Hines, James H., "The Business Cycle and Money, An Analysis of the Inventory Investment Hypothesis", 1983

THE BUSINESS CYCLE AND MONEY
An Analysis of the Inventory Investment Hypothesis

James H. Hines, Jr.
Sloan School of Management
Massachusetts Institute of. Technology
Cambridge, massachusetts 02139

Abstract

Among the most stable phase relationships between economic
variables is that between-money, the change in money, and general
economic activity. Both the change in money and money itself
lead production over the business cycle. This relationship
buttressed with results of the Granger/Sims test for causality,
has been used to support the notion that money causes real
activity. This notion, in turn, is used to argue both that
monetary policy causes the business cycle and that monetary
policy can ameliorate the business cycle.

This paper examines a hypothesis for the phase relationships
which assumes that money does not cause real activity, but,
rather, real activity causes money. According to the hypothesis
inventory investment, which leads business activity, induces
corporate borrowing, which in turn causes a money expansion with
a lead similar to that observed. This has been a working
hypothesis for the phasing in money of the System Dynamics
National Model Project. It is concluded that the hypothesis, by
itself, is insufficient to account for the

observed timing relationships. However, the inventory investment
hypothesis combined with additional hypotheses such as a
mechanism for household portfolio adjustment, can account for the
phasing. These results do not depend upon a causal flow from
money to real activity. As a consequence, business cycle phase
relationships should not be taken to imply money causes the
business cycle nor that monetary policy can influence the
business cycle.

This paper has benefited from the comments and Suggestions, some
expressed with considerable vigor, of Bob Eberlein, Mark Paich,
George Richardson, Peter Senge, and John Sterman.

470

Hines 2

Questions of Timing and Policy. Arthur Burns and Wesley Mitchel
developed the first list of leading, coincident and lagging

indicators in 1937 (Moore 1978). Interest in the phase
relationships between economic time series has continued ever
since. In summing up the work conducted over the past two
generations, Robert Lucas states:

Though there is absolutely no theoretical reason to
anticipate it, one is led by the facts to conclude that
with respect to the qualtitative behavior of comovements

among series, business cycles are all alike. (Lucas [1977]
1981, 218)

Lucas intends his observation to hold across time and across all
countries with decentralized market economies.

Perhaps no relationship between economic time series has been as
thoroughly noted as that between money and real activity. The
data indicate that movements in both the change in money (M1 or
M2) and the stock of money lead movements in general economic
activity (M.Friedman February, 1963; Batten and Hager 1982;
Lucas 1977). Figure 1 presents the relationship between the
change in money and the NBER reference cycles from 1867 to 1960.
Figure 2 presents the relationship between various money series
and the NBER reference cycles from 1956 to March, 1983. The
Change in money (M1) has led the NBER reference cycles at the
peak by an average of 21 months and at the trough by 7 months;
while the money supply in constant dollars (M1) has lead by an
average of about 12 months at the peak and 8 months at the trough
(BCD, 1977). Leads for M2 differ slightly.

BCD (1977) gives scores between 0 and 100 to time series based
upon the reliability of the phase or timing relationship. A
series which always shows a given timing relationship (lead, lag,
or coincident) would recieve a score of 100. A series which has
no consistant phase relationship would recieve a score of zero.
Change in M1 gets an overal timing score of 64; Mi itself
receives a timing score of 86 and is included as one of the
4

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(S67~- 1960
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(oegent; MCD moving avt.~6-ermy
rary

Moxex-ro-Mowra Rare or Cuanes ot US, Money Sroce, 1867-1960

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8

Change in money supply M2
(percent; MCD moving a

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(from Friedman and Schwartz 1963, 194)

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= TH to wl money supply 2 (rata)

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BED nanciise3 Note! P= Peak  T- Trough

Hines 5 472

twelve leading indicators. The mean score, for the 111 cyclical
indicators, is 76 with a standard deviation of 18.

While, the relationship between money and business activity has
long been observed, the relationship between credit and business
conditions has also recently been studied. Benjamin Friedman
coneludes that:

The relationship between credit and nonfinancial economic
activity exhibits stability that is comparable to that of the
relationship between money and economic activity. (Benjamin
Friedman 1962)

Friedman goes on to note that

The econmic behavior underlying the stability of the
eredit-to-income relationship remains a major puzzle --
though, on reflection, no more so than the stablity of the
money-to-income relationship. (Benjamin Friedman 1982)

The puzzle of why the data reveal these consistencies is of
importance as a theoretical question. The existence of stable
timing patterns suggests the existence of stable causal
mechanisms (Lucas 1977). Beyond this, it is often suggested that
the stable lead of money with respect to real activity is
evidence for a causal link from money to real activity
(M.Friedman 1963, M.Friedman 1969, Cagan 1965, Cagin. in Entine
1965, Meigs 1968). While the easy association of timing and
causality has been vigorously contested (Tobin 1970, Frisch
1933), more sophistocated econometric techniques designed to test
causal direction from time series data have more recently been
employed. These suggest that money does cause GNP (Sims 1972)

The step from causation to policy is a small one. Current public
debate over therole of the Fed with respect to the current
economic difficulties reveals nothing if not the existance of a
sizable group of people who believe that monetary policy can
influence real activity with a lag shorter than or equal to the
phase lag observed in the data. For example, a major news
magazine states that “in the fall of 1979 ... Volker abruptly

Hines 6

changed the focus of the Federal Reserve's policy ... to slow the
growth of money and credit ... This sent the economy into
recession", The article attributes to subsequent Fed actions in
the summer of 1982 "the present recovery" including a slight drop
in unemployment, a rise in retail sales, an expected profit in
the auto industry, and a one week jump of 46.63 in the Dow Jones
industrials. (Time, vol. 121 no.17, April 25, 1983, pp.96-97).

In spite of the great hopes (and fears) that people place in the
Fed, we do not yet have a comprehensive, let alone consensus
understanding of the impact of monetary variables on
non-financial economic activity (Lucas 1977, B. Friedman 1982).
There is a need to understand the underlying causes of the
observed lead of financial variables with respect to aggregate
economic activity. We need to be able to explain why the data do
what they do.

An explanation will help provide answers to the monetary
questions of current public concern: Does monetary policy cause
the business cycle? Is monetary policy a high-leverage means of
controlling the business cycle?

Paper Purpose. The purpose of this paper is to examine one
hypothesis for the phase relationships between the stock of
money, the change in money, and production, The hypothesis,
briefly stated, is that inventory investment is financed through
borrowing which causes a money expansion with the observed phase
relationship relative to the business cycle.

Prior to the present study, this was the working hypothesis of

“the System Dynamics National Model Project. It accorded well

with results suggesting that the observed lead in financial
variables with respect to real variables was not a result of
causal flow from money to real economic activity (Senge and Paich
1980). The results reported in this paper suggest that the
inventory investment. hypothesis alone is insufficient to account
for the the phase relationships. However, an elaborated version
473
Hines 7

of the hypothesis is presented which can account for the phase
relationships. The augmented hypothesis is also in accord with
earlier results that the business cycle arises independently of
finaneial variables.

Jay Forrester has expressed the inventory hypothesis succinctly.

Peaks in the growth of money have occured shortly before
busniess-cycle peaks in production ... Business-cycle
fluctuation is generated within the private-business part of
the economy. As inventories rise, investment in inventories
is supported by borrowing money, which increases the money
supply. Inventories rise most rapidly shortly before the
peaks of production and produce the observed changes in the
money supply. (Forrester 1982, 32-33)
This suggestion has much to recommend it. Consider what causes a
change in money in our economy. The monetary authority may
inerease the reserves of banks by buying government bonds from
private holders. This act will increase the money supply
immediately as long as the monetary authority does not buy the
bonds from banks. But, in the scheme of money creation this
immediate effect will prove to be rather small.. What accounts
for the lion's portion of a money supply increase is the
money-multiplier., The money multiplier, of course, operates
through a process involving the borrowing (and redepositing) of
free reserves. The question of money creation, therefore, is the

question of borrowing.
Schumpeter in a similar context noted

Any satisfactory analysis of causes must start with what
induces that credit expansion, as every satisfactory analysis
of effects must start by investigating what is done with the
increased monetary resources. (Schumpeter 1935, 14).
What are the causes of the credit expansion? In the
macro-economy the household sector is a net holder of financial
assets, while the production sector is a net holder of financial
liabilities. This suggests that a consideration of corporate
borrowing over the business cycle might be of value in looking
for the source of net pressures for credit in the financial

Hines 8

system. There are several reasons businesses might borrow.
Perhaps the most basic is simply to meet meet cash expenses:
Businesses borrow when their cash flows are negative and repay
their obligations when cash flows are positive.

It has been argued (N. Forrester 1982, Mass 1975, Low 1980) that
the business cycle has much to do with inventory investment and
less to do with investment in capital plant and equipment. This
suggests that business cycle phase relationships between money
and real activity may result from negative cash flows associated
with inventory investment.

Financial Activity and Real Activity. Philip Cagan would suggest
that by assuming the business cycle to be little influenced by
money or other financial variables, one enters

a debate continuing for centuries [which] pits the classical
writers, who view money as an independent source of economic
disturbance, against the critics of this view, who say money
is a passive adapter to business conditions with little
independent influence. (Cagan, 1965, p.xiv)
The current paper, while questioning the adequacy of the current
system dynamics working hypothesis, nonetheless joins prior work
in taking the side of the "critics". However, the causal arena
in which we intend to take sides is not as wide as might first

appear.

First, let us distinquish between two or three types of cycles.
Friedman and Schwartz (1963) divide business cycles into mild
cycles (eg. 1958-61) and severe cycles (eg. 1927-1933). They

‘eonelude that the case is strong for a monetary cause of major

downturns, and less strong for a monetary cause of minor
downturns. Cagan (1965) comes to much the same conlusiqn.
Forrester (1983), for his part, believes that money is not a
prime cause of the "business cycle" which he associates with mild
downturns, but believes that monetary policy or the behavior of
financial variables may help to aggravate or alleviate major
downturns (personal communication 1983).
474
Hines 9

If the influence of money on real activity were absent in only
one circumstance, it appears there is some agreement that that
circumstance would be mild-downturns or, in Forrester's terms,
the business cycle proper. As a consequence, the current effort
focusses on the mild and more frequent downturns which recur with
a period of two to seven years. I associate these cycles with
what Forrester and Volker (1978) call business cycles and what
Schumpeter (1935) merely notes as a cycle of roughly forty
months.

It is important, nonetheless to be clear about the mechanisms we
are considering and those we are not. In brief, the assumption
implicit in the inventory-investment hypothesis is that the
demand for credit primarily determines the money supply. When
businesses demand funds to meet negative cash flows, that demand
puts "pressure" on the financial system. The pressure is
relieved by a process involving the simultaneous creation of
money and. credit.

It is beyond the scope of the current effort to consider the
several (Cagan 1965) mechanisms by which money is made available.
However, making the assumption that money is made available as
needed is assuming no more than what is assumed in most
econometric studies of the demand for money. These studies
generally assume that money is endogenous (ie. a dependent
variable); the justification offered is that the Fed has often
appeared to be reacting to interest rates (Judd and Scadding,
1982).

A Model of Real Activity. In "Understanding Business Cycles",
Lucas presented a model in words rather that in mathematical
symbols. He later wrote:

Isn't it remarkable how simple it all becomes in plain
English? Yet how deceptive this simplicity is: The
description of inventory behavior .., is as coherent as the
description of accelerator effects, yet the latter is a
verbal transcrition of a fully worked-out model while the
former is only conjecture. (Lucas, 1981, p.15)

Much of the argument to be carried out below could have been

Hines io
developed in "plain English" without reference to a mathematical
model. By presenting the analysis in the context of a
mathematical model, I hope not to sacrifice simplicity, but only
to avoid deception.

The initial hypothesis explored here is an attempt to account for
the phase relationship between real activity and money over the
business cycle. The hypothesis assumes that real activity causes
money through inventory investment and that money does not have
an effect on real activity. This suggests that an appropriate
starting point would be an inventory model of the business cycle
in which financial variables do not effect real variables.

The model of the real sector to be presented here is very similar
to both Metzler's model (1941) and several models (or parts of
models) in the system dynamics literature (N. Forrester 1982
Mass 1975, Mass and Senge 1974, Lyneis 1980). The primary
mechanism responsible for oscillations in these models isthe
interaction between workforce and inventory.

The model is formulated in continuous time. The basic model
equations appear in figure 3. A graphical representation of the
model appears in figure 4 using standard system dynamics symbols
for stocks and flows (Richardson and Pugh 1981). A complete
computer model, written in DYNAMO, is documented in appendix 3.
Hine

a)
(2)
@)
(4)

(5)

(6)
(7)
(8)
(9)

(10)
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(12)

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5)

16)

Cons:

475

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Figure 3: A Model of Real Economic Activity
= PR-SR Inventory (goods)
PR = W*PROD Production rate (goods/year)
SR = CGD*EAS Shipment rate (goods/year)
EAS = £(DSI/CGD) Effect of availability on

DSI = I/NIC

Wes (DW-W)/TAW
DW = DP/PROD
DP = IC+CGD
I¢ = (DI-I)/TCI

DI = CGD*NIC
HSAV = TWR-HEXP
TWR = WAWPP

HEXP = SR*P

CGD = (TWR-CS)/

CS = (DHSAV-HSAV)/TAS

DHSAV = DWC*TWR

tants:

r

shipments (dimensionless)

Desired shipments from
inventory (goods/year)

Workforce (people)
Desired workforce (people)
Desired production (goods/year)

Inventory correction
(goods/year)

Desired inventory (goods)
Household savings (dollars)

Total wage receipts
(dollars/year)

Household expenditures
(dollars/year)

Consumer goods demand
(goods/year)

Correction to savings
(dollars/year)

Desired household savings
(dollars)

Productivity (goods/person)
Normal Inventory Coverage

(years)
Time to Adjust Workforce
(years)
Time to Correct Inventory
(years)

Price (dollars)
Time to Adjust Savings (years)
Desired Wage Coverage (years)

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” Hines is. 476
Since there are three state variables in figure 3 (denoted by
rectangles in figure 4), this set of 16 equations could be
reduced to three first order differential equations or a single
third order equation. The coefficients, which would have
appeared in either of these more compact forms, have been
disaggregated in order to clarify the behavioral assumptions
underlying the model.

The rate of change in inventories is the difference between the
production rate which increases inventory and the shipment rate
which depletes inventory. The production rate is calculated as
the number of workers multiplied by the. average productivity per
worker. Average productivity is assumed constant in this simple
model. The shipment rate is a function of demand from consumers
and the availability of goods. If goods are unavailable (ie. if
inventories are low) shipments will be below consumer demand. If
there is an excess of inventories, shipments may be slightly
higher than consumer demand as sellers induce their customers to
buy a bit more than they would have otherwise wanted.

The effect of availability on shipments is a nonlinear function
of "desired shipments from inventories" and consumer goods
demand. The shape of the function is presented in figure 5.

The independent variable (DSI/CGD) in the function defining the
effect of availability on shipments (EAS) is a measure of the
relationship between what retailers would like to ship or what
their distribution network is designed to handle and what
consumers are demanding. The actual shipment rate is a
compromise between the two. When consumers demand too much, the
distribution system is not adequate to ship everything that is
demanded and consumers do not receive all they want when they
want it.

A bit of algebraic manipulation gives another familiar way of
looking at DSI/CGD:

(puowag spers snvunano)/(srrwdys yaN929)

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477
Hines 85

(DSI/CGD) = (I/NIC)/CGD = I/(NICCGD)
= Inventory / Desired Inventory ice)

the effect of availability on shipments may be interpretted as a
stockout effect (Homer 1978).3 The rate of change of the
workforce is determined by a stock adjustment process. The
actual workforce will adjust exponentially to the desired
workforce with a time constant of TAW. Desired workforce (DW) is
the number of people required to produce at the desired
production rate (DP).

Desired production (DP) is composed of two terms: consumer goods
demand and inventory correction. The former represents the
production required to meet demand, while the latter represents
the production rate necessary to exponentially adjust inventories
to desired levels. The desired level of inventory (DI) is merely
a@ normal coverage of consumer goods demand. In the context of
equation (i) immediately above, this normal coverage may be
interpretted as determining the level of inventory necessary to
maintain a normal or desired stockout rate. In the current
formulation, the normal or desired stockout rate is assumed to be
zero. That is, when inventory equals desired inventory, consumer
goods demand is met in its entirety. While a zero stock out rate
is, no doubt, too low; it simplifies putting the system into
equilibrium and changes no substantive results.

The rate of change of the stock of savings is the difference
between total wage receipts and household expenditures. Total
wage receipts is calculated as the average wage per person (WPP)
multiplied by the number of people employed (W). Household
expenditures are the dollar value of the goods shipped.

In addition to the actual level of savings, households have a
desired level of savings which they form on the basis of their
income. The flip-side of desired savings is, of course, desired
expenditures or consumer goods demand (CGD).

Both Friedman (1957) and Modigliani and Bromberg (1952) saw the

Hines 16

consumption problem as one of allocating consumption through
time. In general, this means that individuals will save while
income is high and disave when income is low, In conformity with
this, consumers in the model developed here wish to save some of
their income for periods during their working years when they
are, in fact, not working (or are working less); they also wish
to save income from their working years for their retirement
years.

Desired household savings (DHSAV) increases with income. On the
one hand this results from the simple observation that it is
easier to save when one is making more money, than it is when one
is making less. Beyond this, however, savings are designed to
yield a certain standard of living during non-working periods.
This desired standard of living from savings is a function of the
current standard of living: People who are used to the good
life, will try to save in order to continue the good life when
they are no longer working. They will, in fact, desire to save
more than those who have not become accustomed to as good a life.
The current attainable standard of living is proportional to
income. Consequently, as income increases, desired savings must
also increase.

Desired savings has been modeled as a constant number of years
worth of income. The use of a constant here may be as reasonable
as any other assumption. A slightly more complicated
justification may be found in appendix 2.

The household attempts to adjust its actual savings stock to its
desired savings stock. It does this by saving a portion of
income which is designed to bring household savings (HSAV) up to
desired over an adjustment time (TAS). The amount set aside is
called "correction for savings" (CS).
478
Hines W

The household is free to spend income (TWR) in excess of the
correction for savings (CS). Indeed the very point of
determining what to “set aside" is to know what may be spent
Consequently, consumer goods demand is formulated as the
difference, adjusted for price, of total wage receipts TWR and
and the correction for savings (CS).

This way of looking at the household's expenditure decision is a
bit different from that of Friedman (1957). Friedman suggests
that households set a consumption target based on "permanent"
income. Some have equated consumption with expenditures. In
this case the savings rate will fluctuate depending upon the
relationship between current income and "permanent income", and
expenditures will be smooth, On the other hand, in the model
presented here, consumers set a savings target, and actual
expenditures will fluctuate with income and the savings
correction. The dynamic implications of this difference are
considered in appendix 1.

Of course, Friedman, himself, did make a distinction between
consumption and expenditure. He allowed that expenditures might
fluctuate with current income, while "consumption" (e.g. use of
rather than expenditure on, durable goods) might not (Friedman
1957, p.28). Hence, Friedman thought that expenditures might
fluctuate with income. Particularly in the current context, it
is important to model expenditures, rather than consumption. The
current formulation provides a simple, behaviorally plausible
expenditure function.

It is interesting that the formulation suggested here may be
manipulated as follows:

CGD = TWR/P ~ CS/P
TWR/P = (DWC#TWR - SAV)/(TAS*P)
(TWR/P)*((TAS-DWC)/TAS) + GICTAS IE CSAN/RD

= (Real Income)*C + A*(Real Wealth)

Hines 1B

The last form of this equation is identical to the consumption
funetion which Dornbusch and Fischer derive for the life-cycle
hypothesis (Dornbusch and Fischer 1978, p. 147,152). The
coefficients which they estimate imply a value for’ TAS of 25.64
years and a value of DWC of 6.67 years. These values are used in
the model and seem reasonable: Since the average worker is
employed for forty years or more and, since, this is the relevant
period over which the worker must accumulate his savings, the
average time to adjust savings twenty-five years is not as long
as it might otherwise sound. As to the figure for coverage,
assume the average worker retires at sixty-five with 6.67 times
his average income in savings. He will have an average of about
16 years remaining to live (National Center for Health
Statistics, 1982, table 5-3). If he has invested his savings at
5% (ef. Ibbotson and Sinquefield 1977, p.10), he will be able to
recieve about sixty per cent of his average pre-retirement income
until he dies. This seems to be a reasonable result. (Relevant
formulae are in appendix 2).

ar Models, The first difference between
this model and Metzler's (1942) model is that Metzler's was a
discrete time model, while the above is a continuous time model.
Beyond that, the delay between desired production and output is
explicitly attributable, in the model developed here, to the
movement of people into and out of the workforce through hiring,

firing, and quits.

One structural difference is the more sophistocated expenditure
function. Whereas Metzler in effect assumed a fixed average
propensity to consume, the present model has an average
propensity to consume which varies with the relationship between
actual savings and desired savings. The propensity to consume in
a stationary unstressed equilibrium (ie. an equilibrium in which
actual quantities are equal to desired quantities) is one.

Figure 6 presents a plot of the average propensity to consume
after the model has been disturbed from equilibrium by a sudden,
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Hines 20

two per cent reduction of inventory. The average propensity to
consume falls as income rises (Cf. Dornbush and Fischer 1978,
144).

Finally, this model explicity recognizes the impact of low
inventories: slowed deliveries or stock outs. Metzler did’ not
represent this effect. Incorporating this effect increases the
stability of the system (see appendix 1).

The major difference between the model considered here and past
workforce-inventory models in system dynamics (N.Forrester 1982,
Mass 1975) is the consumer expenditure function described above.
In keeping with a common interpretation of Freidman, Forrester
and Mass both modeled (desired) consumer expenditures

as proportional to an exponential average of income. While
there is some "smoothing":of expenditures in the formulation in
the model developed here, this smoothing includes an immediate,
substantial, though partial, expenditure response to variations
in income. The difference has some importance to stability. As
discussed more fully in appendix 1, consumer demand in this
model, in contrast to Forrester's and Mass‘ models, is
destablizing to the business cycle.

This discussion has focussed on differences. Obvously, there is
much that is the same. It is most important to note that this
model, like Metzler's and other system dynamics models, is a
model where physical processes are key. Any dynamics that are
generated within the real economy are the result of the real
economy; financial variables have no impact on real processes.
Financial variables will be introduced below. However, movements

‘in financial variables will always be caused in this paper by

movements in the real economy, never the reverse.

Timing. The length of the business cycle is variable.
Nonetheless evidence from the National Bureau of Economic
Research indicates the "business cycle [has] an average length of
JAMES H, HINES) JKy obs06s8E

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. Figure 9
timing Relationsips of Economic and Modeled Variables

BCD Indicators Model Variables
No. Name Average lag” and Name Lag”
standard deviation (months)
(months)
41 Employees on
nonagricultural
payrolls +5 (2.4) Workforce 0
4g Value of Goods
Output (1972 $) i) (1.4) Production oO
51 Personal income
less transfer Total wage
payments (1972 $) 12.1.7) receipts. 0
59 Sales of retail Dollar
stores (1972 $) ne (2.2) Sales a
30 Change in
inventories Change in
(1972 $) “4.9 (5.8) inventories -3.75
70 Mfg. and
trade
inventories

(1972 $) 4.8 (2.7) Inventory 7.5

* Lags are measured relative to production (value of goods output,
1972 dollars). A negative lag is a lead.

(Source: Handbood of Cyclical Indicators, 1977)

Hines ae
about three years from peak to peak" (Sargent 1979, 215).
The damped period of the model is also three years.

Figures 7 and. 8 presents plots of several variables generated by
the model. The model was perturbed from equilibrium at the end
of year 1 by an instantaneous "evaporation" of two per cent of
the inventory in the economy. Figure 9 presents a comparison
between the timing of these variables and corresponding variables
in the economy. The performance of the model seems rather good.

The Inventory Argument and Variations. The hypothesis we wish to

investigate is that business borrowing may be a cause of money
supply expansion and that expansion arising in this manner will
result in the observed timing relationships between money and
production: Change in money leads money leads production.

Most basically, businesses borrow when their cash flows are
negative and repay when their cash flows are positive. A working
hypothesis in the System Dynamics National Model Project has been
that business borrowing is related to the need to finance
inventory expansion. It is possible now to develop more
rigorously the relationship between inventories and cash flows.

Consider the set of curves in figure 10. These curves represent
the behavior of several model variables when the model is
disturbed from equilibrium by an instantaneous, one-time two per
cent "evaporation" of inventory.

The two curves in the first panel represent the production rate
on the one hand and inventory investment (ie. change in
inventories) on the other. As in the real economy, inventory
investment leads production.

Inventory investment is the difference between the production
rate and the shipment rate. Consequently, the relationship
between inventory investment and production has implications for
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Hines 26

the relationship between production and shipments. In
particular, in order for inventory investment to lead production,
the shipment rate must lag the production rate. The computer
plot in the second panel of figure 10 shows the shipment rate
lagging the production rate.

In order to see the necessary connection between the first two
panels of figure 10, note that the production rate reaches a peak
and is consequently not changing at time A. The shipment rate,
however, is still increasing in year three. This means that the
difference between production and shipments, inventory
investments, must be declining; that is, inventory investment
must peak before time A.

Production and shipments have implications for expenses and
hrevenues. It seems reasonable to suppose that in the real
economy cash production costs and, in particular, wage payments
will be approximately in phase with production, And cash
revenues will be approximately in phase with shipments. The
third panel presents corresponding model variables, (Total wage
payments of the production sector are identically equal to the
the total wage receipts of the household sector in figure 3).
Both cash revenues and cash wage payments might in reality be
displaced slightly to the right, if consumers buy on time and if
producers pay wages only after they have been earned.

The difference between cash revenues (dollar sales) and
production expenses (total wage payments) is net cash flow which
is plotted in the third panel of figure 10. To get a sense of
the timing relationships, note that at time A total wage payments
peak and, consequently, are momentarily unchanging. Dollar
sales, on the other hand, are still rising. This means that net
cash flow must be rising; hence, the trough in net cash flow must
occur before point A.
Hines a 483

If businesses borrow when cash flows are negative and repay when
cash flows are negative, business borrowing for cash flow will be
a "flipped-over" version of net cash flows; that is, borrowing
for cash flow. purposes will be 180 degrees out of phase with cash
flows themselves. The final panel in figure 10 plots the
borrowing rate implied by the pattern of net cash flow plotted in
the preceeding panel. As may be seen, borrowing for cash flow
leads the production rate. According to the System Dynamics
working hypothesis, this borrowing may be interpretted as an
inerease in the money supply. Maintaining this interpretation,
we can reinterpret borrowing as the rate of change of money. In
figure 11 this reinterpretation has been carried out and the
money stock, which now integrates a rate of change which is equal
to the net borrowing rate, is shown as well. While the change in
money leads, the money stock lags production.

An integration lags its derivative by ninety degrees. Since
borrowing (change in money) leads production by less than ninety
degrees, the stock of money must lag production in this model.
The too-small lead in borrowing is likel to be a ‘characteristic
of the economy as well as of this model. To see this more
precisely, consider an idealized case where both cash outflow
(wages) and cash inflow (revenues) are sine waves. In this case,
borrowing for net cash flow will be the difference of two sines
and may be written:

Borrowing = Wages - Revenues
= A¥SIN(Wt) - B¥SIN(wt-g)

= K*SIN(wt + h)

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the business cycle
Where w is the frequency of the Dust ’ Figure 12: Lead of Change in Money Over Production Rate
is the amplitude of wages
is the amplitude of revenues (degrees)

A
B
g is the phase lag of revenues behind wages
K

is the amplitude of borrowing and may be written:

KeSQR(A2 - 2aBCOS(g) + B2) (amplitude of Wages)/(Amplitude of Sales)
h is the lead of borrowing in front of production ° 5 1 15 2
which may be written:
ARCTAN(B¥SIN(g)/(A=B*COS(g)) Sales lag
-018° 179° 179° 89.97° +036" +018
18° 162 146° 81.0° 29.4° 16.4
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phase lag of revenues and the relative amplitude of wages 2 108° 78.6 54.0 38.6 29.4
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respect to production for several combinations of relative s 5 . y ° .
: 108 72.0 49.6 36.0 21.7 22.4
amplitudes and revenue lags. .
426° 54.07 36.6" 27.0° 21.2" 17.4
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expenditures, these large leads occur when consumer expenditures 180 0.00° 0.00 0/00" 0.00 0.00
vary more than consumer income. In the model considered here, it

is not possible for the amplitude of consumer expenditures to
exceed consumer income since the consumption function, based on
reasonable decision rules, will immediately pass through to
expenditures only a fraction (seventy five per cent) of a change
in income. While it is not impossible that the variability in
aggregate consumer expenditures would exceeed the variability of
aggregate income, it is not easy to construct a situation in
which this would occur. It would seem that allowing consumers

Hines a1

to borrow in order to spend more than their incomes might produce
a case in which consumers as an aggregate desire to spend more
than they earned. I have looked at consumer—debt-adjustment
processes both in the context of the present model and in the
context of models containing endogenous price movements and of
models containing limits on total workforce participation. None
of these have been capable of generating a run in which consumer
expenditures exceeed income under reasonable choices for
parameters,

Restricting our attention to the three right-most columns of
figure 12, where the amplitude of wages is greater than the
amplitude of sales, it may be seen that the maximum phase lead of
borrowing ahead of production is ninety degrees.” As mentioned,
an integration follows its derivative with a lag of ninety
degrees (as long as the derivative is symmetric). It is clearly
impossible in this model, and unlikely in the economy, for the
stock of borrowing-generated money to lead production. At best,
it will coincide with money. Hence, the inventory-borrowing
argument appears unable to account for the fact that the stock of
money leads business activity.

New Directions. We have assumed above that borrowing would be
translated into money creation, or, more specifically, net
pressures on the financial system. It is, however, important to
remember that in a closed model one sector's (or person's) cash
outlfow is another's inflow. Hence, in the simple two sector
view of the world taken here, the negative cash flow of the
production sector will be balanced by a positive cash flow of the
household sector. In fact, the two are identical in magnitude,
but opposite in sign. The wage expenses (cash outflow) of the
production sector are the wage revenues (cash inflows) of the
household sector. The dollar sales (cash inflow) of the
production sector are the household expenditures (cash outflow)
of the household sector. To make this precise, the production
sector net cash flow is defined as

(17) NCFO = DSALE - TWP Net cash flow (dollars/year)

485

Hines 32

(18) TWP = TWR Total wage payments
(19) DSALE = HEXP Dollar sales

Compare these. equations with equation (11) in figure 3. Clearly,
the one is the additive inverse of the other.

This means that when the production sector borrows, the household
saves in just the same amount. The household could save by
investing in (ie. lending to) the production sector. If this is
the case there will be no net pressure on the financial system.
There will be no need to create money, as illustrated in figure
13.

The important point here is that what the household does with its
cash flow is crucial in understanding the timing of net pressures
in the financial system. While this points up a fundamental flaw
in the corporate cash flow argument, it also provides a means of
resuscitating the underlying argument that the lead of money with
respect to production need not result from money causing
production. While inventory investment by itself cannot account
for the observed phase relationship, it may be possible that an
elaborated theory, consistent with the assumptions and focussing
on the interaction between the borrowing demand of producers and
investment demand of consumers, will be able to account for the
timing relationships. |

There are a number of factors effecting household investment
demand which, in combination with the above inventory argument,
might yield the observed timing relationships between money and
production. I will focus on aggregate default risk and return.
These are, of course, central considerations in portfolio
decisions, Further, the default risk/return factor can be
considered through relatively minor changes to the model
developed thus far, and, hence, the discussion can proceed at a
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faster pace. The following development is intended to be
illustrative rather than definitive.

There may, of. course, be other influences effecting the demand
for money balances which are not treated in what follows.
Perhaps the prime candidate here is transactions demand (Judd and
Seadding 1982), although some might argue that the importance of
the transactions function of money has been exagerated (Wilmouth
1982). I have considered the effect of transactions demand for
financial assets on the part of businesses. -By itself, this
mechanism can generate at best a 90 degree phase lead of money
change and a zero lead of money stock with respect to production.
The mechanism is not sufficient to account for the observed
timing relationships of money and production. However,
transactions demand for money or other financial assets may be an
additional influence in the economy determining the aggregate
timing of financial variables.

Risk, expected return and household money holdings. The
situation considered immediately above and illustrated by figure

13 was one in which consumers invested their entire cash flow in
the production sector. While the household could save by
investing in the production sector, it does not have to. The
household is, after all, making portfolio decisions and it could
choose to hold its assets as money. In this case, as the stream
of cash comes from the production sector to the household, a
portion may be funnelled off. That portion, held as cash, will
not be available to satisfy the producer's demand for credit.

The excess demand for credit will appear as pressures in the

financial system which may be met through the creation of money.

It is necessary to consider factors which the household might
consider in managing its portfolio. It is reasonable to suppose
that expected return will be one force determining portfolio
composition. The aggregate return on assets is, of course,
correlated with movements in production. Indeed, abstracting
from price movements, aggregate production is aggregate return.

j33
487
Hines a5

Hence as expected aggregate production declines, expected
aggregate return will decline as well, In this case, any
descrepancy in expected return between holding money and holding
other financial assets will also decline with the economy. ‘This
should make money relatively more attractive than it was and
people might reasonable choose to hold more of it. It may also
be reasonable to suppose that as expected return declines people
will expect to become poorer. As people become poorer they may
become more risk averse (Merton 1982). If an economic downturn
is associated with the populace becomming poorer and if poorer
people are more risk averse, the household will want to put more
of its financial assets into safe assets, such as money, as times
begin looking grim. In line with these arguments, Cagan (1964)
suggests that during depressons household holdings of currency
may increase; we may suppose that during mild recesions the
household may wish to channal more of its cash flow into its
money balances.

It is important to identify information sources for the formation
of perceptions of the likely course of the economy. Investors
certainly may use the leading indicators mentioned in the
introduction to this paper as a source of information about the
economy. After all, the original purpose of the leading
indicators was to provide just this information (Moore 1978).
Today, of course, the indicators get much play in both the print
and broadcast news services. The indirect influence of the
leading indicators may also be substantial since much secondary
information, such as the quoted opinions of business economists,
may be based in part on a consideration of these leading
indicators. There are other ways in which the household could
gain a sense of the direction of the economy, such as the rate of
change of income, either on a personal level through direct
experience or on an aggregate level though the publications of
news organizations or of government agencies.

It is probably less important in the present context to list all
the possible sources of information about where the economy is

Hines #8
likely to head, than it is to recognize that people use this kind
of information. People can and do predict where the economy is
likely to be a short time in the future: Consumer sentiment,
itself, is a leading indicator (BCD 1977).

For the purposes of this illustration, it is convenient to allow
investors to use a leading indicator that has already been
considered: Inventory investment. Results would not differ
radically if we modelled many leading indicators and allowed
investors to form an average or an index of them.

In brief, we assume the household uses inventory investment to
gain a sense of where the.economy is heading; this information is
assumed to effect expected return and risk preferences. As
expected returns and the desire for risk go down, cash holdings
go up. Consider what would be the case if the household used
actual inventory investment as the basis of its decision to add
to or decrease cash holdings. When inventory investment was
high, the consumer, believing most confidently that the economy
was improving, would be decreasing his cash holdings at the
fastest rate. He would be removing assets from his money balance
and attempting to give them to the production secor. His demand
for investment would, in fact, exceed his positive cash in flow.
This means that his demand for investment would exceed the
producer's demand for credit. There would be net pressure in the
financial system. The monetary authority could relieve this
pressure by destroying money.

Under these circumstances, the destruction of money occurs at its
greatest rate at the peak of inventory investment. This gives

“exactly the reverse timing of the simple inventory-investment

argument according to which money is created at its fastest rate
at the peak of borrowing demand, that is, at the peak of
inventory investment. Under the new assumptions, creation of
money would be 180 degrees out of phase with borrowing demand.
This means that it would be precisely in phase with producer's
net cash flow of figure 10. Clearly, this means there is a very
Hines 37
substantial lead in the rate of change of money (ie. cash flow).

The lead is so great that not only does the peak in money change
lead the peak. in production, but the trouph in money change leads
the peak in production as well. This lead is too great.

Friedman and Schwartz! data (1963 p. 197). suggests that a trough
in money change follows within a month or two a peak in
production, it does not preceed it. .

This too-substantial lead occurs because we have neglected two
considerations thus far in the analysis. First, no one is aware
of the rate of inventory investment as it is occuring. The data
must be gathered, and while results may gradually become clear
even before the publication of the final tabulations, there will
still be a delay between actual inventory investment and the
perception of that investment. Further, even if the household
were able to know inventory investment at the time of the
investment, there is still likely to be a delay: While consumers
may watch the leading indicators, it takes a while for them to
decide that what they see is actually a harbinger of economic
conditions to come. Economic data is noisy, consumers will not
want to respond to every gust of the windy economic indicators.
Investors will wish to smooth their information; they will want
time to see whether the promise of the indicators is finding
evidence in a general economic expansion. This "delay for
deliberation" may be even more significant than the delay
associated with gathering and deseminating the raw information
about inventory investment.

The following equations are consistant with the above discussion.
The equations present the household increasing its money balance
when it percieve the economy will improve and decreasing its
money balance when it percieves the economy faltering.

(20) HON = MCHN*EECP*HMON
(21) EECP = g(DINV)

Household money (dollars)

Effect of economic conditions
on portfolio (dimensionless)

(22) DINV = SMOOTH(INV,TCINV)

488

Deliberated inventory investment ($/yr)

Hines 38

(.) Wel Inventory Investment ($/yr.)

‘
(23) MONEY = NBOR - HDINV
(24) HDINV = BSaV - HMON

Money supply (dollars)

Household desired invesment

(dollars/year)
constants:
MCHM Maximum change in household
money (dollars/year)
TCINV _ Time to consider inventory

investment (years)

SMOOTH is the exponential smoothing function.

This formulation, while adequate for the present illustration,
would, no doubt, require revision in an extended treatment of the
problem of household portfolio selection.

Equation twenty suggests that the rate of change of the
household's money balance is a function of the household's
perception of where the economy is heading. The equation
suggests that an investor, believing the economy will worsen (on

the basis of leading indicators), will increase his money

balance, and, conversely, when the investor believes the economy
is improving he will decrease his money balance.

As written, the equation contains feedback from the money balance
itself, but not from the rest of the portfolio. In a more formal
treatment, the rate of increase in money balances might decrease
as other investments become low. While, this causes no problems
in the current model, since the fluctuations of the mild business
cycle are, by definition, mild; the building of confidence in the
impact of household portfolio decisons will eventually require
testing a formulation under extreme conditions. Further, an
explicit representation of return to investments as well as risk
is important if one wishes to assume that the household is
reacting to or in anticipation of these factors. Finally, it may
be that the control of money balances might better be represented
as a stock adjustment process,
Hines a9 489

As discussed above, equation 21 suggests that a sense of
impending economic conditions may be gleaned from a smoothed
version of inventory investment. Here, EECP is in general a
nonlinear function of inventory investment. In the following
simulations, I have assumed a linear function:

EECP = -C*(DINV/II)
Where C and II (initial inventory) are constants.

The process by which consumers deliberate upon the significance
of the leading indicators has been represented by a first order
information delay (equation 22), It might be argued that.a third
order information delay would better represent the formation of
perceptions in regard to an economic indicator. As it turns out
using a third order delay, rather than the first order delay
above, makes almost no difference. I have chosen to stay,with
the simpler formulation.

The forces shaping the change in money have been made explicit in
equation 23. Net pressure in the financial system is the
difference between producer's demand for credit (NBOR) and the
household's desire for investment (HDINV). The household's
desire for investment (in the private sector) is determined by
two other decisions which have already been considered: the
household savings rate and the adjustment of the households money
balance. This follows from the fact that in this model household
savings must equal the sum of investments and household money.

The form of the equations above should not obscure the fact that
the change in the money supply will be the same as the change in
the household's money balance. These equations give the
equivalence of two views of pressures for money creation: (1)
Pressure for money creation results from credit needs of business
which are not met by the household; or (2) pressure for money
creation results from the desire of the household to hold money.
It seems that the the first way of looking at the matter

Hines 40

represents the true structural relationship in the model, the
second is a kind of reduced form representation. In any case,
the equations explicitly represent the relationship between
credit demands and money.

The result of adding the above equations to the model may be seen
in figure 14 which plots the response of variables of the altered
model to the familiar 2% inventory evaporation. The timing is
very close to desired as figure 15 shows.

Figure 15

Leads and Lags in Money and Change in Money

BCD Economic Lag Model

Time Series Peak Trough All Turns Variable Lag

Change in M1 19.7 =6.7 13-2 Change in Money -19
(5.5) (5.5) (8.9)

M1 (1972 $) -10.5 Money -7

75 9.0
(6.8) (4.2) (6.0)

(Note: A negative lag is a lead. Standard deviations appear in
parentheses)

It must be stressed that in this model money is entirely passive;
it excerts no influence on the rate of production. Causality
flows from production to money. Nonetheless, money leads
production,
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This model is not the first to demonstrate that causality cannot
be deduced from the lead of one time series with respect to
another. In "Money and Income: Post Hoc Ergo Proper Hoc?" (1970)
James Tobin constructed a model which, like this one, generated
leads of money over production even though causation flowed from
production to money. In 1972, however, Sims suggested an
econometric test for causality based upon work done by Granger
several years earlier. In his paper Sims stated

The method of identifying causal direction employed here does
rest on a sophisticated version of the post hoc a propter
hoc principle. However, the method is not easily fooled.

Simple linear structures with reversed.causality like the one

put forth by Tobin cannot be constructed to give apparent
money-to-GNP causality. (Sims 1972, 543)

Sims concluded that the data were consistent with unidirectional
causation from money to GNP. Since 1972 an “enormous number" of
empirical studies, stimulated in part by Sims’ paper, have used
similar proceedures to (attempt to) deduce causality from time
series data (Newbold 1982). Nonetheless, others, includings Sims
(1983) himself, have argued that Granger causality might be
misleading.

It may be of interest to see how the Granger/Sims test for
causality performs on this model for two reasons. First, while
the model produces output which "looks" as if it contains the
proper timing relationships, it is desirable to submit it to
statistical tests. Sims 1972 test showed causality running from
money to real activity. A similar result here would indicate
that the model output is, indeed, behaviorally similar to the
real world. Further, of course, a result here showing causality
flowing from money to production, while confirming one's visual
impression, would raise some doubts about the usefulness of the
Sim's test for identifying the direction of causal flow.

The following proceedures were used. Desired wage coverage was
reduced from 6.667 to 4.5 years in order to make the system less
damped. This change allows the model to generate long series of
Hines 43 491

cyclic data without great amounts of attenuation and without the
need for a noise input, a consideration of which is beyond this
paper. This change has the additional impact of shortening the
period of oscillation. However, the relative timing of money
with respect to production is largely unaffected. Two hundred
quarters of data were generated. The first seventy quarters were
discarded to eliminate any direct impact of the initial
disturbance which occurs in the fourth quarter. ‘This leaves
thirty-one years of data (the last quarter was not used); Sims
(1972) used twenty two years of data in his original study.

Sim's proceedure is a "statistical test for unidirectional
causality". It consists of running a variable ¥ on future and
past values of a variable X. If causation runs unidirectionally
from X to ¥, the coefficients on future values of X will be
insignificantly different from zero, Sims used four leading
values and eight lagged values of the independent variable; 1
have done the same. Results are presented in figure 16 where,
following Sims, an F-test has been used to test whether
coefficients on future values of the independent variable are
significantly (at .01 level) different from zero.

Figure 16 -- Granger/Sims' Test for Causality

OLS
Regression F Significantly
Statistic different
from zero?
(.01 Level)
Production on money +58 No
(Tests whether money
causes production)
Money on production 229 Yes

(Tests whether prod-
uction causes money)

To quote Sims:

These results allow firm rejection of the hypothesis that

Hines a

money is purely passive, responding to GNP [ie. production]
without influencing it. They are consistent with the
hypothesis that GNP is purely passive, reponding to
Mfoney]...but not influencing Mfoney]. (Sims 1972,

This conclusion which Sims reached looking at his test applied to
data from the real world, is the same conclusion reached by
applying his test to the model output. This supports the visual
impression the model produces the proper sorts of leads.

While this result lends credence to the simulation model and
points to the potential usefulness of comparing statistical tests
performed upon a model with those performed upon real data, this
result does not engender confidence in the usefulness of the
Granger/Sim's test for detecting the direction of causal flow
between time series. The test's conclusion about the direction
of causal flow are entirely false. Causality is entirely from
production to money, money has not one iota of influence on
production in this model.

It is important to note that the conditions under which the
Granger/Sims test has been evaluated are quite favorable. There
are more observations than are usually available for this sort of
thing. There were no shifts in parameters during the period
covered by the data. There is no measurement error. And there
is no stochasticity. All these possible ways in which causal
relationship may be obscured have been removed. What is left is
specification error. The Granger/Sims test fails because the
bivariate model upon which it is based does not mirror the
simulation model. Since there is no promise that the bivariate
model will be an any better mirror of the more complex and less
linear real world, the usefulness of the Granger/Sims test for
understanding causal relationships in the economy is open to
serious question.

It should be noted that the Durbin-Watson statistic is quite low.
Although there is no stochasticity here, the low Durbin-Watson
might suggest an autocorrelated disturbance to a naive
investigator. This in turn suggests the use of generalized least
Hines 45 492

squares. Results are given in figure 17, This might be
interpretted as a slight improvement: We may now firmly reject
unidirectional causality in both directions instead of only in
the wrong direction. Of course, it happens that there is
unidirectional causality from production to money in the
simulation model.

Figure 17--Granger-Sims' with GLS
Cochrane-Oreutt

Regression F Statistically
different,
from zero?

(at .01 level)

Production on money 19.43 Yes
(Tests whether money

causes producton)

Money on production 433 Yes

(Tests whether prod-
duction causes money)

Summary. Both the change in mony and the stock of money lead
production over the business cycle. This paper has considered
one hypothesis of these phase relationships. According to the
hypothesis, inventory investment causes business borrowing which
causes an increase in the money supply with a lead relative to
the rate of production. It was concluded that this hypothesis
could not account for the timing relationships between money and
production. Inventory-investment inspired borrowing, considered
alone, causes a lead in the change of money but a lag in money
itself with regard to production.

The chief problem with the inventory investment argument is that
it does not take account of the supply of credit. The inventory
investment hypothesis combined with a mechanism for adjusting
the household's portfolio does have the potential of accounting
for the observed phase relationships.

Hines 6

A model of the inventory-investment-cum-household-portfolio
argument was developed in which the household adjusted its
portfolio based upon expectations about the future course of the
economy. The model generated the observed phase relationships

In addition, the Granger/Sim's test for causality, applied to
simulation model output, yielded results which were qualitatively
similar to results of the test when applied to real data. This
similarity in results enhanced the credibility of the argument,
while calling into question the usefulness of the Granger/Sim's
test for detecting causal direction.

The augmented hypothesis maintained the assumptions that real
activity causes financial activity and that credit demand and
supply determines money. However, an essential similarity
between the credit demand, and supply viewpoint and a money demand
viewpoint was discovered.

Further Steps. It is important not to lose sight of ultimate
goals. What we seek is an explanation for the stable timing
relationships observed between money, credit, and economic
activity. We wish to know whether money causes and whether
monetary policy is a high-leverage means of controlling the
business cycle.

This paper has shown that it is not necessarily the case thet
money causes the business cycle despite the intuitive appeal of
post hoc propter hoc arguments and despite results of the
Granger/Sim's test for causality.

It is necessary to go beyond this conclusion. It is necessary to
explore the mechanisms by which money might influence business
activity. It may be that those mechanisms are weak or operate on
a time scale different from the business cycle. It may be that
the story told here gets at the essential reasons for the
observed stability of the phase relationships. But we cannot
know this until we have taken explicit account of the influences
of financial variables on real activity.
Hines Pn 493

The next step is to connect the current understanding, as
embodied in the simulation model, with causal mechanisms by which
financial variables may influence real variables. The work
presented in this paper provides a foundation for that task.

48

APPENDICES AVAILABLE ON REQUEST
Hines 49

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