# Estimation of a Non-linear production function with Non-linear least squares

Suppose that you have to estimate a Non-linear production function (for instance a Cobb-Douglas or a CES) by using Non-linear LS (and hence without log-linearization). You have just aggregate time series on GDP at constant prices, the Capital stock at constant prices and the level of Employment. What kind of adjustment should be done to the variable in order to obtain consistent estimation of the parameters?

• NLS is consistent... Under some assumptions. Which is one violated? Are your data nonstationnary? – Bertrand Jan 24 '19 at 15:07
• Yes, they are non stationary. And Capital and GDP are still non-stationary even when differencing. More precisely they are around a decreasing trend! In most European economies. Further when differencing there are a lot of negative values and as far as I know for a non.linear optimization you have to use positive values. – Alessandro Jan 24 '19 at 15:10
• I am not the right person to chat with about nonstationarity. I think that you should not differentiate the variables $x$, but the whole nonlinear relationship $y_t-y_{t-1} = f(x_t;\theta)-f(x_{t-1};\theta)$. Joon Y. Park and PCB Phillips wrote on topics related to your question. – Bertrand Jan 24 '19 at 16:25
• Sorry I deleted my answer because I read your comment about the series not being I(1) so it was not applicable, and I couldn't figure out how to delete it. – user21226 Feb 26 '19 at 2:18