| Abstract | Classical endogenous economic theory achieves endogenous economic growth rate by optimizing an economic variable based on an exogenous factor growth equation. This endogenous mode of economic growth rate is Semi-Endogenous. This paper provides a method to realize the complete endogenous growth rate, by relaxing the growth equation of exogenous factors and retaining other basic assumptions of classical endogenous economic growth theory. Then,we find that when a factor has the characteristics of reusable, it can endogenous economic growth; at the same time, the allocation of each period in the growth economy is still Arrow-Debreu allocation, and the prices of each period are the same. In addition, under the environment of dynamic stochastic general equilibrium with growth, this paper makes a preliminary study on the response convergence of economic variables, and finds that the economic system is stable under the condition of reasonable parameter assignment. Finally, the general conditions for the existence and uniqueness of endogenous economic growth rate are given.
The theoretical works of endogenous economic growth pioneered by Lucas (1988) and Romer (1990) enlightened contemporary and following economists with the dynamic analysis on studying an economy at macro level. In contrast to Ramsey’s theoretical framework, the theory of endogenous growth innovatively emphasizes that the steady states of an economy are time dependent. However, it is significant to address that both Lucas’ and Romer’s works imply that a production factor grows at a linear rate that is exogenously given. In other words, the growth rate of an economy in their framework exists in a compact and convex set in which economic agents maximize their utilities and result in such an economic growth rate. Furthermore, the growth of such economy exists no matter how economic agents maximize their utilities due to the fact that the minimal value in the compact and convex set exists and is positive. Therefore, the theory of endogenous growth founded by their framework may not be complete, and their framework induces more or less a theory of semi-endogenous growth.
To ensure the uniqueness of economic growth rate, both Lucas and Romer assume that the key production factor (human capital as in Lucas’ work and technology as in Romer’s work) will grow at a linear rate, and this factor is reusable. Given such dynamics, economic agents then maximize their utilities over other controls with the growth rate of human capital or technology given explicitly. Thereafter economic agents utilize the full rank linear equations of all other variables’ growth rates to solve for the unique growth rates of these variables. Generally speaking, the endogenous growth theory constructed by Lucas and Romer relies on an exogenously given growth rate of a factor for the unique existence of the growth rates of other economic variables. Therefore, Jones (1995) believes that Lucas’s and Romer’s works cannot be firmly concluded as endogenous but semi-endogenous growth theory.
Later theoretical works on economic growth are generally twofold. The first ones follow Lucas’ and Romer’s framework without stochastic analysis. The second ones are based on Aghion and Howitte’s (1992) stochastic growth framework. However, both types of theoretical works require given growth rates of some economic factors.
In addition, the theory of endogenous growth requires not only the existence of an economic growth rate but also its uniqueness. In general, the theory of economic growth focuses on an infinite horizon problem of growth, the uniqueness of the steady state growth rate ensures the invariability of interest rate (price) in each time interval. Once proper initial conditions of the economy are given, the uniqueness of the growth rate will resolve the issue that the Arrow-Debrew allocation may be a zero-solution in a time interval (Stockey and Lucas, 1989). Therefore, the uniqueness of the growth rate guarantees that the solutions to an economy on the balance growth path are all interior solutions.
In summary, the completeness of the classic endogenous growth theory can be hardly concluded in the sense that the relevant theoretical works all presumed some (semi-)exogenous positive growth rates of economic factors to ensure the existence of the economic growth rate along the balanced path. However, this study relaxes the assumption on the exogenously given growth rates of economic factors and provides a proof that with some economic factors having the property of being reusable, the growth rate of an economy may still uniquely exist.
Our study relaxes the assumption on the exogenously given growth of an economic factor and finds that keeping other assumptions in the classic endogenous growth theory, as long as a factor is reusable, the economic growth then uniquely exists and is endogenous. Furthermore, the optimal allocation of economic factors in each period is Arrow-Debrew allocation with the interest rate and prices remain invariant. In addition, we catch a glimpse of a dynamics of such an economy in a stochastic setup and briefly discuss the convergence of the economic variables. The analysis shows that the stochastic economy will grow steadily if proper parameters are assigned. Lastly, we discuss the generalized conditions for the existence and uniqueness of the growth in such an economy.
|