Potential Output: Concepts and Measurement - Department of Labour

Darren Gibbs 83
p
⎛ Qt
Assuming that labour productivity ⎜ ⎞
p
⎟
⎝ Lt
⎠ follows a simple time pattern,
Christiano rearranges the above equation to express actual labour input as a
function of actual output and that time pattern, and obtains estimates of the b s
coefficients. Using these coefficients and an independent measure of L p t
, 11 the
demand equation can be inverted to yield an estimate of the output gap as a
function of lagged values of the input gap.
A second approach which makes use of a capital (or investment) demand
function was proposed by Hickman (1964). In this approach the demand for
capital, K * t
, is expressed as:
* * *
t 0 1 t 2 t 3
log K = α + α logQ + α log P + α t
where Q t * and P t * represent permanent income and relative output prices at time
t. (The model assumes annual data.)
Assuming that the capital stock follows a partial adjustment process, and that
both permanent income and relative output prices depend linearly on current
and lagged values of actual output and actual prices respectively, it is possible
to estimate Q t * as a function of capital and output price series.
The relative advantage of the inverted demand function approaches discussed
above is that although, computationally, they are slightly more burdensome than
the other approaches discussed so far, they do go some way towards addressing
some of the weaknesses in the simpler approaches. They are also simpler to
apply than the next technique we will discuss, which requires us to estimate the
underlying production function. However, as is usually the case, the search for
computational simplicity requires a trade-off to be made with theoretical
desirability. Strong assumptions need to be made about functional forms and the
time behaviour of various variables.
There are a number of difficulties with applying these approaches to New
Zealand data. In the case of the labour demand approach, sufficiently disaggregated
data over a long enough time period is either extremely unreliable or
simply unavailable. Without this disaggregation, the approach differs little from
that suggested by Okun; and the capital demand approach has all the limitations
that were discussed earlier in the context of the output/capital ratio approach.
The production function approach
The final approach that we shall discuss in this section is the production function
approach which, at least on theoretical grounds, is by far the most desirable. The
essence of the production function approach is an explicit modelling of output
in terms of the underlying factor inputs, which involves the specification and
11
Christiano derives a measure of potential hours demand by applying cyclically adjusted
participation and unemployment rates to eight age-gender groups in the population.
Hours are converted to efficiency units by valuing them using relative wages. This is often
known as ‘Perry weighting’, based on Perry (1971).