Golden Rule savings rate
In economics, the Golden Rule savings rate is the rate of savings which maximizes steady state growth consumption in the Solow growth model. It is a term attributedEdmund Phelps who wrote in 1961 that the Biblical adage "do unto others as you would have them do unto you" could be applied inter-generationally inside the model to arrive at some form of "optimum".
In the Solow growth model, a savings rate of 100% implies that all income is going to investment capital for future production, leading to a steady state consumption level of zero. Similarly, a savings rate of 0% implies that no new investment capital is being created, leading to all current capital depreciating without replacement and again a consumption level of zero. Somewhere in between is the "Golden Rule" level of savings, where the savings propensity is set so that per-capita consumption itself is both constant and maximized.
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Derivation of the Golden Rule savings rate
If the other parameters of the Solow model are taken as 'given' (beyond the policy-maker's control), but the savings rate can be set exogenously to maximize steady state consumption the solution can be derived from the steady state equations.
Per capita consumption (c) is the difference between output per capita (y) and savings per capita:
c(k) = y(k)[1 − s]
where s is the propensity to save, c = per-capita consumption and k = the captial/labour ratio (i.e. capital per capita). In the steady state:
Therefore:
Where n is the constant exogenous growth rate, and y* is the steady state output per worker at the golden rule savings rate.
Measuring the Golden Rule savings rate
Since the Golden Rule represents the optimal savings rate to maximize consumption in the economy, an important question for policy-makers is whether the economy is saving too much or too little.
Policy that can change the savings rate
Various economic policies can have an effect on the savings rate and, given data about whether an economy is saving too much or too little, can in turn be used to approach the Golden Rule level of savings. Consumption taxes, for example, may reduce the level of consumption and increase the savings rate, whereas capital gains taxes may reduce the savings rate. These policies are often known as savings incentives in the west, where it is felt that that the prevailing savings rate is "too low" (below the Golden Rule rate), and consumption incentives in countries like Japan where demand is widely considered to be too weak because the savings rate is "too high" (above the Golden Rule)GDP from its own citizens backed only with the promise to pay from future taxation. This does not necessarily lead to capital formation through investment (if the revenue from bond sales is spent on present government consumption rather than infrastructure development, say).
Golden rule taxes within economic models
If consumption tax rates are expected to be permanent then it is hard to reconcile the common hypothesis that rising rates discourage consumption with rational expectations (since the ultimate purpose of saving is consumptiongeneral equilibrium model and Judd (1985) has shown that the optimal tax rate is zero.1986) says that in reaching the steady state (in the short run) a high capital income tax is an efficient revenue source.^ Origin of the term described at newschool.edu
^ Since the golden rule applies only in the steady state an economy not in that state "should not" aspire to the golden rule savings rate, even if the precepts of neo-classical economics growth theory is accepted. For example, the Soviet Union had a famously high savings rate policy in an attempt to "catch up" to the West, the fact that this lowered present consumption below the golden rule rate was justified with the argument that capital accumulation was necessary to reach the world level of industrialization, but that this was a short-term policy of capital deepening.
^ Frankel, D.M (1998), Transitional Dynamics of Optimal Capital Taxation Macroeconomic Dynamics, 2, page 493. (David Frankel writes that a wage tax is the "perfect tool" for influencing the quantity of leisure consumption. Page 495 describes the problem of failing to make government commitment to a tax rate credible).
^ Chamley, C. (1986), Optimal taxation of capital income in general equilibrium with infinite lives. Econometrica 54. Chamley writes that before reaching the golden rule steady state capital income taxes are efficient in the sense that they do not promote deadweight loss through intertemporal consumption substitution.
^ Judd, K.L. (1985), Redistributive taxation in a simple perfect foresight model. Journal of Public Economics 28, page 59.
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