Can PPP adjusted values be compared over time?

Question

I'm a little baffled about this:
Let's say I want to compare the average income of 2 countries, A and B. Of course I'm interested in the real income so I adjust to PPP using the big mac index of that given year (dividing the average salary by some constant).
Now I do it again, but 10 years later (with the big mac index of t = 10).

Question -
Can I compare the adjusted average salary of country A, t=0  to the adjusted average salary of country A, t=10?

One can argue that no, because the index used for PPP adjustment changed over time, so we need to take account for this. That's why when you adjust for inflation you have specify to which year the prices have been fixed.
You can't compare a real salary adjusted to 2003 prices to a real salary adjusted to 2013 prices.

My logic says yes, because assuming that McDonalds hasn't changed their Big Mac over the past 10 years, the unit of choice remained that same - one delicious burger and it's NOT like adjusting to inflation (in which you have to randomly assign a base year).

Alecos Papadopoulos · Accepted Answer

There are two questions here:

Whether it is meaningful to compare PPP-adjusted values intertemporaly

Whether the "Big Mac" index is a good index for PPP-adjustment.

I will occupy myself with the first question.
Why are we doing PPP-adjustment? We do it to make inter-country comparisons against a benchmark country (usually the US). So this country's magnitude remains unadjusted. Note that what we adjust is nominal magnitudes not "real" ones (that are magnitudes adjusted of in-country inflation).
So at time $t$, and using country $A$ as the benchmark, we can obtain the PPP-wage of country $B$, say $bar w_{B|A}(t)$. We could think of that as "I live in country B. My living standard at time $t$ is as if I was living in the benchmark country $A$ and my wage was $bar w_{B|A}(t)$". And comparing that to the actual (nominal) average wage in country $A$, $w_A(t)$, we get a measure of the living standards in country $B$ compared to those in the benchmark country $A$.
Consider now the PPP-adjusted wage from the same country at time $t+k$. It says " I am living in country B in period $t+k$. My living standard at time $k+t$ is as if I I was living in the benchmark country $A$ and my wage was $bar w_{B|A}(t+k)$".
It is evident that in order to meaningfully compare $bar w_{B|A}(t)$ and $bar w_{B|A}(t+k)$, we must deflate the latter by the price deflator of the benchmark country A, covering the period $(t,, t+k)$. Doing that, makes the two comparable.
But the main purpose of PPP-adjustment is inter-country coparisons, not same-country intertemporal comparisons. By considering the ratio in two different time periods,
$$frac{bar w_{B|A}(t)}{ w_A(t)},qquad frac{bar w_{B|A}(t+k)}{w_A(t+k)}, $$
we can see whether living standards have converged or diverged.
A discussion on recent PPP issues can be downloaded here.
A visual tool can be accessed here.

luchonacho · Answer

As you can see from the official dataset, the index changes over time. Therefore, by comparing a variable $x$ in two time periods using a different index for each period, the total change is a combination of changes in the variable $x$ and changes in the index. In other words, you are comparing:

$$ frac{x_0}{p_0} text{ versus } frac{x_{10}}{p_{10}} $$

From the above you cannot tell how much of the difference is due to changes in $x$ and in the index, $p$.

$$ frac{x_0}{p_0} text{   versus   }  frac{x_{10}}{p_{10}} $$

From the above you cannot tell how much of the difference is due to changes in $x$ and in the index, $p$.

Can PPP adjusted values be compared over time?

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