Net stocks are estimated using the perpetual inventory method with geometric
depreciation. The method begins with the investment for each year *i* in type
of asset *j*, that is, $I\_ij\_$. For current-cost and real-cost valuation,
the investment that is used in the calculation is in 1992 dollars; that is,
the investment is in current dollars that have been deflated by the price
index for that type of asset with a 1992 reference year. For historical-cost
valuation, investment in dollars is used in the calculation so that assets are
measured using the prices that existed when they were acquired.

The annual geometric rate of depreciation for type of asset *j*, $\delta \_j\_$,
is related to the declining-balance rate for type of asset *j*, $R\_j\_$, (which
is the multiple of the comparable straight-line rate) and to the average
service life for type of asset *j* in years, $T\_j\_$, by:

$\delta \_j\_\; =\; R\_j\_/T\_j\_.$

Consider the contribution of investment during year *i* in type of asset *j*
to the real-cost net stock at the end of year *t*, $N\_tij\_$. New assets are
assumed, on average, to be placed in service at midyear, so that depreciation
on them is equal to one-half the new investment times the depreciation rate.
Therefore, the contribution to the real-cost net stock at the end of year
*t* is given by:

$N\_tij\_\; =\; I\_ij\_\; (1-\delta \_j\_/2)(1-\delta \_j\_)^t-i^\; ,$

where $t\ge i$.

To calculate the real-cost net stock at the end of year *t* for asset *j*,
N_tj_, the contributions are summed over all vintages of investment flows
for that asset so that:

$N\_tj\_\; =\; \sum \_i=1\_^t^\; N\_tij\_.$

The equations used to estimate historical cost stocks are identical to equations (2) and (3) except that the investment flows are expressed at historical cost rather than at real cost.

Current-cost estimates of the net stock of asset *j* (in dollars), $C\_tj\_$,
are obtained by multiplying the real-cost net stock at the end of year *t* for
asset *j* by the value at the end of year *t* of the price index that was used
to deflate nominal investment in asset *j*, $P\_tj\_$, so that:

$C\_tj\_\; =\; P\_tj\_\; N\_tj\_.$

The current-cost net stock of assets at the end of year *t*, $C\_t\_$, is
estimated as the sum of the stocks given above across all types of assets, so
that:

$C\_t\_\; =\; \sum \_j\_\; C\_tj\_.$

Depreciation on an asset *j* during year *t*, $D\_tj\_$,
equals the net stock of asset *j* at the end of year *t-1* plus
investment in asset *j* during year *t* less the net stock of
asset *j* at the end of year *t*, so that:

$D\_tj\_\; =\; N\_t-1,j\_\; +\; I\_tj\_\; -\; N\_tj\_.$

This equation holds under real-cost and historical-cost valuation.

Current-cost depreciation, $M\_tj\_$, is calculated by multiplying
real-cost depreciation from equation (6) by the average price of asset
*j* during year *t*, $\&overline;P\_tj\_$, so that:

$M\_tj\_\; =\; \&overline;P\_tj\_\; D\_tj\_.$

Current-cost depreciation for an aggregate of assets in year *t*
is calculated by summing across the various types of assets, that is, by:

$M\_t\_\; =\; \sum \_j\_\; M\_tj\_.$