"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.

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.

Neil Wallace | Macro Paper Warehouse

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

Some Unpleasant Monetarist Arithmetic