Ramsey plans
for incomplete
markets economies that generalize an Aiyagari et al. (2002)
economy by allowing a
single asset traded by the government to be risky. Long run debt
and tax dynamics
can be attracted not only to the first-best continuation
allocations discovered by
Aiyagari et al. for quasi-linear preferences, but instead to a
continuation allocation
associated with a level of (marginal-utility-scaled) government
debt that would prevail
in a Lucas-Stokey economy that starts from a particular initial
level of government
debt. The paper formulates, analyzes, and numerically solves
Bellman equations for
two value functions for a Ramsey planner, one for t 1, the other
for t = 0.

## Taxes, debts, and redistributions with aggregate shocks

with Anmol Bhandari, David Evans, and Mikhail Golosov

September 2013

A planner sets a lump sum transfer and a linear tax on labor
income in an economy with incomplete markets, heterogeneous
agents, and aggregate shocks. The planner's concerns about
redistribution impart a welfare cost to fluctuating transfers.
The distribution of net asset holdings across agents affects
optimal allocations, transfers, and tax rates, but the level of
government debt does not. Two forces shape long-run outcomes:
the planner's desire to minimize the welfare costs of
fluctuating transfers, which calls for a negative correlation
between the distribution of net assets and agents' skills; and
the planner's desire to use fluctuations in the real interest
rate to adjust for missing state-contingent securities. In a
model parameterized to match stylized facts about US booms and
recessions, distributional concerns mainly determine optimal
policies over business cycle frequencies. These features of
optimal policy differ markedly from ones that emerge from
representative agent Ramsey models

like a 2002 JPE paper by Aiyagari et al.

like a 2002 JPE paper by Aiyagari et al.

## Fiscal Discriminations in Three Wars

with George J. Hall

June 2013

In 1790, a U.S. paper dollar was widely held in disrepute (something shoddy was not `worth a Continental'). By 1879, a U.S. paper dollar had
become `as good as gold.'
These outcomes emerged from how the U.S. federal government financed three wars:
the American Revolution, the War of 1812, and the Civil War.
In the beginning, the U.S. government discriminated greatly in the returns it paid to different classes of
creditors; but that pattern of discrimination diminished over time in ways that eventually rehabilitated the reputation
of federal paper money as a store of value.

## Speculation And Wealth When Investors Have Diverse Beliefs And Financial Markets Are Incomplete

with Timothy Cogley and Viktor Tsyrennikov

July 2012

In our heterogenous-beliefs incomplete-markets models, precautionary and speculative motives coexist. Missing
markets for Arrow securities affect the size and avenues for precautionary savings.
Survival dynamics suggested by Friedman (1953) and studied by Blume and Easley (2006) depend on whether agents can
trade a disaster-state security. When the market for a disaster-state security is closed, precautionary savings
flow into risk-free bonds, prompting less-informed investors to accumulate wealth. Because speculation motives
are strongest for the disaster-state Arrow security, opening this market brings outcomes close to those for a complete-markets
benchmark where instead it is well-informed investors who accumulate wealth. Speculation is more limited in other cases,
and outcomes for wealth dynamics are closer to those in an economy in which only a risk-free bond can be traded.

## Welfare Cost of Business Cycles in Economies with Individual Consumption Risk

with Martin Ellison

July 2012

The welfare cost of random consumption fluctuations is known from De Santis
(2007) to be increasing in the level of individual consumption risk in the
economy. It is also known from Barillas et al. (2009) to increase if agents
in the economy care about robustness to model misspecification. In this
paper, we combine these two effects and calculate the cost of business
cycles in an economy with consumers who face individual consumption risk and
who fear model misspecification. We find that individual risk has a greater
impact on the cost of business cycles if agents already have a preference
for robustness. Correspondingly, we find that endowing agents with concerns
about a preference for robustness is more costly if there is already
individual risk in the economy. The combined effect exceeds the sum of the
individual effects.

## Three Types of Ambiguity

with Lars Peter Hansen

July 2012

For each of three types of ambiguity, we compute a robust Ramsey plan and an associated
worst-case probability model.
Ex post, ambiguity of type I implies endogenously distorted homogeneous beliefs, while ambiguities of types II and III imply
distorted heterogeneous beliefs.
Martingales characterize alternative probability specifications and clarify distinctions among the three types of ambiguity.
We use recursive formulations of Ramsey problems to impose
local predictability of commitment multipliers directly. To reduce the dimension of the state in
a recursive formulation, we transform the commitment multiplier to accommodate the heterogeneous beliefs that
arise with ambiguity of types II and III. Our formulations facilitate comparisons of the consequences of these
alternative types of ambiguity.

## Bayesian Model Averaging, Learning and Model Selection

with George Evans, Seppo Honkapohja, and Noah Williams

January 2012

Agents have two forecasting models, one consistent with the unique
rational expectations equilibrium, another that assumes a time-varying
parameter structure. When agents use Bayesian updating to choose
between models in a self-referential system, we find that learning dynamics
lead to selection of one of the two models. However, there
are parameter regions for which the non-rational forecasting model is
selected in the long-run. A key structural parameter governing outcomes
measures the degree of expectations feedback in Muth’s model
of price determination.

## U.S. Then, Europe Now

December 2011

Under the Articles of Confederation, the central government of
the United States had limited power to tax. That made it
difficult for it to service the debts that the government had
incurred during our War of Independence, with the consequence
that debt traded at deep discounts. That situation framed a
U.S.\ fiscal crisis of the 1780s. A political revolution -- for
that was what our founders scuttling of the Articles of
Confederation in favor of the Constitution of the United States
of America was -- solved the fiscal crisis by transferring
authority to levy tariffs from the state governments to the
federal government. The Constitution and Acts of the First
Congress of the United States in August 1790 completed a grand
bargain that made creditors of the government become advocates
of a federal government with authority to raise revenues
sufficient to service the government's debt. In 1790, the
Congress carried out a comprehensive bailout of state
government's debts, another part of the grand bargain that made
creditors of the states become advocates of ample federal taxes.
That bailout may have created unwarranted expectations about
future federal bailouts that a costly episode in the early 1840s
corrected. Aspects of these early U.S.\ circumstances and
choices remind me of the European Union today.

## Market Prices of Risk with Diverse Beliefs, Learning, and Catastrophes

with Timothy Cogley and Viktor Tsyrenniko

December 2011

This paper studies market prices of risk in an economy with two types of agents with diverse beliefs. The paper studies both a complete markets
economy and a risk-free bonds only (Bewley) economy.

## Wealth Dynamics in a Bond Economy with Heterogeneous Beliefs

with Timothy Cogley and Viktor Tsyrennikov

December 2012

We study an economy in which two types of agents have diverse
beliefs about the law of motion for an exogenous endowment. One type knows the
true law of motion, and the other learns about it via Bayes’s
theorem. Financial markets are incomplete, the only traded asset being a risk-free
bond. Borrowing limits are imposed to ensure the existence of an
equilibrium. We analyze how financial-market structure affects the distribution of
financial wealth and survival of the two agents. When markets are complete, the
learning agent loses wealth during the learning transition and eventually exits
the economy Blume and Easley 2006). In contrast, in a bond-only economy,
the learning agent accumulates wealth, and both agents survive
asymptotically, with the knowledgeable agent being driven to his debt limit. The absence
of markets for certain Arrow securities is central to reversing the direction
in which wealth is transferred.

## Career Length: Effects of Curvature of Earnings Profiles, Earnings Shocks, Taxes, and Social Security

with Lars Ljungqvist

November 2012

The same high labor supply elasticity that characterizes a representative family model with indivisible labor and employment
lotteries can also emerge without lotteries when self-insuring individuals choose
career lengths. Off corners, the more elastic the earnings profile is to accumulated working
time, the
longer is a worker's career. Negative (positive) unanticipated earnings shocks
reduce (increase) the career length of a worker holding positive assets at the
time of the shock, while the effects are the opposite for a worker with negative
assets. By inducing a
worker to retire at an official retirement age, government provided social security can attenuate responses of career
lengths to earnings profile slopes, earnings shocks, and taxes.

## A Labor Supply Elasticity Accord?

with Lars Ljungqvist

January 2011

Until recently, an insurmountable gulf separated a high labor supply elasticity macro camp from a low labor supply elasticity
micro camp was fortified by
a contentious aggregation theory formerly embraced by real business cycle theorists. The repudiation
of that aggregation theory in favor of one more genial to microeconomic observations opens possibilities for an accord about the aggregate
labor supply elasticity.
The new aggregation theory drops
features to which empirical microeconomists
objected and replaces them with life-cycle choices that microeconomists have long emphasized.
Whether the new
aggregation theory ultimately indicates a small or large macro labor supply elasticity will
depend on how shocks and government institutions
interact to determine whether workers choose to be at interior solutions for career length.

## History dependent public policies

with David Evans

January 2011

A planner is compelled to raise a prescribed present value of revenues by levying a distorting tax on the output of a representative
firm that faces adjustment costs and resides within a rational expectations equilibrium. We describe recursive representations
both for a Ramsey plan and for a set of credible plans. Continuations of Ramsey plans
are not Ramsey plans. Continuations of credible plans are credible plans. As they are often constructed, continuations of optimal inflation target paths
are not optimal inflation target paths.

## Where to draw lines: stability versus efficiency

September 2010

What kinds of assets should financial intermediaries be permitted to hold and what kinds of liabilities
should they be allowed to issue? This paper reviews how tensions involving stability versus efficiency and regulation versus laissez faire have for centuries run through macroeconomic
analysis of these questions. The paper also discusses how two leading models
raise questions of whether deposit insurance is a good or bad
arrangement. This paper is the text of the Phillips Lecture, given at the London School of Economics on February 12, 2010.

## Robustness and ambiguity in continuous time

with Lars Peter Hansen

January 2011

We formulate two continuous-time hidden Markov models in which a decision maker
distrusts both his model of state dynamics and a prior distribution of unobserved states.
We use relative entropy's role in statistical model discrimination % using historical data, we use measures of statistical model detection
to modify Bellman equations in light of model ambiguity and to calibrate parameters that
measure ambiguity. We construct two continuous time models that are counterparts of two discrete-time recursive models of \cite{hansensargent07}.
In one, hidden states
appear in continuation value functions, while in the other, they do not.
The formulation in which continuation values do not depend on hidden states shares features of the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji. For this model, we use our statistical detection calculations to guide how to adjust contributions to entropy coming from hidden states as we take a continuous time limit.

## Practicing Dynare

with A. Bhandari, F. Barillas, R. Colacito, S. Kitao, C. Matthes, and Y. Shin

December 2010

This is a revised version that includes a new section solving examples from the revised chapter `Fiscal Policies in a Growth Model' from the soon to be published
third edition of Recursive Macroeconomic Theory by Ljungqvist and Sargent.
This paper teaches Dynare by applying it to approximate equilibria and estimate nine dynamic economic models.
Among the models estimated are a 1977 rational expectations model of hyperinflation by Sargent, Hansen, Sargent, and Tallarini’s risk-sensitive permanent income model,
and one and two-country stochastic growth models.
The examples.zip file contains dynare *.mod and data files that implement the examples in the paper.
Source Code

## Interest rate risk and other determinants of post WWII U.S. government debt/GDP dynamics

with George Hall

February 2010

This paper uses the sequence of government budget constraints to motivate
estimates of interest payments on the U.S. Federal government debt. We explain why our estimates differ conceptually and quantitatively from
those reported
by the U.S. government. We use our estimates to account for contributions to the evolution of the debt to GDP ratio made by inflation, growth,
and nominal returns paid on debts
of different maturities.

##
Two Illustrations of the Quantity Theory of Money:

Breakdowns and Revivals

with Paolo Surico

March 2010

By extending his data, we document the instability of two low-frequency regression coefficients that
Lucas (1980) used to express two empirical propositions representing the quantity theory of money. Bayesian estimation of a DSGE model over a subsample approximating Lucas's
yields parameters that imply population values of the two regression coefficients that confirm Lucas's results.
Perturbing parameters of a monetary policy rule away from values estimated over Lucas's subsample alters the population values of the two regression coefficients
in ways that reproduce the pattern of instability observed
over our longer sample.

## A defence of the FOMC

with Martin Ellison

July 2010

In this much revised version, we defend the forecasting performance of the
FOMC from the recent criticism
of Christina and David Romer. Our argument is that the FOMC forecasts a
worst-case scenario that it uses to design decisions that will work well
enough (are robust) despite possible misspecification of its model. Because
these FOMC forecasts are not predictions of what the FOMC expects to occur
under its model, it is inappropriate to compare their performance in a horse
race against other forecasts. Our interpretation of the FOMC as a robust
policymaker can explain all the findings of the Romers and rationalises
differences between FOMC forecasts and forecasts published in the Greenbook
by the staff of the Federal Reserve System.

## Wanting robustness in macroeconomics

with Lars Peter Hansen

May 2010

This is a survey paper about exponential twisting as a model
of model distrust. We feature examples from macroeconomics and
finance.

## Managing expectations and fiscal policy

by Anastasios G. Karantounias (with Lars Peter Hansen and
Thomas J. Sargent)

October 2009

This paper studies an optimal fiscal policy problem of
Lucas and Stokey (1983) but in a situation in which the representative
agent's distrust of the probability model for government
expenditures puts model uncertainty premia into history-contingent
prices. This gives rise to a motive for expectation management that
is absent within rational expectations and a novel incentive for the
planner to smooth the shadow value of the agent's subjective
beliefs in order to manipulate the equilibrium price of government
debt. Unlike the Lucas and Stokey (1983) model, the optimal allocation, tax
rate, and debt all become history dependent despite complete
markets and Markov government expenditures.

## Inflation-Gap Persistence in the U.S.

with Timothy Cogley and Giorgio E. Primiceri

December 2007

We use Bayesian Markov Chain Monte Carlo methods to estimate two models of post WWII U.S. inflation rates with drifting stochastic volatility and drifting coefficients. One model is univariate, the other a multivariate autoregression. We define the inflation gap as the deviation of inflation from a pure random walk component of inflation and use both of our models to study changes over time in the persistence of the inflation gap measured in terms of short- to medium-term predicability. We present evidence that our measure of the persistence of the inflation gap increased until Volcker brought mean inflation down in the early 1980s and that it then fell during the chairmanships of Volcker and Greenspan. Stronger evidence for movements in inflation gap persistence emerges from the VAR than from the univariate model. We interpret these changes in terms of a simple dynamic new Keynesian model that allows us to distinguish altered monetary policy rules and altered private sector parameters.

## Diverse Beliefs, Survival, and the Market Price of Risk

with Timothy Cogley

July 2008

We study prices and allocations in a complete-markets, pure endowment economy in which agents have heterogenous beliefs. Aggregate consumption growth evolves exogenously according to a two-state Markov process. The economy is populated by two types of agents, one that learns about transition probabilities and another that knows them. We examine how the presence of the better-informed agent influences allocations, the market price of risk, and the rate at which asset prices converge to values that would be computed under the typical assumption that all agents know the transition probabilities.

## Monetary Policies and Low-Frequency Manifestations of the Quantity Theory

with Paolo Surico

December 2008

As a device to detect manifestations of the quantity theory of money, we follow Lucas (1980) by looking at scatter plots of filtered time series of inflation and money growth rates and interest rates and money growth rates. In the spirit of Whiteman (1984), we relate those scatter plots to sums of two-sided distributed lag coefficients estimated from fixed-coefficient and time-varying VARs for U.S. data from 1900-2005. Then we interpret outcomes in terms of the population values of those sums of coefficients implied by two DSGE models. The DSGE models make the sums of weights depend on the monetary policy rule, yet another example of the cross-equation restrictions that Lucas (1972) and Sargent (1971) emphasized in the context of testing the natural unemployment rate hypothesis. When the U.S. data are extended beyond Lucas's 1955-1975, the patterns revealed by Lucas's scatter plots mutate in ways that we want to attribute to alterations in prevailing monetary policy rules.

## Curvature of Earnings Profile and Career Length

with Lars Ljungqvist

January 2009

A finitely lived worker confronts a labor supply indivisibility, chooses when to work, and smooths consumption by trading an interest bearing security. The worker faces an exogenously given increasing schedule that maps accumulated time on the job into an earnings level. With a specification of the worker's preferences that macroeconomists commonly use to assure balanced growth paths, the more elastic are earnings to accumulated working time, the longer is a worker's career.