New Papers

  • Macroeconomics after Lucas

    July 2024
    This sequel to ``After Keynesian Macroeconomics'' (1978) tells how equilibrium Markov processes underlie macroeconomics and much of applied dynamic economics today. It recalls how Robert E. Lucas, Jr., regarded Keynesian and rational expectations revolutions as interconnected transformations of economic and econometric theories and quantitative practices. It describes rules that Lucas used to guide and constrain his research. Lucas restricted himself to equilibrium Markov processes. He respected and conserved quantitative successes achieved by previous researchers, including those attained by quantitative Keynesian macroeconometric modelers.
  • Implementing a Ramsey Plan

    with Wei Jiang and Neng Wang
    June 2024
    Lucas and Stokey (1983) motivated future governments to confirm an optimal tax plan by rescheduling government debt appropriately. Debortoli et al. (2021) showed that sometimes that does not work. We show how a Ramsey plan can always be implemented by adding instantaneous debt to Lucas and Stokey's contractible subspace and requiring that each continuation government preserve that debt's purchasing power instantaneously. We formulate the Ramsey problem with a Bellman equation and use it to study settings with various initial term debt structures and government spending processes. We extract implications about tax smoothing and effects of fiscal policies on bond markets.
  • A p Theory of Government Debt and Taxes

    with Wei Jiang, Neng Wang, and Jinqiang Yang
    February 2024
    Distortions induce a benevolent government that must finance an exogenous expenditure process to smooth taxes. An optimal fiscal plan determines the marginal cost $-p'$ of servicing government debt and makes government debt risk-free. A convenience yield tilts debts forward and taxes backward. An option to default determines debt capacity. Debt-GDP ratio dynamics are driven by 1) a primary deficit, 2) interest payments, 3) GDP growth, and 4) hedging costs. We provide quantitative comparative dynamic statements about debt capacity, debt-GDP ratio transition dynamics, and time to exhaust debt capacity.
  • Costs of Financing US Federal Debt Under a Gold Standard: 1791-1933

    with Jonathan Payne, Balint Szoke, and George Hall
    January 2024
    From a new data set, we infer time series of term structures of yields on US federal bonds during the gold standard era from 1791-1933 and use our estimates to reassess historical narratives about how the US expanded its fiscal capacity. We show that US debt carried a default risk premium until the end of the nineteenth century when it started being priced as an alternative safe-asset to UK debt. During the Civil War, investors expected the US to return to a gold standard so the federal government was able to borrow without facing denomination risk. After the introduction of the National Banking System, the slope of the yield curve switched from down to up and the premium on US debt with maturity less than one year disappeared.
  • Managing Government Debts

    with Wei Jiang, Neng Wang, and Jinqiang Yang
    January 2024
    To construct a stochastic version of Barro's (1979) normative model of tax rates and debt/GDP dynamics, we add risks and markets for trading them along lines suggested by Arrow (1964) and Shiller (1994). These modifications preserve Barro's prescriptions that a government should keep its debt-GDP ratio and tax rate constant over time and also prescribe that the government insure its primary surplus risk by selling or buying the same number of shares of a Shiller macro security each period.
  • Dynamic Mode Decomposition of a CEX Panel

    with Yatheesan J. Selvakumar
    December 2023
    We state sufficient conditions on matrices defining a linear state-space model that allow us to infer those matrices from a reduced-rank first-order vector autoregression (VAR) for the observables. We use a Dynamic Mode Decomposition (DMD) to compute that VAR and show how dynamic modes relate to hidden Markov states in the state-space representation. We compute a reduced-rank first order VAR for quantiles for income, post tax and transfer income, and consumption from the US Consumer Expenditure Survey. We relate our findings to the neo-classical synthesis that was widely practiced by leading twentieth-century macroeconomists.
  • Fiscal Consequences of the US War on COVID

    with George G. Hall
    November 2023
    Post War on COVID-19 Interest rate rises and inflation imposed losses on federal creditors and motivated the Fed to transfer interest rate risk from private banks to itself. We describe budget-feasible paths for market values of US Treasury debt associated with projections of taxes and expenditures. We compare prospective paths of US federal taxes, expenditures, interest payments, and debt in the post-COVID period to paths observed after big surges in government expenditures during two twentieth-century US wars. Government expenditure/GDP surges in past US Wars had permanent components that were accompanied by permanent rises in tax collections/GDP ratios. Although part of the War on COVID expenditure/GDP surge has endured, so far tax collections haven't risen relative to GDP. The evolution of those two ratios will determine future debt/GDP ratios.
  • Risk, Ambiguity, and Mispecification: Decision Theory, Robust Control, and Statistics

    with Lars Peter Hansen
    September 2023
    What are ``deep uncertainties'' and how should their presence alter prudent courses of action? To help answer these questions, we bring ideas from robust control theory into statistical decision theory. Decision theory in economics has its origins in axiomatic formulations by von Neumann and Morgenstern as well as the statisticians Wald and Savage. Since Savage's fundamental work, economists have provided alternative axioms that formalize a notion of ambiguity aversion. Meanwhile, control theorists created another way to construct decision rules that are robust to potential model misspecifications. We reinterpret axiomatic foundations of some modern decision theories to include ambiguity about a prior to put on a family of models simultaneously with concerns about misspecifications of the corresponding likelihood functions. By building on ideas from dynamic programming, our representations have recursive structures that preserve dynamic consistency.
  • Sources of Artificial Intelligence

    September 2023
    This paper describes artificial intelligence and machine learning and how they were invented.
  • Completely Abstract Dynamic Programming

    August 2023
    with John Stachurski
    We introduce a “completely abstract” dynamic programming frame- work in which dynamic programs are sets of policy operators acting on a partially ordered space. We provide an optimality theory based on high-level assumptions. We then study symmetric and asymmetric relationships between dynamic programs, and show how these relationships transmit optimality properties. Our formulation includes and extends applications of dynamic programming across many fields.
  • HAOK and HANK Models

    July 2023
    I compare Heterogeneous Agent Old Keynesian models with Heterogeneous New Keynesian Models. I describe evidence and data reduction techniques that led leading 20th century macroeconomists to embrace HAOK models. I then describe other evidence that persuaded some able 21st century macroeconomists to want to displace HAOK models. The HANK project carries vast macroeconomic policy consequences.
  • Estimating Historical Yield Curves with Sparse Data

    with Jonathan Payne, Balint Szoke, and George Hall
    July 2023
    Estimating 19th century US federal bond yield curves presents challenges because few bonds were traded, bonds had peculiar features, government policies changed often, and there were wars. This paper compares statistical approaches for confronting these difficulties and shows that a dynamic Nelson-Siegel model with stochastic volatility and bond-specific pricing errors does a good job for historical US bond prices. This model is flexible enough to interpolate data across periods in a time-varying way without over- fitting. We exploit new computational techniques to deploy our model and estimate yield curves for US federal debt from 1790-1933.
  • Cross-Phenomenon Restrictions: Unemployment Effects of Layoff Costs and Quit Turbulence

    with with Isaac Bayley and Lars Ljungqvist
    June 2023
    Cross-phenomenon restrictions associated with returns to labor mobility can inform calibrations of productivity processes in macro-labor models. We exploit how returns to labor mobility influence effects on equilibrium unemployment of changes in (a) layoff costs, and (b) distributions of skill losses coincident with quits (``quit turbulence''). Returns to labor mobility intermediate both effects. Ample labor reallocations observed across market economies that have different layoff costs imply that a turbulence explanation of trans-Atlantic unemployment experiences is robust to adding plausible quit turbulence.
  • Time Averaging Meets Labor Supplies of Heckman, Lochner, and Taber

    with Sebastian Graves, Victoria Gregory, and Lars Ljungqvist
    May 2023
    We incorporate time-averaging into the canonical model of Heckman, Lochner, and Taber (1998) (HLT) to study retirement decisions, government policies, and their interaction with the aggregate labor supply elasticity. The HLT model forced all agents to retire at age 65, while our model allows them to choose career lengths. A benchmark social security system puts all of our workers at corner solutions of their career-length choice problems and lets our model reproduce HLT model outcomes. But alternative tax and social security arrangements dislodge some agents from those corners, bringing associated changes in equilibrium prices and human capital accumulation decisions. A reform that links social security benefits to age but not to employment status eliminates the implicit tax on working beyond 65. High taxes with revenues returned lump-sum keep agents off corner solutions, raising the aggregate labor supply elasticity and threatening to bring about a ``dual labor market'' in which many people decide not to supply labor.
  • Critique and Consequence

    May 2023
    After describing the landscape in macroeconomics and econometrics in Spring 1973 when Robert E. Lucas first presented his Critique at the inaugural Carnegie-Rochester conference, I add a fourth example based on Calvo (1978) to those appearing in section 5 of Lucas's paper. To portray some consequences of Lucas's Critique, I use that example as a vehicle to describe the time inconsistency of optimal plans and their credibility. I describe how different theories of government policy imply distinct apparent dynamic chains of influence between money and inflation. Different theories of policy bring with them different specifications of state vectors in recursive representations of inflation-money-supply outcomes.
  • Efficiency, Insurance, and Redistribution Effects of Government Policies

    with Anmol Bhandari, David Evans, and Mikhail Golosov
    January 2023
    We decompose welfare effects of switching from government policy A to policy B into three components: gains in aggregate efficiency from changes in total resources; gains in redistribution from altered consumption shares that ex-ante heterogeneous households can expect to receive; and gains in insurance from changes in households' consumption risks. Our decomposition applies to a broad class of multi-person, multi-good, multi-period economies with diverse specifications of preferences, shocks, and sources of heterogeneity. It has several desirable properties that other decompositions lack. We apply our decomposition to two fiscal policy reforms in quantitative incomplete markets settings.
  • Returns to Labor Mobility

    with Isaac Baley and Lars Ljungqvist
    December 2022
    Returns to labor mobility have too often escaped the attention they deserve as conduits of important forces in macro-labor models. These returns are shaped by calibrations of productivity processes that use theoretical perspectives and data sources from (i) labor economics and (ii) industrial organization. By studying how equilibrium unemployment responds to (a) layoff costs, and (b) likelihoods of skill losses following quits, we tighten calibrations of macro-labor models.
  • Financing Big US Federal Expenditures Surges: COVID-19 and Earlier US Wars

    with George Hall
    June 2022
    Directed by a consolidated government budget constraint, we compare US monetary-fiscal responses to World Wars I and II, and the War on COVID-19 with responses to the War of Independence, the War of 1812, and the Civil War.
  • Three World Wars: Fiscal-Monetary Consequences

    with George Hall
    April 2022
    With a consolidated government budget constraint as our guide, we compare US monetary-fiscal responses to World Wars I and II and the War on COVID-19.
  • A framework for the analysis of self-confirming policies

    with P. Battigalli, S. Cerreia-Vioglio, F. Maccheroni, and M. Marinacci
    January 2022
    This paper provides a general framework for analyzing self-confirming policies. We study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. We characterize stationary monetary policies in a linear-quadratic setting.
  • Rational Expectations and Volcker's Deflation

    September 2021
    This is my contribution to a volume in memory of Marvin Goodfriend and in honor of his work. It revisits issues analyzed in a classic 2005 paper by Marvin Goodfriend and Robert King.
  • Learning from Lucas

    September 2021
    This paper recollects meetings with Robert E. Lucas, Jr. over many years. It describes how, through personal interactions and studying his work, Lucas taught me to think about economics.
  • Earnings Growth and the Wealth Distribution

    with Neng Wang and Jinqiang Yang
    April 2021
    We solve a Bewley-Aiyagari-Huggett model almost by hand. Forces that shape wealth inequality are intermediated through an individual’s nonfinancial earnings growth rate g and an equilibrium interest rate r. Individuals’ earnings growth rate and survival probability interact with their preferences about consumption plans to determine aggregate savings and the interest rate and make wealth more unequally distributed and have a fatter tail than labor earnings, as in US data.
  • The Fundamental Surplus Strikes Again

    with Lars Ljungqvist
    April 2021
    The fundamental surplus isolates parameters that determine the sensitivity of unemployment to productivity in the matching model of Christiano, Eichenbaum, and Trabandt (2016 and 2021) under either Nash bargaining or alternating-offer bargaining. Those models thus join a collection of models in which diverse forces are intermediated through the fundamental surplus.
  • Stochastic Earnings Growth and Equilibrium Wealth Distributions

    with Neng Wang and Jinqiang Yang
    April 2021
    The cross-section distribution of U.S. wealth is more skewed and fatter tailed than is the distribution of labor earnings. Stachurski and Toda (2018) explain how plain vanilla Bewley-Aiyagari-Huggett (BAH) models with infinitely lived agents can't generate that pattern because of how a central limit theorem applies to a stationary labor earnings process. Two modifications of a BAH model suffice to generate a more skewed fatter-tailed wealth distribution: (1) overlapping generations of agents who pass through $N \geq 1$ life-stage transitions of stochastic lengths, and (2) labor-earnings processes that exhibit stochastic growth. With few parameters, our model does a good job of approximating the mapping from the Lorenz curve, Gini coefficient, and upper fat tail for cross-sections of labor earnings to their counterparts for cross sections of wealth. Three forces amplify wealth inequality relative to labor earnings inequality: stochastic life-stage transitions that arrest the central limit theorem force at work in Stachurski and Toda (2018); a strong precautionary savings motive for high labor income earners who receive positive permanent earnings shocks; and a life-cycle saving motive for the young born with low wealth. The outcome that the equilibrium risk-free interest rate exceeds a typical agent's subjective discount rate fosters a fat-tailed wealth distribution.
  • Inequality, Business Cycles, and Monetary-Fiscal Policy

    with Anmol Bhandari, David Evans, and Mikhail Golosov
    March 2021
    We study optimal monetary and fiscal policy in a model with heterogeneous agents, incomplete markets, and nominal rigidities. We show that functional derivative techniques can be applied to approximate equilibria in such economies quickly and efficiently. Our solution method does not require approximating policy functions around some fixed point in the state space and is not limited to first-order approximations. We apply our method to study Ramsey policies in a textbook New Keynesian economy augmented with incomplete markets and heterogeneous agents. Responses differ qualitatively from those in a representative agent economy and are an order of magnitude larger. Conventional price stabilization motives are swamped by an across person insurance motive that arises from heterogeneity and incomplete markets.
  • Structured Ambiguity and Model Misspecification

    with Lars Peter Hansen
    November 2020
    A decision maker is averse to not knowing a prior over a set of restricted structured models (ambiguity) and suspects that each structured model is misspecified. The decision maker evaluates intertemporal plans under all of the structured models and, to recognize possible misspecifications, under unstructured alternatives that are statistically close to them. Likelihood ratio processes are used to represent unstructured alternative models, while relative entropy restricts a set of unstructured models. A set of structured models might be finite or indexed by a finite-dimensional vector of unknown parameters that could vary in unknown ways over time. We model such a decision maker with a dynamic version of variational preferences and revisit topics including dynamic consistency and admissibility.
  • Shotgun Wedding: Fiscal and Monetary Policy

    with Marco Bassetto
    April 2020
    This paper describes interactions between monetary and fiscal policies that affect equilibrium price levels and interest rates by critically surveying theories about (a) optimal anticipated inflation, (b) optimal unanticipated inflation, and (c) conditions that secure a “nominal anchor” in the sense of a unique price level path. We contrast incomplete theories whose inputs are budget-feasible sequences of government issued bonds and money with complete theories whose inputs are bond-money policies described as sequences of functions that map time t histories into time t government actions. We cite historical episodes that confirm the theoretical insight that lines of authority between a Treasury and a Central Bank can be ambiguous, obscure, and fragile.
  • Debt and Taxes in Eight U.S. Wars and Two Insurrections

    with George J. Hall
    March 2020
    From decompositions of U.S. federal fiscal accounts from 1790 to 1988, we describe differences and patterns in how expenditure surges were financed during 8 wars between 1812 and 1975. We also study two insurrections. We use two benchmark theories of optimal taxation and borrowing to frame a narrative of how government decision makers reasoned and learned about how to manage a common set of forces that bedeviled them during all of the wars, forces that included interest rate risks, unknown durations of expenditure surges, government creditors’ debt dilution fears, and temptations to use changes in units of account and inflation to restructure debts. Ex post real rates of return on government securities are a big part of our story.
  • Macroeconomic Uncertainty Prices when Beliefs are Tenuous

    with Lars Peter Hansen
    March 2020
    Investors face uncertainty over models when they do not know which member of a set of well-defined “structured models” is best. They face uncertainty about models when they suspect that all of the structured models might be misspecified. We refer to worries about the first type of ignorance as ambiguity concerns and worries about the second type as misspecification concerns. These two types of ignorance about probability distributions of risks add what we call uncertainty components to equilibrium prices of those risks. A quantitative example highlights a representative investor’s uncertainties about the size and persistence of macroeconomic growth rates. Our model of preferences under concerns about model ambiguity and misspec- ification puts nonlinearities into marginal valuations that induce time variations in market prices of uncertainty. These reflect the representative investor’s fears of high persistence of low growth rate states and low persistence of high growth rate states.
  • Twisted Probabilities, Uncertainty, and Prices

    with Lars Peter Hansen and Balint Szoke and Lloyd S. Han
    February 2020
    A decision maker constructs a convex set of nonnegative martingales to use as likelihood ratios that represent alternatives that are statistically close to a decision maker's baseline model. The set is twisted to include some specific models of interest. Max-min expected utility over that set gives rise to equilibrium prices of model uncertainty expressed as worst-case distortions to drifts in a representative investor's baseline model. Three quantitative illustrations start with baseline models having exogenous long-run risks in technology shocks. These put endogenous long-run risks into consumption dynamics that differ in details that depend on how shocks affect returns to capital stocks. We describe sets of alternatives to a baseline model that generate countercyclical prices of uncertainty.
  • Funding the Great War and the Beginning of the End for British Hegemony

    with Martin Ellison and Andrew Scott
    July 2019
    An analytical description of British fiscal policy during and after the Great War 1914-1918
  • Complications for the United States from International Credits: 1913-1940

    with George J. Hall
    June 2019
    World War I complicated US monetary, debt management, and tax policies. To finance the war, the US Treasury borrowed $23 billion from its US citizens and lent $12 billion to 20 foreign nations. What began as foreign loans by the early 1930s had become gifts. For the first time in US history, the Treasury managed a large, permanent peacetime debt.
  • Commmodity and Token Monies

    November 2018
    A government defines a dollar as a list of quantities of one or more precious metals. If issued in sufficiently limited amounts, token money is a perfect substitute for precious metal money. Atemporal equilibrium conditions determine how quantities of precious metals and token monies affect an equilibrium price level. Within limits, a government can peg the relative price of two precious metals, confirming an analysis that Irving Fisher in 1911 used to answer a classic criticism of bimetallism.
  • A Case for Incomplete Markets

    with Lawrence E. Blume, Timothy Cogley, David A. Easley, and Viktor Tsyrennikov
    July 2018
    We propose a new welfare criterion that allows us to rank alternative financial market structures in the presence of belief heterogeneity. We analyze economies with complete and incomplete financial markets and/or restricted trading possibilities in the form of borrowing limits or transaction costs. We describe circumstances under which various restrictions on financial markets are desirable according to our welfare criterion.
  • US Federal Debt 1776 - 1960: Quantities and Prices

    with George Hall, Jonathan Payne, and Balint Szoke
    August 2021
    This document describes Pandas DataFrames and the spreadsheets underlying them that contain prices, quantities, and descriptions of bonds and notes issued by the United States Federal government from 1776 to 1960. It contains directions to a public github repository at which DataFrames and other files can be downloaded.
  • Public Debt in Economies with Heterogeneous Agents

    with Anmol Bhandari, David Evans, and Mikhail Golosov
    September 2017
    We study public debt in an economy in which taxes and transfers are chosen optimally subject to heterogeneous agents' diverse resources. We assume a government that commits to policies and can enforce tax and debt payments. If the government enforces perfectly, asset inequality is determined in an optimum competitive equilibrium but the level of government debt is not. Welfare increases if the government introduces borrowing frictions and commits not to enforce private debt contracts. That lets it reduce competition on debt markets and gather monopoly rents from providing liquidity. Regardless of whether the government chooses to enforce private debt contracts, the level of initial government debt does not affect an optimal allocation, but the distribution of net assets does.
  • A Framework for the Analysis of Self-Confirming Policies

    with P. Battigalli, S. Cerreia-Vioglio, F. Maccheroni, M. Marinacci
    August 2017
    This paper provides a general framework for the analysis of self-confirming policies. We first study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. Next we illustrate the theory with a characterization of stationary monetary policies in a linear-quadratic setting. Finally we provide a more general discussion of self-confirming policies.
  • The Fundamental Surplus

    with Lars Ljungqvist
    February 2017
    To generate big responses of unemployment to productivity changes, researchers have reconfigured matching models in various ways: by elevating the utility of leisure, by making wages sticky, by assuming alternating-offer wage bargaining, by introducing costly acquisition of credit, by assuming fixed matching costs, or by positing government mandated unemployment compensation and layoff costs. All of these redesigned matching models increase responses of unemployment to movements in productivity by diminishing the fundamental surplus fraction, an upper bound on the fraction of a job’s output that the invisible hand can allocate to vacancy creation. Business cycles and welfare state dynamics of an entire class of reconfigured matching models all operate through this common channel.
  • Honoring Public Debts

    Becker-Friedman Institute Version

    February 2017
    An essay on interests and forces that affect whether or not public debts are honored. Written for the Becker-Friedman Institute at the University of Chicago. I confess that the absence of equations from this essay makes it difficult to determine whether arguments contradict one another.
  • Fiscal Policy and Debt Management with Incomplete Markets

    with Anmol Bhandari, David Evans, and Mikhail Golosov
    July 2016
    A Ramsey planner chooses a distorting tax on labor and manages a portfolio of securities in an environment with incomplete markets. We develop a method that uses second order approximations of the policy functions to the planner's Bellman equation to obtain expressions for the unconditional and conditional moments of debt and taxes in closed form such as the mean and variance of the invariant distribution as well as the speed of mean reversion. Using this, we establish that asymptotically the planner's portfolio minimizes an appropriately defined measure of fiscal risk. Our analytic expressions that approximate moments of the invariant distribution can be readily applied to data recording the primary government deficit, aggregate consumption, and returns on traded securities. Applying our theory to U.S.\ data, we find that an optimal target debt level is negative but close to zero, that the invariant distribution of debt is very dispersed, and that mean reversion is slow.
  • A Life-Cycle Model of Trans-Atlantic Employment Experiences

    with Sagiri Kitao and Lars Ljungqvist
    December 2015
    To understand trans-Atlantic employment experiences since World War II, we build an overlapping generations model with two types of workers whose different skill acquisition technologies affect their career decisions. Search frictions affect short-run employment outcomes. The model focuses on labor supply responses near beginnings and ends of lives and on whether unemployment and early retirements are financed by personal savings or public benefit programs. Higher minimum wages in Europe explain why youth unemployment has risen more there than in the U.S. Higher risks of human capital depreciation after involuntary job destructions cause long-term unemployment in Europe, mostly among older workers, but leave U.S. unemployment unaffected. Increased probabilities of skill losses after involuntary job separation interact with workers' subsequent decisions to invest in human capital in ways that generate the age-dependent increases in autocovariances of income shocks observed by Moffitt and Gottschalk (1995).
  • A History of U.S. Debt Limits

    with George J. Hall
    December 2015
    Congress first imposed an aggregate debt limit in 1939 when it delegated decisions about designing US debt instruments to the Treasury. Before World War I, Congress designed each bond and specified a maximum amount of each bond that the Treasury could issue. It usually specified purposes for which proceeds could be spent. We construct and interpret a Federal debt limit before 1939.
  • Points of Departure

    February 2015
    This is an essay about my role in the history of rational expectations econometrics, written for the Trinity University series ``Lives of the Laureates".
  • Robert E. Lucas, Jr.’s Collected Papers on Monetary Theory

    November 2014
    This paper is a critical review of and a reader’s guide to a collection of papers by Robert E. Lucas, Jr. about fruitful ways of using general equilibrium theories to understand measured economic aggregates. These beautifully written and wisely argued papers integrated macroeconomics, microeconomics, finance, and econometrics in ways that restructured big parts of macroeconomic research.
  • Price-Level Uncertainty and Instability in the United Kingdom

    with Timothy Cogley and Paolo Surico
    November 2014
    Was UK inflation was more stable and/or less uncertain before 1914 or after 1945? We address these questions by estimating a statistical model with changing volatilities in transient and persistent components of inflation. Three conclusions emerge. First, since periods of high and low volatility occur in both eras, neither features uniformly greater stability or lower uncertainty. When comparing peaks with peaks and troughs with troughs, however, we find clear evidence that the price level was more stable before World War I. We also find some evidence for lower uncertainty at pre-1914 troughs, but its statistical significance is borderline.
  • Harrod 1939

    with Lawrence E. Blume
    August 2014
    Harrod’s 1939 “Essay in Dynamic Theory” is celebrated as one of the foundational papers in the modern theory of economic growth. Linked eternally to Evsey Domar, he appears in the undergraduate and graduate macroeconomics curricula, and his “fundamental equation” appears as the central result of the AK model in modern textbooks. Reading his Essay today, however, the reasons for his centrality are less clear. Looking forward from 1939, we see that the main stream of economic growth theory is built on neoclassical distribution theory rather than on the Keynesian principles Harrod deployed. Looking back, we see that there were many antecedent developments in growth economics, some much closer than Harrod’s to contemporary developments. So what, then, did Harrod accomplish?
  • An Open Letter to Professors Heckman and Prescott

    with Lars Ljungqvist
    July 2014
    You have disagreed in print about the size of the aggregate labor supply elasticity. Recent changes in the ``aggregation theory'' that Prescott uses brings you closer together at least in the sense that now you share a common theoretical structure.
  • Welfare Cost of Business Cycles in Economies with Idiosyncratic Consumption Risk

    with Martin Ellison
    September 2014
    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.
  • Measuring Price-Level Uncertainty and Instability in the U.S., 1850-2012

    with Timothy Cogley
    August 2014
    We measure price-level uncertainty and instability in the U.S. over the period 1850-2012. Major outbreaks of price-level uncertainty and instability occur both before and after World War II, alternating with three price-level moderations,one near the turn of 20th century, another under Bretton Woods, and a thirdin the 1990s. There is no evidence that the price level was systematically more stable or less uncertain before or after the Second World War. Moderations sometimes involved links to gold, but the experience of the 1990s proves that a well-managed fiat regime can achieve the same outcome.
  • What Nonconvexities Really Say about Labor Supply Elasticities

    with Lars Ljungqvist
    May 2014
    Rogerson and Wallenius (2013) draw an incorrect inference about a labor supply elasticity at an intensive margin from premises about an option to work part time that retiring workers decline. We explain how their false inference rests on overgeneralizing outcomes from a particular example and how Rogerson and Wallenius haven't identified an economic force beyond the two -- indivisible labor and time separable preferences -- that drive a high labor supply elasticity at an interior solution at an extensive margin.
  • Four Types of Ignorance

    with Lars Peter Hansen
    May 2014
    This paper studies alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targeting problem of Milton Friedman (1953). We study both "unstructured uncertainty" -- ignorance of the conditional distribution of the target next period as a function of states and controls -- and more "structured uncertainty" -- ignorance of the probability distribution of a response coefficient in an otherwise fully trusted specification of the conditional distribution of next period's target. We study whether and how different uncertainties affect Friedman's advice to be cautious in using a quantitative model to fine tune macroeconomic outcomes.
  • 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.
  • 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 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.
  • 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.
  • 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.