1 A Recursive Dynamic Computable General Equilibrium Model For ...

G t = I/K (22)
Relating changes in the expected rate of return (Et) to capital growth (Gt) in period ‘t’,
it is implicitly assumed that the latter is a positive function of the former. Moreover, it is
important that when expected rates exceed (are below) normal rates of return, the rate of
capital growth is above (below) the historical growth rate of capital. These relationships are
captured by the logistic capital accumulation function (dropping industry subscripts):
β
t
β
t
G = Q.
G M /( Q −1
+ M )
(23)
t
trend
where Gtrend is the historical rate of capital growth; Mt is the ratio of expected to normal
rates of return in period t; the parameter Q is the ceiling limit multiple of the capital growth
rate to the historical growth rate of capital, and β is the elasticity of G t with respect to
changes in Mt. Thus, if the expected rate of return (Et) is equal to the normal rate (Rt), then
Mt is equal to 1, and therefore via changes in the capital stock in equation (19) the rate of
capital growth in period ‘t’ is equal to the historical or trend rate (Gt = Gtrend). Similarly, if
Mt is zero then Gt is also zero, implying that for capital growth to occur, the expected rate
of return must be positive (i.e., with zero expectations, individuals will not invest). Finally,
if Mt assumes a ‘large’ value, then Gt closely approximates the ceiling limit multiplied by the
trend rate. In other words, with Et values exceeding Rt beyond a certain limit, the rate of
growth of capital cannot exceed a certain threshold. Examining different values of Q, Gtrend and β, it is possible to track the relationship between Mt and Gt. 35