Gary D. Hansen | Macro Paper Warehouse

The Inflation Tax in a Real Business Cycle Model

Cooley and Hansen introduce money into a real-business-cycle model – Hansen’s (1985) indivisible-labor economy with employment lotteries – via a cash-in-advance constraint that applies only to consumption, so that leisure and investment are “credit goods” households can substitute toward when anticipated inflation taxes cash-good purchases. When money grows at any constant rate, however high, the cyclical behavior of the real economy – the standard deviations and output correlations of consumption, investment, hours, and so on – is identical to the real model without money at all, because higher anticipated inflation only lowers the steady-state levels of these variables, not their business-cycle comovement; a money supply that instead grows erratically (calibrated to postwar U.S. M1 behavior) does measurably alter the cycle, making consumption and prices more volatile and weakening their correlation with output, bringing the model closer to U.S. data. The paper estimates the welfare cost of a sustained 10% annual inflation at about 0.4% of GNP under a quarterly cash constraint (consistent with prior estimates by Fischer and Lucas) or about 0.1% under a monthly constraint, and it finds – and corroborates with cross-country data for 1976-85 – that steady-state employment is lower in higher-inflation economies, an “upward-sloping long-run Phillips curve” result the paper is careful to attribute entirely to the anticipated-inflation tax rather than to any unanticipated-money or sticky-price channel, which the model does not include.

The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard

Hansen and Imrohoroglu build a dynamic general-equilibrium economy – deliberately designed to give unemployment insurance (UI) the most favorable possible conditions – to compute the potential welfare benefits of UI and the optimal replacement ratio, and to ask how sensitive both are to moral hazard. Agents face a stochastic employment opportunity, cannot borrow, have no private insurance, and can self-insure only via a non-interest-bearing asset; a UI program pays a fraction θ (“replacement ratio”) of after-tax labor income to agents not offered work, financed by a balanced-budget labor tax, and moral hazard is introduced by letting agents who reject a work opportunity collect UI anyway with exogenous probability π. With no moral hazard (π=0) and a risk-aversion coefficient of 1.5, the authors find the welfare-maximizing replacement ratio is a high 0.7, and UI can cut the welfare cost of living in this liquidity-constrained economy (relative to the social planner’s optimum) from 0.76% of GNP to 0.29% – a 62% reduction, and in some higher-risk-aversion cases UI can close the gap entirely. But the potential benefits collapse quickly as moral hazard rises: increasing π from 0.05 to 0.10 drops the optimal replacement ratio from 0.6 to 0.2, and for π above roughly 0.25 the optimal UI level is essentially zero; at a representative moral-hazard level (π=0.15) and risk aversion 1.5, introducing UI at even the empirically plausible replacement ratio of 0.5 makes agents worse off than having no UI at all. The paper’s central message is that, at reasonable degrees of risk aversion, realistic replacement ratios above 0.5 are justified only if the UI system’s “work test” (verification that recipients are not shirking available work) is strictly enforced – a finding the authors connect to evidence that formal work-test disqualifications are extremely rare in actual U.S. UI administration.

The Welfare Costs of Moderate Inflations

Extending their 1989 cash-in-advance real-business-cycle model, Cooley and Hansen add distorting taxes on labor and capital income and no-uncertainty perfect foresight to study the fiscal consequences of a policy proposal much discussed at the time: legislating the Federal Reserve to bring inflation to zero. They find that the presence of other distorting taxes roughly doubles the welfare cost of the inflation tax relative to their earlier estimates and reduces the revenue the inflation tax can raise, because higher inflation now interacts with an already-distorted labor-leisure and consumption margin rather than a frictionless one. Permanently reducing inflation from 5%, 10%, or 20% to zero raises welfare by only about 0.33-1.28% of GNP while costing 2.4-7.9% of GNP in lost annuity-value revenue – and if that lost revenue must be replaced with higher labor or capital income taxes, the new policy leaves the economy worse off (by as much as 3.2% of GNP relative to the original inflationary policy) than before the inflation was eliminated, because labor and especially capital taxation are themselves more distorting than a moderate inflation tax. A temporary (rather than permanent) reduction of inflation to zero is worse still: anticipating the return of inflation, households shift investment – a “credit good” untaxed by the cash-in-advance constraint – into the tax-free window, and the resulting intertemporal substitution leaves both consumption and revenue lower in the long run than under the original policy.