## 2.4 Inflation and Inflationary Expectations

Inflation (or Deflation) is a macroeconomic concept referring to an increase (decrease) in the absolute price level over some defined time period. An increase in the price of all goods has the effect of reducing the purchasing power of money and money incomes and thus must be taken into account when planning future economic activity.

Inflation is difficult to measure directly because it represents the percentage change over time of a nonexistent economic variable--the price level 'Pt'.

π = %Δ Pt= (Pt - Pt-1)/Pt-1

#### 2.4.1 The Consumer Price (Laspeyres) Index

Unlike GDP or other national income measures, no single observable measure exists to represent the aggregate price level. Thus economists rely on a price index based on some well-defined market-basket of goods as a proxy to measure the level of prices and changes in prices over time.

The most common index used to measure inflation is the Consumer Price Index (CPI) or 'CPI' as calculated by the Bureau of Labor Statistics (the BLS). This particular index is based on the prices of a basket of goods which represents the purchasing behavior of some average urban consumer. The CPI, also known as the Laspeyres Index , is calculated using a weighted average of current to past price ratios for this basket of goods:

CPIt = Σ wi,t[Pi,t / Pi,o]

These weights 'wi,t' are based on the expenditure patterns of the consumer in a base period (currently 1982-84) reflecting the importance of each item relative to the overall level of consumer expenditure in that base period or:

wi = (Pi,oQi,o i) / Σ [Pi,oQi,o]

thus

CPIt = Σ[Pi,tQi,o] / Σ [Pi,oQi,o]

where 'Qi,o' represents the quantity of the ith good consumed in the base time period (t = 0), 'Pi,o' represents the price of the ith good in the base time period, and 'Pi,t' represents the price of the same good in the current time period 't'.

#### 2.4.2 Weaknesses of the CPI

It is important to note that the CPI is not a perfect measure of the price level or changes in the price level.

First because this index is computed using base-period quantities (reflecting buying behavior and preferences in the base year), it does not allow for substitution among goods as relative prices change. For example, it might be that the overall rate of inflation is 5%. However, within that value some goods might be rising by 3-4% and other goods by 6-7%. Consumers will attempt to soften the effects of increasing prices on household budgets by substituting away from the relatively more expensive goods and towards the relatively cheaper good. This behavior is not captured in the CPI.

A second problem with the CPI is that it does not allow for changes in product quality over time. It may be that prices are rising due to improved quality of the good being purchased such that this good does not have to be replaced as often. Quality changes can also show up in the size of the good in question. Over the past generation, housing prices have been rising. But during this same period of time, the average size of a housing unit (in terms of square footage, number of bedrooms and baths, size of the garage and lot) has also increased.

Third, the CPI does not allow for the inclusion of new goods and services as they emerge into the market place. A fixed basket of goods based on 1982/84 preferences ignores flat-screen TV's', tablet and cloud PC's, smart phones, online retail and many other goods or services that perhaps lead to improvements in living standards or life style.

Inflation Rate (1960-2019)

#### 2.4.3 The Rate of Inflation

The annual Rate of Inflation is calculated as the percentage change in the CPI from one year to the next.

π = (CPIt - CPIt-1) / CPIt-1

As can be seen in the diagram, the annual rate of inflation in the U.S. over the past 50+ years ranges from roughly 2% up to a high in the early 1980's of 14%. Policy makers often set a target rate in the 2% range and they have mostly achieved that goal over the past 20 years. The values for the CPI and rate of inflation for the past 12 years is shown below:

 Year CPI Inflation Rate (Index 1982-1984=100) 2008 215.25 3.8% 2009 214.57 -0.4% 2010 218.08 1.6% 2011 224.92 3.2% 2012 229.59 2.1% 2013 232.95 1.5% 2014 236.70 1.6% 2015 237.00 0.1% 2016 239.99 1.3% 2017 245.12 2.1% 2018 251.10 2.4% 2019 255.65 1.8%
Source: St. Louis Federal Reserve (FRED: CPIAUCSL, CPALTT01USA657N, 06-30-2020)

These values are indexed to a base period of 1982 - 1984, that is, quantities purchased in that time period. A CPI of 215.25 for 2008 indicates that prices have risen by roughly 115% since the base year.

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#### 2.4.4 Inflationary Expectations

Sometimes a contributing cause of inflationary pressure in the the economy is the build-up of inflationary expectations. These expectations develop based on a recent history or experience with rising inflation and they can get built into wage and labor contracts, pricing decisions and notably, nominal interest rates

Inflationary expectations are based in-part on a recent history of inflation and inflationary trend coupled with other pieces of information that may be relevant:

E[πt] = E[πt | It-1]

The 1970's were a period where both the actual rate of inflation and inflationary expectations were rising and feeding on each-other resulting in both being double-digit values.

In the early to mid-1980's the actual rate of inflation was de-accelerating, a phenomenon known as disinflation During this period, economic agent's expected rates of inflation were greater than what actually occurred. These agents were slow to adapt negotiating unnecessarily high nominal interest rates which put upward pressure on ex-post real interest rates -- a relationship discussed in the module on interest rates.

In an environment of an acceleration of inflation, the agent's expectations will never quite catch up to the actual rate. For this reason, many models assume that the economic agent uses other relavent information such as growth rate in the money supply, the rate of unemployment, and measures of structural capacity utilization within the economy in developing inflationary expectations. These models are known as Rational Expectations models.

#### 2.4.5 The GDP Deflator (Paasche Index)

A different price index, known as the GDP Deflator or the Paasche Index, is constructed using current expenditure shares [to represent the spending habits as reflected in current GDP via Q(i,t)] and is defined by the following equation:

Pt = Σ [Pi,tQi,t] / Σ[Pi,oQi,t]

where 'Qi,t' represents the quantities produced and sold of the i-th good in the current time period 'Pi,t' represents the current price of that i-th good and 'Pi,o' represents the base (1996) price of that same good. This measure can be interpreted as the ratio of actual spending in the current year (NGDP) and the level of expenditure on that same quantity of goods if prices had not changed (RGDP) -- spending in base-year prices (see section 2.1).

Concepts for Review: