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I am not sure about how to decompose the percentage change in the following scenario.

I have data for $2$ time periods, $1990$ and $2007$. Data captures number of employed people in each year.

$1990 : 156,521$ people employed. Out of these $138,332$ are nationals and $18,189$ are immigrants.

$2007 : 234,573$ people employed. Out of these $195229$ are nationals and $39344$ are immigrants.

To find the percentage change in employment I use employment$2007$-employment$1990$ and divide this by employment$1990$. This will give me the percent change in employment from $1990-2007$. I get $49.8$%.

Tricky part:

I am looking to decompose this percent change in employment by nationals and immigrants. That is, what portion of $49.8$% increase can be attributed to nationals and immigrants?

Alessio K
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user508281
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1 Answers1

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You can calculate the percentage change of two measurements as:

\begin{equation} \text{Percentage change} = \frac{\Delta X}{X} = \frac{X_2-X_1}{X_1}\times100\% \end{equation}

where $X_1$ and $X_2$ is the old and new measurement, respectively.

For the overall employment this gives an increase of 49.8% in your case, as you mention. Now you can simply do the same for the national and immigrant group separately:

\begin{equation} \frac{195229-138332}{138332}\times 100\% = 41.1\% \end{equation} and \begin{equation}\frac{39344-18189}{18189}\times 100\% = 116\% \end{equation}

So from this we see that the national and immigrant employments in that period increased by 41.1% and 116%, respectively. Therefore a much larger relative change in new employments is seen in the immigrant group, however the immigrant group has a much smaller population therefore it doesn't affect the total percentage very much.

Mape
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