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I came across this question where the GDP for the years 1995-1997 is given.

  • Then I was asked to compute the growth rate every year which I'm aware of.
  • The next question was to compute the average which is simple divison.
  • However, the final question asks me to predict the GDP for the year of 2012 using the average rate of GDP between 1995-1997.

I understand the tedius way to go about solving this problem is to keep computing the GDP from 1997 all the way upto 2012. Is there a simplar way I can determine the GDP of a particular year, using an average growth rate?

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  • $\begingroup$ Could you show us the first steps of your "tedious way", say to obtain predictions for 1998 and 1999. This may help us to understand why you may be finding it difficult to go directly to the 2012 prediction. $\endgroup$ – Adam Bailey Oct 22 '18 at 20:17
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Generic growth formula:

$$\frac{V_t}{V_{t_0}} = (1 + r)^{t-t_0}$$

Solving for $r$ will give you a growth rate in terms of the units of $t$ and $t_0$. In your example, that's years.

You currently have a growth rate and the value in 1997. Projected value in 2012 would be

$$V_{2012} = V_{1997} \cdot (1 + r)^{2012-1997} = V_{1997} \cdot (1 + r)^{15}$$

This assumes that $r$ is the decimal (not percentage) average growth rate that you calculated.

I'll leave it up to you whether your original calculations of the growth rate are consistent with this method of calculating the growth rate. If not, you may want to recalculate it.

The formula that I gave is a generic one. While you may be applying it to GDP, this will work for the growth rate of any variable. That's why I used $V$ for value rather than a variable more commonly recognized as representing GDP.

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This answer does not directly respond to your question, but I'm concerned that you're treating the calculation of the average growth rate too simplistically. You said it is "simple division", by which I assume you added the two growth rates together and divided by 2.

For a first pass at showing why that method is incorrect, consider the following scenario. In year 1 an economy grows by 10%, increasing an index of GDP from 100 to 110. In the second year, the economy shrinks by 10%, which reduces the index from 110 to 99 (as 10% of 110 is 11). Thus, over the two years, the economy has shrunk from 100 to 99.

If you add the two growth rates and divide by 2, you get 0%, but the average growth rate should actually be negative.

When looking for a growth rate, you are assuming that the trend of GDP is exponential. Thus, one way to get an average growth rate is to compare the start value with the end value. In my example, the growth rate would be $r$ in the following equation: $$99=100(1+r)^2$$ which solves out to be approximately $r=-0.5\%$.

However, an advanced economist would know that merely relying on the start and end values overlooks all the important data in between, furthermore, the start or end value may be in a year where there was a deviation from the trend (i.e. a shock). Thus, it is best to run a regression to get the line of best fit through all the data points. The typical way to do this is to log the values, find the linear line of best fit, and then report the slope of the line as the average growth rate. Even though this method may not be expected from you at your level, it is recommended for any accomplished economist.

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