1. Introduction
Why do some countries, and some regions within countries, have
higher capital intensity than others? (1) This question is at the heart
of economic development analyses since cross-country comparisons
demonstrate that per capita incomes are closely related to capital
intensity. Recent studies that have addressed this question analyse the
roles of sectoral productivity and the price of capital (Hsieh &
Klenow, 2007) and the value on international markets of domestically
produced output (Caselli & Feyrer, 2007). We extend these analyses
deriving some new, and in some cases counter-intuitive, findings despite
adopting a conventional neoclassical structure.
A number of recent studies have examined why New Zealand's
labour productivity growth has lagged that of Australia. (2) The
exploitation of large mineral deposits in Australia has been cited as
one driver of the differential performance, although the empirical
relevance of this factor has been disputed (Kerr, 2007). A proximate
explanation for the difference in productivity performance is that,
compared with New Zealand, capital intensity has increased markedly in
Australia; i.e. New Zealand is 'capital shallow'. A related
explanation is that wages relative to capital returns are low in New
Zealand compared with Australia. However, these are only partial
explanations since capital intensity and wages are themselves
endogenous.
In order to understand the foundational determinants of capital
intensity and output, we develop a model that explains these outcomes as
a function solely of variables that are exogenous to the relevant
country or region. Our analytical framework is designed to provide
insights relevant to small open economies that import capital goods and
produce export goods priced in world markets. The framework explicitly
models impacts on capital intensity of endowments, sectoral structure,
cost of capital, world prices, and factors affecting multi-factor
productivity (implicitly including technology, entrepreneurship,
managerial ability and regulation). (3)
We find that aggregate capital intensity is a function of
multi-factor productivity (MFP) in the traded goods sector (but not the
non-traded sector), the capital share parameter in the production
function for each sector, the cost of capital (including any country
risk premium), and the terms of trade (price of domestically produced
tradable goods to the price of imported capital goods). Total output and
consumer utility are affected by the same variables and by MFP in the
non-traded sector. As in the one-sector neoclassical growth model of
Barro and Sala-i-Martin (1999), the domestic capital stock is not
dependent on domestic savings since, with open capital markets, foreign
agents can invest in the domestic economy. Domestic savings propensities
instead determine the amount of (domestic and overseas) capital owned by
the domestic population.
We subject the model to a range of permanent shocks and examine the
consequent change in capital intensity. Identical shocks to traded and
non-traded sectors have different effects. Wages are a function solely
of (exogenous) tradable goods prices and of parameters of the tradables
production function. Furthermore, domestic welfare increases more
through an incremental increase in traded sector MFP than through an
identical incremental increase in non-traded sector MFP.
Prior to specifying the model, we discuss related studies (Section
2). Section 3 specifies a theoretical model that underpins subsequent
analysis. We subject this model to eight experiments, corresponding to
changes in traded and non-traded sector MFP, the capital share parameter
of each sector, a change in the country risk premium, a change in the
world price of traded (exportable) goods, a change in the world price of
capital goods and a change in consumer preferences between traded and
non-traded goods. Section 4 discusses the results, demonstrating how
they may be used to distinguish between competing hypotheses explaining
capital intensities across countries. It applies these insights to
observed differences in capital intensity and per capita GDP between
Australia and New Zealand.
2. Prior studies
2.1. Investment determinants
Numerous studies and surveys of capital investment determinants
have been published (e.g. Rossana, 1990; Chirinko, 1993: Hamermesh &
Pfann, 1996: Hubbard, 1998; Roberts, 2003: Tevlin & Whelan, 2003).
However, the capital stock and output in these studies are not generally
solved as a function solely of exogenous variables facing the firm or
the economy. Instead, capital is often expressed as a function of output
and/or relative prices which are endogenous.
In discussing the standard neoclassical specification of the demand
for capital, which relates capital stock to output and the real cost of
capital, Chirinko (1993) notes that output is itself a function of
capital but, under constant returns to scale, the optimal capital stock
is not well defined. This reasoning may underlie why the capital stock
is not normally solved out as a function of exogenous variables in
microeconomic contexts. However, there is no need to retain output as a
separate explanatory variable for capital within an aggregate context;
exogenously determined labour supply enables derivation of a solution
for the optimal capital stock as a function solely of variables
exogenous to the domestic economy.
2.2. Capital stock and development
Hsieh and Klenow (HK, 2007) note that one of the strongest
relationships in the empirical growth literature is the positive
correlation between the investment rate in physical capital and the
level of output per worker. Differences in physical capital intensity
play an important role in accounting for why some countries are rich and
others are poor. Standard explanations for capital intensity differences
relate to savings rate differences, capital tax differences or policies
that drive up the cost of capital (e.g. tariffs on capital goods). This
view is consistent with empirical data showing that the relative price
of capital is typically two to three times higher in a poor country than
in a rich country. These types of price effects cannot be examined
within one-sector growth models.
The standard relationships between investment rates and income per
head relate to PPP-adjusted variables. When evaluated at domestic
prices, HK find virtually no relationship between investment rates and
incomes per head. Investment goods are no more expensive in poor
countries than in rich countries, whereas consumption prices tend to be
lower in poor countries. HK interpret this to mean that poor countries
have low investment rates in PPP terms primarily because their (traded)
investment sectors have low productivity compared with their
(non-traded) consumption sectors.
Caselli and Feyrer (CF, 2007) take the issues raised by HK further.
They calculate the marginal product of capital (MPK) across a large
sample of countries, assuming that MPK = aY/K where a is the capital
share in GDP, Y is aggregate output, and K is aggregate capital stock.
CF find substantial differences in MPK between rich and poor countries,
which they attribute to differences in the ratio of output prices to
capital goods prices ([p.sub.y]/[p.sub.k]). Poor countries tend to have
high MPKs while rich countries have low MPKs. These differences may
arise due to tax effects; alternatively, poor countries may have
relatively low MFP in producing capital goods relative to producing
final goods. (4) Relative price differences may also reflect differences
in the composition of output or in unmeasured quality.
CF recognise that where [p.sub.y]/[p.sub.k] differs across
countries, it is MPK.[p.sub.y]/[p.sub.k] that should be equalised across
countries. Assuming Cobb-Douglas technology, they find that differences
in [p.sub.y]/[p.sub.k] explain a sizable proportion of the variation in
MPK across countries. CF comment: 'One way to put this is to say
that the main reason for capital's failure to flow to poor
countries is that what it produces there is of little value, compared to
the cost of installation.'
CF examine two theoretical specifications that might result in
[p.sub.y]/[p.sub.k] varying across countries. The first is a model of
'Complete Country Specialization'. Each country i specialises
in producing a tradable consumption good with dollar price
[p.sup.i.sub.y]. There is a unique tradable investment good with price
[P.sub.k]. (5) If investors worldwide can borrow and lend dollars at the
common rate R *, and if depreciation is denoted by d, then:
[P.sup.i.sub.y]/[P.sub.k] = [[R.sup.*] - (1 - d)]/[MPK.sup.i]
The relative price ratio ([P.sup.i.sub.y]/[P.sub.k]) will differ
across countries inversely to differences in [MPK.sup.i] across
countries. CF specify a 'More General Model' by assuming that
each country produces an identical tradable consumption good (with
dollar price [P.sub.T]) and a non-tradable consumption good or,
equivalently, a country-specific consumption good (with dollar price
[[P.sup.i].sub.NT]). In this specification, however, CF assume that
labour is sector specific and in each sector there is a given fraction
of the labour force. One can then solve the model for the proportion of
total capital allocated to each sector as a function of the sector
specific complementary factors, prices and proportion of labour in each
sector. The usefulness of this approach is limited by the need to assume
that a constant fraction of the labour force is assigned to each sector.
This assumption is unrealistic when an economy's structure changes
as an endogenous reaction to changes in exogenous variables. The model
in the next section does not suffer from this constraining assumption;
it generalises the approach to consider a number of other determinants
of capital intensity including those considered by HK.
3. The model
Following the insights of HK and CF, we develop a small
computational model applicable to small open economies. The following
features are considered relevant: capital goods (K) are imported:
production is split between non-traded goods ([Y.sub.N]) and
(exportable) traded goods ([Y.sub.T]); capital goods prices ([P.sub.K])
and exportables prices ([P.sub.T]) are set in world markets: [P.sub.T]
may differ from [P.sub.K], so allowing a terms of trade change; (6)
non-traded goods prices ([P.sub.N]) endogenously adjust to clear the
goods markets: wages (W) adjust to clear the labour market; depreciation
rates (d) are set exogenously; real interest rates (r) are set
internationally and incorporate an exogenously set country risk premium.
There is no government sector in the model. Given the exogeneity of d, r
and [P.sub.K], and the exclusion of taxes, the user cost of capital is
therefore set exogenously.
Our model is neoclassical, with no treatment of spillovers or other
endogenous growth elements. In part, this reflects the observation that
the underlying neoclassical determinants of productivity and capital
intensity remain important whether or not endogenous growth elements are
incorporated into the model. Thus, we concentrate on the former while
remaining agnostic about the importance of the latter. (7) Since our
interest is in explaining long term developments, we examine only
equilibrium outcomes. Comparative static outcomes following changes in
crucial parameters indicate the sensitivity of long-term outcomes to
changes in exogenous fundamentals; they also indicate the direction of
dynamic adjustments that must occur between different equilibria.
We begin with a two-sector model of domestic production. Output of
non-traded goods ([Y.sub.N]) is a constant returns to scale Cobb Douglas
function of capital used in the non-traded sector ([K.sub.N]) and labour
employed in the non-traded sector ([L.sub.N]); [A.sub.N] determines
productivity; the capital share is given by [alpha]. Similarly, output
of traded goods ([Y.sub.T]) is a constant returns to scale Cobb Douglas
function of capital used in the traded sector ([K.sub.T]) and labour
employed in the traded sector ([L.sub.T]); [A.sub.T] determines
productivity; the capital share is given by [beta].
[Y.sub.N] = [A.sub.N] [K.sup.[alpha].sub.N] [L.sup.1-[alpha].sub.N]
(1)
[Y.sub.T] = [A.sub.T] [K.sup.[beta].sub.T] [[L.sup.1-[beta].sub.T]
(2)
Labour is fully employed, with the total labour force exogenously
given by L (i.e. total labour supply is perfectly inelastic):
[L.sub.N] + [L.sub.T] = L (3)
The wage cost of a unit of labour is W. The rental price of capital
(R) is a function of the price of capital goods, the real interest rate
and the depreciation rate (all exogenous variables):
R = (r + d) [P.sub.K] (4)
Firms in each of the non-traded and traded goods sectors choose
their quantities of labour and capital to maximise profits, taking R, W,
[P.sub.N], [P.sub.T], [A.sub.N], [A.sub.T], [alpha] and [beta] as given.
This yields the standard equations for factor demands:
[L.sub.N] = (1 - [alpha])[Y.sub.N][P.sub.N]/W (5)
[K.sub.N[ = [alpha][Y.sub.N][P.sub.N]/R (6)
[L.sub.T] = (1 - [beta])[Y.sub.T][P.sub.T]/W (7)
[K.sub.T] = [beta][Y.sub.T][P.sub.T]/R (8)
Substituting equations (7) and (8) into equation (2) determines the
wage rate as a function of exogenous variables:
W = (1 - [beta]){[[A.sub.T][[beta].sup.[beta]][P.sub.T][R.sup.-[beta]]}.sup.1/(1 - [beta]) (9)
From equation (9), wages are a function of exogenous prices
([P.sub.T], [P.sub.K], r), the depreciation rate (d) and production
parameters. Notably, the production parameters ([A.sub.T], [beta])
relate solely to the tradables production function. Thus wages relative
to external prices are unaffected by production conditions in the
non-traded sector. As derived below, however, real consumption wages are
affected by nontraded production function parameters. Substituting
equations (5) and (6) into equation (1) yields equation (10) which can
be rearranged to give an expression for [P.sub.N] as a function of
exogenous variables plus W (which, in turn is a function of exogenous
variables) as in equation (11):
W = (1 - [alpha]){[A.sub.N][[alpha].sup.[alpha]][P.sub.N][R.sup.-[alpha]]}.sup.1/(1 - [alpha]) (10)
[P.sub.N] = [[alpha].sup.-[alpha] [(1 - [alpha]).sup.[alpha]-1]
[A.sup.-1.sub.N][W.sup.1-[alpha]] [R.sup.[alpha]] (11)
All prices in the system have now been determined.
Substituting equation (6) into equation (1), and equation (8) into
equation (2) determines the output/labour ratios in the non-traded and
traded goods sectors respectively:
[Y.sub.N]/[L.sub.N] =
[{[A.sub.N][([[alpha][P.sub.N]/R).sup.[alpha]}.sup.1/(1 - [alpha]) (12)
[Y.sub.T]/[L.sub.T]
[{[A.sub.T][([beta][P.sub.T]/R).sup.[beta]]}.sup.1/(1 - [beta]) (13)
Having determined prices, output/labour ratios and total use of
labour, we determine the split of production (and/or labour) between the
traded and non-traded goods sectors. Caselli and Feyrer (2007) do so by
assuming that labour is sector specific, so that each of [L.sub.N]/L and
[L.sub.T]/L is set exogenously. This is an extreme assumption. An
alternative method is to determine the relative shares from the
consumption side. By definition, the only agents who demand the
non-traded good are those who live in the domestic economy. Once we
determine [Y.sub.N] (as a function of prices and incomes), we determine
[L.sub.N] and thence [L.sub.T], [Y.sub.T], [K.sub.N] and [K.sub.T].
Assume that domestic agents' utility (U) is given by a
constant elasticity of substitution utility function defined over
consumption of the non-traded good ([C.sub.N]) and consumption of the
traded good ([C.sub.T]): (8)
U = {[gamma][C.sup.-[[phi].sub.N] + (1 -
[gamma])[C.sup.-[phi].sub.T]}.sup.-1/[phi] (14)
Maximising utility subject to income (given the constant labour
supply assumption) yields the relationship between consumption of the
two goods:
([C.sub.N]/[C.sub.T]) = [[[gamma]/(1 - [gamma]].sup.1/(1 + [phi])
[[P.sub.T]/[P.sub.N].sup.1/(1 + [phi])] (15)
Provided no output is wasted:
[C.sub.N] = [Y.sub.N] (16)
Total consumption equals total income accruing to residents (D:
[P.sub.N][C.sub.N] + [P.sub.T][C.sub.T] = I (17)
Total income (I) is given by wage income (which all accrues
domestically) plus net returns to domestically-owned capital, defined as
D. Since this is a stationary model, D is treated as constant (i.e. held
at the inherited equilibrium level). If D < [K.sub.N] + [K.sub.T],
some domestic capital is owned offshore; if D > [K.sub.N] +
[K.sub.T], domestic agents own some capital offshore. For simplicity,
our application of the model assumes that domestic wealth equals
domestic capital stock, but this assumption is inconsequential as shown
in the experiments that follow.
Net return to capital accruing to domestic residents equals the
real interest rate multiplied by the domestically-owned capital stock
(thus depreciation is reinvested and not consumed). Hence:
I = WL + r[P.sub.K]D (18)
Combining equations (15)-(18) yields an expression for [Y.sub.N] in
terms of known variables:
[Y.sub.N] = (I/[P.sub.T])[g.sup.[delta]][([P.sub.T]/[P.sub.N]).sup.[delta]]{1 + [g.sup.[delta]]([P.sub.T]/[P.sub.N]).sup.[delta] -
1]}.sup.-1] (19)
where g = [[gamma]/(1 - [gamma])] and [delta] = [(1 +
[phi]).sup.-1].
With [Y.sub.N] given by equation (19), we obtain [L.sub.N] from
equation (12), thence [L.sub.T] from equation (3) and [Y.sub.T] from
equation (13). [K.sub.N] and [K.sub.T] are given respectively by
equations (6) and (8). Thus, all variables are determined.
To operationalise the model, we assume the following base case
parameters:
The base case is symmetric in that the traded and non-traded
production functions are identical, prices of traded, non-traded and
capital goods are identical, (11) and consumption of non-traded goods
equals consumption of traded goods. Production of traded goods equals
production of non-traded goods plus depreciation (since replacement
capital goods must be imported). Over half the labour force and capital
stock (57.6% in each case) is therefore employed in the traded goods
sector.
Having established the base case, we vary exogenous parameters and
establish the impacts of each experiment on a range of variables
including: output (non-traded, traded, total); capital stock
(non-traded, traded, total (12)); capital/output ratio (non-traded,
traded, total); labour (non-traded, traded); consumption (non-traded,
traded, total); prices (price of non-traded goods, wages, real exchange
rate (13)); and utility. The last of these variables is the appropriate
measure of welfare in the model.
The chosen experiments reflect issues that have been mooted as
being relevant to explaining countries' capital intensity. They
include: underlying productivity (in non-traded and traded sectors);
(14) sector structure (specialisation in sectors with inherently low or
high capital shares); (15) cost of capital (r); (16) and terms of trade
([P.sub.T]/[P.sub.K]). (17) Another experiment relates to a shift in
consumption preferences between traded and non-traded goods to test the
impacts of this factor on capital intensity, the real exchange rate and
other variables. (18)
We change each of eight parameters (individually) by 1% and examine
the effects on the selected outcome variables. (19) The fact that the
base case is symmetric in parameters and in consumption outcomes across
sectors allows us easily to compare the effects of an increase in
parameters applying to the non-traded sector relative to those for the
traded goods sector. Despite the symmetry, the effects of parameter
variations across the two sectors are quite different from one another.
Tracing through the reasons for these differences is helpful in
formulating hypotheses relating to certain countries' economic
outcomes, including capital intensity outcomes.
Table 1 summarises the impacts of each of the eight experiments
under the assumption that utility is Cobb Douglas ([phi] = 0). With this
assumption, the share of nominal consumption across traded and
non-traded goods is constant for marginal changes. Table 2 assumes that
utility is CES with [phi] = 10. Under this assumption, an increase in
[P.sub.N]/[P.sub.T] results in an increase in the share spent on
non-traded goods.
Experiments 1 & 2: Non-Traded Sector Productivity Increase
([A.sub.N] [up arrow] 1%) and Traded Sector Productivity Increase
([A.sub.T] [up arrow] 1%)
Columns 1 and 2 of Tables 1 and 2 summarise the effects of
increasing non-traded sector multi-factor productivity ([A.sub.N]) and
traded sector multi-factor productivity ([A.sub.T]) by 1% respectively.
In each case, the productivity increase raises overall utility: however,
utility increases more following an increase in traded sector than in
non-traded sector productivity (under each of the alternative utility
assumptions (20)). In each example, the rise in AN and AT raises
domestic production and incomes (and hence total consumption and
utility). Foreign prices ([P.sub.T] and [P.sub.K]) remain unaffected by
the productivity changes. Thus, we are assuming that the rise in
[A.sub.T] (and also [A.sub.N]) affects domestic producers only and is
not shared by world producers. An example might be a domestic minerals
discovery.
A rise in [A.sub.N] raises production of non-traded goods, so a
fall in [P.sub.N] relative to [P.sub.T] is required in order for
[C.sub.N] to rise in tandem with [Y.sub.N]. In the Cobb-Douglas case,
the rise in [C.sub.N] (and [Y.sub.N]) is offset by a commensurate fall
in [P.sub.N]. Since [C.sub.N] [P.sub.N] is unchanged, [C.sub.T]
[P.sub.T] must also be unchanged: [C.sub.T] is therefore unchanged. No
labour or capital needs to be reallocated in this case, so capital,
labour and output in the traded sector remain unchanged. Labour in the
non-traded sector therefore remains unchanged. The effect of the 1% fall
in [P.sub.N] on non-traded goods sector profitability exactly outweighs
the positive profitability effect of the productivity increase; thus
[K.sub.N] also remains unchanged. Total consumption rises by 0.5% (equal
to the 1% rise in non-traded goods consumption plus 0% rise in traded
goods consumption) while gross output rises by the lesser amount of
0.42% (since there is no increase in output matching the depreciation
portion of gross production).
In the CES ([phi]) = 10) case, the change in relative prices
induces consumers to spread their real income gains over consumption of
both goods. Total consumption and total output rise by the same amounts
as with [phi] = 0 but [C.sub.T] and [Y.sub.T] now increase and a smaller
rise occurs in [Y.sub.N] ([C.sub.N]). There is some reallocation of
labour and capital to the traded goods sector away from the non-traded
goods sector.
Irrespective of the utility function, production conditions in the
traded goods sector are unaffected by the rise in [A.sub.N], so capital
intensity remains unchanged in the traded sector. However, the rise in
productivity in the non-traded sector results in non-traded output
rising with no change in the non-traded sector capital stock. The
non-traded sector and aggregate capital/output ratios therefore fall,
while sectoral and aggregate capital intensities remain unchanged. The
fall in the capital/output ratio is an optimal result of increased
non-traded sector productivity and is accompanied by a rise in output,
consumption and utility.
A rise in traded sector multi-factor productivity has more complex
effects than does the rise in [A.sub.N]. Since traded goods prices are
unaffected by the rise in [A.sub.T], the profitability of traded goods
production rises, so more capital is demanded in that sector. More
labour is also demanded, raising wages and thence [P.sub.N]. Higher
incomes are spread across consumption of non-traded and traded goods
(under each utility function) so non-traded goods production and capital
also rise. Capital intensity rises in each sector. The overall effect is
a rise in the economy's capital stock and hence in aggregate
capital intensity. (21) Non-traded goods consumption and output rise
more strongly in the [phi] = 10 than the [phi] = 0 case, so a small
reallocation of labour to non-traded goods production occurs in the
former case; in the Cobb-Douglas case, a reallocation of labour to the
traded sector occurs.
In both the [phi] = 10 and the [phi] = 0 cases, overall consumption
rises as a result of the traded sector productivity increase. Gross
output rises by more than consumption since the capital stock, and hence
depreciation, increases. The additional increment to gross output is
required to replace the depreciated capital. Gross output, consumption,
and utility each rise by more in response to a 1% traded goods
productivity increase than to a 1% non-traded goods productivity
increase. Capital intensity rises in the face of an AT shock and remains
unchanged in face of an [A.sub.N] shock, despite the built-in symmetry
of the model and the symmetrical nature of the changes to the base case.
A key contributor to the differing results is the limited demand
for non-traded goods. Traded goods face a flat demand curve: domestic
producers can sell as much production as they wish without moving the
price against them. By contrast, producers of non-traded goods face a
downward sloping demand curve, so extra production moves the price
against themselves. In the case of a 1% [A.sub.N] increase, [P.sub.N]
falls by approximately 1%, both absolutely and relative to [P.sub.T]. In
the case of a 1% [A.sub.T] increase, [P.sub.N] rises as pressure on
labour resources increases.
If [A.sub.N] and [A.sub.T] both rise by the same percentage,
capital intensity rises in each sector (and hence in aggregate) whereas
the capital/output ratio in each sector (and in aggregate) remains
unchanged. (22) Gross output, capital, consumption and utility all rise.
Traded output rises by more than non-traded output given the need to
generate extra traded product to meet the increased demand both for
domestic traded goods consumption and replacement capital.
Figure 1 graphs iso-utility curves in [A.sub.N], [A.sub.T] space.
The curve passing through [A.sub.N] = [A.sub.T] = 1 is the base case
curve. The iso-utility curves represent 5 percentage point increases in
utility. Comparing the base case curve with the next curve (downwards
and to the right), a 5% increase in utility can be gained either by an
approximate 7% increase in [A.sub.T] (with [A.sub.N] unchanged) or by an
approximate 10% change in [A.sub.N] (with [A.sub.T] unchanged).
At the margin, therefore, productivity improvement in the traded
goods sector has superior utility (and other) outcomes to an equal
productivity increase in the non-traded goods sector, despite the
symmetry built into the base case of the model. Put simply, it is
preferable to have improved productivity in a sector facing a flat
demand curve than one facing a downward sloping demand curve.
This finding has an implication for a number of economic policies.
For instance, consider the case where government has scarce resources
which can be used for a limited number of infrastructure projects, each
with an equal potential probability of raising productivity to the same
degree. According to this model, in allocating the resources government
should give greater weight to projects that raise productivity in the
traded goods sector or, more generally, in industries with flatter
demand curves. This is the case even if there were a marginally greater
likelihood of the projects increasing non-traded goods productivity than
traded goods productivity. (23)
[FIGURE 1 OMITTED]
Experiments 3 & 4: Non-Traded Capital Share Increase ([alpha]
[up arrow] 1%) and Traded Capital Share Increase ([beta] [up arrow] 1%)
Columns 3 and 4 of Tables 1 and 2 summarise the effects of
increasing the capital share in each industry by 1% (i.e. from 0.33 to
0.3333). This can be considered as an exogenous change, caused by a
change in optimal production technologies for the relevant industries.
In each case, the increased capital share results in higher
aggregate capital intensity and a higher capital/output ratio. Output,
consumption and utility all rise. Each of output, capital, the
capital/output ratio, consumption and utility rise more in response to a
1% increase in [beta] (traded sector) than a 1% increase in [alpha]
(non-traded sector). The reason for this differential impact again lies
with the price behaviour stemming from different demand curves. An
increase in the capital share of the non-traded sector ([alpha]) induces
a rise in the capital stock and output in the non-traded sector, but
this forces [P.sub.N] downwards (under both utility assumptions). The
reduction in [P.sub.N] causes labour resources to shift to the traded
sector, which encourages extra capital in the traded sector so as to
keep the capital/output ratio constant in that sector.
An increase in the capital share of the traded sector ([beta])
induces a rise in the capital stock and output in the traded sector, but
has no effect on [P.sub.T] which is set in world markets. (24) Labour
flows into the traded goods sector, lifting wages, so limiting the
inflow of labour to the sector. The rise in wages leads to increased
demand for non-traded goods inducing a rise in [P.sub.N], with the
result that non-traded capital and output also rise.
Figure 2 graphs iso-utility curves in [alpha], [beta] space. The
curve passing through = [beta] = 0.33 is the base case curve. The
iso-utility curves represent 5 percentage point increases in utility.
Comparing the base case curve with the next curve (downwards and to the
right), a 5% increase in utility can be gained either by an approximate
0.045 (13.6%) increase in [beta] (with [alpha] unchanged) or by an
approximate 0.065 (19.7%) change in [alpha] (with [beta] unchanged). To
the extent that one could engineer a change in the capital share of one
sector or another, utility would be increased more by having a
capital-intensive traded goods sector than by having a capital-intensive
non-traded goods sector. Countries with capital-extensive traded sectors
(e.g. countries that specialise in tourist services) might therefore be
expected to have lower capital intensity (ceteris paribus) than
countries with capital-intensive traded goods sectors (e.g. countries
that specialise in mining).
Experiment 5: Risk Premium Increase (r [up arrow] 1%)
Columns 5 and 6 of Tables 1 and 2 summarise the effects of an
increase in the country risk premium, reflected in a rise in r from 0.07
to 0.08. The results quantitatively (but not qualitatively) depend on
whether we assume that domestic agents own the domestic capital or
foreign capital, since the risk premium change means that returns differ
across countries. In the former case, there is much less of an income
loss to domestic agents arising from the increase in r than in the
latter case. Column 5 adopts the assumption that domestic agents receive
this return when investing domestically but receive the world return
(0.07) when investing internationally. Column 6 adopts the assumption
that domestic agents own foreign capital only (with domestic capital
being owned offshore) and so receive the world return on all their
wealth.
[FIGURE 2 OMITTED]
In each case, the direct effect of the rise in r is a reduction in
the capital stock (and hence capital intensity) in each sector. The cost
of capital rises by 7.69% (recalling that the depreciation rate and the
price of capital goods are held constant) so the capital/output ratio in
each sector falls by a similar amount (given the Cobb Douglas production
assumption). (25) With lower capital stock, labour demand falls, so
wages fall (by 3.58% in each case) to re-establish labour market
equilibrium.
When domestic capital is owned onshore, there is very little net
income loss to domestic residents with the higher risk premium. Wages
decline, but there is less depreciation owing to the reduced capital
stock. (26) The reduction in depreciation means that traded goods
production (which is required, in part, to fund depreciation) falls
relative to non-traded goods production. The latter is maintained at
close to its base case level as a result of the offsetting forces noted
above.
When domestic capital is entirely owned abroad, there is a much
more substantial income loss arising from the increased risk premium.
The same mechanisms are at work as discussed above, but the levels of
[C.sub.N] and [C.sub.T] now each fall by 2.83% rather than by 0.15% when
domestic capital is owned domestically. The reason is that foreign
owners of capital obtain a greater proportion of the returns generated
domestically than in the former case.
Experiments 6 & 7: Capital Goods Price Increase ([P.sub.K] [up
arrow] 1%) and Traded Goods Price Increase ([P.sub.T] [up arrow] 1%)
Columns 7 and 8 of Tables 1 and 2 summarise the effects of
increasing the price of capital goods and the price of traded goods by
1% respectively. In real terms, the effects of these two experiments are
virtually mirror images of each other. Each involves a terms of trade
change, one driven from the import side and one from the export side. An
increase of 1% in both [P.sub.K] and [P.sub.T] (a zero terms of trade
change) leaves all real variables unchanged with a 1% rise in all
domestic nominal variables (consistent with treating traded goods prices
as numeraires within the system).
A 1% increase in [P.sub.K] increases the cost of capital, so
reducing the capital stock in both sectors. The reduced capital stock
lowers depreciation and hence traded output decreases by more than
non-traded output. Consumption of each of non-traded goods and traded
goods declines by the same amount as the decline in non-traded output
(0.18%) under each utility function. The capital/output ratio decreases
by virtually 1% in response to the 1% increase in [P.sub.K] given the
Cobb Douglas production function. The aggregate capital stock (i.e.
aggregate capital intensity) falls by approximately 1.5% with an
accompanying approximate 0.5% decline in total gross output.
A 1% increase in [P.sub.T] increases the profitability of traded
goods production, raising capital in that sector. The rise in capital
stock induces a switch of labour from the non-traded to traded sector
and an increase in wages. Higher incomes result in consumers spreading
consumption over both non-traded and traded goods, resulting in a slight
rise in non-traded output following a 1% rise in [P.sub.N]. This
increased output is achieved through an increase in non-traded sector
capital stock. Mirroring the [P.sub.K] experiment, the capital/output
ratio rises by 1% in response to the 1% increase in [P.sub.T]; aggregate
capital intensity increases by 1.5% and total gross output expands by
0.5%.
Figure 3 depicts the iso-utility curves in [P.sub.T], [P.sub.K]
space. Increases in utility occur as shifts are made downwards and to
the left (each line represents a 1 percentage point increase in
utility). For small changes in [P.sub.T] and [P.sub.K] the lines are
virtually parallel to each other, demonstrating the equivalent nature of
increases in [P.sub.T] and decreases in PK on utility. The base case
line (passing through [P.sub.T] = [P.sub.K] = 1) demonstrates that
equivalent percentage changes in both [P.sub.T] and [P.sub.K] result in
unchanged utility.
Experiment 8: Consumption Preference Shift ([gamma] [up arrow] 1%)
Column 9 of Tables 1 and 2 summarises the effects of an increase in
[gamma], representing a change in consumer preferences away from traded
goods towards non-traded goods. Consumer preferences do not affect
production conditions; hence, all prices are left undisturbed by the
shift in [gamma]. In the Cobb-Douglas case (Table 1) a 1% rise in
[gamma] induces a 1% rise in [C.sub.N] (and in [Y.sub.N], [K.sub.N] and
[L.sub.N]) offset by a 1% fall in [C.sub.T]. The fall in [C.sub.T] is
accompanied by a 0.74% fall in each of [Y.sub.T], [K.sub.T] and
[L.sub.T] (recalling that traded good exports are required at the base
case level to finance imported capital goods).
As [phi] increases (Table 2) the transfer from traded to non-traded
consumption decreases. Nevertheless, the same patterns occur. Aggregate
output and capital intensity remain unchanged (for any value of [phi])
consequent on a change in [gamma]. Thus, neither capital intensity nor
output per person is a function of domestic preferences relating to
traded versus non-traded consumption goods; nor is the equilibrium real
exchange rate affected by changes in consumption preferences.
[FIGURE 3 OMITTED]
4. Discussion
The foregoing experiments indicate that a country will have
relatively low capital intensity if it has the following characteristics
(ceteris paribus): low traded sector MFP; a low capital share parameter
(especially in the traded goods sector); a high risk premium; high
capital goods prices; (27) and/or low traded goods prices. (28) Each of
these situations results in output, consumption and utility being low. A
country with relatively high non-traded sector MFP will have the same
capital intensity as an otherwise alike country but will have higher
aggregate output, consumption and utility. Output, consumption and
utility, however, do not increase as much following an increase in
non-traded sector MFP as they do through an equivalent increase in
traded sector MFP. We summarise qualitative responses of certain ratios
to changes in exogenous variables in Table 3. (29) Each indicated change
lowers the capital/output ratio (K/Y), but effects on other variables,
including capital intensity, differ.
An increase in [A.sub.N] (relative to [A.sub.T]) has a unique
combination of effects. It is the only case in which a decline in the
capital/output ratio is associated with an increase in output,
consumption and real wages (with no change in capital intensity). (30)
An increase in the country risk premium has the same directional
effects on every listed variable other than [P.sub.N]/[P.sub.K] as does
a rise in [P.sub.K] and a fall in [P.sub.T]. For each of these shocks,
international prices move against the domestic economy. They can
therefore each be conceptualised as an external price shock, whether
occurring in the goods or financial markets. Together, these shocks can
be differentiated from all other listed shocks by the prediction that
they have no effect on the real exchange rate, measured as
[P.sub.N]/[P.sub.T]. However, if the real exchange rate were interpreted
as [P.sub.N]/ [P.sub.K], each of the [P.sub.T] and [P.sub.K] shocks lead
to a fall in the real exchange rate whereas an r shock has no effect. A
financial shock can therefore be differentiated from a terms of trade
shock.
The qualitative effects on each listed variable of a decline in the
traded goods sector capital share ([beta]) are identical to those for a
decline in traded goods MFP, [A.sub.T]. These results differ from all
other sets of qualitative results. Over long periods one might rule out
declines in [A.sub.T]; thus, if these observations are apparent, one may
attribute them to a decline in [beta]. By contrast, low capital
intensity due to a decline in the non-traded goods capital share
([alpha]) has a unique set of outcomes. It results in lower output,
consumption and real wages, but a high real exchange rate, measured by
non-traded goods prices relative to each of capital goods prices and
traded goods prices.
The importance of the traded goods sector's MFP and capital
share parameter for economic outcomes is relevant to interpreting the
observed capital intensity and GDP per capita differences between
Australia and New Zealand. The mining sector has a high capital share
parameter relative to other industries and also has high relative MFP.
(31) The mining sector in New Zealand constitutes approximately 0.9% of
total value added and 0.25% of total employment, compared with 7.1% and
1.3% respectively for Australia.
We investigate the thought experiment of making New Zealand's
mining industry 6 percentage points of GDP greater than it currently is
(i.e. equal to the Australian share of GDP). Using the estimates of
mining industry [beta] and MFP from Note 31, the resulting
weighted-average traded sector values of [beta] and [A.sub.T] would be
1.084 and 0.3804 respectively, (32) compared with 1.0 and 0.33 for the
base case. These small parameter changes have major economic effects.
Relative to the base case, capital intensity increases by 48% and per
capita output increases by 27%. Because resources are attracted towards
the highly productive mining sector, remaining sectors are forced to
increase capital investment and wages to attract resources. For
instance, capital employed in the non-traded sector rises 23% to
compensate for a reduction in labour in that sector (which gravitates to
the traded sector). The extra non-traded capital is required since
agents in the (more productive) traded sector still wish to purchase
non-traded goods. If the terms of trade were also to increase by 10% as
a result of exposure to revalued minerals exports, the overall change in
real per capita GDP relative to the base case would become 34%; that
would be a lucky country indeed.
These illustrative numbers suggest that the presence of a small
profitable, highly productive segment within the traded goods sector can
have major macroeconomic impacts. In comparing country outcomes, it is
therefore important to consider the general equilibrium impacts of such
segments rather than measuring their impacts through a partial
equilibrium (segment-specific) lens. The model presented here provides a
concise vehicle for undertaking this analysis.
Acknowledgements
This paper was prepared with funding from the Ministry of Economic
Development and from the Foundation for Research, Science and Technology
(grant MOTU0601: Infrastructure). I thank Richard Fabling for preparing
the graphs and for his extremely helpful comments during the preparation
of the paper. I also thank Roger Procter, Geoff Lewis, participants at a
New Zealand Treasury seminar, and a referee and the editor of this
journal for their helpful comments. However, I remain solely responsible
for the contents.
(Received 27 May 2008: final version received 15 October 2008)
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Notes
(1.) We define capital intensity as capital/labour. Elsewhere,
capital intensity is occasionally defined as capital/output (for
example, see: www.j-bradford-delong.net/macro_online/ gt_primer.pdf). We
refer to this latter concept explicitly as the capital/output ratio.
(2.) See Black et al. (2003), Claus and Li (2003), Mawson et al.
(2003), McLellan (2004), Fox (2005), Hall and Scobie (2005).
(3.) This explicit modelling approach differs from typical
neoclassical growth models that leave the capital stock determined
implicitly by equating the marginal product of capital to the cost of
capital (see expositions in Aghion & Howitt, 1998: and Barro &
Sala-i-Martin, 1999).
(4.) However, CF do not analyse why poor countries do not just
import the capital goods.
(5.) CF refer to evidence suggesting that [p.sub.k] does not vary
substantially across countries; hence [P.sup.i.sub.y], must vary for
[p.sub.y]/[p.sub.k] to vary. Eaton and Kortum (2001) demonstrate that
most of the world's equipment stock is imported from only a few
countries.
(6.) [P.sub.T] and [P.sub.K] are exogenous to the domestic economy
in contrast to the price of non-traded output ([P.sub.N]) and wages (W)
which are determined endogenously. In the absence of terms of trade
shifts, the traded goods and capital goods prices can be considered the
numeraire in the system.
(7.) See Stiroh (2000) on the relative importance of
'neoclassical' versus 'endogenous growth' factors as
determinants of improvements in labour productivity.
(8.) The capital good is not part of the consumption basket. If
[phi] = 0, the utility function is Cobb-Douglas. The utility function is
specified in static terms since we are investigating a stationary
outcome. The model results in savings equalling depreciation (i.e. gross
investment); total consumption (over traded and non-traded goods) equals
net income.
(9.) That is, a Cobb-Douglas specification with equal consumption
shares.
(10.) The value of domestically-owned capital (domestic wealth) is
set equal to the sum of traded sector plus non-traded sector capital in
the base case solution.
(11.) [P.sub.N] = 1 in the base-case solution.
(12.) Since L is held constant at 1, the total capital stock is
identical to overall capital intensity.
(13.) The real exchange rate is defined as the price of non-traded
to traded goods.
(14.) Factors may include skills, management capability, distance
from major sources of knowledge, terrain, infrastructure, significant
minerals, etc.
(15.) For instance, tourism services (low) or mining (high).
(16.) Countries may be charged a premium on their cost of capital
owing to high country debt levels (Orr et al., 1995; Lane &
Milesi-Ferretti, 2002; Plantier, 2003).
(17.) Prebisch (1950), Singer (1950).
(18.) This experiment reflects the experience of small open
economies with floating exchange rates (such as New Zealand) in which
cyclical changes in traded versus non-traded consumption are associated
with real exchange rate changes. Here, we test whether shifts in
consumption preferences have permanent real exchange rate (and capital
intensity) effects.
(19.) The risk premium experiment involves a one percentage point
change in r.
(20.) The result is robust to [phi] being anywhere in the
admissible range; i.e. [phi] [member of] (-1, [infinity]).
(21.) Domestic ownership of capital is held constant by the
inherited level of wealth in each of the [A.sub.N] and [A.sub.T]
experiments. Thus, the additional capital stock in the [A.sub.T]
experiment is owned offshore. The returns to that capital accrue to the
offshore owners rather than flowing through to domestic income.
(22.) The results of joint experiments are not presented separately
in the tables.
(23.) Private sector agents will, of course, direct their own
investment spending to areas with privately optimal pay-offs.
(24.) One could consider this experiment a special case since the
rise in the traded goods capital share may be accompanied by a change in
the traded goods price if the effect were shared globally. However there
is no level of [P.sub.T] that re-establishes the original equilibrium. A
1.7% fall in [P.sub.T] that accompanies the 1% rise in [beta] leaves
utility and consumption unchanged, output fractionally lower and capital
approximately 1% lower than baseline. Similarly there is no combination
of [P.sub.T] and [P.sub.K] change accompanying the rise in [beta] that
re-establishes the original equilibrium.
(25.) The percentage fall in the capital/output ratio exactly
matches the percentage rise in the cost of capital for small changes in
r.
(26.) Thus, net domestic product (NDP) does not fall as heavily as
gross domestic product (GDP). This raises the observation that measuring
cross-country welfare by comparing per capita GDP biases the results
against 'capital shallow' countries; the more relevant
comparison is to use per capita NDP.
(27.) Consistent with the risk premium and capital goods price
results, a country with a high depreciation rate (possibly due to
extreme climate factors, poor maintenance skills/ practices, or through
the possibility of expropriation of capital) will also tend to have low
capital intensity.
(28.) Grimes (2006) analyses the relationship between New
Zealand's terms of trade and production.
(29.) We express Y and C as Y/L and C/L respectively, so that all
variables are in ratio form. K is expressed both as K/Y and K/L for
clarity. We do not include a change to [gamma] since experiment 8
demonstrates that this change has no effect on capital intensity or
other aggregate variables.
(30.) The Balassa-Samuelson case (a rise in [A.sub.T] relative to
[A.sub.N], where both [A.sub.N] and [A.sub.T] are rising) leads to
increased output, consumption, capital intensity and traded output as a
proportion of total output.
(31.) The OECD-STAN database shows that, over 1986-2001, New
Zealand's average labour share of value added in mining represented
37.5% of that for the total economy. If the latter were set to 0.67 (as
in our baseline model), this would correspond to a labour share of 25%
in the mining industry: i.e. [beta] = 0.75 within the mining industry.
Using the STAN estimate of mining capital stock and employment, this
would correspond to an MFP coefficient of 1.7 in the mining industry.
(32.) That is, in each case equal to baseline x 0.88 + mining x
0.12 (noting that mining is in the traded goods sector and hence the
extra 6% GDP weight corresponds to a 12% traded goods sector weight).
Arthur Grimes *
Motu Economic and Public Policy Research Trust, PO Box 24390,
Wellington, New Zealand: and University of Waikato, New Zealand
* Email: arthur.grimes@motu.org.nz
Productivity: [A.sub.N] = [A.sub.T] = 1
Prices: [P.sub.K] = [P.sub.T] = 1
Capital share: [alpha] = [beta] = 0.33
Real interest rate: r = 0.07
Depreciation rate: d = 0.06
Labour force: L = 1
Consumption: (9) [gamma] = 0.5; [phi] = 0
Domestic capital: (10) D = 4.0164
Table 1. Experiment results (Cobb-Douglas utility).
Experiment (each parameter [up arrow] 1%) *
Variable [A.sub.N] [A.sub.T] [alpha] [beta]
YN 1.00 O.18 0.46 0.08
YT 0.00 1.73 0.36 1.30
Y 0.42 1.07 0.40 0.78
KN 0.00 1.18 1.00 0.55
KT 0.00 1.73 0.36 2.31
K 0.00 1.50 0.63 1.57
LN 0.00 -0.31 -0.49 -O.14
L7 0.00 0.23 0.36 0.11
CN 1.00 0.18 0.46 0.08
CT 0.00 1.18 0.00 0.55
C 0.50 0.68 0.23 0.32
PN -0.99 1.00 -0.46 0.46
[P.sub.N]/ -0.99 1.00 -0.46 0.46
[P.sub.T]
W 0.00 1.50 0.00 0.69
U 0.50 0.68 0.23 0.32
Experiment (each parameter [up arrow] 1%) *
Variable [r.sup.a] [r.sup.b] [P.sub.K] [P.sub.T]
YN -0.15 -2.83 -0.18 0.18
YT -6.11 -4.14 -0.72 0.72
Y -3.58 -3.58 -0.49 0.49
KN -7.28 -9.77 -1.17 1.18
KT -12.82 -10.98 -1.70 1.73
K -10.47 -10.47 -1.47 1.50
LN 3.56 0.78 0.31 -0.31
L7 -2.62 -0.57 -0.23 0.23
CN -0.15 -2.83 -0.18 0.18
CT -0.15 -2.83 -0.18 0.18
C -0.15 -2.83 -0.18 0.18
PN 0.00 0.00 0.00 1.00
[P.sub.N]/ 0.00 0.00 0.00 0.00
[P.sub.T]
W -3.58 -3.58 -0.49 1.50
U -0.15 -2.83 -0.18 0.18
Experiment (each parameter [up arrow] 1%) *
Variable [gamma]
YN 1.00
YT -0.74
Y 0.00
KN 1.00
KT -0.74
K 0.00
LN 1.00
L7 -0.74
CN 1.00
CT -1.00
C 0.00
PN 0.00
[P.sub.N]/ 0.00
[P.sub.T]
W 0.00
U 0.00
NB: Suffix T denotes traded; N denotes non-traded;
no suffix denotes total.
Figures in the table show percentage change in the vertically
listed variable.
[*.sub.r] experiments involve a 1 percentage point increase
(from 0.07 to 0.08).
[r.sup.a] assumes domestic capital stock is owned wholly onshore.
[r.sup.b] assumes domestic capital stock is owned wholly
offshore; domestic agents own foreign capital.
Table 2. Experiment results (CES utility: [phi] = 10).
Experiment (each parameter [up arrow] 1%
Variable [A.sub.T] [A.sub.T] [alpha] [beta]
YN 0.54 0.63 0.25 0.29
YT 0.33 1.39 0.52 1.14
Y 0.42 1.07 0.40 0.78
KN -0.45 1.64 0.79 0.76
KT 0.33 1.39 0.52 2.16
K 0.00 1.50 0.63 1.56
LN -0.45 0.14 -0.70 0.07
LT 0.33 -0.10 0.52 -0.05
CN 0.54 0.63 0.25 0.29
CT 0.45 0.72 0.21 0.34
C 0.50 0.68 0.23 0.32
PN -0.99 1.00 -0.46 0.46
[P.sub.N]/ -0.99 1.00 -0.46 0.46
[P.sub.T]
W 0.00 1.50 0.00 0.69
U 0.50 0.68 0.23 0.32
Experiment (each parameter [up arrow] 1%
Variable [r.sup.a] [r.sup.b] [P.sub.K] [P.sub.T]
YN -0.15 -2.83 -0.18 0.18
YT -6.11 -4.14 -0.72 0.72
Y -3.58 -3.58 -0.49 0.49
KN -7.28 -9.77 -1.17 1.18
KT -12.82 -10.98 -1.70 1.73
K -10.47 -10.47 -1.47 1.50
LN 3.56 0.78 0.31 -0.31
LT -2.62 -0.57 -0.23 0.23
CN -0.15 -2.83 -0.18 0.18
CT -0.15 -2.83 -0.18 0.18
C -0.15 -2.83 -0.18 0.18
PN 0.00 0.00 0.00 1.00
[P.sub.N]/ 0.00 0.00 0.00 0.00
[P.sub.T]
W -3.58 -3.58 -0.49 1.50
U -0.15 -2.83 -0.18 0.18
Experiment (each parameter [up arrow] 1%
Variable [gamma]
YN 0.09
YT -0.07
Y 0.00
KN 0.09
KT -0.07
K 0.00
LN 0.09
LT -0.07
CN 0.09
CT -0.09
C 0.00
PN 0.00
[P.sub.N]/ 0.00
[P.sub.T]
W 0.00
U 0.00
NB: Suffix T denotes traded; N denotes non-traded; no
suffix denotes total.
Figures in the table show percentage change in the
vertically listed variable.
* r experiments involve a 1 percentage point
increase (from 0.07 to 0.08).
[r.sup.a] assumes domestic capital stock is owned wholly onshore.
[r.sup.b] assumes domestic capital stock is owned wholly offshore;
domestic agents own foreign capital.
Table 3. Potential reasons for 'capital shallowness'.
Qualitative Effect on:
Reason K/Y K/L Y/L
[A.sub.N} [up arrow] [down arrow] 0 [up arrow]
[A.sub.T} [down arrow] [down arrow] [down arrow] [down arrow]
[alpha] [down arrow] [down arrow] [down arrow]
[beta] [down arrow] [down arrow] [down arrow]
r [up arrow] [down arrow] [down arrow] [down arrow]
[P.sub.T/[P.sub.K] [down arrow] [down arrow] [down arrow]
[down arrow]
Qualitative Effect on:
Reason C/L [Y.sub.T]/Y [P.sub.N]/
[P.sub.T]
[A.sub.N} [up arrow] [up arrow] [down arrow] [down arrow]
[A.sub.T} [down arrow] [down arrow] [down arrow] [down arrow]
[alpha] [down arrow] ? [up arrow]
[beta] [down arrow] [down arrow] [down arrow]
r [up arrow] [down arrow] [down arrow] 0
[P.sub.T/[P.sub.K] [down arrow] [down arrow] 0
[down arrow]
Qualitative Effect on:
Reason [P.sub.N]/ W/PC
[P.sub.K]
[A.sub.N} [up arrow] [down arrow] [up arrow]
[A.sub.T} [down arrow] [down arrow] [down arrow]
[alpha] [up arrow] [down arrow]
[beta] [down arrow] [down arrow]
r [up arrow] 0 [down arrow]
[P.sub.T/[P.sub.K] [down arrow] [down arrow]
[down arrow]
Notes: [up arrow] denotes variable increases.
[down arrow] denotes variable decreases.
? denotes direction of effect uncertain
(depends on parameters).
0 denotes no change.