International Finance Discussion Papers (IFDP)
December 1989
A Substitute for the Capital Stock Variable in Investment Functions
Guy V.G. Stevens
Abstract:
Capital stock variables appearing in investment and other equations are almost always constructed by the "perpetual inventory method." Successive values are related by the well-known equation:
where K(t) is the measure of the real capital stock at time t, I(t) is the real rate of investment, and 
the rate of depreciation. By successive backward substitutions for K(t-l), K(t) can be expressed equivalently as a weighted sum of past levels of investment plus the depreciated value of an initial real capital stock:
![$ K(t)= {\textstyle\sum\limits_{i=0}^{t-1}} [I(t-i)(1-\delta)^{i}]+K(0)(1-\delta)^{t}.$](/pubs/ifdp/1989/368/img3.gif)
The initial real capital stock, K(O), that is implicitly a component of every measure of the capital stock calculated by this method can rarely be measured, however, with any degree of accuracy. As demonstrated in this paper, the measurement error can frequently lead to severe bias in the estimated coefficients of investment functions.
This paper proposes a method to bypass this source of measurement error. In important cases it is then possible to estimate unbiased and consistent coefficients.
PDF: Full Paper
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