# Empirical implementation of Milbourne et al's 2003 model of growth for time series data

I'm interested in testing the relationship of public investment in human capital and infrastructure, and the rate of growth of the GDP for Colombia, during a 20 years period. Given that I'm only an undergraduate student and my knowledge is limited, I found that the closest theoretical model to test this hypothesis is Milbourne, Otto and Voss's "Public investment and economic growth" model, that has this production function:

$$Y_{t}=A_{t}K^{\alpha }_{t}H^{1-\beta }_{t}\prod_{m }^{j=1}(G_{jt})^{\gamma _{j}}(A_{t}L_{t})^{1-\alpha -\beta-\gamma }$$

They use the following regression for economies that have not reached steady state output per capita levels:

$$ln y_{t}-ln y_{0}=a_{0}+a_{1}ln s_{K}+ a_{2} ln s_{H} + a_{3} ln s_{G} + a_{4} ln(n-x+\delta )+ a_{5} ln y_{0} + \epsilon$$

Where y is output per capita, and $s_{i}$ represent the proportion of income dedicated to private capital investment (K), human capital investment (H) and government capital investment (G).

However, they use it on a cross-country study, and I don't know whether this is suitable for a country-specific time series study.

My econometric knowledge is at Gujarati's and Dinardo's level. I know how to estimate ARDL, VAR and VECM models. I would appreciate any advice regarding a time series estimation of this model.