<p>As you can see from the <a href="http://infographics.economist.com/2017/databank/BMFile2000toJul2017.xls" rel="nofollow noreferrer">official dataset</a>, 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 $x$ <strong>and</strong> changes in the index. In other words, you are comparing:</p>

<p>$$ \frac{x_0}{p_0} \text{   versus   }  \frac{x_{10}}{p_{10}} $$</p>

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

CC BY-SA 3.0
2017-08-21T12:00:50.727Z
2017-08-21T12:06:24.320Z
2017-08-21T12:06:24.320Z
luchonacho
<p>There are two questions here:</p>
<ol>
<li><p>Whether it is meaningful to compare PPP-adjusted values intertemporaly</p>
</li>
<li><p>Whether the &quot;Big Mac&quot; index is a good index for PPP-adjustment.</p>
</li>
</ol>
<p>I will occupy myself with the first question.</p>
<p>Why are we doing PPP-adjustment? We do it to make inter-country comparisons <em>against a benchmark country</em> (usually the US). So this country's magnitude remains unadjusted. Note that what we adjust is <em>nominal</em> magnitudes not &quot;real&quot; ones (that are magnitudes adjusted of in-country inflation).</p>
<p>So at time <span class="math-container">$t$</span>, and using country <span class="math-container">$A$</span> as the benchmark, we can obtain the PPP-wage of country <span class="math-container">$B$</span>, say <span class="math-container">$\bar w_{B|A}(t)$</span>. We could think of that as &quot;I live in country B. My living standard at time <span class="math-container">$t$</span> is as if I was living in the benchmark country <span class="math-container">$A$</span> and my wage was <span class="math-container">$\bar w_{B|A}(t)$</span>&quot;. And comparing that to the actual (nominal) average wage in country <span class="math-container">$A$</span>, <span class="math-container">$w_A(t)$</span>, we get a measure of the living standards in country <span class="math-container">$B$</span> compared to those in the benchmark country <span class="math-container">$A$</span>.</p>
<p>Consider now the PPP-adjusted wage from the same country at time <span class="math-container">$t+k$</span>. It says &quot; I am living in country B in period <span class="math-container">$t+k$</span>. My living standard at time <span class="math-container">$k+t$</span> is as if I I was living in the benchmark country <span class="math-container">$A$</span> and my wage was <span class="math-container">$\bar w_{B|A}(t+k)$</span>&quot;.</p>
<p>It is evident that in order to meaningfully compare <span class="math-container">$\bar w_{B|A}(t)$</span> and <span class="math-container">$\bar w_{B|A}(t+k)$</span>, we must deflate the latter by the price deflator <em>of the benchmark country A</em>, covering the period <span class="math-container">$(t,\, t+k)$</span>. Doing that, makes the two comparable.</p>
<p>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,</p>
<p><span class="math-container">$$\frac{\bar w_{B|A}(t)}{ w_A(t)},\qquad \frac{\bar w_{B|A}(t+k)}{w_A(t+k)}, $$</span></p>
<p>we can see whether living standards have converged or diverged.</p>
<p>A discussion on recent PPP issues <a href="https://www.princeton.edu/%7Edeaton/downloads/Deaton_Aten_Trying_to_understand_ICP_2011_V5.pdf" rel="nofollow noreferrer">can be downloaded here.</a></p>
<p>A visual tool <a href="https://ourworldindata.org/what-are-ppps" rel="nofollow noreferrer">can be accessed here.</a></p>

CC BY-SA 4.0
2020-12-05T16:51:29.153Z
2020-12-05T16:51:29.153Z
Alecos Papadopoulos
<p>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).</p>

<p>Question -
Can I compare the <strong>adjusted</strong> average salary of country <strong>A, t=0</strong>  to the <strong>adjusted</strong> average salary of country <strong>A, t=10</strong>?</p>

<p>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.</p>

<p>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).</p>

CC BY-SA 3.0
2017-08-22T12:20:20.970Z
Is the answer what you are looking for? If not, let me know.
luchonacho
CC BY-SA 4.0
2018-11-15T02:35:29.213Z
Even if the Big Mac hasn’t changed over time, the social meaning of the Big Mac has. Consider the Big Mac or Play Station PPP commodity bundle index of 1789?
Samuel Russell
<inflation><time-series><purchasing-power-partity>
Can PPP adjusted values be compared over time?
RiskyMaor
# Can PPP adjusted values be compared over time?

(Asked by: username_0 on 2017-08-21)

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).

**Tags:** inflation, time-series, purchasing-power-partity
> **Comments:**
> **username_1**: Is the answer what you are looking for? If not, let me know.  
> **username_2**: Even if the Big Mac hasn’t changed over time, the social meaning of the Big Mac has. Consider the Big Mac or Play Station PPP commodity bundle index of 1789?  

---

## 2 answers

### Answer by username_3 on 2020-12-05. Score: 3 | Accepted answer

There are two questions here:

1. Whether it is meaningful to compare PPP-adjusted values intertemporaly
2. 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.](https://www.princeton.edu/%7Edeaton/downloads/Deaton_Aten_Trying_to_understand_ICP_2011_V5.pdf)

A visual tool [can be accessed here.](https://ourworldindata.org/what-are-ppps)


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### Answer by username_1 on 2017-08-21. Score: 2

As you can see from the [official dataset](http://infographics.economist.com/2017/databank/BMFile2000toJul2017.xls), 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, $p$.


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