q5
Kewei Hou,Haitao Mo,Chen Xue,Lu Zhang 2018
This 98 page article can be found here
The paper looks at a macroeconomic equations derived by Cochrane 1991 to determine Tobin's q. Tobin follows work by Kaldor 1966 on valuation and growth.
Growth model: the Solow-Swan Model 1956
Described here. The Solow-Swan model was chosen for its mathematical tractability and its ability to explain catch up growth. It assumes that output $y$ is a function of capital $K$ and labour $L$, the latter is made efficient through advancement $A$.
$$Y = K^\alpha (AL)^{1-\alpha}$$
with $A = A_0 e^{gt}$, $L = L_0 e^{nt}$
The stock of Kapital entail a proportional cost of depreciation $d$, and a proportion $s$ of output $Y$ is used for investment.
Output per person $$ y = Y/(AL) = k(t)^\alpha$$
Kapital per unit of labour then converges towards an optimal value $$k^ = \left(\frac{s}{n+g+d}\right)^{\frac{1}{1-\alpha}}$$
with $$\alpha = \frac{r K}{Y} = {K \frac{\partial K}{\partial Y}}{Y}$$
This model used to be used to explain the post war rapid catch up of Germany and Japan towards US output per worker. However, people now talk of conditional convergence* as institutions have to support the capitalistic enhancement of output per workers found in the leading economy.
People also refer to catch-up growth for a less developped country using arbitrage of known costs of production as Riccardian growth, where $k(t)$ increases towards its equilibrium value, whereas growth occuring at the frontier and causing creative destruction is called Schumpetarian growth is due to applicable technological progress $n = \frac{d \ln A(t)}{dt}$.
We saw such a catch-up growth happen in China in the years of 8% growth, with government instructing commercial banks how much to lend every year, and the private sector effectively allocating the capital to enhance production. This growth is now fading and there are questions on the level of profitability and depreciation cost of the later infrastructure investments.