Thomas J. Sargent | Macro Paper Warehouse

Time Averaging Meets Heckman, Lochner, and Taber and Ben-Porath

Wed, 01 Jan 2025 00:00:00 +0000

Research question and motivation: How does endogenizing retirement (career-length) choice change the labor-supply and human-capital implications of the canonical Heckman, Lochner, and Taber (1998a, HLT) life-cycle general-equilibrium model, and what does this imply for social-security reform, labor-income taxation, aggregate labor-supply elasticities, and inequality? HLT already contains two ingredients of Ljungqvist-Sargent (2006) “time-averaging” models — credit markets and within-period labor-supply indivisibilities — but shuts time-averaging down by assuming inelastic labor supply until a mandatory retirement age of 65. The authors “activate” time-averaging by letting workers choose when to retire and by adding a pay-as-you-go social security system. This matters because the micro-foundation of the high aggregate labor-supply elasticity that Prescott invoked (switching from Rogerson’s employment lotteries to time-averaging) hinges on whether workers sit at corner solutions for career length.

"Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule

This paper studies, within a simple “ad hoc” macroeconomic model not derived from individuals’ and firms’ optimizing behavior but built to resemble the macroeconometric models of the time, how the choice between a money-supply rule and an interest-rate rule as the monetary authority’s policy instrument affects the economy, following the framework of Poole (1970). It compares two ways the public’s price expectations might be formed: fixed autoregressive (“adaptive”) schemes, and rational expectations in the sense of Muth, in which expectations equal the model’s own true conditional forecast, including full knowledge of whatever policy rule is in force. Under adaptive expectations the paper reproduces Poole’s finding that whether a money-supply rule or an interest-rate rule is preferable is a genuinely empirical question, turning on the full set of the model’s parameters, including the covariance structure of the shocks. Under rational expectations the results are strikingly different: the probability distribution of output turns out to be completely independent of which deterministic money-supply rule the authority follows, because output responds only to unanticipated price surprises in the paper’s Lucas-type aggregate-supply schedule, so only unanticipated money matters; if the policy loss function is a discounted quadratic in output and the price level, the optimal deterministic money rule is simply the one that sets the expected future price level equal to its target; and if the authority instead pegs the nominal interest rate period by period, no matter how that peg varies over time, the model cannot determine a unique equilibrium price level at all – reviving, in a fully dynamic setting, the Wicksellian price-level indeterminacy earlier known only from static, flexible-price analysis. A further section shows that a money-supply rule optimal in the absence of any informational asymmetry between the authority and the public remains optimal, and yields the same expected loss, whether or not such an asymmetry exists, and that actually exploiting a genuine informational advantage is possible only in a limited, subtle way that requires the authority to know precisely how the public’s information differs from its own. The authors close by cautioning that, because the model is admittedly ad hoc, its specific numerical conclusions should not be taken literally, but argue that its two load-bearing ingredients – rational expectations and the Lucas surprise-supply hypothesis – are the parts doing the real work, and that the qualitative contrast between rational and adaptive expectations should survive changes to the model’s other equations.

ABCs (and Ds) of Understanding VARs

This 2007 American Economic Review paper by Fernández-Villaverde, Rubio-Ramírez, Sargent, and Watson asks when the structural economic shocks in a DSGE model’s state-space representation can be recovered from the one-step-ahead forecast errors (“innovations”) of a VAR estimated on the model’s observables — the “invertibility” problem. Writing the model as a state equation x_{t+1} = Ax_t + Bw_{t+1} and observable equation y_{t+1} = Cx_t + Dw_{t+1}, with w_t an i.i.d. Gaussian vector of structural economic shocks, they show that in the square case (number of observables k equals number of shocks m, and D is nonsingular) the VAR innovations equal the structural shocks if and only if the eigenvalues of A − BD^{-1}C are strictly less than one in modulus — a “poor man’s invertibility condition” that can be checked directly from the model’s own matrices without deriving a full VARMA representation. When this eigenvalue condition fails, the VAR instead recovers the model’s “innovations representation,” a distinct state-space system built from the Kalman-filtered state estimate x̂_t = E(x_t|y^t) rather than the true state x_t; because the state cannot then be fully inferred from current and past observables (Σ = var(x_t|y^t) > 0), the variance of the VAR’s innovations strictly exceeds that of the true structural shocks (D̂D̂’ > DD’), and the VAR’s estimated impulse responses can differ sharply — even in sign — from the model’s true responses. The paper illustrates this failure analytically in a permanent-income consumption model (Sargent 1987, chap. XII) calibrated with gross interest rate R = 1.2 and income shock scale σ_w = 1: when only the consumption-income surplus y_t − c_t is observed, A − BD^{-1}C = R > 1, so the eigenvalue condition fails and Σ = σ²_w(1 − R^{-2}) > 0. The resulting VAR — an AR(1) for the surplus — has impulse responses that are “markedly different” from the true model’s: consumption responds with the opposite sign to a VAR shock than it does to the true structural shock, and the surplus response has a positive present value in the VAR representation versus a present value of exactly zero in the true model (which imposes budget balance). The authors note that observing additional variables (such as consumption, income, or the value of accumulated assets) can restore invertibility, and conclude that despite this problem VARs remain informative about the shapes of impulse responses that theories should be disciplined to match, even when they cannot recover every structural shock exactly. The analysis is purely theoretical and methodological — it presents no empirical VAR estimation or Monte Carlo evidence — and is restricted to the square case (k = m) with Gaussian shocks and the time-invariant (steady-state) limits of the Kalman filter.

Drifts and volatilities: monetary policies and outcomes in the post WWII US

This 2005 Review of Economic Dynamics paper by Timothy Cogley and Thomas J. Sargent extends their earlier Cogley-Sargent (2001) time-varying-parameter VAR (TVP-VAR) of postwar U.S. inflation, unemployment, and the 3-month Treasury bill rate by adding stochastic volatility to the innovation covariance matrix, directly responding to Sims (2001) and Stock (2001)’s criticism that CS2001’s finding of drifting VAR coefficients could be an artifact of omitted heteroskedasticity. Using quarterly U.S. data from 1948:Q1-2000:Q4 (the first ten years used only to initialize priors, with estimation reported for 1959:Q1-2000:Q4), the authors estimate a trivariate reduced-form VAR – no structural shocks are identified – in which the coefficient vector theta_t follows a driftless random walk truncated to stationary draws and the innovation covariance R_t = B^{-1} H_t B^{-1’} has diagonal elements H_t that themselves evolve as independent log-random walks, all estimated via a Metropolis-within-Gibbs MCMC sampler (100,000 draws, 50,000 burn-in, every 10th draw retained). They find the drift in theta_t survives the addition of stochastic volatility: the posterior for the innovation-variance matrix Q governing the coefficient process is shifted well to the right of the prior, with even its smallest posterior value about three times the trace of the prior mean, and this drift is low-dimensional, with the first two principal components of the smoothed coefficient path accounting for 83% of its variation and the first component loading heavily on inflation dynamics. Separately, the paper documents a “Great Moderation” decline in shock volatility, with the unemployment innovation standard deviation falling by roughly 40% from peak to trough in the early 1980s and about 60% overall since the late 1950s (approximate readings from the paper’s figures). Core inflation (the TVP-VAR’s implied long-run mean of the inflation process) rises from roughly 1.5% in the early 1960s to about 8% in the late 1970s before falling to 2.5-3.5% in the 1980s-1990s, tracking the estimated natural rate of unemployment closely (correlation 0.748); inflation persistence, measured by the normalized spectrum of inflation at zero frequency, sweeps upward through the late 1960s and stays high through the 1970s – with two-sigma error bands placing it roughly between 2 and 10 at its peak, comparable to a univariate AR(1) coefficient of 0.85-0.97 – then falls sharply after 1980, with inflation “approximately white noise” in the early 1960s and again in the mid-1990s; core inflation and persistence are strongly positively correlated (0.92), a pattern the authors describe as “problematic” for escape-route learning models that predict persistence should rise, not fall, along the transition from high to low inflation. Using a time-varying forward-looking Taylor rule, they estimate that the probability policy was “activist” (a coefficient on expected inflation of at least one) rose from 0.208 in 1975 to 0.919 in 1985 and 0.941 in 1995, with activism inversely correlated with both core inflation (-0.79) and persistence (-0.72) – corroborating Clarida, Gali and Gertler’s (2000) conclusion that policy was passive in the 1970s and activist for most of the Volcker-Greenspan era. Finally, classical stability tests (Andrews sup-LM, Nyblom-Hansen, and Andrews sup-Wald) mostly fail to reject time-invariance of theta_t at conventional significance levels, but Monte Carlo simulations show these tests have low power (as low as 0.076-0.252 in several specifications) against the kind of continual drift the model describes, so the authors argue that failure to reject should not be read as evidence against drift.

Israel 1983: A bout of unpleasant monetarist arithmetic

Israeli inflation, which had held near 130 percent annually for the previous five years, suddenly jumped to about 400 percent in October 1983 – a jump economists had found puzzling because it was not accompanied by any significant contemporaneous rise in the government deficit or expenditures, nor by any intensification of the Israeli-Arab conflict that had driven earlier inflation surges. Sargent and Zeira argue the jump was instead caused by a different event that also occurred in October 1983: a massive government bailout of Israeli bank shareholders, after it emerged that the country’s major banks had illegally manipulated their own share prices for years and could no longer sustain them. The government’s “Bank Shares Arrangement” (the “Hesder”) promised to repurchase the affected shares at their pre-collapse, dollar-indexed value, but only after four or five years (in 1987 or 1988); the paper estimates this implicitly increased government obligations overnight by roughly $5.44 billion, close to a quarter of 1983 Israeli GDP. Because forward-looking Israelis understood that such a large future payment would eventually be financed, at least partly, by printing money, the paper argues they reacted immediately by reducing their money holdings, driving up the price level right away – a textbook instance of the “unpleasant monetarist arithmetic” of Sargent and Wallace (1981), in which money demand’s negative dependence on expected inflation means anticipated future monetary expansions cause inflation to rise well in advance of the expansion itself. The paper first uses a standard inflation-tax model to account for Israel’s earlier inflation history (rising from under 10 percent before 1967 to roughly 40 percent after the 1973 war and 120 percent after a 1978 financial liberalization), estimating that money creation financed only about a third of the large fiscal deficits of the 1970s and early 1980s, with debt issuance financing the rest. It then documents the bank-share episode in detail, showing from the yield differential between the (now dollar-indexed) bank shares and other safe dollar assets that the public assigned the bailout a probability of roughly 50 percent or more once the arrangement was announced. A calibrated closed-economy Ramsey monetary model, in which a constant monetized deficit is occasionally supplemented by a one-time future payment financed by a monetary expansion, shows that raising the perceived probability of that future payment from a pre-announcement estimate of about 19 percent to roughly 50 percent is sufficient to generate an inflation jump of the same order of magnitude as the one observed, from about 120 percent to between roughly 400 and 700 percent depending on the exact probability assumed. The paper reviews and rejects several competing explanations for the October 1983 jump – an exchange-rate-management story in which reduced depreciation rates were financed by rising public debt, and a story in which inflation rises in anticipation of a future stabilization – arguing that neither fits the timing or the debt and reserve data as well as the bank-bailout channel. The authors conclude that the episode is both a new explanation for a previously puzzling historical event and an unusually clean natural experiment for rational-expectations theory, since the size and approximate timing of the anticipated future government payment were both known with unusual precision at the moment inflation jumped.

Macroeconomic Features of the French Revolution

This paper interprets the French Revolution “from the vantage point of macroeconomic theories about government budget constraints” (p. 474), using two macroeconomic ideas – unpleasant arithmetic and sustainable plans – and three successive models of money as lenses on the same chronology of events. From 1688 to 1788, Britain reformed its institutions to smooth taxes and finance war debt while France defaulted repeatedly, and this asymmetry in “fiscal technology,” not any lack of arithmetic competence among French ministers, produced the fiscal crisis of 1788 that forced Louis XVI to convene the Estates General. The National Assembly’s response – confiscating church lands and issuing assignats redeemable at land auctions – created a “tax-backed money” scheme that functioned much as a real-bills or asset-backed theory of currency would predict: real balances of assignats grew and prices rose only moderately from 1790 through mid-1792. The war that began in April 1792 forced the government to divorce note issues from land sales, converting the tax-backed scheme into a fiat-money scheme whose depreciation accelerated sharply and threatened the inflation-tax base the government depended on. The Jacobins met this threat with a “guillotine-backed currency” of price controls and legal restrictions criminalizing refusal of the assignat at par, a policy episode the paper interprets through legal-restrictions models of currency demand: real balances rose and prices fell even as the government raised immense new issues to finance the war. When military victory removed the rationale for the Terror’s repressive apparatus in mid-1794, the legal restrictions became unenforceable and were abandoned, and the assignat entered a classical Cagan-style hyperinflation in 1795-96 in which real balances collapsed and prices exploded, ending in France’s 1797 default on two-thirds of its debt and a return to a specie standard. Throughout, the authors emphasize that these are not merely their own retrospective interpretations: the revolutionaries themselves debated the same theoretical questions – about backing, forced currency, and the inflationary consequences of deficit monetization – while designing and defending each successive monetary regime.

Some Unpleasant Monetarist Arithmetic

Sargent and Wallace show that even in a fully monetarist economy, a monetary authority that tightens money today while an independent fiscal authority’s deficits are taken as given must finance the resulting growth in interest-bearing government debt with future money creation once the public’s demand for bonds is exhausted, so that tighter money now can mean higher inflation later – and, once money demand depends on expected inflation, can even fail to lower inflation today. Building on Friedman’s (1968) claim that monetary policy cannot permanently control real variables but can control inflation, the authors show that even this narrower claim requires qualification once monetary and fiscal policy are considered jointly. In a model deliberately built on the most unqualified monetarist assumptions available – a quantity-theory demand for base money, a constant real bond return exceeding the economy’s growth rate, and a fiscal authority whose deficit path is fixed independently of monetary policy – they prove that a tighter current monetary policy, financed by additional bond sales, must eventually run into the public’s upper bound on the real stock of bonds it will hold relative to the size of the economy; once that bound binds, the accumulated principal and interest can only be serviced through additional money creation, producing higher inflation than a looser current policy would have. In a second model using a Cagan-style money-demand schedule that depends on expected future inflation, the authors go further, presenting a numerically “spectacular” example in which anticipation of the higher money growth that a tight policy eventually requires raises expected inflation enough to make current inflation and the current price level higher under the tight policy than under a looser one – so tight money can fail to lower inflation even temporarily. The paper’s concluding remarks are explicit that both the interest-rate-exceeds-growth-rate condition and the assumption that the fiscal authority “moves first” are the crucial, and potentially replaceable, hypotheses driving the result, and that monetary policy can still permanently control inflation under an alternative game in which the monetary authority moves first and thereby imposes fiscal discipline – for example, through a fixed exchange rate, a commodity standard, or a binding, permanent money-growth rule.

The Conquest of American Inflation: A Summary

Summarizing Sargent’s “The Conquest of American Inflation,” this essay compares two interpretations of the postwar rise and fall of U.S. inflation, both built around policymakers learning a version of the natural-rate hypothesis but differing in how that learning is modeled. The “triumph of natural-rate theory” story has the government eventually learn the correct rational-expectations version of the theory and simply cease exploiting an illusory long-run Phillips curve trade-off, ushering in the low-inflation “Ramsey outcome.” The essay’s preferred “vindication of econometric policy evaluation” story instead keeps the government using the very Tinbergen-Theil-style econometric procedures Lucas’s Critique condemned – estimating a Phillips curve from recent data and resetting policy accordingly, generating exactly the kind of drifting coefficients Lucas identified as a symptom of policy-dependent behavior but left unexplained. Working through the Kydland-Prescott one-period model, the essay first shows the Nash outcome (positive inflation, unemployment at its natural rate) arises when the government ignores the effect of its rule on expectations, while the Ramsey outcome (zero inflation) arises when it accounts for that effect; it then introduces “self-confirming equilibria,” in which the government’s beliefs about the Phillips curve are validated by the data its own policy generates, reproducing the Nash outcome as a steady state. The essay’s central mechanism is “escape dynamics”: because the government’s learning algorithm discounts older observations (suspecting, incorrectly, that the true relationship is unstable), chance disturbances can occasionally push its estimated Phillips curve toward vertical, triggering a real disinflation whose own resulting data temporarily reinforce that belief – generating, in simulations, long stretches near the efficient Ramsey outcome that “resemble Arthur Burns as well as ones that look like Paul Volcker.” But because the true short-run trade-off never actually disappeared, the same dynamics eventually push the government to rediscover it and drift back toward the high-inflation Nash outcome, so the disinflation is not permanent. The essay closes by stressing this is an exercise in positive, not normative, economics – its simulations do not vindicate the underlying econometric procedures as good policy design – and expresses the explicit hope that the truth is instead the more reassuring “triumph” story, since otherwise “the dynamics governing adaptation threaten eventually to rekindle inflation.”

The Ends of Four Big Inflations

This paper studies the abrupt endings of four hyperinflations that struck Austria, Hungary, Poland, and Germany in the years following World War I, using them as historical “laboratories” for testing the rational-expectations view of inflation against a rival “momentum” view. The momentum view holds that once high inflation becomes embedded in expectations, only a long, gradual, and costly disinflation – with substantial lost output – can bring it down; a contemporary estimate cited in the paper put the cost to the United States at 220 billion dollars of foregone annual GNP for every one-percentage-point reduction in inflation achieved through restrictive policy. The rational-expectations view, by contrast, holds that current high expected inflation reflects the public’s correct reading of the government’s current and prospective monetary and fiscal policy, so that a sufficiently binding, credible change in that policy – a change in regime rather than an isolated restrictive action – can bring expected and actual inflation down quickly and at much lower cost. Each of the four countries ran enormous, persistent budget deficits financed by having the central bank discount treasury bills and expand its note issue at rates that produced monthly, and at times near-daily, price increases; the paper documents this dynamic country by country, drawing on official League of Nations and U.S. Senate compilations of budget, money-supply, price, and exchange-rate data. In every country the hyperinflation ended suddenly, not gradually, once the government simultaneously created or reconstituted an independent central bank legally forbidden from extending further unsecured credit to the government, and moved decisively toward a balanced budget, typically under the supervision of a League of Nations-appointed Commissioner General and backed by an international reconstruction loan. Sargent argues that it was this credible, coordinated regime change – not simply a reduction in the rate of money creation – that stabilized prices and exchange rates within weeks, because it changed the fiscal backing of government notes from worthless treasury paper to gold, foreign exchange, and commercial assets. The paper further shows that in each country the nominal stock of high-powered money continued to grow rapidly, sometimes multiplying several-fold, in the months after stabilization, a fact Sargent reconciles with the quantity theory by distinguishing “backed” from “unbacked” money. Available unemployment data show that stabilization was accompanied by increases in unemployment that Sargent characterizes as comparatively minor next to the “220 billion dollar” tradeoff invoked in contemporary U.S. debate, though he is careful to note that how much of the recorded unemployment reflects the stabilization itself, as opposed to other real dislocations, “cannot be determined.” As a further comparison case, the paper describes Czechoslovakia, which under Finance Minister Alois Rasin adopted a restrictive fiscal and monetary regime immediately after the war and thereby avoided hyperinflation altogether. Sargent concludes that the essential common ingredients ending each hyperinflation were the joint, coordinated creation of a fiscally independent central bank and a credible commitment to balance the budget, and that – while he acknowledges a deeper objection to whether “regime change” is even a coherent concept within a fully rational-expectations model – the four episodes together constitute unusually clean natural experiments in the effects of credible policy commitment on the expected cost of ending inflation.