Understanding GDP Graphs: Key Considerations and Calculating Average Growth

[ecastro]

Is reading a GDP graph the same as any other graphs? For example, given a certain GDP growth over a certain period of time, the average growth can be calculated as taking the sum of all values and then dividing the sum by the number of data points.

Are there also crucial points to consider, such as the latter GDP values of a certain period of time has the most effect on the GDP growth?

 

[fresh_42]

Well, it always depends on what you want to read from the chart. At least it should be normalized with respect to (the varying) inflation. If not, it might be of questionable value. Then of course one has to keep an eye on the scales, for sometimes logarithmic scales are used. Furthermore those graphs often consist two are more curves to compare the values. However, comparison of two or more different sources does heavily depend on the measurements, e.g. different countries or states may determine their GDP differently.

Averaging is also a tool which should be used wisely. E.g. many monetary values depend on seasons, and if this isn't taken into account, average values can be very misleading.

So it's with GDP charts as with every other chart, too: ask for the quality of data, the deformations, resp. adjustments that have been applied to (or not) to build the chart, determine what it is supposed to display, and make sure beforehand, which dependencies exist between these parameters.

 

[jtbell]

Do you mean a graph like this, that shows the changes in GDP for each year, not the actual value of GDP for each year?

For example, given a certain GDP growth over a certain period of time, the average growth can be calculated as taking the sum of all values and then dividing the sum by the number of data points.

That gives you what the article linked below calls the arithmetic mean return (AMR). Most people don't use it because if you apply that % change for each year (i.e. as a constant growth rate) you don't get the same final value for the same initial value, as with the original data. To get that property, you have to use the compound annual growth rate (CAGR).

https://en.wikipedia.org/wiki/Compound_annual_growth_rate

To calculate the CAGR, you need to know the initial and final actual values of GDP.

 

[ecastro]

I am just comparing a GDP data from two different sources (one from the World Bank, and the other from the local government), but for the same country. The World Bank has the data in current US Dollars, while the data from the local government is in GDP per Capita (constant 2000 prices). It would seem that I need to convert one of them to the other.

How about trends? If there is an increasing trend from 10 to 15 years, and there's a drop for 3 years, what can be told about the GDP growth?

 

[EnumaElish]

There are 2 issues. First, the graphs have different values (height on the y-axis) as they are denominated on different units. This can be at least partially resolved by converting each series into an index with year 2000 as the base period (i. e. "2000=100"). The second issue is they are not single-variabled functions of one another. That is there are additional time-dependent variables to consider.

The exact nature of the series issued by the local government (call it Series B) is not clear from your post. We know that the series B is per capita and in constant currency (year 2000). But the question "is series B denominated in year-2000 US dollars per capita or or year-2000 units of the local currency (call it pesos)?" is not addressed. Let us assume it is pesos. Let A(t) be the value of the World Bank series at time t and let B(t) be the value of the government-issued series at t. Let P(t) be the population and e(t) the pesos-per-dollar exchange rate. Let r(t) be the price level at t relative to the price level in year 2000. Then B(t) = [A(t) e(t)/P(t)]/r(t). As you can see there are 3 additional time-dependent variables to consider.

If the exchange rate is free-floating, e(t) = r(t) e(2000) can be expected, so e(t)/r(t) = e(2000) and the translation reduces to B(t) = A(t) e(2000)/P(t). As a further simplification let us consider "no significant change in population," implying P(t) = P(2000). Now the formula is B(t) = A(t) e(2000)/P(2000). Finally let's apply a logarithmic function, so Log B(t) = Log A(t) + C where C is the constant Log e(2000) - Log P(2000).

If these assumptions are nearly accurate, the Log series should be an almost-linear transformation of each other, the vertical distance between them nearly a constant in each and every period.

 

[EnumaElish]

As for trends, I'd consider looking at "X"-year moving averages. You can try X's of different lengths, 5-year or 10-year. That way you'd be averaging out short-lived idiosyncratic bumps while capturing a longer cyclical element.