Cochrane's 'Determinacy and Identification with Taylor Rules' (Journal of Political Economy, 2011) established three negative results: the Taylor principle does not deliver price-level determinacy in microfounded new-Keynesian models under a Ricardian fiscal regime; the Taylor-rule parameters are not identified in the determinate equilibrium, so Taylor-rule regressions cannot support the claim that U.S. inflation was stabilized around 1980 by a switch from passive to active policy; and determinate new-Keynesian (Ricardian) and fiscal-theory (non-Ricardian) regimes are observationally equivalent without further assumptions, so fiscal-regime tests fail for the same reason as monetary tests. The paper left a coherent set of open questions: what theory can determine the price level in a modern fiat-money economy whose central bank targets an interest rate; whether fiscal-theory (non-Ricardian) models can account for the data and be empirically distinguished from monetary-determinacy equilibria, given their observational equivalence; and whether full-system likelihood methods can overcome the identification problems in order to test for determinacy. It explicitly declines the historical question of what, if not a Taylor-rule regime change, the pre-1980 Taylor-rule regressions measured: 'once a coefficient loses its structural interpretation, who cares how it comes out?' Later literature has made substantial progress — identification-robust determinacy tests, regime-switching estimation of monetary-fiscal policy mixes, a fully developed fiscal-theory research program with empirical accounting, central-bank balance-sheet and informational-friction alternatives — but no accepted resolution exists: regimes remain observationally equivalent without extra assumptions, determinacy tests rest on contested identification assumptions, and competing explanations of the 1980s stabilization coexist. The joint problem — a theoretically coherent and empirically identified microfounded theory of price-level determination — remains open.

Background

In a modern fiat-money economy the central bank sets a short nominal interest rate rather than a monetary quantity, and the classical question 'what pins down the price level?' has no obvious answer. Sargent and Wallace (1975) showed that a pure nominal interest-rate peg leaves the price level indeterminate under rational expectations (expectations of future prices are self-fulfilling). The new-Keynesian model — the standard modern framework with an intertemporal 'IS' consumption Euler equation, a forward-looking Phillips curve from optimizing price-setters with nominal rigidities, and a monetary policy rule — proposed a fix: a Taylor rule in which the central bank raises the nominal rate more than one-for-one with inflation. This 'Taylor principle', formalized as a reaction coefficient ϕπ>1\phi_\pi>1, is said to make the determinate equilibrium unique by rendering all other paths explosive; equilibrium variables 'jump' to the unique locally bounded path. Leeper (1991) classified policy regimes: 'active' monetary policy (a Taylor-principle interest rule) paired with 'passive' (Ricardian) fiscal policy, in which taxes always adjust ex post to validate government debt, versus 'active' fiscal (non-Ricardian) policy, in which the government's debt-valuation equation — the real value of nominal debt equals the present value of expected primary surpluses — itself determines the price level, an idea known as the fiscal theory of the price level. Clarida, Galí and Gertler (2000) gave the story its central empirical support: Taylor-rule regressions with an inflation coefficient below one before 1980 and above one after, interpreted as a shift from indeterminacy to determinacy that conquered U.S. inflation. Canzoneri, Cumby and Diba (2001) proposed an analogous fiscal-regime test. Cochrane (2011) attacked both pillars. First, the Taylor principle's uniqueness requires ruling out explosive inflation or deflation equilibria by assuming the government would follow policies that 'blow up' the economy — threats that violate the model's own assumptions — so inflation is effectively as indeterminate as under a fixed interest-rate target. Second, in the determinate new-Keynesian equilibrium the Taylor-rule coefficient ϕπ\phi_\pi does not appear in the observable equilibrium dynamics: locally bounded equilibrium variables are stationary, so the explosive off-equilibrium behavior that would reveal ϕπ\phi_\pi is never observed, and regression estimates of Taylor rules recover shock processes rather than policy parameters. Third, new-Keynesian (Ricardian, determinate) and fiscal (non-Ricardian) regimes are observationally equivalent — every equilibrium condition holds in each case — so Canzoneri–Cumby–Diba-style fiscal tests fail for the same reason as Clarida–Galí–Gertler-style monetary tests (Cochrane 1998 made the analogous point). The paper concludes by asking what theory can determine the price level 'in an economy like ours', notes that fiscal-theory models solve the determinacy and uniqueness problems at a stroke, and leaves open whether they can account for the data — in the published wording, whether 'the results are the same' — and whether full-system likelihood methods (which in the existing literature impose rather than test determinacy) can ever test it; the historical question of what, if not a Taylor-rule regime change, stabilized inflation in the early 1980s it explicitly declines, since 'once a coefficient loses its structural interpretation, who cares how it comes out?' The question sits at the foundations of monetary economics: every central bank that sets interest rates implicitly relies on an answer to it.

Problem Statement

Construct, and empirically identify, a microfounded theory of price-level determination for a modern fiat-money economy whose central bank targets a short-term nominal interest rate. The theory must uniquely determine the price level — not merely the inflation rate, leaving the initial price level indeterminate as under a pure interest-rate peg — without equilibrium-selection devices that rely on incredible off-equilibrium policy threats; in the source's sense, an assumption used to rule out the alternative equilibria is incredible unless it is a plausible description of what people currently believe the government would do and is not wildly at odds with what governments actually do in similar circumstances. It must also be distinguishable in data from its rivals. Concretely, the source-faithful problem comprises: (i) a positive theory — a fully specified model of monetary and fiscal policy (which may be Ricardian with a selection mechanism, non-Ricardian along fiscal-theory lines, central-bank balance-sheet based, or otherwise) in which the price level is uniquely determined under interest-rate targeting; (ii) an identification and testing methodology — an econometric procedure that can distinguish the candidate mechanisms in actual data, overcoming the observational equivalence between determinate new-Keynesian/Ricardian equilibria and fiscal-theory/non-Ricardian equilibria and the non-identification of Taylor-rule parameters in the determinate equilibrium; and (iii) an empirical accounting — a demonstration that the identified mechanism can account for the data, that is, the joint historical record of inflation, nominal interest rates, and government debt in economies like the postwar United States. The source poses one further issue as an open sub-question whose feasibility it doubts rather than as a required ingredient of an answer: whether full-system likelihood methods, which in the existing literature impose rather than test determinacy, can overcome the identification problems in order to test for determinacy versus indeterminacy. The positive theory, the identification methodology, and the empirical accounting are posed jointly and must be coherent in accounting for what anchors the price level under interest-rate targets.

References

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