SICENTERLjubljana, Slovenia

   Time Distance – New Generic

Approach for Analysis and Presentation of Time Related

Data

Professor Pavle Sicherl

SICENTER and University of Ljubljana

Email: Pavle.Sicherl@sicenter.si; www.sicenter.siCopyright © 1994-2005 P. Sicherl All rights reserved

Presented at the Time Distance Analysis conference at the George Washington University, October 25, 2005, Washington D.C.

TIME DISTANCE: Concept and novel generic statistical measure

A Comparison of European and US Economies Based on Time Distances

The fact that comparisons should be made in two dimensions has been verified by the world-wide media interest in my analysis for the EUROCHAMBRES Spring Business Forum. The static ratio of 1.41 does not catch much attention, while the time gap of about two decades obviously produced a different perception of reality. The same will be true for comparing within the EU.

Source: P. Sicherl, A Comparison of European and US Economies Based on Time Distances, EUROCHAMBRES, Brussels, March 2005

35

40

45

50

55

60

65

70

75

80

85

90

95

100

1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Time

US

GD

P p

er c

api

ta (2

003

=100

)

EU15

US

S-time-distance 18 years

US

EU15

Index 141

US-EU gaps in GDP per capita: static index and time distance

A NEW VIEW IN TIME SERIES ANALYSIS

II. a. CONCEPT OF MULTIDIMENSIONAL COMPARISON AND EVALUATION b. PRESENTATION c. VISUALIZATION d. SEMANTICS: POLICY, MANAGEMENT

PERCEPTION OF A SITUATIONIII. STOHASTIC MODELS WITH S-TIME-DISTANCE-e.g. criterion for evaluating forecasting models (Granger and Jeon, 2003)

IV. DECISION MAKING MODELS- extension of decision making models

FURTHERAPPLICATIONS

I. DESCRIPTIVE STATISTICAL MEASURE

A new view of the information using levels of the variable as identifiers and time as the

focus of comparison and numeraire

Time matrix from the inverse relations: time when a specified

level of the variable was achieved in each compared unit

Level Time ti (XL)

Time tj (XL)

XL1 tj (XL1) XL2 ti (XL2) tj (XL2) XL3 ti (XL3) tj (XL3) … … … XLn ti (XLn)

The resulting time matrix provides new information from which new generic measures can be derived.

Two operators applied to this time matrix lead to the derivation of two novel statistical measures, expressed in standardized units of time.

Subtracting horizontally the respective times in the time matrix we get a special category of time distances S-time-distance for a given level of XL defined as

Sij(XL) = t(XL) = ti(XL) – tj(XL) (1)

Subtracting vertically the respective times in the matrix for consecutive levels of the variable for each column we get the second suggested measure S-time-step

Si(XL) = (tXL+X – tXL)/X (2)

The concept of S-time-step measures the growth characteristics of a series, using the inverse relation to the conventional X/t or growth rate metrics.

Source: P. Sicherl, Time Distance: A Missing Link in Comparative Analysis, 28th General Conference of the International Association for Research in Income and Wealth, Cork, Ireland, August 22-28 2004

METHODOLOGY: a broader perception,

policy and welfare

The perception whether the gender difference in life expectancy in the EU15 is large or small depends on the measure used: static

percentage difference is only 8 percent, while S-time-distance amounts to 29 years. For a more realistic conclusion all measures

should be presented simultaneously.

Source: P. Sicherl, Time Distance As A New Additional Way To Measure And Assess The Overall Position Among And Within Countries, Discussion Paper, SICENTER, Ljubljana, 2004, http://www.sicenter.si/pub/Time%20distance%20Sicherl.pdf

Static measures of disparity and time distance between life expectancy for females and males for EU15 in 2000

65

70

75

80

85

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Lif

e e

xp

ec

tan

cy

(y

ea

rs)

Life expectancy (male) Life expectancy (female)

S-time-distance = 29 years

F-M = 6.3 yearsF/M = 1.08

Importance for development strategy: the relations between growth, efficiency and inequality are different when based on a

dynamic concept of overall degree of disparityStatic relative measure and time distance lead to different conclusion: higher 4% growth example ratio=1.5, S=10 years; lower 1% growth example ratio=1.5, S=40 years.

Per

cap

ita

inco

me

(lo

g s

cale

)

Higher growth rates lead to smaller time distances, and thus have an important effect on the overall degree of disparity. This is based on both static disparity and time distance, as both matter. Static measures alone are inadequate.

1960 1970 1980 1990 2000 2010 2020 2030 2040

100

1000

10000

S121(t)

S122(t)

R12(t)

S122(t)

S121(t)

R12(t)

unit 1

unit 2

unit 1

unit 2

Time

Source: P. Sicherl, Time Distance: A Missing Link in Comparative Analysis, 28th General Conference of the International Association for Research in Income and Wealth, Cork, Ireland, August 22-28 2004

Static measure and time distance show two very different messages about importance of different components

Percentage differences between US and EU15 for employment rate, annual hours worked and productivity per hour are very similar. It seems as if the difficulty of catching up would be similar in the analysed components.

S-time-distances are very different, for productivity per hour only 5 years, while for employment rate and annual hours worked are about a quarter of a century. Policy analysis should expect different difficulties of catching up in these fields.

EU15-US - Static Disparities (2003)

141

111113 114

100

105

110

115

120

125

130

135

140

145

150

GDP per capita EmploymentRate

Annual HoursWorked

Productivity(GDP per hour)

Ind

ex E

U15

=10

0

Time distance between the EU15 and the US (years)

18

25

23

5

0

5

10

15

20

25

30

GDP per capita EmploymentRate

Annual HoursWorked

Productivity(GDP per hour)

EU

15

tim

e l

ag

in

ye

ars

Conclusions

Time distance concept and statistical measure S-time-distance is: - theoretically universal - intuitively understandable - immanently practical

“The usual matrix for comparing two lines involves differences along the vertical axis. This can be a poor way of measuring how these trends vary in terms of time which is on the horizontal axis… Sicherl’s several works have presented a non-technical discussion of the theory of time distance. This concept can help us to think more clearly about the forecastibilty of series.” C.W.J. Granger and Y. Jeon, University of California at San Diego “Time distance is a generic concept. That means that, as it has been the case e.g. with spreadsheet, one cannot in advance specify all the uses to which a generic framework can be put by imaginative users in numerous fields.” J. Backhouse, Information Science Dpt., London School of Economics

ANALYTICAL AND PRESENTATION TOOL

EMPIRICAL APPLICATIONS

UNITS OF COMPARISON

• MACRO, MEZZO, MICRO

• COUNTRIES• REGIONS• SECTORS• CITIES

• SOCIO-ECONOMIC GROUPS

• COMPANIES• HOUSEHOLDS• PROJECTS• INDIVIDUALS

“Time distance is a generic concept. That means that, as it has been the case e.g. with spreadsheet, one cannot in advance specify all the uses to which a generic framework can be put by imaginative users in numerous fields.”

J. Backhouse, Information Science Dpt., London School of Economics

FIELDS OF CONCERN

• ECONOMICS• BUSINESS• STATISTICS AND ECONOMETRICS• SOCIAL SCIENCES• TECHNOLOGIES AND SCIENCE

STUDIES• POLITICAL SCIENCE• INEQUALITY• COMPARATIVE POSITIONS• GAP ANALYSIS

NEW INSIGHTS FROM EXISTING DATA DUE TO AN ADDED DIMENSION OF ANALYSIS

PARADIGMATIC EXAMPLES TO BE USED IN PRESENTATION

• USA EU15 COMPARISON (EUROCHAMBRES STUDY)

• USA vs. JAPAN• NEW MEMBER STATES

AND EU15 AVERAGE• ONE INDICATOR MANY

COUNTRIES • MANY INDICATORS

TWO COUNTRIES

• 29 OECD COUNTRIES AND 3 INDICATORS: A NOVEL TYPOLOGY OF INDICATORS

• CONVERGENCE IN TWO DIMENSIONS

• GOODNESS-OF-FIT AND MONITORING IN TWO DIMENSIONS

• INTERNET USERS AND DIGITAL DIVIDE

TYPES OF ANALYSIS

• COMPARISON BETWEEN UNITS, BENCHMARKING

• COMPARISON ACROSS DIFFERENT TOPICS

• ACTUAL VS. ESTIMATED, FORECAST, PLAN, BUDGET, TARGET VALUES, MONITORING, MODELS, REGRESSIONS

• ANALYZING A SINGLE TIME SERIES

An example how analytical statistical tables can present time dimension in a new way

Time matrix: time when a given indicator level was attained (penetration rates for PC per 100 inh.)

Level (%) 5 10 15 20 25 30 35 40 45 50 55 60

EU15 Apr-96 Mar-98 Dec-99 Aug-01BE Jul-94 Jul-96 Feb-98 Jul-99 Jun-01DK Feb-95 Sep-95 Nov-96 Oct-97 Aug-99DE Dec-94 Sep-96 Apr-98 Jan-00 Oct-01GR Sep-98ES Jan-95 Apr-98 Mar-01FR Mar-96 Feb-98 Jun-99 Nov-00IE Sep-94 Aug-96 Apr-98 Aug-99 Oct-00IT May-97 Sep-99LU Jan-95 Jan-00 Nov-00NL Mar-94 Dec-95 May-97 May-98 Aug-99 Jan-01AT Dec-93 Oct-95 Sep-97 Aug-99PT Jul-95 Jun-00 Apr-01 Oct-01FI Jun-94 Jul-95 May-96 Sep-97 Dec-98 Feb-01SE Dec-93 Mar-96 Aug-96 Feb-97 Mar-98 Jan-99 Dec-99 Nov-00 Oct-01UK Dec-95 May-98 Nov-99 May-01US Jan-95 Jul-96 Oct-97 Oct-98 Sep-99 Jun-00 May-01JP Apr-95 Sep-96 Nov-97 Mar-99 Jun-00

Source: P. Sicherl, A New Perspective on Digital Divide, Time-distance Analysis: Method and Applications, eWISDOM, Journal for Comparative Research, 2a/2004

Time distances for the past and projected time distances for level of GDP per capita of EU15 average in 2003 (Scenario: growth rate for countries is 4%)

30

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50

55

60

65

70

75

80

85

90

95

100

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030

Time

EU

15

av

era

ge

fo

r 2

003

=1

00

EU15

CZ

EE

CY

LV

LT

HU

MT

PL

SI

SK

EE 21 years

PL 22 years

SK 19 years

HU 15 years

CZ 12 years

SI 9 years

Backw ard looking S-time-distances for EU15 average Forward looking S-tim e-distances for EU15 ave rage for 2003

S-time-distance for SI 18 years

LV 25 years

© P. Sicherl 2005

CY 8 years

MT 10 years

LT 22 years

S-time-distance for CY 16 years

S-time-distance for MT 20 years

S-time-distance for CZ 25 years

S-time-distance for HU 31 years

S-time-distance for SK 35 years

S-time-distance f or PL and LT 38 years

S-time-distance for LV 41 years

S-time-distance for EE 37 years

Source: P. Sicherl, Time Distance As A New Additional Way To Measure And Assess The Overall Position Among And WithinCountries, Discussion Paper, SICENTER, Ljubljana, 2004, http://www.sicenter.si/pub/Time%20distance%20Sicherl.pdf

COMPARING MANY COUNTRIES FOR A GIVEN INDICATOR FOR A YEARGDP per capita (ppp): time distances for 2003 from EU15 average

Source: P.Sicherl, ibid.

LTPL

EESK

HUCZ

MTPT

SIGRCY

ESEU25

ITDEEU15

FIUKFRBESEIENL

DKJPAT

LUUS

-40-35-30-25-20-15-10-50510152025303540

S-time-distance (years): - time lead, + time lag

LV

© P. Sicherl 2005

Time distance for EU23 countries from EU15 average for mobile phones per capita December 2003

Source: P.Sicherl, ibid.

PLLVLTFRSK

EEHUDEBENL

IEEU15

UKGRATDKESCZSISEFIPTITLU

-40-35-30-25-20-15-10-50510152025303540

S-time-distance (years): - time lead, + time lag© P. Sicherl 2005

Comparisons over many indicators can show characteristic profiles across countries, regions, socio-economic groups, firms, etc.

Source: Interview with P.Sicherl - Semanario Economico, Lisbon, March 18, 2005

Time distances in years between the USA and EU15 average for selected indicators for 2003 (- time lead, + time lag for the USA)

-18 -25 -23 -5 -23

1010

-30

-25

-20

-15

-10

-5

0

5

10

15

GDP percapita

EmploymentRate

Annual HoursWorked

GDP per hour R&D percapita

Lifeexpectancy

females

Infant survivalrate

S-t

ime

-dis

tan

ce

in y

ea

rs

economic indicators social indicators

(2002)

(2002)

© P. Sicherl 2005

The time lag behind the USA over time has been the highest for employment rate and R&D per capita (25 and 23 years)

Source: P. Sicherl, A Comparison of European and US Economies Based on Time Distances, EUROCHAMBRES, Brussels, March 2005.

0

5

10

15

20

25

30

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Time

EU

tim

e la

g i

n y

ears

Employment Rate R&D Investment (R&D per capita) Income (GDP per capita)

Productivity (GDP per employed) Productivity (GDP per hour)

US=0

Some hypothetical calculations: year in which EU15 would equalize with the USA for various assumptions

Source: P. Sicherl, A Comparison of European and US Economies Based on Time Distances, EUROCHAMBRES, Brussels, March 2005.

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

2100

2110

2120

2130

0.5% 1% 1.5% 2% 2.5% 3% 3.5% 4% 5% 6% 7% 8%

Required positive difference in growth rates between EU15 and USA

Ye

ar

of

eq

ua

liza

tio

n u

nd

er

giv

en

as

su

mp

tio

ns

GDP per capita

Employment RateGDP per employed

GDP per hourR&D per capita

Source: P. Sicherl, Time Distance As A New Additional Way To Measure And Assess The Overall Position Among And Within Countries, Discussion Paper, SICENTER, Ljubljana, 2004, http://www.sicenter.si/pub/Time%20distance%20Sicherl.pdf

Time distances between Hungary and EU15 average around 2003 (EU15=0)S-distance in years, - time lead, + time lag for Hungary

31 27 24 14 15 24 12 9 3 2 29 1

-20

-10

0

10

20

30

40GDP per

capita (ppp)GDP peremployed

(ppp)

Annualhours

worked

Export percapita

Employmentrate

Lifeexpectancy

(female)

Infantsurvival rate

Personalcomputersper capita

Internetusers

Internethosts per

capita

Cars percapita

Mobilephones per

capita

1 2 3 4 5 6 7 8 9 10 11 12

S-t

ime

-dis

tan

ce (

ye

ars

): -

tim

e le

ad

, + ti

me

lag

HU

Graph HU

© P. Sicherl 2004

USA and Japan: very different conclusions about the magnitude of the gaps in the two dimensions

Source: P.Sicherl, ibid.

Typology of development indicators based on two dimensions: S-time-distance and index ofstatic disparity (29 OECD countries) - domains for the three types of indicators

GDP per capita (Type II) Female life expectancy (Type I) Internet users per capita (Type III)

-40-30-20-10010203040

S-time-distance (in years): - time lead, + time lag from benchmark

0

20

40

60

80

100

120

140

160

180

200

Ind

ex

(ben

ch

ma

rk E

U1

5=1

00

)

Very different conclusions about the magnitude of the gaps in the two dimensions among different indicators are also

observed in comparing 29 OECD countries (see the graph)

• Development and welfare are multidimensional and long-term phenomena. Comparative analysis in attributes has to deal with these characteristics in a meaningful and consistent way.

• The two-dimensional approach shows a novel typology of indicators:

• type-I processes with long distances in time and short absolute or relative distances (e.g. life expectancy)

• type-II processes with short time distances and long distances in absolute or relative values (e.g. Internet users per capita)

• type-III processes with intermediate values of time distances and of absolute or relative distances (e.g. GDP per capita)

• An important question from the point of view of policy is to what extent are the wide differences in growth rates inherent in the nature of some particular attribute and to what extent can they quickly be changed by appropriate policy measures in accord with social objectives.

GDP per capita, time distance (S-distance) in years ( - time lead, + time lag) and percentage difference from the Western Europe average (WE12)

Time distance from WE12 Percentage difference from WE12

Ireland Spain Portugal Greece Ireland Spain Portugal Greece 1966 15 16 23 25 -44 -46 -52 -50 1973 15 13 13 13 -44 -37 -42 -37 2001 -2 14 19 25 16 -22 -29 -38

Source: own calculations based on data from Maddison (2003)

Convergence viewed in two dimensions: proximity in time and in space (3 x 3 classification of cases)

Distance in indicator space

1 Ratio S-distance

4 Ratio S-distance GRE 1973-2001

7 Ratio S-distance PRT 1973-2001

2 Ratio S-distance

5 Ratio S-distance IRL 1964-1973

8 Ratio S-distance ESP 1973-2001

Distance In time

3 Ratio S-distance

6 Ratio S-distance

9 Ratio S-distance ESP, PRT, GRE 1966-1973 IRL 1973-2001

Growth rate effects and a broader concept of convergence

Source: P.Sicherl, ibid.

Time

S-time-distance adds a second dimension to comparing actual value with estimated value, forecast, budget, plan,

target, etc. and to evaluating goodness-of-fit in regressions, models, forecasting and monitoring

Var

iabl

e X

e1

S1

e2

e3

e4

e5

S2

S3

S4

S5

The generic idea for many other applications of S-time-distance

Source: P.Sicherl, Time Distance – Another Measure of Achieving Lisbon Targets, European Regional Economic Forum EREF-2005 Nova Gorica, Slovenia, 27-28 October 2005

Monitoring attainment of the Lisbon target for employment rate

58

59

60

61

62

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65

66

67

68

69

70

71

72

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Time

Em

plo

ymen

t R

ate

(%)

Target

EU15

BE2

DE1

ITC4

ITD4

AT22

SI

SE01

USA

Stockholm 76.9

Baden-Württemberg

Steiermark

SloveniaVlaams Gewest

Friuli-Venezia Giulia

Lombardia

USA

EU15

Path to Target 70%

Source: P.Sicherl, ibid.

Monitoring: time distance deviation from the path to Lisbon target in 2003

Path to Target

Friuli-Venezia Giulia

Slovenija

Vlaams Gewest

Lombardia

EU15

Steiermark

Baden-Württemberg

-10-8-6-4-20246810

S-time-distance in years: - time lead, + time lag from assumed path to target

(-12) USA

(-17) Stockholm

Monitoring and goodness-of-fit test in two dimensions The importance of using S-time-distance as a second dimension for monitoring and benchmarking across indicators in many fields is self explanatory, and immediately operational. A more long term

scientific assignment is to develop optimizing procedures in models based also on the time distance deviations. E.g. Nobel prize winner Granger and Jeon (1997, 2003) further elaborated S-time-distance

for the use as a criterion for evaluating forecasting models of leading and lagging indicators.

Consensus forecast and actuals in two dimensionsUSA, growth rate of GNP deflator (1973-1985)

83

8584

82

76

74

73

7879

77 80 75

81

-4

-3

-2

-1

0

1

2

3

4

-3-2.5-2-1.5-1-0.500.511.522.53

Error in timing: S-time-distance in years P.Sicherl 1994

forecast too high and too early

forecast too high and too late

forecast too low and too late

forecast too low and too early

actual (0,0)

Co

nsen

su

s f

ore

cast

of

infl

ati

on

rate

min

us

actu

al

Time distance measure is intuitively understood by policy makers, managers, media and general public and is comparable across different variables, fields of concern, and units of comparison.

Source: P.Sicherl, A New Generic Statistical Measure in Dynamic Gap Analysis, The European E-Business Report, 2004 Edition, European Commission, Enterprise Directorate General, Luxembourg, 2004

Digital divide in EU15 in time (S-time-distance): how many months earlier was the level of selected categories in 2002 attained by average Internet usage

5

13

19

30

26

43

52

60

0 12 24 36 48 60 72

Internet usage

Internet usage at home

Internet usage

Internet usage at home

Internet usage

Internet usage at home

Internet usage

Internet usage at home

Fem

ale

Ag

e 50

+1s

t in

com

eq

uar

tile

Lo

wed

uca

tio

n

S-time-distance in months: time lag behind the average Internet usage (base=0)

S-time-distances for buying online for sectors compared with the average percentage of diffusion for all sectors

Source: P. Sicherl, Pilot study: Sectoral time-distances in the adoption of e-commerce activity, in The European e-Business Market Watch, Special Report, A Guide to ICT Usage Indicators, European Commission, DG Enterprise & Industry, 2005, http://www.ebusiness-watch.org/resources/documents/TR01_Indicators_2005_web.pdf

-60

-48

-36

-24

-12

0

12

24

36

48

60

1997 1998 1999 2000 2001 2002 2003

S-t

ime-

dis

tan

ce in

mo

nth

s:

- ti

me

lead

, +

tim

e le

g f

or

the

resp

ecti

ve s

ecto

r

Textile Chemical Electronics Transport Retail Tourism ICT srv. Business s. Health Craft

Average for all sectors

BENEFITS OF USING TIME DISTANCE

ANALYSIS

SUMMARY: Benefits of immediate operational uses of time distance

• 2.1 A new view in competitiveness issues, benchmarking, target setting and monitoring for economic, employment, social, R&D and environment indicators at the world, EU, country, regional, city, project, socio-economic groups, company, household and individual levels

• 2.2 A broader dynamic framework for interrelating Lisbon strategy issues of growth, efficiency, inequality and convergence

• 2.3 Enhanced semantics for policy analysis and public debate

• 2.4 Additional exploitation of databases and indicator systems

• 2.5 An excellent presentation and communication tool - among different levels of decision makers and interest groups- for describing of the situations, challenges and scenarios- for proactive discussion and presentation of policy alternatives to policy

makers, media, the general public and mobilizing those participating in or being affected by the programs

- for communicating the urgent need for change and reforms