2. by Giuseppe Bruno (Bank of Italy - Research Department) OECD, Statistics Division Paris, November 27, 2003 A comparative Analysis of the tools for time disaggregation available at the Bank of Italy

3. 2 National Statistical Offices (NSI) and Eurostat have agreed upon 4 essential requisites for Time Disaggregation algorithms. Sometimes method choice is driven just by availability of the algorithms in the preferred software package. Quite often Time disaggregation procedures are provided by specialized programs. Institutional users feel the need of integrating these procedures into general purposes packages providing other statistical and econometric tools. Motivation

4. Providing a simple and flexible software tool that allows a quick implementation of the main disaggregation algorithms, the software should be easily extensible with new features and integrated with the statistical – econometric analysis framework. The Goals

5. 4 The Speakeasy/Modeleasy+ software is the general purpose analytical framework adopted more than 20 years ago, Modeleasy+ is a general purpose package but it addresses a wide range of statistical applications, It provides an interactive shell as well as full fledged programming language. The Solution adopted at the Bank of Italy

6. 5 Temporal Disaggregation: Techniques available Modeleasy+ provides: Chow-Lin (1971) and Denton (1971) working on first order differences and matrix manipulations Fernàndez (1981) Litterman (1983) Given the following high frequency model: Where B is the Backshift operator

7. 6 Potential for new dynamic techniques So far the basic tools seem satisfactory, trade-off between a richer set of high frequency indicators and a more sophisticated model, Modeleasy+ provides a matrix manipulation language (comparable to GAUSS and MATLAB) Methods proposed in Di Fonzo (2002) might be ported in the Modeleasy+ framework.

8. 7 An empirical example with Italian data Total household consumption has been disaggregated using different sets of related indicators achieved from the following variables: Disposable income, wealth and interest rate We compare the models using the performance indicators suggested in Santos Silva and Cardoso (2001):

9. An empirical example (contd) Standard Chow-Lin Method: H.freq. IndicatorsStand. Dev.Minimum valueMaximum value Y only 1.7189-4.80264.5528 Y and W.3823-.994181.2234 Y, W and R.3813-.863841.3548 Y and R 1.7354-4.92784.3831

10. An empirical example (contd) Dynamic Model (DynChow): H.freq. IndicatorsStand. Dev.Minimum valueMaximum value Y only.28078-.65045.82553 Y and W.27552-.6508.82792 Y, W and R.27698-.70031.84764 Y and R.28044-.70185.84795

11. 10 Another empirical example Private Investment has been disaggregated using different sets of related indicators achieved from the following variables: Capital Stock, Value added, a climate index and an interest rate.

12. Investment empirical example Standard Chow-Lin Method: H.freq. IndicatorsStand. Dev.Minimum valueMaximum value VA Only 1.8411-5.80045.4343 VA & CL 2.001-7.0346.2929 VA, CL & R 1.9222-7.11285.9872 VA, CL & K 1.9934-7.22575.9604 VA, CL, K & R 1.917-7.26376.0217 VA & R 1.9641-6.40436.6964

13. Investment empirical example Dynamic Model (DynChow): H.freq. IndicatorsStand. Dev.Minimum valueMaximum value VA Only 2.0038-5.0516.1063 VA & CL 1.9225-5.23145.9179 VA, CL & R 1.9042-5.31186.0375 VA, CL & K 1.8209-5.80836.3205 VA, CL, K & R 1.8034-5.94316.5006 VA & R 1.9792-5.41466.5357

14. Some programming examples $ BUILD command matrix mcmd = matrix(nserie, 1:" ") mcmd(1,)="ACPUBRD=DG(ACOAPRY C AMFARQ TREND :SUM )" mcmd(2,)="AFF=DG(CFAFFY,C,CFABCD,TREND :SUM )" mcmd(3,)="AFF70=DG(CFAFFRY,C,CFABCRD :SUM )" mcmd(4,)="AMMFAM=DG(AMMFAMY,C,AMMOAQ :SUM )" mcmd(5,)="AMMPA=DG(PAUAMM,C,TREND,TREND**2 :SUM )" mcmd(6,)="AMPUBRD=DG(AMAAPRY,C,AMMATRQ,TREND :SUM )" mcmd(7,)="ATTTOT=DG(TOPEAY,C,INDICAT,TREND,TREND**2 :MEAN)" mcmd(8,)="CIG=DG(CIGA,C, cigdip*riscig :SUM)" nser = noels(yearts) fratio = 4 startim = cpuseconds() for i=1, nser itim = cpuseconds() do mcmd(i) type("disaggr" yearts(i) ":" cpuseconds - itim, "cpuseconds" ); space 1 itim = cpuseconds() object(denlst(i))=denton(object(yearts(i)),fratio, object(method(i))) type("denton" yearts(i) ":" cpuseconds - itim, "cpusecondo" ); space 1 next i

15. 14 Some programming examples " Use of Multcall instead of the loop, faster" itim = cpuseconds() xin = yearts xout = namelist(acoden cfaden cfarden ammden pauaden amaaden topeaden cigaden) Multcall xout denton xin fratio sum ftim =cpuseconds(); ttim = ftim - itim type("tempo totale with multcall", ttim, "cpuseconds") itim = cpuseconds() xout = makename('dou' ints(nser)) c = trend/trend cl = namelist(c c c c c c c c) tl = namelist(trend trend trend trend trend trend trend trend) Multcall xout disaggr xin c trend:sum

16. Conclusions Use of high frequency dynamic model has recently started its diffusion, What is the level of acceptance of these methods by the international community? Software packages do not routinely include these algorithms An incentive to the spread of these methods will come from the introduction of these methods into general purpose packages (Gauss already available on Windows and UNIX ) (Modeleasy+, MATLAB)