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An Evaluation of Alternative Methods of Estimating Capital Services

John BaldwinWulong Gu

Micro Economic Analysis DivisionStatistics CanadaMay 14, 2008

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Concept of capital services

A measure of capital input which would be consistent with production theory is the flow of services that capital goods provide over a time period.

The price of capital goods vs. the unit price of capital services (or user cost of capital):

– While the price of the capital good is available, the price of the services that the capital good yields is not usually observed and needs to be inferred.

– Statisticians need to estimate the price of capital services.

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User cost of capital services

Jorgenson and Griliches (1967) have developed a method for measuring the price and volume of capital services that is based on the economic theory of production.

The concept of capital services and capital rental prices is now well established with further developments due to Jorgenson (1995), Hulten (1990), Diewert (2004), and Schreyer, Diewert and Harrison (2005).

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User cost of capital services

The user cost of capital can be thought of as the price that a well functioning market would produce for an asset that is being rented by an owner to a user of that asset.

Jorgenson and Griliches (1967) show that the formula for the rental price of a unit of capital is

1 1( )t t t t t tc q r q q q

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User cost of capital services

The user cost of capital formula can be modified to take into account taxes (Christensen and Jorgenson, 1969; Schreyer, Diewert and Harrison, 2005).

[ ]* *1 1

11t kt kt

kt kt t kt k kt kt tt

uz ITCc q r q q

ud p f- -

æ - - ö÷ç= + - +÷ç ÷çè ø-

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The issues in estimating the user cost of capital

The choice of the rate of return.

The choice of capital gains.

The treatment of corporate tax provisions in the user cost estimation.

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Endogenous vs. exogenous rate of returns

Endogenous (or ex post) rate of returns:– The rates of returns are calculated endogenously from

data on capital income and capital stock from the system of national accounts.

Exogenous (ex ante) rates of returns:– The rates of returns are chosen exogenously from

observed rates in financial markets.– The exogenous rate of returns in this paper is weighted

average of debt costs and rate of returns on equity.

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Endogenous vs. exogenous rate of returns

The endogenous rate of returns approach was chosen at Statistics Canada to estimate the user cost of capital services:

– It is provides a fully integrated set of accounts.

– The assumptions that are required to make use of capital income in the national accounts in estimating capital services are fully compatible with the assumptions that underlie the growth accounting framework for estimating MFP.

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Capital gains

There is little disagreement that, on theoretical grounds, capital gains should be included in the rental price of capital.

Question is how capital gains should be included.

– Capital gains (estimated as change in asset prices) are volatile.

– If there is no inexpensive way to realize capital gains, changes in asset prices derived from price indices are not a very useful way to measure the capital gains component of the rental price of capital.

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Capital gains

We will examine three alternative treatment of capital gains:

– Instantaneous asset-specific real capital gains.

– Smoothed asset-specific real capital gains

– No asset-specific real capital gains: all assets have the same nominal capital gains (that are set equal to smoothed CPI).

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Tax parameters

The rental cost of capital formula requires us to estimate a number of tax parameters.

This formula is costly to implement and therefore sometimes ignored.

We will examine the effect of excluding tax parameters on estimated capital services and MFP growth.

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The alternative specifications of user cost formulae

Real capital gains

Yes, not smoothed

Yes, smoothed

No

User cost with tax parameters

Endogenous rate of return M1 M2 M3

Exogenous rate of return M4 M5 M6

User cost without tax parameters

Endogenous rate of return M7 M8 M9

Exogenous rate of return M10 M11 M12

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The effects of alternative specifications

We will compare the effects of alternative user cost specifications on:

– The average rates of return,

– The cost share accruing to capital,

– The increase in the price of capital services,

– The increase in capital composition, and

– The growth in multifactor productivity (MFP).

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Data for the paper

The Canadian KLEMS database.

The data on investment and capital stock for 28 reproducible capital stock plus land and inventories at the industry level.

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The effects on rate of return

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1961 1966 1971 1976 1981 1986 1991 1996 2001

M1 M2 M3 M4-M6

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The cost share of capital

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1961 1966 1971 1976 1981 1986 1991 1996 2001

M1-M3 M4 M5 M6

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The user cost of capital

0

20

40

60

80

100

120

140

1961 1966 1971 1976 1981 1986 1991 1996 2001

M1 M2 M3 M4 M5 M6

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Annual growth in capital quality and MFP, 1981-2001

M1 M2 M3 M4 M5 M6

Annual growth in capital quality (%)

1.1 1.1 0.9 1.1 1.1 0.9

Annual MFP growth (%)

0.3 0.3 0.4 0.3 0.3 0.4

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The bias of excluding tax parameters in user cost

The bias of ignoring taxes in the annual MFP and capital composition estimates is small for both endogenous rate and exogenous rate methods.

The bias of ignoring taxes is much larger for the exogenous rate method than for the endogenous rate method.

This suggests that the endogenous method has an advantage over the exogenous method.

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The aggregation of capital service over industries

Top-down vs bottom-up approach.

– The bottom-up approach are used by Statistics Canada and the U.S. BLS to estimate aggregate capital services.

– Alternatively, the top-down approach can be used to estimate aggregate capital services.

Empirical evidence appears to favour the top-down approach:

– Large difference in the rate of return. The rate of return is positively related to capital stock growth across industries.

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The difference in capital growth and MFP growth using the two approaches

Bottom-up Top-down

Period 1981 to 2001

Capital services 3.55 3.09

Multifactor productivity growth 0.12 0.31

Reallocation of capital 0.46 …

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Conclusions

Comparison of exogenous rate and endogenous rates.

– The endogenous rate has a number of advantages: more stable cost share of capital, more stable user cost of capital.

– The effects of two approaches on MFP growth and capital service growth is small.

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Conclusions

Comparison of alternative treatment of capital gains.

– Moving from instantanous capital gains to moving average of capital has little effect on capital service growth and MFP growth.

– What matters is whether we include asset-specific real capital gains. Capital service growth is higher and MFP growth is lower if we do not include asset-specific capital gains.

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Conclusions

The effect of excluding tax parameters on capital service growth and MFP growth.

– The bias in MFP growth and capital service growth when we exclude tax parameters is small.

– This suggests that it is probably a good idea to exclude tax parameters in gthe user cost calculation as the EU KLEMS did.

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Conclusions

The difference between bottom-up and top-down approach.

Empirical evidence appears to favour the top-down approach.

The reallocation of capital accounts for a significant share of capital service growth.

The bottom-up approach yields higher capital growth and lower MFP growth than top-down approach.