In this paper we shall limit our attention to the Cobb-Douglas production function with constant returns to scale and four alternative specifications of Hicks-neutral disembodied technical change:
|Y ||=||AK bL1 - bexp(rt)||Model||(1)|
|Y||=|| AK bL1 - bexp[rot + (1/2)r1t2]||Model|| (2)|
|Y||=||AK bL1 - bexp(rt + mvt)||Model ||(3)|
|Y||= ||AK bL1 - bexp[rot + (1/2)r1t2 + mvt ]||Model ||(4)|
The variable vt appearing in models (3) and (4) is a special variable designed to catch the impact of cyclical fluctuations in the rate of change of the total factor productivity
It is defined in the following way:
where gt = 1, if t is a recession year and gt = 0 if t is a normal year
The economic meaning of the parameters is straightforward:
is the initial level of the total factor productivity, i. e. the level in the year to. This parameter is of little interest for us, because it depends on units of measurement and cannot be directly compared between different countries
is the capital elasticity of output, which should not be interpreted as a factor share of capital, because the
neoclassical theory of distribution is hardly applicable to the Soviet-type economic systems.
in the model (1) is an average annual rate of technical change or the rate of change of the total factor productivity4 in a given country. It captures the trend values in data, which cannot be attributed to conventionally measured capital or labor. In addition to the true effect of technical change it may reflect the impact of data distortions as for example the hidden inflation mentioned above.
in the model (2) are based on the assumption that the rate of technical change r(t) is a linear function of time:
Apparently ro is the rate of technical change at the beginning of the observed period while r1 is the annual increment or decrement of the rate of technical change.
in the models (3) and (4) measures the difference of the rate of change of the total factor productivity in normal and recession years. In the model (3) this rate would be r in normal years and r + m in recession years. In the model (4) m represents a deviation of the linear trend in recession years from the trend in normal years. In both cases we expect m to be negative.
The assumption of linear trend in the rate of technical change — models (2) and (4) — is, of course, very crude; such a model can represent only a very rough approximation of reality, but it still may be by far superior to even cruder assumptions underlying the model (1). If the estimates of parameters r1 and m turn to be significant, the hypothesis of the constant rate of technical change will have to be rejected in favor of declining and/or cyclically fluctuating rate of technical change.