The Intertemporal Structure of Capital
Hayek greatly simplified the Austrian vision of a capital-using economy by
modelling the economy’s production activities as a sequence of inputs and a
point output. Each element in the sequence is designated a ‘stage of production’,
the number of stages posited being largely a matter of pedagogical
convenience. This simple construction was first introduced as a bar chart with
the individual bars arrayed temporally, their (equal) widths representing increments
of production time. The length of the final bar represents the value
of consumable output; the attenuated lengths of the preceding bars represent
the values of the goods in process at the various stages of production.
Figure 9.1 shows ten stages of production arrayed from left to right. (In
the original Hayekian rendition, five stages were arrayed from top to bottom.)
The specific number of stages is not intended to quantify any actual,
empirically established detail about the economy’s production process but
rather to capture our general understanding that in many instances the
(intermediate) output of one stage is used as an input to a subsequent stage.
That is, vertical integration – and, certainly, complete vertical integration –
is not the norm. Hayek’s ‘stages’ do not translate cleanly into ‘firms’ or
‘industries’. Some vertically integrated activities may be carried out within
a single firm. An oil company, for example, may be engaged in exploring,
extracting, refining, distributing and retailing. A paper manufacturer, for
another example, may be supplying paper for blueprints and for greeting
cards, thus operating simultaneously in different stages. And there are obvious
deviations from the strict one-way temporal sequence: coal may be
used in the production of steel while steel is used in the production of coal.
Stages of production
Consumable
Early output
stages
Late
stages
(This is the supposedly telling counter-example offered by Frank Knight in
his critical introduction to the English translation of Menger’s Principles.)
Still, as with all simple models, this Austrian model of the capital structure
is notable not for its many sins of omission but rather for the essential
truths that are captured by its construction.
Means are employed to achieve ends, and those means are temporally prior
to the corresponding ends. Production moves forward through time. Valuation,
however, emanates in the reverse direction. That is, the anticipated value
of an end attaches itself to the means capable of achieving that end. This is
Menger’s Law. The demand for the factors of production and hence for the
outputs of the intermediate stages of production is a derived demand. The
direction of valuation is implicit in Menger’s designation of consumption
goods as ‘goods of the first order’. The market values of goods of the second,
third and higher orders are ultimately derived from the anticipated value of
the first-order goods. But even with the doctrine of derived demand fully in
play, those values entail a systematic time discount consistent with the temporal
remoteness of higher-order goods.
The Austrian vision puts the entrepreneur in a key role. At a minimum, the
entrepreneur operating in some particular stage of production must anticipate
the demand for his own output, assessing the profitability of his activities with
due attention to the cost of borrowed funds. Longer-run planning may require
gauging the strength of demand several stages forward, including ultimately
the demand for the consumable output. Speculative activities may consist in
part in the movement of resources – in response to a change in credit conditions
– from one stage to another and possibly in the creation of new stages of
production that are of a higher order than the highest order of the existing
stages. The increasing ‘roundaboutness’, to use Böhm-Bawerk’s term, and the
increasing significance of the time element in the production process, are
characteristic of developing (and developed) capitalist economies.
The attention to the temporal structure of production suggests that the time
element is an important variable in our understanding of how a decentralized
economy works to coordinate production activities with consumer preferences
and hence in our understanding of what might go wrong with the
coordinating mechanisms. The use of multiple stages of production gives full
play to marginalist thinking. Austrian macro is micro-friendly. The pattern of
resource allocation can be modified in systematic ways, changing the temporal
profile of production activities. A marginal decrease in late-stage activities
coupled with a marginal increase in early-stage activities has important implications
for the economy’s overall growth rate. Significantly, a related
pattern of marginal changes gives rise to boom and bust. Changes in the
intertemporal pattern of resource allocation have a claim on our attention,
according to the Austrians, even if these marginal changes cancel one another
out in some conventional macroeconomic aggregate such as investment spending
(in all stages) or total spending (by both consumers and the investment
community).
The pattern of resource allocation associated with intertemporal equilibrium
exhibits a certain uniformity in terms of the value differentials that
separate the stages of production. The difference in the value of the output of
one stage and the value of the output of the next stage reflects, among other
things, the general terms of intertemporal exchange, expressed summarily as
the market rate of interest. With a given rate of interest, excessive stage-tostage
value differentials would present themselves as profit opportunities
which could be exploited only by reallocating resources toward the earlier
stages of production. In the limit, when all such profit opportunities have
been competed away, the relative prices of inputs used in the various stages
are brought into line with the equilibrium rate of interest. A summary graphical
rendering of the intertemporal capital structure takes the form of a triangle
encasing the sequence of stages that constitute such an intertemporal equilibrium.
The Hayekian triangle in Figure 9.1 keeps the many complexities of
capital theory at bay while keeping in play the overall time element in the
production process.
The extreme level of simplification warrants some discussion. First, we
note that the triangle’s hypotenuse, which tracks the value of the yet-to-be
completed consumables, rises linearly from no value at all to the full market
value of the consumables. Yet we know that the interest rate is expressed in
percentage terms and, starting from some initial input value, allows for compounding.
Clearly – and contrary to the Hayekian triangle – such percentage
value differentials imply that the cumulative value should be tracked by a
curve that rises exponentially from some initial value to some final value.
Here, linearity wins out on the grounds of its being simpler in construction
yet adequate to the task. It is also true to Hayek’s original formulation. We
need to recognize, however, that the triangle would be inadequate for dealing
with any issue for which the compounding effect is critical. Ambiguities
about the precise relationship between the interest rate and the overall degree
of roundaboutness arise when the effects of compound interest are factored
in. These and related ambiguities concerning capital intensity lay at the heart
of the Cambridge capital controversy (see Harcourt, 1972), a protracted and,
ultimately, sterile debate that attracted much attention a few decades ago. But
for dealing with the business cycle and related macroeconomic issues, the
triangle, simple as it is, does just fine.
Second, the horizontal leg of the triangle, which invites us to imagine a
sequence of unit time intervals, does not translate readily into calendar time.
In application, an early stage of production consists only partly in goods in
process – pine saplings that mature over time into lumber or wine that
undergoes an ageing process. Earliness is also implicit in durable capital
goods or even in human capital. These factors of production are categorized
as early-stage because they will have a yield over an extended future. The
heterogeneity of capital warns against trying to create a single metric, such as
some average period of production, or to quantify in some other way the
production time for the macroeconomy. Still, many early-stage activities and
late-stage activities are readily discernible. Inventory management at retail is
a late-stage activity. Product development is an early-stage activity. Increases
in the time dimension of the economy’s capital structure might take the form
of shifting resources from relatively late to relatively early stages, of creating
capital goods of greater durability, or of simply changing the mix of goods
produced in favour of those involving more time-consuming (but higheryielding)
production processes.
Third, the vertical leg of the Hayekian triangle, which represents the value
of consumable output, implies that consumption occurs at a single point in
time at the end of the production process. This is not to deny the existence of
consumer durables. But expanding the intertemporal aspect of the macroeconomy
to include consumption time would complicate matters without
adding much to the analysis. The triangle focuses attention on the particulars
of production and on aspects of the market process that lose much of their
relevance once the goods are in the hands of the consumer. The notion of
‘stages of consumption’ would be contrived if not meaningless.
In application there is a fine line – in Austrian theory as in more conventional
theory – between an investment good and a consumer durable.
Residential housing, whether or not owner-occupied, is universally categorized
as investment, the rental value (actual or implicit) of its services
qualifying as consumption. Owner-driven automobiles, however, despite their
considerable durability and implicit lease value, are categorized as consumption
goods. Instances can be imagined in which a consumable (for example a
light truck purchased new for non-commercial use) is later sold into an early
stage of production (for example as a work truck). But as a general rule,
goods delivered into the hands of consumers stay in the hands of consumers.
Attention to these and related matters may be necessary in particular applications
of the Austrian theory, but the theory itself is based on the vision of a
multi-stage production process that yields a consumable output.
In its simplest interpretation, Figure 9.1 represents a no-growth economy.
Gross investment, financed by saving, is just enough to offset capital depreciation.
With given tastes and technology, the macroeconomy settles into an
intertemporal equilibrium and produces consumption goods at an unchanging
rate. More typically, saving and gross investment exceed capital depreciation,
allowing the economy to grow at every margin. If we can assume for the
moment an unchanging rate of interest, the growth can be represented by a
triangle of increasing size, its general shape remaining the same.
The pay-off to Hayekian triangulation, however, comes from allowing for
changes in the triangle’s shape. More conventional macroeconomic constructions
make the implicit assumption of structural fixity or structural irrelevance.
In the Austrian theory, changes in saving behaviour have implications for the
allocation of resources within the economy’s capital structure. In turn, the
changing shape of the triangle affects the time profile of consumable output.
The natural focus of the analysis is on intertemporal coordination and possible
causes of intertemporal discoordiantion.
Hayek greatly simplified the Austrian vision of a capital-using economy by
modelling the economy’s production activities as a sequence of inputs and a
point output. Each element in the sequence is designated a ‘stage of production’,
the number of stages posited being largely a matter of pedagogical
convenience. This simple construction was first introduced as a bar chart with
the individual bars arrayed temporally, their (equal) widths representing increments
of production time. The length of the final bar represents the value
of consumable output; the attenuated lengths of the preceding bars represent
the values of the goods in process at the various stages of production.
Figure 9.1 shows ten stages of production arrayed from left to right. (In
the original Hayekian rendition, five stages were arrayed from top to bottom.)
The specific number of stages is not intended to quantify any actual,
empirically established detail about the economy’s production process but
rather to capture our general understanding that in many instances the
(intermediate) output of one stage is used as an input to a subsequent stage.
That is, vertical integration – and, certainly, complete vertical integration –
is not the norm. Hayek’s ‘stages’ do not translate cleanly into ‘firms’ or
‘industries’. Some vertically integrated activities may be carried out within
a single firm. An oil company, for example, may be engaged in exploring,
extracting, refining, distributing and retailing. A paper manufacturer, for
another example, may be supplying paper for blueprints and for greeting
cards, thus operating simultaneously in different stages. And there are obvious
deviations from the strict one-way temporal sequence: coal may be
used in the production of steel while steel is used in the production of coal.
Stages of production
Consumable
Early output
stages
Late
stages
(This is the supposedly telling counter-example offered by Frank Knight in
his critical introduction to the English translation of Menger’s Principles.)
Still, as with all simple models, this Austrian model of the capital structure
is notable not for its many sins of omission but rather for the essential
truths that are captured by its construction.
Means are employed to achieve ends, and those means are temporally prior
to the corresponding ends. Production moves forward through time. Valuation,
however, emanates in the reverse direction. That is, the anticipated value
of an end attaches itself to the means capable of achieving that end. This is
Menger’s Law. The demand for the factors of production and hence for the
outputs of the intermediate stages of production is a derived demand. The
direction of valuation is implicit in Menger’s designation of consumption
goods as ‘goods of the first order’. The market values of goods of the second,
third and higher orders are ultimately derived from the anticipated value of
the first-order goods. But even with the doctrine of derived demand fully in
play, those values entail a systematic time discount consistent with the temporal
remoteness of higher-order goods.
The Austrian vision puts the entrepreneur in a key role. At a minimum, the
entrepreneur operating in some particular stage of production must anticipate
the demand for his own output, assessing the profitability of his activities with
due attention to the cost of borrowed funds. Longer-run planning may require
gauging the strength of demand several stages forward, including ultimately
the demand for the consumable output. Speculative activities may consist in
part in the movement of resources – in response to a change in credit conditions
– from one stage to another and possibly in the creation of new stages of
production that are of a higher order than the highest order of the existing
stages. The increasing ‘roundaboutness’, to use Böhm-Bawerk’s term, and the
increasing significance of the time element in the production process, are
characteristic of developing (and developed) capitalist economies.
The attention to the temporal structure of production suggests that the time
element is an important variable in our understanding of how a decentralized
economy works to coordinate production activities with consumer preferences
and hence in our understanding of what might go wrong with the
coordinating mechanisms. The use of multiple stages of production gives full
play to marginalist thinking. Austrian macro is micro-friendly. The pattern of
resource allocation can be modified in systematic ways, changing the temporal
profile of production activities. A marginal decrease in late-stage activities
coupled with a marginal increase in early-stage activities has important implications
for the economy’s overall growth rate. Significantly, a related
pattern of marginal changes gives rise to boom and bust. Changes in the
intertemporal pattern of resource allocation have a claim on our attention,
according to the Austrians, even if these marginal changes cancel one another
out in some conventional macroeconomic aggregate such as investment spending
(in all stages) or total spending (by both consumers and the investment
community).
The pattern of resource allocation associated with intertemporal equilibrium
exhibits a certain uniformity in terms of the value differentials that
separate the stages of production. The difference in the value of the output of
one stage and the value of the output of the next stage reflects, among other
things, the general terms of intertemporal exchange, expressed summarily as
the market rate of interest. With a given rate of interest, excessive stage-tostage
value differentials would present themselves as profit opportunities
which could be exploited only by reallocating resources toward the earlier
stages of production. In the limit, when all such profit opportunities have
been competed away, the relative prices of inputs used in the various stages
are brought into line with the equilibrium rate of interest. A summary graphical
rendering of the intertemporal capital structure takes the form of a triangle
encasing the sequence of stages that constitute such an intertemporal equilibrium.
The Hayekian triangle in Figure 9.1 keeps the many complexities of
capital theory at bay while keeping in play the overall time element in the
production process.
The extreme level of simplification warrants some discussion. First, we
note that the triangle’s hypotenuse, which tracks the value of the yet-to-be
completed consumables, rises linearly from no value at all to the full market
value of the consumables. Yet we know that the interest rate is expressed in
percentage terms and, starting from some initial input value, allows for compounding.
Clearly – and contrary to the Hayekian triangle – such percentage
value differentials imply that the cumulative value should be tracked by a
curve that rises exponentially from some initial value to some final value.
Here, linearity wins out on the grounds of its being simpler in construction
yet adequate to the task. It is also true to Hayek’s original formulation. We
need to recognize, however, that the triangle would be inadequate for dealing
with any issue for which the compounding effect is critical. Ambiguities
about the precise relationship between the interest rate and the overall degree
of roundaboutness arise when the effects of compound interest are factored
in. These and related ambiguities concerning capital intensity lay at the heart
of the Cambridge capital controversy (see Harcourt, 1972), a protracted and,
ultimately, sterile debate that attracted much attention a few decades ago. But
for dealing with the business cycle and related macroeconomic issues, the
triangle, simple as it is, does just fine.
Second, the horizontal leg of the triangle, which invites us to imagine a
sequence of unit time intervals, does not translate readily into calendar time.
In application, an early stage of production consists only partly in goods in
process – pine saplings that mature over time into lumber or wine that
undergoes an ageing process. Earliness is also implicit in durable capital
goods or even in human capital. These factors of production are categorized
as early-stage because they will have a yield over an extended future. The
heterogeneity of capital warns against trying to create a single metric, such as
some average period of production, or to quantify in some other way the
production time for the macroeconomy. Still, many early-stage activities and
late-stage activities are readily discernible. Inventory management at retail is
a late-stage activity. Product development is an early-stage activity. Increases
in the time dimension of the economy’s capital structure might take the form
of shifting resources from relatively late to relatively early stages, of creating
capital goods of greater durability, or of simply changing the mix of goods
produced in favour of those involving more time-consuming (but higheryielding)
production processes.
Third, the vertical leg of the Hayekian triangle, which represents the value
of consumable output, implies that consumption occurs at a single point in
time at the end of the production process. This is not to deny the existence of
consumer durables. But expanding the intertemporal aspect of the macroeconomy
to include consumption time would complicate matters without
adding much to the analysis. The triangle focuses attention on the particulars
of production and on aspects of the market process that lose much of their
relevance once the goods are in the hands of the consumer. The notion of
‘stages of consumption’ would be contrived if not meaningless.
In application there is a fine line – in Austrian theory as in more conventional
theory – between an investment good and a consumer durable.
Residential housing, whether or not owner-occupied, is universally categorized
as investment, the rental value (actual or implicit) of its services
qualifying as consumption. Owner-driven automobiles, however, despite their
considerable durability and implicit lease value, are categorized as consumption
goods. Instances can be imagined in which a consumable (for example a
light truck purchased new for non-commercial use) is later sold into an early
stage of production (for example as a work truck). But as a general rule,
goods delivered into the hands of consumers stay in the hands of consumers.
Attention to these and related matters may be necessary in particular applications
of the Austrian theory, but the theory itself is based on the vision of a
multi-stage production process that yields a consumable output.
In its simplest interpretation, Figure 9.1 represents a no-growth economy.
Gross investment, financed by saving, is just enough to offset capital depreciation.
With given tastes and technology, the macroeconomy settles into an
intertemporal equilibrium and produces consumption goods at an unchanging
rate. More typically, saving and gross investment exceed capital depreciation,
allowing the economy to grow at every margin. If we can assume for the
moment an unchanging rate of interest, the growth can be represented by a
triangle of increasing size, its general shape remaining the same.
The pay-off to Hayekian triangulation, however, comes from allowing for
changes in the triangle’s shape. More conventional macroeconomic constructions
make the implicit assumption of structural fixity or structural irrelevance.
In the Austrian theory, changes in saving behaviour have implications for the
allocation of resources within the economy’s capital structure. In turn, the
changing shape of the triangle affects the time profile of consumable output.
The natural focus of the analysis is on intertemporal coordination and possible
causes of intertemporal discoordiantion.
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