1

DEPRECIATION OF DURABLE DEPRECIATION OF DURABLE GOODS IN AN UNSTABLE GOODS IN AN UNSTABLE ECONOMY: THE CASE OF ECONOMY: THE CASE OF

ARGENTINA ARGENTINA ““A Hulten&Wycof ApproachA Hulten&Wycof Approach””

Ariel CorembergAriel CorembergECLAC Buenos Aires ArgentinaECLAC Buenos Aires Argentina

CONICET/IDESCONICET/IDESacorem@fibertel.com.aracorem@fibertel.com.aracoremb@yahoo.com.ar

The 2008 World Congress on National Accounts and Economic Performance Measures for Nations

May 12–17, 2008Key Bridge Marriott (Arlington, VA—minutes from Washington D.C.)

2

Identification of the Depreciation Identification of the Depreciation Pattern in emerging economies using Pattern in emerging economies using

Vintage Assets Prices (H&W Vintage Assets Prices (H&W approach)approach)

Argentina during 1998-2002: the biggest & Argentina during 1998-2002: the biggest & longest economic depression of its modern longest economic depression of its modern

economic history, DDD currency devaluation economic history, DDD currency devaluation (default & desdoralization) which provoked a (default & desdoralization) which provoked a

high instability in relative priceshigh instability in relative prices

OBJECTIVEOBJECTIVE

3

• (Koopmans 1947) This research applies the famous Koopman`s motto:“It is necessary to avoid Measurement without theory”

• (J. Hicks 1981) quoted by Hulten“ The measurement of capital is one of the nastiest jobs that economists have set to statisticians”

• Diewert (2003): “The main problem in accounting is determining the value of capital goods that are used by the firm more than one fiscal year”

4

SUMMARYSUMMARYConceptual and Theoretical IssuesConceptual and Theoretical Issues• Importance • Concepts (SNA93, OECD, Hill, Hulten, Diewert)• Main Standard Depreciation Methods• Asymmetric Information in Durable Goods

Empirical Results in ArgentinaEmpirical Results in Argentina• Box Cox Test: Simple and Double Form• Crossection and Panel Data Results• Age Price Profile Under Inflation

5

• The empirical estimation of rate & depreciation pattern reduces the uncertainty about the real value of capital stock calculated by PIM by standard (fix) assumptions

• If the depreciation shape is not geometric, the aggregate depreciation depends on age structure of the stock and also is endogenous.

• The Instability of the relative prices in developing countries could have effects on durable goods market and also on age price profile

• The use of standard price index could biased the capital stock and also the analysis of wealth and productivity of an economy

6

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10Age

Pri

ce

of

Ca

pit

al

Go

od

(Y

ea

r 0

=1

00

)

Hiperbolic b=0.75

Straight Line

Geometric

Geometric R=2

Sum of the digits

AGE PRICE PROFILESAGE PRICE PROFILES

7

1. Econometric estimation of the hedonic price indicator in the base year

2. Econometric Test of Functional Shape of Depreciation (Box-Cox test)

3. Testing the Functional Shape of the Withdrawals Function

4. Valuation of the physical stock according to their attributes

5. Measuring the capital stock series by PIM (benchmarking HV base year)

n

i iii uabp1

log

ap* pppp 1* ii

iaa 1*

Hedonic Valuation MethodHedonic Valuation Method

8

HEDONIC VALUATION (58.5%)•DWELLING UNITS

•NON RESIDENTIAL PRIVATE CONSTRUCTION

•LIVESTOCK

•AGRICUTURAL ASSETS

•FARM TRACTORS & OTHER AGRICULTURAL MACHINES

•AIRCRAFTS

•TRANSPORT EQUIPMENT

PIM (41.5%)

•REST OF DURABLE EQUIPMENT AND MACHINES

•PUBLIC WORKS

CAPITAL STOCK IN ARGENTINA BY METHODCAPITAL STOCK IN ARGENTINA BY METHOD

9

Depreciation Value“Lemmons Problem” +Biased -BiasedCensored Data -Biased +BiasedAlternative uses Biased BiasedAge Price Profile Stability Biased Biased

TABLE 1Assymetric Information in Used Durable Goods Market

10

EFFECTS OF INFLATION ON DEPRECIATIONEFFECTS OF INFLATION ON DEPRECIATION

EFFECTS OF INFLATION ON DEPRECIACION PATTERN

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10Age

Du

rab

le G

oo

d P

rice

Ag

e 0=

100)

Original

Neutral Inflation

Non Neutral Inflation (average life decreases)

Non Neutral Inflation (average life increases)

11

TABLE 2TABLE 2Information Sources on the Age Price Profile of Durable GoodsInformation Sources on the Age Price Profile of Durable Goods

Sources Period

Farm Tractors Surveys Prices of Farm Tractors 1997

Aircrafts Aircraft Bluebook Price Digest 2002

Cars Tax Agency based on Market Prices 1998-2002

Light commercial vehicles Tax Agency based on Market Prices 1998-2002

Buses Tax Agency based on Market Prices 1998-2002

Trucks Tax Agency based on Market Prices 1998-2002

12

ap 1

1 p

p

Box-Cox Test Simple VersionBox-Cox Test Simple Version

tap 21

;

13

Trucks: Age Price Profile 1998-2002

0

10000

20000

30000

40000

50000

60000

70000

80000

1 2 3 4 5 6 7 8 9 10 11

Age

Pri

ce

Price Obs.

Boxcox

Buses: Age Price Profile 1998-2002

0

10000

20000

30000

40000

50000

60000

1 2 3 4 5 6 7 8 9 10 11

Age

Pri

ce

Price Obs.

Boxcox

Light Commercial Vehicles: Age Price Profile 1998-2002

0

5000

10000

15000

20000

25000

30000

35000

1 2 3 4 5 6 7 8 9 10 11

Age

Pri

ce

Price Obs.

Boxcox

Cars: Age Price Profile 1998-2002

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 1 2 3 4 5 6 7 8 9 10

Age

Pri

ce

Price Obs.

Box-Cox

14

Farm Tractors: Age Price Profile

0

10000

20000

30000

40000

50000

60000

1 2 3 4 5 6 7 8 9 10

Age

Pri

ce

Price Obs.

Box-Cox

15

Aircrafts: Age Price Profile

0

500000

1000000

1500000

2000000

2500000

3000000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57

Age

Pri

ce

Precio Promedio

Box-Cox

16

In every case, the test confirmed convex functional forms, but the null hypothesis of identification of any exact functional form proposed (geometric, reciprocal or linear) was rejected,

Except in the case farm tractors, In the last case, the geometric form was accepted (=0).According to table 6 by year: also buses (1999)

TABLE 3: Box-Cox Test Simple FormTABLE 3: Box-Cox Test Simple Form 1 2 Log-likelihood n. obs.

Aircraft -0,17 5,34 -0,01   -36935 2.783

Cars -0,17 -11,45 -0,03 0,01 -222518 20.675

LCV -0,03 -37,21 -0,10 0,02 -47642 Semilog 4.636

Buses -0,15 -19,71 -0,04 0,01 -12601 1.148

Trucks 0,39 -1244,31*

-3,88* 0,71 -38351 3.293

Farm Tractors

-0,06* 7,56 -0,03   -6200 semilog 571

17

211ap

Box-Cox Test: Double FormBox-Cox Test: Double Form

TABLE 7TABLE 7Box-Cox Test Double Form for Airplanes and Farm Box-Cox Test Double Form for Airplanes and Farm

TractorsTractors  1 2 1 Log-

likelihoodn. obs.

Aircraft -2,58 3,83 0,39 0,00 (31.057)

2.783

Farm Tractors -0,05 0,87 8,18 -0,05 (6.198)

571

18

TABLE 8TABLE 8Double Form Box-Cox Test for Transport Equipment by Category with Double Form Box-Cox Test for Transport Equipment by Category with

Annual frequencyAnnual frequency

Cars 1998 1999 2000 2001 2002

-0,20 -0,16 -2079,05 -0,27 -0,28

0,40 0,51 0,02* 0,76 0,80

-0,05 -0,06 -1317,15 -0,02 -0,01

4,40 5,03 9,27 3,49 3,41

Log-likelihood -33.439 -39.489 -45.689 -49.353 -54.688

n. obs. 3.098 3.673 4.243 4.682 4.998

LCV 1998 1999 2000 2001 2002

0,22 -2,10 0,45 0,34 0,09

0,14* 18707,78 0,17* 0,35 0,26

-3,12 0,00 -27,29 -7,55 -0,89

37,39 0,48 204,88 83,71 17,06

Log-likelihood -6.250 -7.508 -9.729 -10.797 -12.523

n. obs. 623 763 972 1093 1197

19

TABLE 8: Double Form Box-Cox Test for Transport Equipment by TABLE 8: Double Form Box-Cox Test for Transport Equipment by Category with Annual frequencyCategory with Annual frequency

Buses 1998 1999 2000 2001 2002

-0,79 0,10 -0,21 -0,37 -0,09*

1,13* -2.156.209* 0,22* 0,66 0,59

0,00 -395,11 -0,06 -0,01 -0,13

1,26 19,74 4,27 2,68 6,92

Log-likelihood -1358 -2178 -2584 -3146 -3258

n. obs. 127 191 242 293 308

Trucks 1998 1999 2000 2001 2002

0,06* -2,31 0,53 0,53 0,77

-1091,41 775,30 -9,39 19,79 -10,19

-2143,14 0,00 -8,78E+07 0,00 -5,20E+13

15,31 0,43 9351476,00 500,82 5,10E+12

Log-likelihood -8.083 -8.090 -12.321 -4.461 -4.868

n. obs. 692 743 1065 392 429

20

In almost every case the shape of depreciation has been convex:

1< 1 y 2<1; but in few cases an exact form could be detected

In the case of Light C.V.(1999), Buses (1999) and Trucks (1999 y 2001), there could be some atypical shapes (backward S, accelerated depreciation or in 2 steps) but they were not detected by the test

21

Table 4: Average Annual Rate of Change in Vintage Asset Vehicles PricesTable 4: Average Annual Rate of Change in Vintage Asset Vehicles Prices

Cars 1999 2000 2001 2002 LCV 1999 2000 2001 2002 Buses 1999 2000 2001 2002 Trucks 1999 2000 2001 2002

0 -13,7 13,1 3 56,6 0 39,6 -33 -8,7 71,2 0 23,9 -5,6 1 27,8 0 3 -12 -6,7 27,7

1 -8,2 2,6 -0,2 57,7 1 39,9 -29 -11 62 1 30,9 -9,8 -0,1 31,1 1 6,8 -13 16,5 5,9

2 -2,6 5,6 -8,1 49,8 2 49,1 -32 -9,9 52,4 2 31,7 -12 5,7 24,1 2 -17 8,9 -2,1 22,8

3 -1,7 1,7 0,6 43,2 3 37,5 -23 -13 55,1 3 17,5 -31 20,5 26,9 3 -10 -15 31,6 6,4

4 -0,4 -6 3,4 60,4 4 48,7 -32 -8,3 51,9 4 33,5 -31 -1 49,6 4 -13 -13 3,3 51,1

5 -2,2 -13,5 7,4 60,1 5 -1,2 -0,1 -14 55,2 5 97,8 -40 -5,3 32 5 -22 -2 3,4 19,5

The relative asset price changed through time.

The age price profile may not seem stable.

22

Table 5: Price of New VehiclesTable 5: Price of New VehiclesAnnual Rate of ChangeAnnual Rate of Change

CARS LCV TRUCKS BUSES

DGI INDEC DGI INDEC DGI INDEC DGI INDEC

1999 -1,30 -13,70 -2,30 39,60 0,50 3,00 0,20 23,90

2000 1,90 13,10 0,70 -32,60 0,00 -11,60 19,40 -5,60

2001 -7,00 3,00 -11,00 -8,70 -8,00 -6,70 -4,20 1,00

2002 78,30 56,60 86,10 71,20 64,70 27,70 193,00 27,80

The use of standard price index (with representative models) could biased the value capital stock and also the analysis of wealth and productivity of an economy.

23

Cars: Age Price Profile by Year

0

10000

20000

30000

40000

50000

60000

70000

0 1 2 3 4 5 6 7 8 9 10

Age

Pri

ce

1998

1999

2000

2001

2002

24

Buses: Age Price Profile by Year

0

10000

20000

30000

40000

50000

60000

70000

80000

1 2 3 4 5 6 7 8 9 10 11

Age

Pri

ce

1998

1999

2000

2001

2002

25

Light Commercial Vehicles: Age Price Profile by Year

0

5000

10000

15000

20000

25000

30000

35000

40000

1 2 3 4 5 6 7 8 9 10 11

Age

Pri

ce

1998

1999

2000

2001

2002

26

Trucks: Age Price Profile by Year

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 1 2 3 4 5 6 7 8 9 10Age

Pri

ce

1998

1999

2000

2001

2002

27

Shifts in the age price profile curve Shifts in the age price profile curve due to inflation were not neutraldue to inflation were not neutral

1. Consumer Durable Goods : Cars & Light C.V.: Life Span Decreases

2. Capital Goods: Buses and Trucks: Average Life Increases

28

CAPITAL STOCK IN ARGENTINA-INDECCAPITAL STOCK IN ARGENTINA-INDEC1993

K/POP 16.423K/OUTPUT 2,30 Depreciation/Stock 5,0%Depreciation/GDP 11,4%Net Investment/GDP 7,6%Internal Rate of Return 15,6%Annual Average Rate of Growth (93-00) 2,9%

(K/POP)USA>(K/POP)ARG: u$s 84.464>u$s15.506

29

CAPITAL OUTPUT RATIOCAPITAL OUTPUT RATIOK/GDP

1994 TOTALArgentina DNCN-INDEC 2,30 Chile (BC Chile) 2,10 Brasil (IPEA) 3,10 Australia 4,00 Belgium 3,80 Canada 4,50 Denmark 5,70 Finland 5,90 France 3,10 Italy 3,90 Japan 3,00 Holland 3,70 Norway 5,30 Spain 3,20 Sweeden 4,50 United Kingdom 3,40 United States 3,60 Germany 4,00 China 2,00 Hong Kong 2,20 India 1,80 Indonesia 1,70 Corea 2,40 Malasia 2,70

30

•The econometric test weakly verifies convex depreciation in every type of durable goods

•The econometric test only verifies an exact geometric shape in the case of farm tractors (1997) and buses (1999) with B-X Simple (but any B-X double form)

•The age price profile in Argentina changes through time and it is not neutral when there is inflation

•This results are relevant in order to estimate the capital stock and empirically test the main assumptions in PIM: average life, retirement pattern and depreciation in unstable economies

31

Main Suggestion From Main Suggestion From Emerging EconomiesEmerging Economies

This study supports OECD Canberra Group II remarks:

• AT LEAST VERIFY PIM ASSUMPTIONS FOR A BASE YEAR

• BUT IN UNSTABLE ECONOMIES: !!WE MUST UPDATE THE RESEARCH MORE FRECUENTLY