# 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 : $$Y(t) = [K(t)]^{\alpha} [A(t)L(t)]^{1-\alpha}$$

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?

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.
• @DiogenicOrder Yes, you are right in saying that it is calculated ex post. But calculating the residual is an empirical exercise or else you could use your assumed $\gamma_{A}$ for a theoretical model. This holds for any growth rate. If you are looking for instantaneous economic growth rate updates please see “GDP nowcasting”. If you are looking for ways to model technological growth per se, please see some endogenous growth theory models. Commented Mar 12, 2018 at 16:38