BANK OF ISRAEL
Office of the Spokesperson and Economic Information
Press Release
November 4, 2012
Bank of Israel Study: The effects of seasonality in the Consumer Price Index on inflation expectations estimates
 The inflation expectations estimates suffer from deviations caused by seasonality that is latent in the Consumer Price Index.
 While seasonality factors are priced into indexed bonds, they have a significantly lower absolute value than the seasonality factors published by the
Central Bureau of Statistics (CBS).
 If we calculate the average inflation forecasts for the next 12 indices over time, and present the results by month, we find that they vary by month in a fixed pattern, in contrast with economic logic.
A new study conducted by Roy Stein of the Bank of Israel's Research Department shows how inflation expectations estimates suffer from deviations due to seasonality in the Consumer Price Index. The expectations estimates are among the most important indicators considered when formulating monetary policy. These estimates include primarily (1) inflation expectations for the next 12 months, calculated from the prices of CPI (Consumer Price Index)-indexed and unindexed government bonds, and (2) forecasts for the next 12 CPIs as formulated by professional forecasters. These expectations and forecasts are affected by deviations caused by the seasonality that is latent in the Consumer Price Index.
The deviation in expectations is the result of the influence of seasonality on the pricing of index-linked bonds. This deviation occurs when the redemption ranges of these bond series are not consolidated with complete years. Basically, most of the time, bonds are not traded in a range of complete years, so it is necessary to take the
POB 780, 91007 Jerusalem Tel: 972–2–6552713 www.boi.org.il

yields to redemption of the existing series, convert them to annual terms, and take into account the seasonality factors that are included in the CPIs that will be published during the lifespan of each series of bonds. The study shows that the seasonality factors have a strong effect on the pricing of CPI-indexed bonds, but these factors have a significantly lower absolute value than the seasonality factors calculated by the CBS through accepted statistical methods. These findings hint that the CPI-indexed bond market in Israel is not a sophisticated market in this respect, since the yields of indexed government bonds do not reflect all of the seasonality factors, even though these factors have an influence on the future payments of the bonds. When calculating the annual real yields and inflation expectations, we must take into account the seasonality factors that are priced into the bond prices, but these are not the same as the factors published by the CBS. To the extent that the seasonal factors priced into the CPIindexed bond prices are not taken into account, we obtain a deviation in the calculation of the real yield, and in turn in the inflation expectations. See the graph presenting the average deviation that existed during the sample period.
The deviation in forecasts apparently results from an only partial internalization of seasonality factors when forecasters' projections for annual inflation are formulated.
As a result of this partial internalization, the forecasters are surprised by monthly indices that are much higher or lower than prior forecasts. They estimate that the inflation environment is higher or lower than prior estimations, and update the inflation forecasts for the next 12 months accordingly. In his study, Roy Stein relates to the average of the inflation forecasts provided in each of the months of the year, calculates the average for each of the months over 12 years, and shows that the results vary in a fixed pattern over the year.
The findings of the study show that bond market participants in Israel, as well as professional forecasters, do not use the full information included in seasonal fluctuations of the CPI when pricing CPI-indexed bonds and formulating their inflation forecasts and expectations. Policy makers take these findings into account when using these forecasts as input in formulating monetary policy.
POB 780, 91007 Jerusalem Tel: 972–2–6552713 www.bankisrael.org.il

1.20%
The deviation of inflation expectations from capital market data that results from seasonality factors that are priced into indexed bonds, monthly averages
January 2008 – March 2012
1.00%
0.80%
0.60%
0.40%
0.20%
0.00%
-0.20% Ja nu ar y
Fe br ua ry
-0.40%
Ma rc h
A pr il
Ma y
Ju ne
Ju ly
A ug us t
Se pte m be r
O cto be r
N ov em be r
D ec em be r
POB 780, 91007 Jerusalem Tel: 972–2–6552713 www.bankisrael.org.il