The measurement of capital input

19.73    The quantity of capital services is estimated by assuming that capital services produced by an asset are proportional to the value of productive capital stock of the asset; that is:

    \(\large K_t = u_t PKS_t\)

where \(K_t \)is the quantity of capital services, and \(PKS_t \)is the productive capital stock and \(u_t\) is the capacity utilization rate.

19.74    The capacity utilization rate is assumed to be constant over time. This assumption has two implications. First, as \(u_t\) is constant and invariant to time, a change in the quantity of capital services delivered from any given capital asset is tantamount to a change in its productive capital stock. Second, variations in the utilization of the capital stock are not accounted for in the estimation of its capital services, and as a consequence changes in the capital services over time may reflect the impact of short-term business cycles, other than movements of capital input.

19.75    The productive capital stock estimates are derived from data on gross fixed capital formation (except inventories and land), using the PIM. The essence of this method is to transform all capital assets of different vintages into equivalent efficiency units and then add them up into an estimate of the productive capital stock. Chapter 14 provides a full description of the procedures used to derive the productive capital stock. Chapter 10 provides a full description of the data sources and procedures used to compile estimates of gross fixed capital formation.

19.76    In estimating the value of labour services, statisticians can directly observe labour rental prices as wage rates paid to workers. In the case of capital however, the rental prices for capital have to be imputed. The rental price reflects the price at which an investor is indifferent between two alternatives:

1. earning a nominal rate of return on a different investment; and
2. buying a capital asset, renting it out, collecting rent and selling it in the next period. 

19.77    A standard specification for the capital rental price in the absence of taxes is the arbitrage equation⁹⁰:  

     \(\large P_j,_{t-1}(1+i_t) = r_{j,t}+(1-δ_j)P_{j,t}\)         - - - - - - - (19.1)

where \(i_t\) is the nominal interest, \(P_{j,t-1}\) is the acquisition price of capital asset \(j\) at the beginning of the period, \(r_{j,t}\) is the rental price, \(P_{j,t}\) is the price of capital asset j at the end of the period and \(δ_{j,t}\) is the rate of economic depreciation.

19.78    This can be rearranged into the expression:

    \(\large r_{j,t}=i_tPj_{,t-1}+δ_{j,t}P_{j,t}- \pi _{j,t}\)         - - - - - - - (19.2)

where \(\pi_{j,t} = P_{j,t} - P_{j,t-1}\) is the asset-specific capital gains term.

19.79    Equation (19.2) shows that the capital rental price consists of three components: the rate of return to capital, the depreciation rate and the capital gain or loss due to revaluation. The industry dimension is supressed here.

19.80    When tax considerations are given to the measurement of capital rental prices (both capital income taxes and indirect business taxes), the tax-adjusted rental price equation becomes:

    \(\large r_{i,j,t}=T_{i,j,t}(i_{i,t}P_{i,j,t-1}+δ_{j,t}P_{i,j,t}-π_{i,j,t})+x_{i,t}P_{i,j,t-1}\)         - - - - - - - (19.3)

where \(i\) indexes industries, \(T_{i,j,t}\) is the income tax parameter and \(x_{i,t}\) is the effective net indirect tax rate on production. The description of data sources for constructing the tax parameter is provided in Annex C.

19.81    The rate of return to capital \(i_t\) can be estimated by either endogenously or exogenously. Under the endogenous approach, the total value of capital services in each industry is assumed to be equal to the compensation for all assets in that industry. The resulting internal rate of return exhausts capital income and is consistent with constant returns to scale. The nominal rate of return is the same for all assets in an industry but may vary across industries.

19.82    In the case of the exogenous approach, the nominal rate may equal the Treasury bond rate, or the dividend yield on a stock index. This method allows the value of capital income to deviate from property compensation, assuming imperfect competition and non-constant returns to scale. For a detailed discussion of these two alternative methods and associated sensitivity analysis, see Appendix 2 Sensitivity Analysis of Capital Inputs, in the Information paper, Experimental Estimates of Industry Multifactor Productivity.

19.83    The ABS follows the endogenous method in producing its official productivity estimates. For the corporate sector, iit, is solved for all assets in each industry by assuming that gross operating surplus, \(GOS_{it}\) equals the rental price multiplied by the real productive capital stock in each industry:

    \(\large GO{S_{i,t}} = \sum\limits_j {{r_{i,j,t}}{K_{i,j,t}}}\)         - - - - - - - (19.4)

and substituting for the rental price in equation (19.4) giving:

    \(\large GO{S_{i,t}} = \sum\limits_j {{K_{i,j,t}}\left( {{T_{i,j,t}}\left( {{i_{i,t}}{P_{i,j,t - 1}} + {\delta _j}{P_{i,j,t}} - {\pi _{i,j,t}}} \right) + {x_{i,t}}{P_{i,j,t - 1}}} \right)}\)         - - - - - - - (19.5)

so

    \(\large {i_{i,t}} = \frac{{GO{S_{i,t}} - \sum\nolimits_j {{K_{i,j,t}}\left( {{T_{i,j,t}}\left( {{\delta _j}{P_{i,j,t}} - {\pi _{i,j,t}}} \right) + {x_{i,t}}{P_{i,j,t - 1}}} \right)} }}{{\sum\nolimits_j {{K_{i,j,t}}{T_{i,j,t}}{P_{i,j,t - 1}}} }}\)         - - - - - - - (19.6)

19.84    To prevent negative rental prices, the ABS imposes a floor limit on the internal rate of return of CPI plus 4 per cent; otherwise, the endogenous rate is used.

19.85    The depreciation of a capital asset measures the change in its real economic value during the accounting period. The depreciation rates are derived using asset age-price profiles. The age-price profiles are constructed by using corresponding age-efficiency profiles, multiplied by a suitable discount rate (the ABS chooses a real discount rate at 4 per cent). See Chapter 14 for the detailed description of age-efficiency and age-price profiles and their roles in constructing various capital components.  

19.86    The capital gain or loss due to revaluation can be calculated as an asset-specific deflator or a general deflator. As defined in equation (19.3), the asset-specific capital term is used and calculated as the percentage change in the value of the asset in time t-1 relative to its value in time t. Alternatively, \(π_t\) can be replaced by a general price deflator such as the consumer price index. The former is preferred because it is able to account for the large changes in relative prices across heterogeneous asset classes and therefore reduces measurement errors. However, the disadvantage of using asset-specific deflators is that it often introduces volatility into the rental price equation. 

19.87    The elemental capital inputs are compiled at a detailed level. There are capital input measures for up to 16 asset types for the corporate and unincorporated entities for each of the 16 ANZSIC industry divisions that comprise the market sector. For each capital input there is a volume indicator of the flow of capital services, and a rental price that is used to weight the service flow with the service flows of other capital inputs.