An Intertemporal Model of Saving and Investment
National Bureau of Economic Research, 1982 - Econometrics - 32 pages
The standard model of optimal growth, interpreted as a model of a market economy with infinitely long-lived agents, does not allow separation of the savings decisions of agents from the investment decisions of firms. Investment is essentially passive: the "one good" assumption leads to a perfectly elastic investment supply; the absence of installation costs for investment leads to a perfectly elastic investment demand. On the other hand, the standard model of temporary equilibrium used in macroeconomics characterizes both the savings-consumption decision and the investment decision, or, equivalently, derives a well-behaved aggregate demand which, in equilibrium, must be equal to aggregate supply. Often, however, we want to study the movement of the temporary equilibrium over time in response to a particular shock or policy. The discrepancy between the treatment of investment in the two models makes imbedding the temporary equilibrium model in the growth model difficult. This paper characterizes the dynamic behavior of the optimal growth model with adjustment costs. It shows the similarity between the temporary equilibrium of the corresponding market economy and the short-run equilibrium of standard macroeconomic models: consumption depends on wealth, investment on Tobin's q. Equilibrium is maintained by the endogenous adjustment of the term structure of interest rates. It then shows how the equivalence can be used to study the dynamic effects of policies; it considers various fiscal policies and exploits their equivalence to technological shifts in the optimal growth problem
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adjustment costs aggregate demand bonds centralized economy Consider consumption and investment consumption tax crowds out consumption dynamic effects economy is initially endogenous adjustment equations of motion equivalence f(kt Fumio Hayashi gross output h(it/kt h(xt head tax increase in lump-sum increasing function initially in steady installation costs installed capital Intertemporal Model investment decision it(l Jeffrey Sachs kx(l labor loci lump-sum rebates lump-sum taxes marginal utility market economy market-determined interest rate Maurice Obstfeld measured in units Michael Bruno Model of Saving NBER optimal growth model optimal growth problem original path output tax perfectly elastic investment proportional tax Rational Expectations retaining earnings rtBt saving and investment shadow price shocks or policies stable arm standard model standard optimal growth steady-state capital stock structure of interest study the effects tax increase technological shifts term structure Tobin's q transversality condition units of output units of utility various fiscal policies