Round 2 - Budget Challenge! Role of Inflation

Just as inflation erodes the earnings of families—meaning they need to make more and more each year just to stay even—inflation erodes the buying power of governments.

We often need to look at trends in government spending over time, both for the budget as a whole and for individual budget areas.  In order to determine the impact of inflation on government spending over a series of years, an analyst must adjust for inflation. 

Let’s look at the country of Chaosa.  Fortunately, Chaosa has published budget data for the last 10 years so we can see how spending has changed in that period.

It is evident from this simple table that spending in Chaosa has doubled during this 10-year period, from Ŧ100 billion to Ŧ200 billion.  The biggest increase was in the defense budget, which grew by Ŧ35 billion, while the smallest increase was in the “other” category, which increased by only Ŧ3 billion.  There is a key question, however.  Has the size of government spending actually doubled during this period?  After all, assuming there has been some inflation over that time, a tenge—Chaosa’s currency— (or, in this case, a billion tenges) doesn’t buy as much in 2006 as it did in 1997. 

Adjusting for inflation

To adjust figures for inflation, you need to know what inflation was for each of the years during the period you are analyzing.  The most common tool for doing this, published by most governments or by academics, is typically called the consumer price indexor, sometimes, the inflation index.  This is a table that has an arbitrary starting point equal to 100.  If the following year inflation runs at five percent, the index rises to 105 (100 x 1.05).  If inflation the next year rises to 10 percent, the inflation index would rise to 115.5 (105 x 1.10), and so on.  Years prior to the base year—which, again, is an arbitrary point—will show up as numbers below 100 as long as inflation was positive.  If inflation had been four percent the year prior to the base year, the index would have been 96.2 (100/1.04).   
Just below is the consumer price index for Chaosa.  A quick glance shows that inflation seemed to be pretty significant during many of the years shown.  In fact, you can quickly calculate that prices more than doubled during this period, since the 2006 figure—130.9—is more than double the 1997 index of 64.2.  If inflation more than doubled between 1997 and 2006, but government spending merely doubled, that means real spending—spending after adjusting for inflation—actually fell.  The government can actually purchase fewer items in 2006 than it could in 1997.  But we need to be more precise, and we also want to calculate the impact of inflation on each of the programs the government of Chaosa operates.

To adjust for inflation, think first what, in principle, you are trying to do.  You want to ensure that the value of the money you are describing in any two years is the same.  Because there has been inflation, we know that a tenge in 2006 doesn’t buy as much as a tenge did in 1997, so we want to equalize the “purchasing power” of the two years.  Note that we can accomplish that by inflating the nominal figure from 1997 to equal 2006 tenges or deflating the 2006 figure to equal 1997 tenges, or, if we want, describe both of them in some other year, such as using the 1999 base year. 

Because readers instinctively know what today’s tenge is worth, it is typically better to inflate all nominal prior year figures to today’s tenge, or the most recent year for which the inflation index exists.

Now, how do you do this?  Here is the equation to inflate prior year data to today’s values, with an example showing how to inflate Chaosa’s 1997 defense budget to today’s tenges:

Nominal Value x Current Year Inflation Index ÷ Prior Year Inflation Index = Real Value (measured in Current Year values)

or

Ŧ65 x 130.9 ÷ 64.2 = Ŧ133

In other words, the Ŧ65 billion Chaosa spent on defense in 1997 was the equivalent of spending Ŧ133 in 2006.  Since Chaosa spent Ŧ100 billion on defense in 2006, it has actually reduced the real value (measured in 2006 values) of defense spending over the last 10 years.

It is usually important—in this and other calculations—to check conceptually to make sure that the result is logical, that it is in very rough terms what one would expect.  One of the simplest, yet most important, checks is to make sure that the new figure calculated moves in the direction you expect it to.  That is, it is easy to get confused and multiply the nominal value by the prior year’s inflation index, and then divide by the current year index.  If you do that, though, the nominal value will shrink in value.  Except in the rare circumstances when the economy is marked by deflation—where prices fall and the value of money shrinks from year to year—adjusting for inflation should always make earlier year’s data larger, or current and future year data smaller. 

Finally…

there may be times when you want to calculate current spending in the value of some historic period, or you want to deflate the projections of future costs into today’s tenges.  In either case, the equation is just the opposite of the equation to inflate past year’s data.  If you wanted to measure today’s spending on defense in 1997 tenges, for instance, the equation would be:

Nominal Value x Prior Year Inflation Index ÷ Current Year  Inflation Index = Real Value (measured in Prior Year Values)

or

Ŧ100 x 64.2 ÷ 130.9 = Ŧ49

In other words, the Ŧ100 billion Chaosa spent on defense in 2006 was the equivalent of Ŧ49 billion in 1997.  Again, the quick, common sense test is that when deflating current (or future) year spending data to some past period, the value should shrink, as it does here from Ŧ100 billion to Ŧ49 billion.  Still, beyond this inflation-driven decline, it is evident that real defense (measured in 1997 values) spending fell during the period, from Ŧ65 billion to Ŧ49 billion. 

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Time to try some exercises:

EXERCISES:  Inflation in Practistan!

The Consumer Price Index (CPI) in Practistan over the past five years is as follows: 

1.  Inflation in 2007 is expected to be ten percent.  What is the CPI for 2007?

2.  Instead of providing the inflation estimates, the government publishes the CPI for 2007 as 130. What is the rate of inflation in 2007?

The budget (in millions) of Practistan in 2004 is as follows:

3.  Assuming that the CPI in 2007 is 132, calculate the (real) value of all the categories of Practistan’s 2004 budget expressed in 2007 values.

4.  If the Defense budget in 2007 is at $33,000, has it gone up in real terms from the 2004 value and if so by how much? Compare both years in REAL values.

 


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Question 1
ANSWER:

132

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Question 2
ANSWER:

8.33 percent

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Question 3
ANSWER:

19,800 for health, 23,760 for education, 7,920 for social welfare, 31,680 for defense, 19,800 for interest payments, and 2,640 for others.

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Question 4
ANSWER:

Yes, 4.2 percent.

Thanks for participating in Round 2 of the Budget Challenge!