I am trying to estimate a simple Cobb-Douglas production function $Y=AL^{\alpha}K^{\beta}$ on US data and get an unrealistic estimate of $\alpha$ and a high p-value for $\beta$. Structure of regression is as follows:
$\frac 1 Y \frac{\mathrm dY}{\mathrm dt} = \frac 1 A \frac{\mathrm dA}{\mathrm dt} + \alpha \frac 1 L \frac{\mathrm dL}{\mathrm dt} + \beta \frac 1 K \frac{\mathrm dK}{\mathrm dt}$
and assuming technological growth constant:
$\text{growth}_Y = a_0 + \alpha\cdot \text{growth}_L + \beta\cdot \text{growth}_K$
I have the following output of linear regression in R:
\begin{array}{lllll} &\text{Estimate}\quad & \text{Std. error}\quad & \text{t value} & \mathrm{Pr}(>|t|) \\ \text{(Intercept)}\ & 0.008256 & 0.006070 & 1.360 & 0.186 \\ growth_L & 1.388552 & 0.283867 & 4.892 & 5.47\mathrm e^{-05}\ ^{***} \\ growth_K & 0.194165 & 0.255572 & 0.760 & 0.455 \\ \\ R^2 = 58\% \end{array}
Estimate for the coefficient in front of $\text{growth}_L$ ($\hat\alpha$) seems unrealistically high (1.388552) and estimate for coefficient for $\text{growth}_K$ ($\hat \beta$) has high p-value (0.455).
Before running the regression I excluded outliers (observations outside 2.5% and 97.5% for growth_gdp
, growth_L
and growth_K
).
I also checked correlation between growth_L
and growth_K
and it is 42% which is not that high to impact stability of coefficients of the regression that much.
Unfortunately I could not find a simple and reproducible analogue of the above analysis.
My questions are the following:
- Is there an empirical analysis of simple Cobb-Douglas function producing realistic estimates of coefficients? So that I would understand my key mistakes
- If not, what would be the simplest form of production function which could be supported by empirical analysis?
P.S. For the full reproducibility of the analysis below is more info on data and R code used in estimation of the coefficients. I take data from OECD Economic outlook database
Variables used: GDPV – states for Real GDP, HRS states for hours worked per worker, LF – states for number of workers in Economy, KTPV states for productive capital stock. I calculated L as $LF*HRS$
Full R code and the input data set can be found at pastebin.