Rules, discretion and reputation in a model of monetary policy

This 1983 Journal of Monetary Economics paper by Robert Barro and David Gordon shows that a monetary authority acting with full discretion each period will generate more inflation on average than one bound by a fixed rule, because private agents rationally anticipate the policymaker’s temptation to spring inflation surprises and build that expectation into wages and prices, so the surprises never systematically materialize and only the extra average inflation remains. The model gives the policymaker a per-period cost, z = (a/2)π² - b(π - π^e), that is increasing and convex in realized inflation π but falls with a positive inflation shock (π - π^e), where the benefit parameter b (varying randomly with mean b̄) captures gains such as reducing unemployment below a distorted natural rate or extracting revenue by depreciating the real value of nominally denominated money and government debt. Under discretion the policymaker minimizes expected cost taking expectations as given, yielding π̂ = b̄/a and, in rational-expectations equilibrium, π^e = π̂, so inflation shocks average zero but expected cost is strictly higher than under the “ideal rule” of zero inflation, which would eliminate the inflation term entirely; that ideal rule, however, is generally not enforceable, because if people expect zero inflation the policymaker’s one-period temptation to cheat, (1/2)(b̄)²/a, exceeds the enforcement available from the mere threat of losing credibility for one period, (1/2)q(b̄)²/a (with q the discount factor, necessarily less than one). The paper’s central extension is to reputational equilibria: given a postulated expectations mechanism under which the private sector reverts to discretionary expectations for one period after any policy violation and then restores trust, the best rule the policymaker can credibly sustain is the constant-inflation rate π* = (b̄/a)(1-q)/(1+q), which is a weighted average of the ideal rule and the discretionary outcome, moving toward discretion as the discount factor falls (e.g., during wars) and toward the ideal rule as it rises. When the benefit parameter and discount factor are instead observed before inflation is set, the best enforceable contingent rule has the policymaker “bite the bullet” with surprisingly low (even negative) inflation when the benefit parameter is low, investing in credibility that is cashed in as surprisingly high, welfare-improving inflation when the benefit parameter is high (e.g., during a war or recession). The authors note their results depend on assuming a fixed one-period punishment interval and flag that varying this interval generates a family of reputational equilibria among which the model, as developed, cannot select.

The Dynamic Impacts of Monetary Policy: An Exercise in Tentative Identification

This 1994 Journal of Political Economy paper by David B. Gordon and Eric M. Leeper proposes a structural vector autoregression (SVAR) that identifies monetary policy shocks by modeling supply and demand simultaneously in the reserves market and, separately, in the M2 market, rather than treating a single monetary aggregate or interest rate as predetermined the way standard Cholesky, nonborrowed-reserves, or federal-funds-rate identification schemes do. In each market a demand equation (the monetary aggregate as a function of its own interest rate, the price level, and output, with the interest elasticity a_1 restricted negative) and a supply equation (the interest rate as a function of the aggregate, the 10-year Treasury yield, and a commodity price index, with elasticity a_4 restricted positive) are estimated jointly by maximum likelihood, identified by two restrictions: private demanders of money observe only the current interest rate, prices, and output within the month (the long-term rate is excluded from demand), while the Federal Reserve observes current financial-market variables (funds rate, 10-year yield, commodity prices) but not current goods-market data (price level, output, unemployment) because of a roughly one-month reporting lag, so those goods-market variables are excluded from the supply/Fed-behavior equation; the goods-market block itself is treated as block-recursive, unaffected contemporaneously by either money market. Using monthly U.S. data over 1982:12-1992:4 with six lags, the estimated interest elasticity of reserves demand is -0.028 (se 0.014) and the reserves supply elasticity is +30.28 (se 10.95); for M2 the demand elasticity is -0.0082 (se 0.0007) and the supply elasticity is +253.84 (se 10.79); the reserves-market model narrowly fails an overidentification test (chi-squared(5)=11.864, p=.04, which the authors describe as “not… a strong statistical rejection”), while the M2-market model comfortably passes (chi-squared(5)=2.715, p=.74). A one-unit expansionary supply shock in the reserves market produces a liquidity effect – the funds rate falls sharply and reserves rise – that lasts about 8 months before the rate climbs back above baseline after roughly two years, with the price level and industrial production rising significantly within about six months and unemployment falling with roughly a three-month lag, responses the authors call “fully consistent with traditional analyses,” in contrast to the liquidity-puzzle and price-puzzle results the paper documents earlier from reduced-form and single-variable-innovation identifications. The analogous M2 supply shock produces qualitatively similar but “less significant” responses, and a regression linking the two shows the M2 supply shock loading on current and lagged reserves supply shocks with R-bar-squared only 0.19, implying that a substantial share of M2 supply-shock variation reflects nonpolicy behavior of financial institutions rather than monetary policy, so the authors caution that inference from M2-based studies “should be drawn cautiously.” Variance decompositions show policy shocks explaining a large share of reserves and funds-rate forecast-error variance on impact but declining quickly, while their share of price-level and output variance rises to roughly 30 percent by three years out. When the same reserves-market model is re-estimated on 1971:1-1979:9 data, the identifying restrictions “fail to identify demand and supply relationships for reserves in the 1970s”: the demand elasticity flips to the wrong sign (+0.0069) and neither elasticity differs significantly from zero, which the authors attribute to a different Federal Reserve operating procedure in that earlier period rather than to a flaw in the identification strategy itself, whereas the M2-market model still recovers sensible elasticities in the 1970s but now strongly rejects overidentification (chi-squared(5)=14.958, p=.01).

David B. Gordon | Macro Paper Warehouse

Rules, discretion and reputation in a model of monetary policy

The Dynamic Impacts of Monetary Policy: An Exercise in Tentative Identification