
Thomas J. Sargent
New York University | NYU · Department of Economics
Thomas J. Sargent
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Publications (295)
Returns to labour mobility have too often escaped the attention they deserve as conduits of important forces in macro-labour models. These returns are shaped by calibrations of productivity processes that use theoretical perspectives and data sources from (i) labour economics and (ii) industrial organisation. By investigating earlier prominent stud...
What are “deep uncertainties” and how should their presence influence prudent decisions? To address these questions, we bring ideas from robust control theory into statistical decision theory. Decision theory has its origins in axiomatic formulations by von Neumann and Morgenstern, Wald, and Savage. After Savage, decision theorists constructed axio...
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”). Retur...
The fundamental surplus isolates parameters that determine how sensitively unemployment respond to productivity shocks in the matching models of Christiano, Eichenbaum, and Trabandt (2016 and this issue) under either Nash bargaining or alternating-offer bargaining. Those models thus join a collection of models in which diverse forces are intermedia...
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 clo...
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...
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 ex...
When the intertemporal elasticity of substitution is disentangled from risk aversion as in the recursive preferences of Epstein and Zin (1989) and Weil (1990), news about the intertemporal profile of consumption and leisure affect the equilibrium value of the government's portfolio of securities and, therefore, the extent to which the government ha...
If two rational agents want to trade and there are no externalities, then trade is Pareto improving. Economists generally oppose restrictions on such trade. Complete markets allocations are Pareto optimal and thus complete markets are generally viewed as good. But when individuals want to trade because of heterogeneous beliefs, this standard argume...
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-mandate...
The welfare cost of random consumption fluctuations is known from De Santis (2007) to be increasing in the level of uninsured idiosyncratic consumption risk. It is known from Barillas, Hansen, and Sargent (2009) to increase if agents care about robustness to model misspecification. We calculate the cost of business cycles in an economy where agents...
Was UK inflation 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 st...
This paper studies alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targetting 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 uncerta...
We measure price-level uncertainty and instability in the United States over the period 1850 to 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 the twentieth century, another under Bretton Woods, and a third in the 1990s....
Written by Lars Peter Hansen (Nobel Laureate in Economics, 2013) and Thomas Sargent (Nobel Laureate in Economics, 2011), Uncertainty within Economic Models includes articles adapting and applying robust control theory to problems in economics and finance. This book extends rational expectations models by including agents who doubt their models and...
We use a flexible statistical model with stochastic volatilities to measure price level uncertainty and instability in the U.S. over the period 1850-2012. Major outbreaks associated with the Civil War, the two World Wars and Great Depression, and the Great Inflation and Great Recession alternate with three great price-level moderations, one near th...
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 t...
This chapter outlines a setting with heterogeneity among households' preferences of a kind that violates the conditions for Gorman aggregation. Households' Engel curves are still affine, but dispersion of their slopes prevents Gorman aggregation. However, there is another sense in which there is a representative household whose preferences are a pe...
This chapter derives dynamic demand schedules from a household service technology. It applies the concept of canonical representation of household technologies to a version of Becker and Murphy's model of rational addiction. Canonical household technologies are useful for describing economies with heterogeneity among households' preferences because...
Some of the general equilibrium models in this book can be reinterpreted as partial equilibrium models that employ the notion of a representative firm, and that generalize the preference and technology specifications of Lucas and Prescott (1971). The idea is that there is a large number of identical firms that produce the same goods and sell them i...
A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. This book uses these tools to create a class of econometrically tractable models of prices and quantities. The book presents examples from microeconomics, macroeconomics, and asset pricing. The models are cast in terms of a representative consumer....
This chapter describes the vector first-order linear stochastic difference equation. It is first used to represent information flowing to economic agents, then again to represent competitive equilibria. The vector first-order linear stochastic difference equation is associated with a tidy theory of prediction and a host of procedures for econometri...
This chapter describes a decentralized economy. It assigns ownership and decision making to three distinct economic entities, a household and two kinds of firms. It defines a competitive equilibrium. Two fundamental theorems of welfare economics connect a competitive equilibrium to a planning problem. A price system supports the competitive equilib...
This chapter describes methods for computing equilibria of economies with consumers who have heterogeneous preferences and endowments. It adopts simplifications that facilitate coping with heterogeneity. In the present chapter, consumers differ only with respect to their endowments and the processes {bt} that disturb their preferences. It assumes t...
Until now, each of the matrices defining preferences, technologies, and information flows has been specified to be constant over time. This chapter relaxes this assumption and lets the matrices be strictly periodic functions of time. The aim is to apply and extend an idea of Denise Osborn (1988) and Richard Todd (1983, 1990) to arrive at a model of...
This chapter describes an economic environment with five components: a sequence of information sets, laws of motion for taste and technology shocks, a technology for producing consumption goods, a technology for producing services from consumer durables and consumption purchases, and a preference ordering over consumption services. A particular eco...
This chapter sets out the book's focus, namely constructing and applying competitive equilibria for a class of linear-quadratic-Gaussian dynamic economies with complete markets. Here, an economy will consist of a list of matrices that describe people's household technologies, their preferences over consumption services, their production technologie...
This chapter describes fast algorithms for computing the value function and optimal decision rule for the type of social planning problem to be described in Chapter 5. The chapter is organized as follows. First, it displays a transformation that removes both discounting and cross-products between states and controls. It then describes invariant sub...
This chapter uses the model of preferences to represent multiple goods versions of permanent income models. It retains Robert Hall's (1978) specification of a “storage” technology for accumulating physical capital and also a restriction on the discount factor, depreciation rate, and gross return on capital that in Hall's simple setting made the mar...
This chapter describes links between competitive equilibria and autoregressive representations. It shows how to obtain an autoregressive representation for observable variables that are error-ridden linear functions of state variables. In describing how to deduce an autoregressive representation from a competitive equilibrium and parameters of meas...
This chapter describes a concept of value that will be used to formulate a model in which the decisions of agents are reconciled in a competitive equilibrium. It describes a commodity space in which quantities and prices both will reside. The stochastic Lagrange multipliers of Chapter 4 are closely related to equilibrium prices and live in the same...
This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange multipliers; the second uses dynamic programming. The first method reveals a direct connection between the Lagrange multipliers and the equilibrium prices in...
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 dis...
The same high labor supply elasticity that characterizes a representative family model with indivisible labor and employment lotteries also emerges without lotteries when self-insuring individuals choose interior solutions for their career lengths. Off corners, the more elastic is an earnings profile to accumulated working time, the longer is a wor...
We defend the forecasting performance of the Federal Reserve Open Market Committee (FOMC) against the criticism of Christina and David Romer (2008, American Economic Review 98, 230–235) by assuming that the FOMC’s forecasts depict a worst‐case scenario that it uses to design decisions that are robust to misspecification of the staff’s model. We use...
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 t...
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 clarif...
We compare market prices of risk in economies with identical patterns of endowments, priors, and information flows, but two different market structures, one with complete markets, another in which consumers can trade only a single risk-free bond. We study how opportunities to speculate, uncommon priors, and learning affect market prices of risk. Tw...
We provide small noise expansions for the value function and optimal decisions of a decision maker who has the risk-sensitive/robust preferences specified by Hansen and Sargent (1995), Hansen, Sargent, and Tallarini (1999) and Tallarini (2000). We use the expansions (1) to provide a fast method for solving dynamic stochastic problems, (2) to quanti...
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 paramete...
This paper uses a sequence of government budget constraints to motivate estimates of returns on the US Federal government debt. Our estimates differ conceptually and quantitatively from the interest payments reported by the US government. We use our estimates to account for contributions to the evolution of the debt-GDP ratio made by inflation, gro...
A dispute about the size of the aggregate labor supply elasticity has been fortified by a contentious aggregation theory used by real business cycle theorists. The replacement of that aggregation theory with one more congenial to microeconomic observations opens possibilities for an accord about the aggregate labor supply elasticity. The new aggreg...
We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are...
What kinds of assets should financial intermediaries be permitted to hold? What kinds of liabilities should they be allowed to issue? Should a government or a central bank offer explicit deposit insurance or implicit deposit insurance by acting as a lender of last resort? This paper reviews how tensions involving stability versus efficiency, and re...
By extending his data, we document the instability of low-frequency regression coefficients that Lucas (1980) used to express the quantity theory of money. We impute the differences in these regression coefficients to differences in monetary policies across periods. A DSGE model estimated over a subsample like Lucas's implies values of the regressi...
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We refine and apply particle filtering algorithms that emphasize portions of the filtered distribution most pertinent to a decision maker. We illustrate our algorithms in an equilibrium model with investors who design robust decision rules by exponentially tilting probabilities of a baseline statistical model.
This paper modifies a Townsend turnpike model by letting agents stay at a location long enough to trade some consumption loans, but not long enough to support a Pareto-optimal allocation. Monetary equilibria exist that are nonoptimal in the absence of a scheme to pay interest on currency at a particular rate. Paying interest on currency at the opti...
For linear quadratic Gaussian problems, this paper uses two risk-sensitivity operators defined by Hansen and Sargent (2007b) to construct decision rules that are robust to misspecifications of (1) transition dynamics for state variables and (2) a probability density over hidden states induced by Bayes’ law. Duality of risk sensitivity to the multip...
A standard timing protocol allows in a cash-in-advance model allows the government to elude the inflation tax. That matters. Altering the timing of tax collections to make the government hold cash overnight disables some classical propositions but enables others. The altered timing protocol loses a Ricardian proposition and also the proposition tha...
A representative consumer uses Bayes' law to learn about parameters of several models and to construct probabilities with which to perform ongoing model averaging. The arrival of signals induces the consumer to alter his posterior distribution over models and parameters. The consumer's specification doubts induce him to slant probabilities pessimis...
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 between stability versus efficiency and regulation versus laissez faire have long run through macroeconomic analysis of these questions.
The high labor supply elasticity in an indivisible-labor model with employment lotteries emerges also without lotteries when individuals must instead choose career lengths. The more elastic are earnings to accumulated working time, the longer is a worker's career. Negative (positive) unanticipated earnings shocks reduce (increase) the career length...
Robust control theory is a tool for assessing decision rules when a decision maker distrusts either the specification of transition laws or the distribution of hidden state variables or both. Specification doubts inspire the decision maker to want a decision rule to work well for a ∅ of models surrounding his approximating stochastic model. We rela...
‘Rational expectations’ is an equilibrium concept that can be applied to dynamic economic models that have elements of ‘self-reference’, that is, models in which the endogenous variables are influenced by the expectations about future values of those variables held by the agents in the model. The concept was introduced and applied by John F. Muth (...
We develop a method for measuring the amount of insurance the portfolio of government liabilities provides against scal shocks, and apply it to postwar US data. We de ne scal shocks as surprises in defense spending. Our results indicate that the US federal government is partially hedged against wars and other surprise increases in defense expenditu...
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...
Reinterpreting most of the market price of risk as a price of model uncertainty eradicates a link between asset prices and measures of the welfare costs of aggregate fluctuations that was proposed by Hansen, Sargent, and Tallarini [17], Tallarini [30], Alvarez and Jermann [1]. Prices of model uncertainty contain information about the benefits of re...
We construct a model of a firm competing for market share in a customer market and making investments in physical capital. The firm is financially constrained and there are implementation lags in investment. Our model predicts that product prices should depend on costs and competitors' prices but respond weakly to demand shocks. Also, prices should...
We infer determinants of Latin American hyperinflations and stabilizations by using the method of maximum likelihood to estimate a hidden Markov model that assigns roles both to fundamentals in the form of government deficits that are financed by money creation and to destabilizing expectations dynamics that can occasionally divorce inflation from...
We study prices and allocations in a complete-markets, pure-exchange economy in which there are two types of agents with different priors over infinite sequences of the aggregate endowment. Aggregate consumption growth evolves exogenously according to a two-state Markov process. The economy has two types of agents, one that learns about transition...
To detect 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. Like Whiteman (1984), we relate those scatter plots to sums of two-sided distributed lag coefficients constructed from fixed-coefficient and time-varying VA...
We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight from emerging markets) prior to and during the 2008 fi...
We study how a concern for robustness modifies a policymaker's incentive to experiment. A policymaker has a prior over two submodels of inflation-unemployment dynamics. One submodel implies an exploitable trade-off, the other does not. Bayes' law gives the policymaker an incentive to experiment. The policymaker fears that both submodels and his pri...
Concerns about misspecification and an enduring model selection problem in which one of the models has long run risks give rise to countercyclical risk premia. We use two risk-sensitivity operators to construct the stochastic discount factor for a representative consumer who evaluates consumption streams in light of model selection and parameter es...
By positing learning and a pessimistic initial prior, we build a model that disconnects a representative consumer's subjective attitudes toward risk from the high price of risk that a rational-expectations econometrician would deduce from financial market data. We follow Friedman and Schwartz [1963. A Monetary History of the United States, 1857–196...
We study a Markov decision problem with unknown transition probabilities. We compute the exact Bayesian decision rule and compare it with two approximations. The first is an infinite-history, rational-expectations approximation that assumes that the decision maker knows the transition probabilities. The second is a version of Kreps' anticipated-uti...
A general equilibrium search model makes layoff costs affect the aggregate unemployment rate in ways that depend on equilibrium proportions of frictional and structural unemployment that in turn depend on the generosity of government unemployment benefits and skill losses among newly displaced workers. The model explains how, before the 1970s, lowe...
The introduction of the precious metals for the purposes of money may with truth be considered as one of the most important steps towards the improvement of commerce, and the arts of civilised life; but it is no less true that, with the advancement of knowledge and science, we discover that it would be another improvement to banish them again from...
An incomplete-market life-cycle model with indivisible labor makes career lengths and human capital accumulation respond to labor tax rates and government supplied non-employment benefits. We compare aggregate and individual outcomes in this individualistic incomplete-market model with those in a comparable collectivist representative-family model...
This paper discusses two sources of ideas that influence monetary policy makers today. The first is a set of analytical results that impose the rational expectations equilibrium concept and do 'intelligent design' by solving Ramsey and mechanism design problems. The second is the adaptive learning process that first taught us how to anchor the pric...
To understand trans-Atlantic employment experiences in the post-World War II era, we enrich the environment of Ljungqvist and Sargent (2008) in ways that allow skill losses occasioned by involuntary job separations (`turbulence') to have further effects on labor market outcomes. Our model features ex ante heterogeneity by having two types of worker...
We use Bayesian 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...
models and the prior distribution are correctly specified. We explain how the policy maker's desires to protect against misspecifications of the submodels, on the one hand, and misspecifications of the prior over them, on the other, have different effects on the decision rule.
Self-confirming equilibria are limiting outcomes of purposeful interactions among a collection of adaptive agents, each of whom averages past data to approximate moments of conditional probability distributions. Self-confirming equilibria are powerful tools to investigate dynamic economic problems such as the limiting behaviour of learning systems,...
From 1970 to 1985, Israel experienced high inflation. It rose in three jumps to new plateaus and eventually exceeded 400% per annum. This paper claims that anticipated monetary and fiscal effects of a massive government bailout of owners of fallen bank shares caused the last big jump in inflation that occurred in October 1983. Bank shares had just...
To understand European and American unemployment during the last 60 years, we use a search-island model and four matching models with workers who have heterogeneous skills and entitlements to government benefits. When there is higher turbulence, in the sense of worse skill transition probabilities for workers who suffer involuntary layoffs, high go...
A representative family model with indivisible labor and employment lotteries has no labor market frictions and complete markets. Nevertheless, its aggregate responses to an increase in government supplied unemployment insurance (UI) and to an increase in microeconomic turbulence are qualitatively similar to those in two macromodels with labor mark...
In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes’ law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood...
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state space system for a vector of observables. An associated state space system (A,ˆB,C,ˆD) determines a vector autoregression for those same observables. We present a simple condition for checking when these...
Adding generous government supplied benefits to Prescott's (2002) model with employment lotteries and private consumption insurance causes employment to implode and prevents the model from matching outcomes observed in Europe. To understand the role of a 'not-so-well-known aggregation theory' that Prescott uses to rationalize the high labour supply...