Specific transversality conditions ensure an economy remains on the saddle path.
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REFUTED
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Economic literature contains conflicting findings regarding transversality conditions, with some models noting that specific conditions help establish unique saddle-path solutions, while others demonstrate that certain fiscal or monetary specifications can cause transversality conditions to fail to ensure a unique path, resulting in a continuum of equilibria.
The present article considers an endogenous growth model in which the service output is used as intermediate good in commodity sector, tax is imposed on manufacturing product and the revenue earned is invested to create human capital. It is shown that there exists a unique, saddle path stable steady-state growth rate of human capital accumulation and a unique growth-maximizing tax rate. The optimal tax rate for the command economy is compared with growth-maximizing tax rate in competitive economy. A numerical analysis shows that the command economy will have a higher growth rate than the competitive economy. An extension of the model where households privately spend for accumulation of human capital yields the same growth rate as that of the command economy of the previous model. JEL Classification: E6, H2, O4
The authors study a simple monetary model with a Ricardian fiscal policy in which equilibria are indeterminate if the monetary policy consists solely of a rule for fixing the short-term interest rate. \textit{T. J. Sergent} and \textit{N. Wallace} [``Rational expectations, the optimal monetary instrument, and the optimal money supply rule'', J. Polit. Econ. 83, 241--254 (1975; \url{doi:10.1086/260321})] first pointed possible indeterminacy of inflation expectations in forward-looking rational expectations models over an open-ended future when a monetary authority uses an interest rate rule. If the fiscal policy adapts itself to the level of the government's debt to ensure that the debt does not grow faster than the interest rate (\textit{T. J. Sargent} [``Beyond demand and supply curves in macroeconomics'', Am. Econ. Rev. Papers Proc. 72, No. 2, 382--389 (1982); \url{http://www.jstor.org/stable/1802363}] coined this as a Ricardian policy), then the transversality condition does not force a unique path since every path automatically satisfies the transversality condition and there is a continuum of equilibria. In standard New Keynesian models, an active monetary policy, by which the short-term nominal interest rate is raised by more than the increase in inflation, leads to a unique path of the linearized system which stays close to the steady state and this approximate equilibrium is selected as the basis for policy analysis. A series of papers have pointed out that the local
Rationality, the premise of economics, is an ideal behavioral norm. In the real world, however, intertemporal decision-making is based on adaptive behavioral principles from companies to individual households. It bases on managerial accounting procedures, whereby action plans are formulated and implemented, differences from actual results are recognized, and revisions accumulate over time. We take the intertemporal decision-making problem of households’ consumption/saving (investment) planning in this paper. And we compare the validity of rationality and adaptability as decision-making principles. First, rational decision-making in the optimal growth model leads to a unique path. However, optimal growth planning is practically unstable on the saddle-point path and can only realize if it assumes rationality leading to perfect foresight. On the other hand, the growth paths guided by budget-controlled adaptive decision-making are diverse and distributed in the myriad around the optimal growth path. This redundancy creates stability in the management and operation of the plan. Because through the trial-and-error process of planning and actual comparison, we can implement a more advantageous plan while allowing for multiple next-best goals, including the optimal growth path. Moreover, the numerical results show that the sequentially adaptive consumption/investment planning is comparable to the optimal growth plan on a social welfare basis calculated by accumulating consumption utility and is practically manageable. For example, paths that exceed 0.9 as a ratio to the optimal growth plan are reachable from the initial planning stage at a ratio of 0.58. Based on the above results, we can now analyze intertemporal economic problems with this realistic, practical, and simple method, replacing dynamic optimization ones.
This paper studies necessity of transversality conditions for the continuous time, reduced form model. By generalizing Benveniste and Scheinkman's (1982) "envelope" condition and Michel's (1990) version of the squeezing argument, we show a generalization of Michel's (1990, Theorem 1) necessity result that does not assume concavity. The generalization enables us to generalize Ekeland and Scheinkman's (1986) result as well as to establish a new result that does not require the objective functional to be finite. The new result implies that homogeneity of the return function alone is sufficient for the necessity of the most standard transversality condition. Our results are also applied to a nonstationary version of the one-sector growth model. It is shown that bubbles never arise in an equilibrium asset pricing model with a nonlinear constraint.
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