sou · GQB3118d4 · 2003-01-01 00:00:00 — SCB kan komplettera denna förhållandevis övergripande datain- samling med data från olika urval av produktionsenheter, exempel- vis försäkringskassor, arbetsförmedlingar, krigsförband, högskolor etc. Detta skulle avsevärt förbättra kvaliteten i beräkningar- na och därtill ge väsentligt större analysmöjligheter (med , stokastisk produktionsfront etc.) och möjligheter att förstå pro- duktionsförhållandena vad gäller offentliga tjänster. Ett samarbete kan tänkas mellan SCB och någon annan myndig- het som också har intresse av att följa produktivitetsutvecklingen i den statliga förvaltningen: ESV, KI, Statskontoret eller någon an- nan. Uppgiften att utveckla analyser av produktionsförhållandena för offentliga tjänster är så omfattande att det skulle kunna motive- ra en separat organisation, ett institut, en avdelning vid Riksban- ken, KI eller någon annanstans. I så fall vore detta den naturliga sammanställaren av beräkningarna. Att slutligen föra in beräkningarna i nationalräkenskaperna görs av SCB. Myndigheterna åläggs att redovisa sin produktivitetsutveckling Myndigheterna skulle kunna åläggas att redovisa sin produktivi- tetsutveckling, som en del av resultatredovisningen i årsredovis- ningen. För att redovisningarna ska bli jämförbara måste anvisning- ar för hur beräkningarna ska göras utfärdas. Vilka myndigheter, som, med hänsyn till verksamhetens art, inte ska behöva göra pro- duktivitetsberäkningar, behöver också avgöras. Detta kan förslags- vis göras av ESV, som också skulle kunna ges i uppdrag att granska kvaliteten i redovisningarna. Alternativt förlitar man sig på Riksre- visionsverkets (den framtida ) granskning. Därtill krävs att någon får i uppdrag att göra en sammanställning av produktivitetsutvecklingen i delsektorer och för hela den statliga sektorn. SCB, ESV, KI och Statskontoret är några kandidater. Att föra in resultatet i nationalräkenskaperna är naturligtvis en uppgift för SCB. Detta alternativ kan ses som en vidareutveckling av det första al- ternativet, med den skillnaden att tillgången på data säkras genom att ålägga myndigheterna att beräkna produktivitetsutvecklingen. Alternativet har den fördelen att myndigheternas årsredovisningar därigenom blir bättre. En beräkning helt enligt nationalräkenskapernas behov och defi- nitioner överensstämmer inte alltid med det slag av produktivitets- beräkning som kan behöva göras för att belysa myndighetens resul- tat i förhållande till det uppdrag som myndigheten erhållit. Myn- dighetsperspektivet kan i vissa fall skilja sig från nationalräken- skapsperspektivet. För att åläggandet att redovisa produktivitetsut- vecklingen i årsredovisningen ska vara meningsfullt måste myndig- heten ges möjlighet att jämväl redovisa produktivitetsutvecklingen på ett sätt som på ett relevant sätt belyser dess resultat. Ett exempel är flyktingmottagning som kan ses som en prestation ur Migra- tionsverkets synvinkel men som ur ett nationalräkenskaps- (och politiskt) perspektiv kan ses som en stödverksamhet för beslut i asyl- och invandrarfrågor. Ett annat exempel gäller valet av pris- och löneindex för att beräkna kostnader i fast pris. I ett nationalrä- kenskapsperspektiv är ett genomsnittsindex för statlig förvaltning relevant. I ett myndighetsperspektiv är ibland ett myndighetsspeci- fikt pris- och löneindex relevant. Förordningen (2000:605) om årsredovisning och budgetunderlag anger att myndigheterna – försåvitt regeringen inte beslutat om krav på återrapportering – ska redovisa och kom- mentera hur prestationerna utvecklats med avseende på volym, in- täkter, kostnader och kvalitet. (3 kap. 1 §). ESV föreskriver att Där så krävs för att kravet på en rättvisande redovisning skall upp- fyllas skall, som tilläggsinformation, kostnads- och intäktsutveck- lingen belysas även i fasta priser efter omräkning med lämpliga in- dex. Myndigheten skall ange och motivera val av index. ESV före- skriver därtill att redovisningen ska omfatta , att informationen ska vara jämförbar över tiden och att om principerna för beräkningar ändras ska omräkning ske av det närmast före- gående räkenskapsåret så att en jämförelse med det aktuella räkenskapsåret blir möjlig. Detta åläggande vore i det närmaste fullt tillräckligt om inte av regeringen angivna återrapporteringskrav skulle förekomma. Ett enda sådant återrapporteringskrav upphäver den skyldighet som myndigheten eljest skulle falla under. Det skulle därför i stort sett vara tillräckligt att ändra förord- ningen så att av regeringen ställda krav på återrapportering inte för- tar verkan av kravet att redovisa prestationer med avseende på vo- lym, intäkter, kostnader och kvalitet. Därtill bör läggas kravet att myndigheten också ska redovisa en sammanvägd produktivitetsutveckling. Detta är viktigt för att sä- kerställa konsistens i alla deluppgifter, att alla prestationer och alla kostnader innefattas samt att myndigheten kommenterar helheten. Av erfarenhet bör redovisningen helst sträcka sig längre än . kan fluktuationerna i prestationsvolym och kostna- der vara ganska stora utan att ha så mycket att göra med den lång- siktiga produktivitetsutvecklingen. För årsredovisningen som hel- het gäller ett krav redovisning. Detta bör tillämpas även på resultatredovisningen. Ds Fi 1983:18, Minskad produktivitet i offentlig sektor Ds Fi 1985:9, Produktions-, kostnads- och produktivitetsutveck- ling inom vägsektorn Ds Fi 1986:1, Produktions-, kostnads- och produktivitetsutveck- ling inom armén och flygvapnet 1972–1982 Ds 1986:13, Offentliga tjänster – sökarljus mot produktivitet och användare, Expertgruppen för studier i offentlig ekonomi () Ds Fi 1986:17, Produktions-, kostnads- och produktivitetsutveck- ling inom den offentligt finansierade utbildningssektorn – 1980 Ds 1991:20, Metoder i forskning om produktivitet och effektivitet med tillämpningar på offentlig sektor, Expertgruppen för studi- er i offentlig ekonomi Ds 1994:22, Kvalitets- och produktivitetsutvecklingen i sjukvården –1992 Ds 1994:24, Den offentliga sektorns produktivitetsutveckling Ds 1994:71, Den offentliga sektorns produktivitetsutveckling, bila- gor (1995), 1995 (ESA95), , 2001, Handbook on price and volume measurements in National Accounts (1998), Task Force on volume Measures for , NACE L, (stencil), . (2001), Budgetredogörelsen –2001, janu- ari 2001, Fisk, , och Hatry, H. (1971), Improving Productivity and Pro- ductivity Measurement in Local Governments, The , , 1971 Goudrian, R, de , H and van Tulder, F, (1985), Public sector productivity: recent empirical findings and policy implications, finance, 41st congress (1975), Price and Volume Measures for , (stencil), Statistical office of Communi- ties, , (1977), On Goods and Services, , ser. 23, no. Kuznets, S. (1971) Economic Growth of Nations: Total Output and Production Structure, , : . (1987), Den offentliga sektorn – produktivitet och ef- fektivitet, Bilaga 21, (1992), Measuring Public-Sector Output: The Swedish Report, Output Measurement in the Service Sectors, red. , in In- come and Wealth (1961), Accounting, , T. och Tabellini, G. (1999), Political Economics and Pub- lic Finance, I Auerbach, A. och Feldstein, M. ), Handbook of Public Economics vol. Pritchard, Alwyn (2002), Measuring productivity change in the provision of public services, Economic Trends, no. 582, 2002, Office for national Statistics, & SL, (1989), Bättre kollektivtra- fikstandard – kollektivtrafikanternas värderingar vid arbetsresor. Statskontoret (1985), Statlig tjänsteproduktion, produktivitetsut- vecklingen 1960–1980, Huvudrapport, rapport 1985:15 Statskontoret (1987), 3-årsmyndigheternas resultatanalys, PM Statskontoret (1996), Staten i omvandling, rapport 1996:15 Statskontoret (1997), Produktivitet och kvalitet i resultatstyrning- en av myndigheterna, Statskontoret 1997:6, RRV 1997:11 Statskontoret (1998), Produktivitetsutvecklingen i statsförvalt- ningen 1990–97, rapport 1998:23 United Nations, , and (1993), System of National Accounts 1993 (SNA 93) Økonomistyrelsen (2001), Vejledning i udarbejdelse af virksom- hedsregnskaber baseret på ny struktur, minimumskrav, bilaga 2, Forecasting GDP within the Framework of the Swedish Activity Index –An Overview– Forecasting GDP within the Framework of the Swedish Activity Index –An Overview– 2The Swedish Activity Index 2.1The Selection of Indicators and a Model for GDP 2.2Bias Adjustment of the Activity Index 2.3Seasonal Adjustment of the Activity Index 2.4Output from the Production of the Activity Index 3Preliminary Results on the Prediction of GDP 4The Decomposition of a Quarterly Change A monthly disaggregation of Qarterly GDP (QGDP) has been produced by Statistics since 1998. Its popularity with the public and its increased use as a direct predictor of QGDP, and some preliminary analysis, have led to the support for further tests of the Activity Index as a predictor of the change of QGDP. This paper is a short overview of the Activity index, some preliminary results and its further use as a predictor for QGDP. An outline of the research during the next year is also given. Statistics has published an Activity Index for the Swedish economy intermittently in the journal SCB-Indikatorer. During 1997 this index appeared to show great instability for 1995–1996, and its quality was in question. A short project on the future of the index was carried through at Statistics in late 1997 in dis- cussion with . The question was could the old approach be improved or should the publication of the index stop. As a result of this project, a new de- sign of the activity index was suggested. The primary purpose of the new index was to provide a better monthly disaggregation of GDP than the old index (see 1998). A system for producing the Activity Index was also designed that included seasonal ad- justment. The new approach (called the Activity index in this re- port) was first published in January 1998. During 1998–1999, it was based on the following indicators: industrial production index, production of electric energy, employment in the form of the number of working hours for employees in the public sector and turnover in retail trade. In the second quarter of 1999, there were many changes of the definition and measurement of the target variable, GDP and it was calculated according to SNA 93/ESA95 including new price defla- tors, new classifications and new sources. The calculations of the Activity Index were changed, e.g. new indicators and a bias reduc- tion procedure were included. These new changes have consistently linked the Activity Index and GDP and many user of economic statistics seem to consider the Activity Index as an official monthly GDP. On the initiative from the General of Statistics and the Investigation of Economic Statistics, the use of the Swed- ish Activity Index in predicting the change of QGDP has been in- vestigated1. The purpose of these investigations has been to check the prediction power of the Activity Index and give suggestions for further use of the Activity Index as a predictor for the first pre- liminary quarterly change of GDP (seasonally adjusted). In this paper, an overview of the Activity Index and the above studies are given. 2 The Swedish Activity Index 2.1The Selection of Indicators and a Model for GDP The selection of the monthly indicators for the Activity Index has been based on the following principle. monthly variables with maximum correlation with the major components of QGDP. This screening has come up with the monthly indicators industrial pro- duction index (IPI), employment in the form of the number of working hours for employees in the public sector (emp), turnover in retail trade (RT), export of goods (exp) and import of goods (imp). All these variables are survey estimates2 measured on a monthly basis. In Figure 1 the correlations between the activity indicators and the corresponding components of GDP are illustrated. Here, , INV, GOV, EXP, IMP stand for household consumption, investment, government consumption, total export and total im- port respectively. The numbers in circles are the correlation coef- ficients between the indicator and the related component of GDP. The indicator RT is related to household consumption with a cor- relation of 0.88, etc. 1There are two reports, (2002:2) and and (2002). 2Consequently, there are sampling errors involved. SOU 2002:118 Bilaga 7 Correlation between and the Indicators of the Activity Index The corresponding quarterly counterparts in index-form are related to QGDP in the standard quarterly regression model Yt = + 1 X1t + 2 X 2t + L+ t where Y is the dependent variable represented by QGDP and X the independent variables representing the indicators. t is a random vari- able with regular properties. is the intercept and i covers the par- tial effect of a change of X i . In order to relate the individual impact of the indicators to QGDP, all variables are transformed to with 1995=100. The estimated model for Activity Index in 1999 is shown in Table 2.1 below. Table 2.1 The Regression Model for the Activity Index for GDP according to SNA 93/95 -0,25 (12,2) (5,5) (4,7) (3,1) (-2,4) (4,3) R2 =0,992 the parameter estimates of Table 2.1, the t-tests of the esti- mates are shown in brackets. The model explains about 99 per cent of the variability of QGDP. If this model is used with the indicators on a monthly fre- quency, we have what we call the original Activity Index (AI). It is the monthly model-based counterpart of QGDP. Now, if we es- timate the parameters of (2-1-1), we will get an estimated residual, i.e. a difference between actual GDP and the monthly predictions measured as an average over the months of the quarter. This esti- mated residual, will now be called the quarterly bias of the Activ- ity Index3. Because this bias would be considered an inconsistency in the statistics, this bias has been eliminated from the original in- dex. This is described in the next paragraph. 2.2Bias Adjustment of the Activity Index Consistency between QGDP and the Activity Index is achieved by the following adjustment: AIt = ˆ + ˆ1empt + ˆ2 RTt + ˆ3 IPIt + ˆ4 expt + ˆ5impt BIASt , (2-2-1) where ˆ, ˆ j , j = 1,2L,5 are the estimated regression parameters for ex post quarterly data. The bias is not known on a monthly basis and the quarterly bias is used for all months within a quarter, i.e. BIASt = BIAStk ,t = 1,L,12; k = 1,2,3,4 where t indicates a month and k a quarter. When the quarterly bias is unknown, the bias is given by BIASt = BIAStk 1 ,t = 1,L,12; k = 1,2,3,4 That is, when the bias is not known, the last known bias is used. 3 It is well known that there is no overall bias due to the estimations method. the who- le estimation period, the residuals cancel. The word bias is used just for pedagogical reasons. BIAS of Activity Index 2.3Seasonal Adjustment of the Activity Index The Activity Index is seasonally adjusted by model-based methods provided by the software TRAMO/SEATS, which is also used for the national accounts. Within this framework, an ARIMA-model for the series is specified and decomposed into a seasonal, a trend- cycle, an error and other relevant components. The selection of a proper model has been made by use of the standard information criteria based on the likelihood function, i.e. AIC and BIC. Consi- deration of smoothness has also been taken into account. An (111)(010) has been used since 1998 as shown in Table 2.3.1 below. ARIMA-parameters for the Bias Adjusted Activity Index The seasonally adjusted original Activity Index and the corresponding for the bias adjusted index are different.4 The unadjusted index shows greater variability. Seasonal adjustment is made as an integrated part of the production system written in the software SAS and EXCEL. That is, it is made whenever the Activity Index is published. The regression model for the Activity Index is calibrated when there is a new QGDP and/or when QGDP has been revised. That includes also bias adjust- ment. 2.4Output from the Production of the Activity Index Statistics publishes the seasonally adjusted values, the trend estimates and their changes according to Table 2.4.1 below. The official version of the index is the bias adjusted index consis- tent with QGDP.5 The seasonally adjusted series and the trend are also available on SCB´s home page on the Internet. Change in per cent from 4See , S. (2002:2) pp. 7-8, 12-15 (In Swedish). 5Note that consistency only refers to the original QGDP and the original Activity Index, not to the seasonally adjusted counterparts. Two graphs are also published in the press release. These are shown below: The Activity Index 1995=100 Per cent change from previous month The Activity Index is also published on Reuters and SIX. Since its first publication, the Activity Index has been quite stable including the original series as well as the seasonally adjusted series and the trend estimates. The monthly changes of the trend (raised to a ye- arly level) are also shown as the second diagram on page 1 of this report. 3 Preliminary Results on the Prediction of GDP We have investigated the prediction performance of the Activity Index for the target variable first estimate of the QGDP change based on the seasonally adjusted series of QGDP. In (2002:2), and (2002) several approa- ches of the use of the Activity Index as a predictor of the target variable are discussed. In this section, a short summary is given. It was decided that the prediction based on the Activity Index should only consider already published and official results. This limits the prediction approach and its analysis. Tables according to 2.4.1 have been used, where two level esti- mates and two monthly changes are given, calculated from the sea- sonally adjusted series and the trend estimates. The predictions co- ver 1999–2001, i.e. 12 ex ante quarterly predictions. Changes based on the seasonally adjusted series of the Activity Index as well as the changes based on the trend estimate have been tested. The trend estimate seems to be the best predictor. If we use the mean of the two monthly changes of the trend gi- ven by Table 2.4.1, the following predictions of the first estimate of QGDP change will appear. The first QGDP change is 0.9. If we use the published Table for January 19996 as described above, the prediction of QGDP will be 0.6. The next prediction based on the Activity Index for January and February 1999 will also be 0.6, while the prediction for February and will be 0.9. The prediction errors will be -0.3, -0.3 and 0. 6 Including the estimated change of the Activity Index in . SOU 2002:118 Bilaga 7 The Activity Index and GDP. Quarterly Predictions and Prediction Errors raised to quarterly level The first Estimate of the Change of QGDP (BNP) and Predictions of QGDP (Prediktion) If the predictions based on the different publications of the Activi- ty Index, i.e. from the first month of the quarter, second month and the third month, are separated, the following summary table of the predictions emerges. The Activity Index and GDP. Prediction in per cent, by Month Table 3.2 reveals a few things. The use of the already published Activi- ty Index (trend estimates) changes could be used as predictors for the change of QGDP, seasonally adjusted. The predictions based on the first published Activity Index (two changes) are quite successful with a RMSE of 0.209 and almost unbiased. The largest prediction error was 0.3 and the smallest was -0.3. These prediction errors are smaller than what was expected by the author, considering the bias of the mo- del as shown in section two. The corresponding prediction error using the second/third pub- lication of the Activity Index is not that successful. However, RMSE=0.388 and 0.400 are still acceptable. The predictions above are based on the average of two monthly changes of the Activity Index with equal weights, i.e. Now, if the predictions of QGDP were made by means of the corresponding monthly counterparts, we would actually use six monthly changes with unequal weights. This is discussed in the next paragraph. 4 The Decomposition of a Quarterly Change7 In what follows, Yt is a quarterly variable, which can be aggregated according to Yt = y1t + y2t + y3t , Yt = value regarding quarter t, = value regarding the first month of = value regarding the second month of t, =value regarding the third month of t. Yt is here represented by QGDP. The change (Yt ) of the quarterly series from t-1 to t is calculated as (Yt ) = * (Yt / Yt 1 1) (4-2) can also be written (Yt ) = * (Yt Yt 1 ) / Yt 1 . 7 This paragraph is a short version of and (2002). Yt 1 (Yt ) /100 = Yt Yt 1 (Yt ) is the relative change of the quarterly series from t-1 to t. Now, if Yt and Yt 1 are substituted by their monthly values accor- ding to (4-1), we get Yt 1 (Yt ) /100 = Yt Yt 1 = y1t + y2t + y3t ( y1t 1 + y2t 1 + y3t 1 ) = (1 B3 )( y where B3 ( y1t ) = y1t 1 . Note that t indicates a quarter. B)(1+ so (4-5) could be written B)(1+ B2 )( y If this expression is developed, we reach to the following identity between a quarterly change and its decomposition in terms of monthly changes. Yt 1 (Yt ) /100 = (1 B)( y2t 1 + 2y3t 1 + 3y1t + 2y2t + y3t ) = y2t 1 y1t 1 + 2( y3t 1 y2t 1 ) + 3( y1t y3t 1 ) + 2( y2t y1t ) + y3t y2t That is, the quarterly change from t-1 to t can be expressed as a weighted sum of monthly changes, i.e. a MA symmetric filter of monthly changes. How to use (4-8) within the framework of the Activity Index? 8 The operator B is used here for a monthly series. Normally the definition is ( yt ) = A direct application of (4-8) requires a quarterly series and a cor- responding monthly series measured in levels. They should also be related in such a way that (4-1) is exactly fulfilled. Now, we have the Activity Index as a prediction, say yˆit of yit . Suppose we have the predictions yˆit of yit and the purpose is to predict Yt before it is calculated. QGDP is published about 65 days after t, i.e. during the third month of t+1. A first prediction of Yt can now be made with the Activity Index represented by yˆ1t and earlier estimates yˆit 1 ,i=1,2,3. Therefore, we can replace the monthly values of (4-8) with the corresponding Activity Index up to yˆ1t . However, yˆ2t and yˆ3t are not yet known. A first prediction of QGDP could be made by means of (4-9) below: (Y ) /100 = B)( y = w1 [yˆ2t 1 yˆ1t 1 + 2( yˆ3t 1 yˆ2t 1 ) + 3( yˆ1t yˆ3t 1 )] where w1 is a weight for compensating the loss of two terms. When the Activity Index for the second month is calculated, the QGDP predictor will be: (Y ) /100 = B)( y = w2 [yˆ2t 1 yˆ1t 1 + 2( yˆ3t 1 yˆ2t 1 ) + 3( yˆ1t yˆ3t 1 ) + 2( yˆ2t yˆ1t )] where w2 is a corresponding weight. A linear interpolation requires that w2 are determined by can not be calculated. 9 That is, 2( y Using the third month of the quarter is not necessary because QGDP will normally be published within one week after the Acti- vity Index publication for the third month. The predictions based on (4-9) and (4-10) have not yet been car- ried through because these measures of change are not available from an ex ante point of view. They are only available for the Acti- vity Index for 2002. During the next 12 month-period, these predictions will be made. The approach used for the Swedish Activity Index is similar to the approach suggested by Chow & (1971). Since then, there have been many proposed solutions to the disaggregation problem. We could say that the Activity Index-model is static in levels. The eco- nometric research since that time has drawn the attention to dy- namic models of non stationary time series. The issues of cointe- gration and common trends are important. The implications of the latest research on dynamic modelling are given substantial attention and if possible improvements of the ba- sic model for the Swedish Activity Index.