How is the Solow residual measured? In the Solow model, we have the Solow residual often referred to as the level of technology A.

More particularly : \begin{equation} Y(t) = [K(t)]^{\alpha}  [A(t)L(t)]^{1-\alpha} \end{equation}

Here it is defined as "is the portion of output not explained by the amount of
inputs used in production" though there's an explanation of its fluctuations, I still do not understand how it is calculated.

This paper from the National Bank of Belgium does leave me a bit confused because several measurements are said to be used but it sometimes sounds as if one took the total output for a year and substracted what wasn't explained directly by labour and capital, to obtain the residual?

I'm not really sure how it is measured and where said measurements even come from,

Can someone point me to an answer?

Thanks for your time,

Nate
Below please find a portion of a lecture slide a professor of mine used last year. Please note that $\gamma_{\tilde{y}}$ denotes per-capita output growth, $\gamma_{\tilde{k}}$ denotes per-capita capital growth and $\alpha(t)$ denotes the income share of capital. $R(t)$ - the Solow residual - can then be easily computed.

The production function you have stated was the one we used for this example. So it can be applied here directly.



Source: "Growth and Business Cycles" lecture by Professor Gerhard Sorger, University of Vienna