# Inflation

We mentioned, in “Salary Curve”, that total lifetime savings equaling sum of (income – expenditure) as shown in the last curve does not work out in practice because of inflation. Let’s dig deeper into the meaning of inflation, how inflation may be measured, and what it means to you and me in daily life.

## Defining Inflation

The qualitative meaning of inflation is simple enough: a sustained rise in general price levels in goods and services in an economy over a period of time [1]. So for example, Rupee prices of bread, soap, and toothpaste in the corner grocery shop near my house are higher today than they were a few years ago.  So it is clear that prices inflate (or currency deflates). A very narrow “point” definition of inflation can be given without much disagreement as follows:

For a specific commodity at a specific location, if its prices at two times T1 and T2  are P1 and P2 respectively (where T1 > T2),

The above gives a multiplier. An alternative formula measures the percentage rate of change:

## Computing Inflation

Giving a single quantitative definition that everyone would find useful, however, is not easy. The problem is that ‘point’ inflation varies across commodities, across locations, and across times. It is rather like the concept of density in a non-uniform material.

So one has to develop a method to somehow average these countless point inflation values into a single meaningful value. There are several choices to be made:

1. How to ‘mix’ the price of two commodities, say soap and SUV.
2. How to select a manageable number of commodities from the millions of goods and services out there. Do we include soap? Which brands? Which sizes? Which packages?
3. How to select the locality or area over which prices are to be collected. Town, District, State, Country, …? Or by socio-economic group?
4. How to select the time interval.

Long story short, the accepted methodology is to calculate a number, called a consumer price index (CPI) at a given time and in a given area as follows:

The Pi values are average prices for specific commodities over the desired area, and wi values are weighting factors that fine tune the contribution coming from each commodity.

This set of commodities is called a basket of commodities.

The rationale for introducing weighting factors comes from quantifying how much money a typical family with typical needs would spend in a month. This can be explained with a simplified example: Consider a family who consumes, on average, the following quantities in a month:

• soap : 2
• Toothpaste: ½
• Bread: 24 loaves

Then a price index based on a basket of {soap, toothpaste, bread} will have the weighting factors {2, ½, 24} respectively. Note the prices and weighting factors must be in consistent units.

Although a single CPI value is not very useful by itself, but CPI values c1, c2 for two times T1, T2, (T1 < T2) can be used to measure inflation in terms of the rate of rise of CPI with time.

If the time interval is 1 year, this gives a yearly inflation rate. If the time interval is 1 month, the yearly rate is derived by appropriate adjustment.

An example of a real-life CPI basket that is specified by Govt of India is described in [3], see Annexure V, pages 137- 144, in particular.

## Fuzziness in Inflation Numbers

CPI numbers as published by Govt of India or World Bank have many assumptions and approximations. For example, the basket used for CPI is not that meaningful for the very rich or the very poor. Averaging over a large area or population smears out local idiosyncrasies. The composition of the basket has to be adjusted from time to time to accommodate changing trends.

## What it Means to You and Me

CPI-based inflation numbers show a trend. What is really important is not whether inflation is really 6.21 % or 6.53 %, but that in the long term, inflation becomes a force that is very dangerous to your and my financial well-being. But this line of thought will be followed up in a separate article.

## Everything is Too Expensive

The other side effect of sustained inflation is that we generally get stressed out because our sense of prices of things lags behind reality. Our expectation of the price of a loaf of bread is probably its price we stored in memory some years ago (most people buy a bunch of things at a time and never pay attention to individual prices). Our expectations often become “anchored” to an earlier year. I suspect that older people are anchored to earlier times than younger people.

Another way to think about this is, everything is not getting expensive really, it is just that the currency is losing its value, year on year.

Unfortunately, when it comes to salaries, this anchoring effect may lull us into a false sense of comfort: what one is getting paid today, even if it feels like a comfortable salary, is probably not much higher than our expectations that are still anchored to salary levels of a few years back. In fact, current salary may be less than earlier years’ salary after taking inflation into account.

## Finding Your Anchor Year

So let’s try an experiment. Find a common commodity where you are not aware of its current price. Write down what you feel would be its price today, F. Then find out the actual current price P.

The ratio P/F gives you a multiplier, which is a measure of mismatch between your view of prices and the reality. If you are in India, use the table below to find the closest matching cumulative inflation multiplier and read off the year in the previous column (If outside India, you can construct your own table from [4]). The table below was built from data in [5].

Notice that the multiplier values increase as you go back in past. Consider that the multiplier is 2.01 for 2008. For example, if you feel that a thing that you expect to be priced Rs 50 is actually Rs 100 today, then P = 100, F = 50,  P/F = 2.0, hence you are mentally still in 2008 for this particular item!

This procedure gives you your anchoring year for a particular commodity. Repeat for several different commodities and see if you get a consistent value for the anchoring year. You can now use the multiplier of your average anchoring year to revise all your price estimates upward.That should somewhat reduce the stress from the feeling of paying too much every time you shop.

This anchoring effect works in reverse on income too. So you should  divide your current salary number by the same multiplier, so that you develop a more realistically prudent approach to spending.

 YEAR Mult YEAR Mult YEAR Mult YEAR Mult 2016 1.00 2006 2.26 1996 3.92 1986 9.71 2015 1.06 2005 2.38 1995 4.30 1985 10.40 2014 1.13 2004 2.47 1994 4.70 1984 10.94 2013 1.23 2003 2.56 1993 5.11 1983 12.31 2012 1.37 2002 2.65 1992 5.52 1982 13.30 2011 1.45 2001 2.78 1991 6.24 1981 14.99 2010 1.59 2000 2.88 1990 7.09 1980 16.35 2009 1.83 1999 2.89 1989 7.48 1979 18.27 2008 2.008 1998 3.34 1988 8.13 1978 18.54 2007 2.118 1997 3.55 1987 8.89 1977 20.00

Table : cumulative inflation multiplier with 2016 as reference (India)

## Takeaways

Inflation is the slow but inexorable rise of prices, or conversely, the inexorable loss of value of a currency.

Inflation may lead to shopping stress – “everything is so expensive” – because we often are mentally anchored to price points of an earlier time. Because of this anchoring, it may also lull us into a false sense of security when it comes to current and future incomes.

So inflation may be a mere annoyance in the short term, but over a longer time span. if inflation is not taken into account, it can seriously upset our financial calculations.

### References

[1]  Inflation https://en.wikipedia.org/wiki/Inflation

[2]  Consumer Price Index https://en.wikipedia.org/wiki/Consumer_price_index

[3]  CPI Manual India 2010 http://mospi.nic.in/Mospi_New/upload/manual_cpi_2010.pdf

[4]  World Bank Inflation data http://data.worldbank.org/indicator/FP.CPI.TOTL.ZG

[5]  India CPI 1958-2015 http://www.inflation.eu/inflation-rates/india/historic-inflation/cpi-inflation-india.aspx