Calendar Effects on Economic Activity

Deutsche Bundesbank Monthly Report December 2012 51 Calendar effects on economic activity Calendar configurations can have a marked impact on economic activity. In the case of the quarterly rate of change in real gross domestic product (GDP), they account for as much as 1 percentage point. In the monthly movements of industrial output, calendar effects are often on a scale of more than 5 percentage points. With regard to statistical measurement of calendar effects, a distinction should be made between two aspects. Following European recommendations, patterns that recur annually and are typical of a given month or quarter are assigned to the seasonal component of a time series. In a month with 31 days, more work is performed and more is consumed on average than in a month with 30 days, let alone a month with 28 days. This should be differentiated from effects that result, say, from the shift in the number of working days within the same given month or quarter. In the context of official seasonal adjustment, these are recorded separately as calendar effects. The forms in which calendar effects appear are manifold and vary depending on the economic sector and the type of economic activity which is measured. For a large number of German economic indicators, the working-day model has proved to be effective in quantifying calendar effects. This model takes account of the fact that a working week of five days is usual in Germany, but that production is sometimes continuous, ie takes place even on public holidays. In the manufacturing sector, for example, one additional working day in the months January to November thus leads, on average, to a 3.4% higher monthly output. The effect is less pronounced in Decem- ber, since production is cut back anyway in the period around Christmas. The scale of activity in other sectors of the economy, such as transport, likewise follows a working-day pattern. Retail sales, on the other hand, are influenced more by the number of days on which outlets are open for business. However, these effects are not equally strong in every month. For GDP, the calendar effect is derived by aggregation across all sectors of the economy. A 1% increase in the number of working days leads, on average, to a 0.3% rise in overall output. Such calendar effects prove to be largely stable across time. The increased use of working time accounts and of more flexible working hours has no noticeable impact on this. Furthermore, the estimated relative effects are virtually independent of the cyclical situation. In principle, the effects on output of “bridge days”, the timing of school holidays or of weather conditions can also be estimated by calendar adjustment methods. For example, industrial output on such a bridge day is, on average, about one-third lower than on a normal working day. This effect is not independent of the cyclical situation, however. Difficulties in determining a stable correlation also arise when estimating the effects of school holidays. And, in assessing the effects of the weather using calendar models, subsequent catching-up effects are not clearly quantifi- able. Accordingly, in official statistics, such effects are not assigned to the calendar component, but are shown instead in the collective item “irregular effects” of the relevant seasonally adjusted time series. Deutsche Bundesbank Monthly Report December 2012 52 The importance of calendar Calendar effects in selected effects economic indicators 2005 = 100 Macroeconomic Calendar configurations have a marked impact Log scale, quarterly relevance on economic activity. For example, real GDP in- 113 112 Real gross domestic product creased at an annual rate of 1.7% in the first 111 only seasonally adjusted quarter of 2012. However, this growth received 110 a boost from the leap year effect (29 February) 109 108 calendar and and from the early Easter business season, seasonally adjusted 107 which began in March. Calendar influences 106 probably contributed an estimated 0.5 percent- 105 age point, so that the calendar-adjusted output 104 Lin scale, enlarged Calendar component 101.0 rose by “only” 1.2%. A counter-movement 100.5 took place in the second quarter: at 1.0% up 100.0 on the previous year, the calendar-adjusted in- 99.5 crease was 0.5 percentage point higher than 135 Log scale, monthly 130 that of the original values. Moreover, since the Manufacturing output 125 third quarter of 2012 had one working day less 120 than the corresponding quarter one year previ- 115 ously, the growth rate of the original values in 110 this case, too, is, at 0.4%, below the calendar- 105 adjusted increase of 0.9%. Output in the manu- 100 facturing sector and construction output de- 95 Lin scale pend to a very large extent on the calendar. It Calendar component 110 is not uncommon for working-day deviations in 105 a given month to amount to 5%, or even more, 100 95 of the series level. 90 Log scale 145 Effects on stock Calendar patterns not only affect flow variables 140 Construction output and flow (which are measured over a period of time), 135 variables however, but also stock variables (which are 130 125 measured at a point in time). The prices of 120 some services, such as package holidays, de- 115 pend positively on the timing of movable public 110 holidays such as Easter or Whitsun, around 105 which times demand for travel usually in- 100 creases. And the volume of overnight deposits 95 held by credit institutions at the end of a month 90 is lower when the day of observation is shortly 85 Lin scale before the weekend, as this is when many indi- 115 Calendar component viduals withdraw cash for the weekend ahead. 110 105 Seasonal and Moreover, the calendar affects seasonal behav- 100 structural iour. In months with 31 days, for instance, 95 calendar effects more work is performed and more is consumed 90 than in a February with 28 days, and Christmas 2010 2011 2012 shoppers push retail sales to seasonal peak levels every December. Following European rec- Deutsche Bundesbank Deutsche Bundesbank Monthly Report December 2012 53 ommendations,1 effects that recur annually terly factors and are consolidated in the na- and can be allocated to a particular month or tional accounts according to the importance of quarter are assigned to the seasonal compon- the individual series. The most accurate statis- ent of a time series. Only the other calendar tical quantification of calendar effects is pos- influences that result, for example, from the sible following this procedure. Moreover, the shift in the number of working days (and there- consistent treatment of monthly and quarterly fore in the number of weekends or public holi- indicators of sectoral and macroeconomic out- days) within the same given month or quarter put is assured; this is very important in analys- are recorded in the context of official seasonal ing and forecasting economic activity. adjustment as calendar effects. These effects are examined in greater detail below. RegARIMA models have prevailed internation- Statistical model ally for estimating calendar influences (for de- framework tails, see annex with methodological notes on Estimating calendar factors pages 59-60). These models can be used to determine semi-elasticities which, for example, Quantification of In order to quantify calendar effects precisely, it indicate the average percentage effect of an calendar effects would actually be necessary to conduct daily additional working day (compared with the reflected in daily data … statistical surveys, as then it would be possible month-specific average) on monthly output. to precisely measure production volume on 29 February, for instance, or retail sales on a In Germany the working-day model has proved Working-day given day before Easter. to be effective for a large number of economic approach indicators. It is based on a five-day working … possible to But because often only monthly data are avail- week and takes into account that, in some estimate from able, the relevant calendar effects cannot be cases, production is carried out continuously – monthly indicators, … calculated directly. Instead, the Easter effect in meaning even on public holidays. Since an add- March or April of each year becomes blurred itional working day in a month with a fixed with all the other effects in the month in ques- duration always means a weekend day or pub- tion. For this reason, it is only possible to con- lic holiday day less in that month, the estimated duct estimates based on comparable calendar working-day effect reflects exactly the differ- configurations that have occurred sufficiently ence, for example, between production on a often in the past. normal working day and production on a weekend day. A distinction needs to be made … and difficult In the case of quarterly data, for instance, the between two extreme cases. In an economic to gauge from Easter effect, which sometimes occurs in the sector with purely working-day production (ie quarterly data first quarter and sometimes in the second, without continuous production), the working- overlaps with all the other effects that arise be- day effect is proportional. Assuming a month tween 1 January and 30 June. As a result, dir- to have 20 working days on average, one add- ect quantification on the basis of quarterly time itional working day would lead to an increase series leads to greater uncertainties than when in production of 5%. On the other hand, if pro- using comparable monthly data. The quarterly duction is continuous and consistent across all approach is therefore generally considered dif- the days of the week, there is no difference be- ficult.

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