Rates of return and alternative measures of capital input

Nicholas OULTONLondon School of Economics

and

Ana RINCON-AZNARNational Institute of Economic and Social Research

August 2010

Presented at The First World KLEMS Conference, Harvard University, Boston, August 19-20, 2010

This research was made possible by financial support under the 6th Framework Programme of the European Commission to the “EU KLEMS Project on Productivity in the European

Union”. The views expressed are our own.

Outline

• Aims of the study:1. Estimate average rate of return in 11

branches and 14 countries: can observed patterns be explained by economic factors?

2. Measure capital’s contribution by three methods: • Ex-post • Ex-ante • Hybrid (Oulton, 2007)

2

The spirit of the new SNAIssues raised here are relevant given the new

System of National Accounts 2008:• Capital stocks, capital services and capital

consumption should all be estimated in an internally consistent way. All underlying data should be consistent (see OECD manuals).

• and Capital Compensation should include a breakdown into the returns to different assets (Schreyer et al. 2005; EC 2009, chapter 20).

3

Ex post versus ex ante: previous literature

Hall and Jorgenson (1967)Berndt and Fuss (1986)Jorgenson, Gollop and Fraumeni (1987)Jorgenson (1989)Berndt (1990)OECD Capital Manuals (2001, 2009)Oulton (2007)

4

Reminder

• Growth rate of capital services is weighted average of growth rates of asset stocks. Weight for each asset is rental price (user cost) times value of asset stock.

• Contribution of capital to growth of output is capital’s share times growth rate of capital services.

• But both rental prices and capital’s share can be either ex post or ex ante

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Main idea

Ex ante, for each type of capital, a firm tries to equate the expected value of its marginal product to the expected rental price (user cost); the latter includes the required rate of return, depreciation and the expected capital gain. Firms plan that the nominal rate of return should be the same for all assets (and equal to the required rate).

But ex post, things can go wrong! And the ex post rate of return may be different for different assets.

Each type of capital gets paid the value of its actual marginal product (under competition). The sum of these returns equals actual, observed capital compensation (profit).

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Ex-post versus ex-ante rental prices (1)

1

: growth of -th asset price; : rental price of -th asset in period ;

: purchase price of -th asset at end of period ; : -th depreciation rate

[ (1

jt jt

jt j

exantejt t j t

j q j t

p j t j

q r E

Ex ante rental price

1 , 1

, 1

( )) ( )]

: rate of return ( value of actual, ex post marginal product)

[ (1 ) ]

: , ex post rate of return

jt t jt j t

t

truejt jt j jt jt j t

jt

E p

r required

q r p

r actual

True ex post rental price

Common ex pos

, 1[ (1 ) ]

: rate of return assumed equal to observed, rate

ex postjt t j jt jt j t

t t

q r p

r r commonaverage

t rental price

7

Mean nominal rate of return in an industry:

1 1

-1Value of capital stocks

: capital compensation (profit): depreciation charge on asset

: capital gain (loss) on asset

: number of types of capital asset

m mt jt jtj j

tt

t

jt

jt

CAP D CGr

CAPD j

CG j

m

8

Ex-post versus ex-ante rental prices (2)

9

In , all expectations are correct:

( )

and competition plus cost minimisation ensures that

So

jt jt

t jt t t

true ex post ex antejt jt jt

full equilibrium

E

r r r r

q q q

Which is the best method?

• To estimate the capital services index, we should ideally weight each asset by the true, ex-post rental price.

• We could equally well weight by the ex-ante rental prices since these are proportional to the true, ex-post ones, if the production function is CES (Oulton 2007).

• We should not use the common, ex-post rental prices. • To measure capital’s contribution to output growth, we should

weight the growth rate of capital services by the share of actual profit in output: the hybrid method.

• Capital compensation equals sum of ex ante returns to each asset, grossed up, if the production function is CES.

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The EUKLEMS data

• We estimate capital stocks and average real rates of return across 7 asset types in 10 branches plus the market economy for 14 countries, 1971-2005: 11 EU countries

Austria, Denmark, Finland, France, Germany, Italy, Netherlands, Portugal, Spain, Sweden, and UK. 3 non-EU Australia, Japan, US

• 7 types of capital (residential structures excluded)3 ICT types:

Computing equipment, communications equipment, software4 non-ICT types: other machinery and equipment, transport equipment, non-residential structures, and other assets

• 10 branchesAtB, C-K plus total of these (“market economy”)

11

Name EUKLEMSCode

1 Agriculture, hunting, forestry & fishing

AtB

2 Mining & quarrying C3 Manufacturing D4 Electricity, gas & water E5 Construction F6 Wholesale & retail trade G7 Hotels & restaurants H8 Transport & storage &

communicationI

9 Financial intermediation J10 Renting of machinery and

equipment and other business activities (exc. industry 70)

K

11 Market economy (sum of above) MKT

Branches of the market economy

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Ex-post method: number of negative rental prices

• 746 out of 27,930 rental prices are negative: 2.7%• Over half of these (414) are for “Other construction”• 248 are in Transport and storage, 226 in Financial

intermediation• 180 are in Finland

NOTE: negative rental prices make no sense economically. So to implement the common ex post method they have to be smoothed away.

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Number of negative rental prices under the ex-post method, by country and branch

AtB C D E F G H I J K TOTAL EU Austria 0 0 0 0 0 0 0 15 4 0 19 Denmark 0 0 5 26 6 3 4 20 27 0 91 Finland 1 4 7 15 11 20 9 47 66 0 180 France 0 0 3 0 3 0 0 33 18 2 59 Germany 0 0 0 15 10 10 2 26 21 8 92 Italy 0 0 0 8 0 8 5 24 37 11 93 Netherlands 0 0 0 0 0 0 0 17 13 0 30 Spain 0 0 1 0 8 5 0 11 7 0 32 Sweden 0 0 0 2 0 2 1 2 6 2 15 Portugal 3 0 0 1 0 0 0 5 3 0 12 UK 0 4 6 8 4 5 1 19 13 0 60 Non-EU Australia 0 3 2 4 7 1 1 24 5 0 47 Japan 0 0 0 0 0 1 1 3 4 2 11 US 0 0 0 1 0 0 0 2 2 0 5 TOTAL 4 11 24 80 49 55 24 248 226 25 746

14

Number of negative rental prices under the ex-post method, by country and asset

IT ISOF CT OMACH TRAEQ OCON OTHER TOTAL EU Austria 0 0 0 0 0 18 1 19 Denmark 0 1 32 6 5 36 11 91 Finland 1 9 22 24 18 96 10 180 France 0 0 3 3 0 45 8 59 Germany 0 0 15 16 6 40 15 92 Italy 0 0 8 8 5 61 11 93 Netherlands 0 0 0 0 0 26 4 30 Spain 0 0 1 8 5 11 7 32 Sweden 0 0 2 2 1 8 2 15 Portugal 3 0 1 0 0 8 0 12 UK 0 9 10 4 7 30 0 60 Non-EU Australia 0 3 6 7 2 26 3 47 Japan 0 0 0 1 1 7 2 11 US 0 0 1 0 0 2 2 5 TOTAL 4 22 101 79 50 414 76 746

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Implementing the ex ante method

• The required real rate of return is estimated as the time mean of the real rate of return in the market economy. So it varies across countries but not across branches or over time. Justification: the real rate is trendless.

• Each expected price growth rate is prediction from AR(1) model.

• Result: no negative rental prices.

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7.3

8.4

7.1

15.9

7.1

9.19.7

8.3

2.4

11.5

9.4

11.6

8.5

13.3

05

1015

AUS AUT DNK ESP FIN FRA GBR GER ITA JPN NLD PRT SWE USA

1971-2005, % p.a.Mean real rate of return in the market economy

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Method

Prices Weights in capital services index

Weight for contribution of capital

Ex post Actual Ex post Actual CAP

Ex ante Forecast by ARMA model

Ex ante Expected CAP

Hybrid Forecast by ARMA model

Ex ante Actual CAP

Comparison of methods

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Mean annual contribution of capital, 1971-2005: number of times when absolute difference

between methods exceeds 0.5% p.a. (11 x 14 = 154 cases in all)

Branch Ex-ante versus

ex-post Hybrid versus

ex-post AtB 5 0 C 7 0 D 0 0 E 6 0 F 2 0 G 1 0 H 5 0 I 12 0 J 11 7 K 7 0 MKT 0 0 Total 56 7

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Conclusions

• The three methods produce very similar results at the market economy level.

• But there are marked differences between the ex-ante and the ex-post methods at the branch level.

• The hybrid and the ex-post method are quite similar at the branch level.

• The hybrid method gives a theoretical justification for smoothing away the negative rental prices generated by the ex-post method.

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THE END