# How to calculate the average wage increase?

What is the average wage increase and how does one calculate it? Gottfries (2013, p. 166) refers to the following formula as the "average wage increase:"

$$\frac{\Delta W_t}{W_{t-1}}$$

If the above formula is meaningful, then my question is more a clarification about terminology and notation.

As to terminology, what is a more popular way to refer to this equation other than the average wage increase?

As to notation, Gottfries refers to $W$ as the "average wage level," but what do the other symbols mean? Is it safe to assume the expressions $W_t$ and $W_{t-1}$ refer, respectively, to the average wage levels at times $t$ and $t-1$? What then does $\Delta W_t$ represent? Is $\Delta W_t$ the difference in average wage levels at times $t$ and $t-1$ (i.e., $\Delta W_t = W_t - W_{t-1}$)?

I think this question is worth asking since 1) there has to be a more popular way to refer to this equation (Gottfries book was all that came up when I Googled "average wage increase") and 2) I don't want to assume, as far as notation goes, more than I have to (Gottfries doesn't define these symbols).

• I would agree that $\Delta W_t = W_t - W_{t-1}$ makes sense in this context. A problem comes when the workers change, so for example every continuing worker could see a positive wage increase individually but if the retiring workers are paid more than the new workers then the average wage need not change – Henry Aug 8 '16 at 21:45

This is a very standard % change over time formula.

It is simply: Change Between Years / Original Value

$ΔW_t$ means the change in wage from year $t-1$ to year $t$ (where $t$ represents an arbitrary amount of time). You can easily calculate that by: $ΔW_t=W_t−W_{t−1}$.

Thus it is simply saying % change over time is $\frac{New - Old}{Old}$.

Middle school math with more symbols.

So I think you've got it right on the $\Delta$ notation. So the difference in wages between those two periods normalized by the first period will give you something that we can call increase. The reason it's `average' is simply because W is an average.

To my knowledge, there is no popular equation with that name as "average increase" will be so context specific.

This equation is commonly named wage growth rate (in discrete time) in its simplest form (the difference between two consecutive periods). Your notations understanding is correct.

"average wage increase" because $W$ is an "average level" by definition.

I do not know of any standardised formula for calculating the average wage increase. But using some basic Mathematics, I devised this little formula that should work - at least at a basic level:

Let: a = previous wage b = current wage t = time

Increase = (b-a)/t

Note that the t **is only required if you want an increase per unit of time given. **

However, in order to get the average wage increase, we should find the median (rather than the mean, as the median isn't affected by the skewness of data):

Let: n = total number of values

median = n/2

If we then use this result as an ordinal (placement) number to find which value in an small-to-great organised set of data. This correlating value is our median.

Repeat this for both a and b and then apply the other, above formula to find the average wage increase.

But, to be even more accurate you could use grouped data and then interpolate to find the median. In this case I shall link to an external method as it is very lengthy, but is very useful for accuracy reasons, as it allows you to use grouped data that in turn, allows for much larger quantities of data to be processed. This seems to have a good method that I would recommend. I don't recognise the formula you listed, but I would be great fun if you could explain it in greater detail for me. Hope this helps!