Library for solving, simulating, and estimating the Solow (1956) model of economic growth.
The following summary of the Solow model of economic growth largely follows Romer (2011).
The Solow model of economic growth focuses on the behavior of four variables: output, Y, capital, K, labor, L, and knowledge (or technology or the "effectiveness of labor"), A. At each point in time the economy has some amounts of capital, labor, and knowledge that can be combined to produce output according to some production function, F.
Y(t) = F(K(t), A(t)L(t))
where t denotes time.
The initial levels of capital, K0, labor, L0, and technology, A0, are taken as given. Labor and technology are assumed to grow at constant rates:
Ȧ(t) = gA(t)L̇(t) = nL(t)
where the rate of technological progrss, g, and the population growth rate, n, are exogenous parameters.
Output is divided between consumption and investment. The fraction of output devoted to investment, 0 < s < 1, is exogenous and constant. One unit of output devoted to investment yields one unit of new capital. Capital is assumed to decpreciate at a rate 0 ≤ δ. Thus aggregate capital stock evolves according to
K̇(t) = sY(t) − δK(t).
Although no restrictions are placed on the rates of technological progress and population growth, the sum of g, n, and delta is assumed to be positive.
Because the economy is growing over time (due to exogenous technological progress and population growth) it is useful to focus on the behavior of capital stock per unit of effective labor
k ≡ K/AL.
Applying the chain rule to the equation of motion for capital stock yields (after a bit of algebra!) an equation of motion for capital stock per unit of effective labor.
k̇(t) = sf(k) − (g + n + δ)k(t)
That's it! The Solow model of economic growth reduced to a single non-linear ordinary differential equation.
Assuming you have pip on your computer (as will be the case if you've installed Anaconda) you can install the latest stable release of solowPy by typing
pip install solowpyat a terminal prompt.
There are a number of example notebooks that demonstrate how to use the solowPy library to solve, simulate, and estimate generic Solow models of economic growth.