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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.

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