## Base No increase Base Increase Myopic expectation Perfect expectation

Figure 5.23 Effect of sudden increase in 1980

XCF, of capacity over expected output is reached. This is the excess capacity reason for scrapping old vintages.

The investment decision requires some elaboration. Equation (5.5) provides an output measure of investment. From this the number of machines of vintage t planned at time t is calculated:

¡, = b\y, (5.6) Then the (historic cost) investment expenditure on vintage t is calculated as

Et=KtIt where Kt is the real price of capital goods at time t (deflated by the price index for manufacturing output). It is assumed that total expenditure E is not all incurred in one period, but rather is spread over the LD periods between planning and bringing into commission a new machine. The pattern of distribution over the LD periods can be modelled as a beta distribution function with parameters p and q (to be estimated). This allows for a wide range of patterns of such expenditure. Accordingly for /=1,... ,LD define o) by:

Then total investment expenditure in period t will be given by

Figure 5.24 Effect of unexpected increase

TE will be comparable with the quarterly series on investment expenditures.

Miscellaneous aspects

Two final aspects are needed to complete the description of the model. First, the determination of the capacity of machines after the date of installation needs to be discussed. This is done by assuming that depreciation takes the form of a particular proportion ô of existing capacity being taken out of operation each period (until it is scrapped). Thus:

Second, it is necessary to make assumptions about how expectations of output and factor prices are formed. A simple form of adaptive expectations is assumed, whereby at time t producers use the past LT observations on the variable to fit a linear trend, which is then extrapolated forward the appropriate number of periods.

### Estimation

The model has been estimated using full-information maximum likelihood on quarterly data for the UK manufacturing sector (excluding iron and steel) over the period 1955Q1-1989Q4. The estimated parameters are the matrix A= [ay], «j,...,«^ LD, LT, XCF, p, q and 8. Because the likelihood function cannot be assumed to be differentiable in parameters, a simplex algorithm (Nelder—Mead) was used to maximize the likelihood function.

APPENDIX 5B PARAMETER ESTEMATES

Matrix of parameters A =

0.0572 -0.0500 0.0256

-0.0410 0.1471 0.1944

Depreciation rate 0.041 Investment period 2 Expected life of vintages 45 Excess capacity factor 1.37 Technical progress rates: Oj=0.0064, o2=0.0072, u3=0.0029, u4=0.0109 weights for investment: period 1, 0.51; period 2, 0.49 Premium on treasury bill rate to obtain discount rate 0.04525

0.0312 -0.0230 0.2572 0.0803