418 Structural Time Series Models
the International Monetary Fund (DeMasi, 1997), the Congressional Budget Office
(2001), and the European Commission (see McMorrow and Roeger, 2001).
The PFA assumes that technology can be represented by a Cobb–Douglas produc-
tion function with constant returns to scale on labor, measured by hours worked
or by the number of employed persons, and capital:
yt=ft+αht+( 1 −α)kt, (9.23)whereftis the Solow residual,htis hours worked,ktis the capital stock (all variables
expressed in logarithms), andαis the elasticity of output with respect to labor
( 0 <α< 1 ).
To achieve the decompositionyt=μt+ψt, the variables on the right-hand side of
equation (9.23) are broken down additively into their permanent (denoted by the
superscriptP) and transitory (denoted by the superscriptT) components, giving:
ft=ft(P)+ft(T), ht=h(tP)+h(tT), kt=k(tP). (9.24)It should be noticed that potential capital is always assumed to be equal to its actual
value; this is so since capacity utilization is absorbed in the cyclical component
of the Solow residual. Only survey-based measures of capacity utilization for the
manufacturing sector are available for the euro-area.
Hence potential output is the value corresponding to the permanent values of
factor inputs and the Solow residual, while the output gap is a linear combination
of the transitory components:
μt=ft(P)+αh(tP)+( 1 −α)kt,
ψt=ft(T)+αh(tT). (9.25)Hours worked can be separated into four components that are affected differently
by the business cycle, as can be seen from the identityht=nt+prt+ert+hlt, where
ntis the logarithm of working-age population (i.e., population of age 15–64),prtis
the logarithm of the labor force participation rate (defined as the ratio of the labor
force to the working-age population),ertis the logarithm of the employment rate
(defined here as the ratio of employment to the labor force), andhltis the logarithm
of labor intensity (i.e., average hours worked). Each of these determinants is in turn
decomposed into its permanent and transitory component in order to obtain the
decomposition:
h(tP)=nt+prt(P)+er(tP)+hlt(P), h(tT)=pr(tT)+ert(T)+hlt(T). (9.26)The idea is that population dynamics are fully permanent, whereas labor force
participation, employment and average hours are also cyclical. Moreover, since
the employment rate can be restated in terms of the unemployment rate, we can
relate the output gap to cyclical unemployment and potential output to structural
unemployment. As a matter of fact, since the unemployment rate is one minus the
employment rate,ut=log( 1 −exp(ert)), the variablecurt=−ert(the contribution