Perceived Inflation Index

The " Index of Perceived Inflation (IWI)" developed by Hans Wolfgang Brachinger is a statistical construct for measuring perceived inflation. The aim of the index is to quantify the extent to which a representative household, according to its subjective perception, is affected by inflation with its daily purchases.

As is well known, inflation is a sustained significant increase in the price level , which is usually measured with the help of a consumer price index . However, the operationalization of inflation is only possible on the basis of assumptions for which there is a certain degree of flexibility. “True” inflation does not exist; rather, measured inflation is always a construct.

Individuals can view price changes or inflation from different perspectives. Brachinger distinguishes between two different perspectives, that of consumers and that of buyers. For a consumer, the costs or the price of the shopping basket consumed by him and the goods as well as the change in costs or price increases in the shopping basket are of interest. A good is all the more important, the higher the cost share of the good in the total costs of the shopping cart. This perspective generally serves as the basis for consumer price indices. From the point of view of a buyer, however, the acts of purchase of the goods and their price changes are important, which is why the purchase frequency and not the cost share of the goods in the shopping cart plays a central role.

To represent the buyer's perspective, Brachinger creates his theory of perceived inflation. The aim of this theory is to map the perception of price changes based on the decision-making behavior of buyers. Therefore, this theory is based on fundamental knowledge of psychology , essentially on the " prospect theory " and the availability heuristics of Kahneman and Tversky .

On the basis of this theory of perceived inflation and taking into account the traditional theory of price indices and the considerations of official price statistics , the index of perceived inflation was finally constructed.

Perceived inflation theory and its basic hypotheses

Brachinger's theory of inflation perception is based on the following three hypotheses :

In a first phase of perception, the prices of goods are coded relative to goods-specific reference prices as gains or losses. Price increases represent losses and price decreases represent gains.
Profits or losses are valued according to a value function V and losses are higher than profits. This asymmetrical valuation is referred to in the literature as loss aversion . Price increases are rated more strongly than price decreases.
The more often a buyer has experienced price increases or the easier it is to come up with examples of price increases, the higher the inflation estimate. Conversely, decreases in the price of goods that are seldom bought or goods without an explicit purchase process, e.g. B. rents, the perception of inflation hardly. Thus, the frequency of experience of price changes or the availability of reminders regarding price changes determines the perception.

The index of perceived inflation is based on this theory of perceived inflation and combines actual price data from price statistics in such a way that the three hypotheses outlined are taken into account.

Perceived Inflation Index

Index concept

The generalized index formula of the Laspeyres type serves as the basis of the index of perceived inflation , which is also used as the basis of the price indices of the public offices for measuring inflation. Based on a certain basket of goods that represents the consumer habits of an average household, the index can be presented as follows: ${\ displaystyle n}$

{\ displaystyle I_ {gLA} ^ {0, t} = \ sum _ {i = 1} ^ {n} G_ {i} \ left ({\ frac {p_ {i} ^ {t}} {p_ {i } ^ {0}}} \ right) \ cdot g_ {i}}

where and denote prices of the -th good in the reporting period or in the base period , is an arbitrary transformation function of the price index of the -th good and arbitrary base periods are weights with which the individual price indicators are weighted (with and ). ${\ displaystyle p_ {i} ^ {t}}$ ${\ displaystyle p_ {i} ^ {0}}$ ${\ displaystyle i}$ ${\ displaystyle t}$ ${\ displaystyle 0}$ ${\ displaystyle G_ {i}}$ ${\ displaystyle i}$ ${\ displaystyle g_ {i}}$ ${\ displaystyle g_ {i} \ geq 0}$ ${\ displaystyle \ sum _ {i} ^ {n} g_ {i} = 1}$

The idea of the index of the perceived inflation consists in choosing the transformation function and the weights in the index formula of the generalized Laspeyress type in such a way that they do justice to the theory of inflation perception outlined above. The index of perceived inflation is thus designed as a special case of a price index of the generalized Laspeyress type.

Reference prices

In a first phase of perception, according to the theory of inflation perception outlined above, the prices of goods relative to goods-specific reference prices are encoded as gains or losses.

A past price of a good is to be selected as the reference price. This can be the current base price of the consumer price index, any other past price of this good or a suitable average. Because of the comparability with consumer price indices, Brachinger suggests the base prices as reference prices , which are used when calculating the consumer price indices . ${\ displaystyle p_ {i} ^ {0}}$

This means that in the event of price increases, i. H. if the price of a good in the reporting period is higher than in the base period , this is recorded as a loss and that price reductions for which is less than are regarded as gains. ${\ displaystyle p_ {i} ^ {t}}$ ${\ displaystyle p_ {i} ^ {0}}$ ${\ displaystyle p_ {i} ^ {t}}$ ${\ displaystyle p_ {i} ^ {0}}$

Value function

After coding the prices of goods as profits or losses, these coded prices are valued according to a value function according to the theory of inflation perception presented above. It is assumed that this value function is independent of the considered good and its price level. The value function is taken into account with the help of a suitable transformation function.

The index formula of the generalized Laspeyress type can be represented as any other price index formula as a function of relative price changes:

{\ displaystyle {\ frac {p_ {i} ^ {t}} {p_ {i} ^ {0}}} = {\ frac {p_ {i} ^ {t} -p_ {i} ^ {0}} {p_ {i} ^ {0}}} + 1.}

This can be used with the transformation function in such a way that it does not depict price relations but the perception of relative price changes.

If the Weber-Fechner law is also assumed for the perception of price changes (the same relative changes in a stimulus (here relative price change) lead to the same absolute changes in perception and absolute changes in perception are a linear function of relative changes in the stimulus), then the price relations depend only on the perceived price changes, are independent of the price level and can be represented as a linear function of the relative price changes. For the transformation function, the Weber-Fechner law and (2) result: ${\ displaystyle p_ {i} ^ {t} / p_ {i} ^ {0}}$

{\ displaystyle G_ {i} \ left ({\ frac {p_ {i} ^ {t}} {p_ {i} ^ {0}}} \ right) = G_ {i} \ left ({\ frac {p_ {i} ^ {t} -p_ {i} ^ {0}} {p_ {i} ^ {0}}} + 1 \ right) = c \ left ({\ frac {p_ {i} ^ {t} -p_ {i} ^ {0}} {p_ {i} ^ {0}}} \ right) +1}

Following Kahneman and Tversky 's loss aversion , losses (price increases) are weighted more heavily than gains (price decreases). This means that the value function must be steeper in the case of price increases than in the case of price decreases. H. positive price changes must be multiplied by a higher constant , the loss aversion coefficient, than negative price changes. If the coefficient for negative price changes is normalized to one, the following finally results for the transformation function: ${\ displaystyle c}$ ${\ displaystyle c}$

{\ displaystyle G_ {i} \ left ({\ frac {p_ {i} ^ {t}} {p_ {i} ^ {0}}} \ right) = \ left \ {{\ begin {array} {ll } {\ frac {p_ {i} ^ {t}} {p_ {i} ^ {0}}} & {\ mbox {for}} ~ p_ {i} ^ {t} \ leq p_ {i} ^ { 0} \\ c \ left ({\ frac {p_ {i} ^ {t} -p_ {i} ^ {0}} {p_ {i} ^ {0}}} \ right) +1 & {\ mbox { for}} ~ p_ {i} ^ {t}> p_ {i} ^ {0}. \ end {array}} \ right.}

For the loss aversion coefficient , Brachinger suggests a value of 2, which was determined in various empirical studies on the subject. ${\ displaystyle c}$

Weighting scheme

For a complete specification of the generalized index formula of the Laspeyres type, suitable weights must be selected. The third and final hypothesis of the theory of perceived inflation outlined above states that the more often a buyer has experienced price increases or the easier it is to come up with examples of noticeable price increases, the more likely he is to think of inflation. It is assumed that the purchase frequency with which the corresponding good is bought is decisive for how easily a buyer can come up with examples of price increases. Therefore, with a view to measuring perceived inflation, it makes sense to choose the relative purchase frequency with which a good is bought by the average buyer in the base period as the weight of a good. ${\ displaystyle g_ {i}}$ ${\ displaystyle g_ {i}}$

Perceived Inflation Index IWI

The index of the perceived inflation results from the fact that in the generalized index formula of the Laspeyres type the transformation function developed above is used for all goods and that the relative purchase frequencies with which the goods are bought in the base period are chosen as weights . The index of perceived inflation is then defined by: ${\ displaystyle i}$ ${\ displaystyle G_ {i}}$ ${\ displaystyle f_ {i} ^ {0}}$ ${\ displaystyle g_ {i}}$

{\ displaystyle IWI (c) ^ {0, t} = \ sum _ {i: p_ {i} ^ {t}> p_ {i} ^ {0}} \ left [c \ left ({\ frac {p_ {i} ^ {t} -p_ {i} ^ {0}} {p_ {i} ^ {0}}} \ right) +1 \ right] f_ {i} ^ {0} + \ sum _ {i : p_ {i} ^ {t} \ leq p_ {i} ^ {0}} {\ frac {p_ {i} ^ {t}} {p_ {i} ^ {0}}} f_ {i} ^ { 0}}

In contrast to the consumer price index, the IWI as an inflation indicator does not reflect the view of a consumer, but rather the view of a buyer. It quantifies the extent to which, according to its subjective perception, a representative household is affected by inflation with its daily purchases.

Measurement of perceived inflation in Germany

Course of the perceived inflation measured with the help of the index of the perceived inflation with a loss aversion coefficient of 2.0 (IWI (2.0)) compared to the officially measured inflation (consumer price index CPI) and the perceived inflation measured with the help of the balance score of the European Union. Sources: CEStat University of Friborg Switzerland / Federal Statistical Office, Wiesbaden / European Commission for Economics and Finance.

Weighting scheme index of perceived inflation for Germany. Source: CEStat University of Friborg Switzerland.

In a joint project with the German Federal Statistical Office, Hans Wolfgang Brachinger calculated the index of perceived inflation for Germany . The aim of this project was to explain the " euro equals expensive " phenomenon that occurred after the introduction of euro cash . H. the divergence between the officially reported inflation rate and the general perception of inflation, as shown in consumer surveys.

The first figure shows the development of inflation measured with the help of the consumer price index (CPI), the results of the consumer survey EU-CS Balance Score of the European Union . The perceived inflation is also shown. It is measured using the index of perceived inflation with a loss aversion coefficient of 2.0 IWI (2.0). The pie chart shows the weighting scheme of the IWI for Germany, which reflects the frequency of purchase of goods and services.

With the help of the index of perceived inflation (IWI (2.0)) it could be shown that even before the introduction of the euro cash the prices of common goods rose sharply. In January 2002, with the introduction of euro cash, the IWI (2.0) reached a high of 11% at the time, compared to a reported inflation rate of just 2.1% (| consumer price index CPI). Shortly thereafter, perceived inflation decreased, but in 2007 and 2008 it reached new highs of up to 12.8% perceived inflation. The perception of inflation is currently on the rise again and is reaching values of up to 5%, while the officially reported inflation rate is currently at values of just over 2%.

It is also interesting that the course of the perceived inflation, measured with the help of the index of perceived inflation IWI, shows a comparable development to the balance score (EU-CS balance score), which reflects the consumer survey data of the European Union . The perceived inflation measured with the help of the index of the perceived inflation IWI is therefore a good indicator to reflect the subjective assessment of buyers with regard to inflation.

Individual evidence

^ HW Brachinger: Statistics between Lies and Truth - On the relation to reality of economic and social statistical statements. In: ASTA Economic and Social Science Archive. Vol. 1, No. 1, 2007, pp. 5ff.

↑ CESTAT University of Friborg in Switzerland. ( Page no longer available , search in web archives )@1@ 2Template: Dead Link / www.unifr.ch

↑ Federal Statistical Office. Consumer price index for Germany ( Memento from October 15, 2011 in the Internet Archive )

↑ European Commission for Economy and Finance.

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HW Brachinger: "Euro equals expensive" - it is not that wrong. In: Neue Zürcher Zeitung. No. 224/2004, p. 29.

HW Brachinger: The euro as expensive? Perceived inflation in Germany. In: Economy and Statistics. No. 9, 2005, pp. 999-1013.

HW Brachinger: Statistics between Lies and Truth - On the relevance of economic and social statistical statements to reality. In: ASTA Economic and Social Science Archive. Volume 1, No. 1, 2007, pp. 5-26.

HW Brachinger: A New Index of Perceived Inflation: Assumptions, Method and Application to Germany. In: Journal of Economic Psychology. Volume 29, No. 4, 2008, pp. 433-457.

HW Brachinger: Perceived inflation puts economic confidence on shaky legs. in www.oekonomenstimme.org, January (2011): oekonomenstimme.org ( accessed : October 3, 2011).

H. Jungermann, HW Brachinger, J. Belting, K. Grinberg, E. Zacharias: The Euro Changeover and the Factors Influencing Perceived Inflation. In: Journal of Consumer Policy. No. 30, 2007, pp. 405-419.

Web links

[1] HW Brachinger: Statistics between Lies and Truth - On the relation to reality of economic and social statistical statements. In: ASTA Economic and Social Science Archive. Vol. 1, No. 1, 2007, pp. 5ff.