Contents

(A) The Consumption Function

(B) The Investment Function

(C) The Liquidity Preference Function

(D) The Transmission Mechanism

There are several important relationships within the Keynesian model: the
consumption function, the investment function, the liquidity preference function being the
major three. Methodologiclaly speaking, the Neoclassical-Keynesian
Synthesis had given the green light for the application of Neoclassical economic
theory to Keynesian economics and thus major efforts were undertaken by various
Neo-Keynesians to "ground" these major Keynesian relationships in Neoclassical
microeconomic theory - specifically, to derive these relationships from
utility-maximization or profit-maximization exercises of some sort or other. This turned
out to be perhaps *the* major research agenda in American macroeconomics during the
1950s and 1960s and only a brief outline is possible here.

The first efforts in this research programme concentrated on the
consumption function. The simple Keynesian function, C = C_{0} + cY was regarded
as "too simple" and there were apparently some conflicts with empirical evidence
laid out by Simon Kuznets (1946) - specifically,
the finding that savings were a reasonably stable share of income for the 1869-1938
period. As the simple Keynesian consumption function predicted that as income rose,
savings would take an ever greater share of it, efforts were needed to come up with a
"better" consumption function.

James S. Duesenberry (1949) mad the first attempt, by arguing that there was "habit formation" in consumption behavior. Specifically, he proposed that people easily increase consumption when income rises but have problems reducing it symmetrically when income falls. Thus, he proposed a consumption function of the form:

C = C

_{0}+ c_{1}Y + c_{2}Y^{M}

where Y^{M} is the peak consumption achieved in the past. In this
way, consumer behavior is "ratcheted up" as income rises above previous peaks.

Franco Modigliani and Richard Brumberg (1954) decided to go further than Duesenberry and proposed what has since become known as the "Life Cycle Hypothesis" (LCH). A similar idea was proposed independently by Milton Friedman (1957) in his "Permanent Income Hypothesis" (PIH). Specifically, Modigliani and Brumberg visualized consumption decisions as integrated in an intertemporal optimization program for a "representative consumer" along the lines of Irving Fisher's (1930) two-period model. In other words, households were faced with a forecasted "income stream" which they attempted to allocate over their lifetime. They did so by shifting their promised endowments around different time periods via financial markets in order to "smooth" their consumption out (or, rather, to make it compatible with their intertemporal tastes). Their optimization problem can be roughly stated to be something akin to the following (we are summing time t from t = 0 to t = T, the end of one's life):

max U = ・/font>

_{t}b^{t}U_{t}(C_{t})

s.t.

・/font>

_{t}C_{t}/(1-r_{t})^{t}｣ A_{0}+ ・/font>_{t}Y_{t}/(1-r_{t})^{t}

thus agents choose a consumption path (C_{1}, .., C_{T})
which maximizes their intertemporal utility function (weighted by a subjective time
discount rate b ^{t}) subject to an intertemporal
budget constraint which is governed by a discounted stream of future income (・/font> _{t} Y_{t}/(1-r_{t})) and the wealth they
are born with (A_{0}). Modigliani and Brumberg proposed an aggregate consumption
function of the following sort:

C

_{t}= cV_{t}

where V_{t} is the sum of net worth at time t, income at time t
and the present value of all expected future earnings - all averaged out over the
characteristics of the given population. In Miton Friedman's
(1957) language, V_{t} can be thought of as "permanent income". The
parameter c can be assumed constant if the demographic composition of the population is
relatively constant. Thus, in short, the aggregate consumption function does not depend
solely on current income, but also on demographics, on conditions in financial markets
(and thus the interest rate), uncertainty and expectations, etc. To capture this, Ando and
Modigliani (1963) proposed the following
testable consumption function:

C

_{t}= cY_{t}+ cA_{t}+ c(T-1)Y_{t}^{e}

where consumption at time t is a linear function of current income (Y_{t}),
current wealth (A_{t}) and the average expected annual non-property income (T-1)Y_{t}^{e}.
This last term is obtained by recognizing that (T-1)Y_{t}^{e} = ・/font> _{t}Y_{t}/(1+r)^{t} and is the most
difficult part of this equation to estimate. The implication, then, is that temporary
increases in income will not have much of an effect of consumption behavior but rather be
accumulated as savings, whereas changes in the expected income stream (permanent income)
will lead to substantial changes in consumption.

Keynes's theory of investment was a more complicated affair. Unlike consumption, the modifications of the investment function were not dominated by empirical concerns - indeed, empirical evidence seemed to imply that interest rates has, in fact, little influence on investment (hence many Neo-Keynesian economists were happy enough to assume a vertical IS curve which permitted them to more-or-less ignore the LM side of things in the early years). From this vantage point, the effort should have been to integrate the empirically-powerful accelerator theory of investment into the Keynesian model - as was indeed attempted by Roy Harrod, Evsey Domar and the Cambridge Keynesians. However, the American Neo-Keynesians were more worried about the theoretical problems of the simple Keynesian investment function (see our notes on investment for more details).

In fairness, integrating investment (a flow concept) with a stock-based
capital and production theory had already been a troublesome issue for Neoclassical
theory. Recall that Keynes proposed an investment function of the sort I = I_{0} +
I(r) where the relationship between investment and interest rate was of a rather naive
form: namely, firms "ranked" investment projects depending on their internal
rate of return (or "marginal efficiency of
investment") and thereby, faced with a given rate of interest, chose those whose
rate of return exceeded the rate of interest. Assuming something akin to a continuum of
available investment projects, they would thus invest until their marginal efficiency of
investment was equal to the rate of interest, i.e. MEI = r.

Several problems emerged with this theory. Firstly, as Armen Alchian (1955) and, later, Jack Hirshleifer (1970), pointed out, the method by
which Keynes "ranked" projects, i.e. via their "internal rate of
return", implied that Keynesian rankings are ultimately quite different from rankings
which are set according to the maximization of the present value of firms. A second
objection, perhaps best expressed by Robert Eisner
and R.H. Strotz (1963) was regarding the rather *ad hoc* way Keynes dealt with the
determination of the expected profits and returns, arguing instead for some carefully
prescribed distribution and process of expectation formation. This, of course, is a
"Neoclassical" objection - Post Keynesians,
such as G.L.S. Shackle (1949, 1955) and Paul Davidson (1972, 1994) have vociferously insisted that
there is no *ad hoccery* at all. Quite the contrary - pointing to Keynes's (1936, 1937) repeated insistence on radical
uncertainty - indeterminate or "animal spirited" expectations are quite
essential to Keynes's theory of investment.

A third, perhaps more serious problem, was the contention that a downward-sloping aggregate MEI curve is ultimately incompatible with Keynes assumption of unemployment (e.g. Piero Garegnani, 1978).. In situations of unemployment, increases in investment will increase effective demand and thus the profitability of projects - which will thereby push the MEI outwards. Consequently, as long as there is unemployment, the MEI curve should in fact be flat. Salvaging the downward sloping MEI curve may only be possible by either careful considerations of aggregation problems or appealing to Kalecki's (1937) principle of increasing risk - which again, coincides with the uncertainty thesis in Keynes' (1936, 1937) and the instrumental importance of finance.

Jack Hirshleifer (1958, 1970) had expanded upon Fisher (1930) to argue that investment ought to be conceived in the context of the maximization of the present value of the firm. Subsequently Dale W. Jorgenson (1963, 1971) provided a micro-theoretic Neoclassical theory of "investment" based on this notion. Effectively, Jorgenson's solution was to steal a leaf from the consumption book and recast the optimal capital stock decision in intertemporal form. Firms attempted to choose an intertemporal path for capital stock that maximized the present value of the firm - i.e. the present value of a stream of proceeds. Thus, in general, firm's face the following intertemporal optimization problem:

max V = ・/font>

_{0}^{･ }[p_{t}Y_{t}- s_{t}I_{t}- w_{t}N_{t}] e^{-rt}dt

s.t.

Y

_{t}= F(K_{t}, N_{t})

dK

_{t}/dt = I_{t}- d K_{t}

where (suppressing time subcripts) they are maximizing a stream of returns
(defined as total sale revenue, pY minus wage costs, wL and investment costs, sI where s
is defined as the supply price of investment) subject to a production function constraint,
Y = F(K, N) and the definition of net investment, dK/dt. Solving this problem yields the
following conclusions: (1) F_{N} = w/p, firms employ labor until their marginal
product is equal to their wage; and (2) the following holds:

pF

_{K}= s[d + r - (ds/dt)/s]

so that the optimal capital stock K* is chosen where the marginal value
product, pF_{K} is equal to the real user cost of capital, c = s[d + r - (ds/dt)/s]. This last term can be thought of as the implicit
rental rate. The logic is that the cost of investing (i.e. buying another unit of capital)
is the opportunity cost of lending out the funds (r), the depreciation per unit (d ) minus the expected capital gains (ds/dt)/s. If we had an explicit
invertible production function, then K* could be determined easily from F_{K} =
c/p. For instance, suppose we had a Cobb-Douglas production function Y = K^{a} L^{(1-a ) }so that F_{K}
= a (Y/K), then K* = pa Y/c. Thus,
in general, K* = ｦ (Y, p, r, d , s,
ds/dt, p) or simply K* = ｦ (Y, p, c) where K* depends
positively on Y and p and negatively on c.

This is fine for determining the optimal capital stock, but how does one
solve for the* investment* flow? Investment is defined as the instantaneous change
in the *optimal* stock of capital, thus, in principle, there is no investment unless
there is some reason to *change* the optimal stock of capital (by say, imposing
exogenous some rate of technical change or some population growth rate), or,
alternatively, investment is derived from the adjustment path *towards* the optimal
capital stock, K*. Following the first case, suppose that K_{t}* ｹ K_{t+1}* for some reason. Then, in principle, moving to
continuous time, from any given K, then investment is defined as I = dK* + d K, thus:

I = ｦ (dY, dp, dc) + d K

thus investment is a function of changes in the real user cost of capital (c), changes in the price of output (p), changes in output (Y) and the level of capital (K). Jorgenson's subsequent addition of some controversial delivery lags has been since disputed and thus will be ignored here.

Of course, Jorgenson's (1963)
theory is less about investment and more about optimal capital. If investment is seen as
the *adjustment* from a given level of capital to the optimal level of capital stock,
then, in Jorgenson, investment is instantaneous - and thus Jorgenson's connection with
Keynes is tenuous at best. As Abba Lerner (1944,
1953) and Trygve Haavelmo (1960) pointed out, it
is virtually impossible to allow marginal productivity theory to determine the
"optimal" level of capital, and then have marginal efficiency of investment
theory determine the optimal level of investment without thereby eliminating the flow
investment term entirely.

One implied resolution was to appeal to marginal adjustment costs. In effect, rising supply price of capital goods industries implies that firms approach the optimal capital stock only gradually. This gradualness is governed by marginal adjustment costs which are, in turn, the reason for a falling marginal efficiency of investment (MEI) function. Thus, as investment increases, supply price of capital goods rises and thus MEI falls so that MEI = r before the optimal capital stock is reached. These marginal adjustment costs will therefore slow down adjustment and allow for both optimal capital and optimal investment to be defined.

Attempts were made to incorporate marginal adjustment costs into Jorgenson's theory in order to obtain a proper theory of investment in an optimization context. To this end, the work of Robert Eisner and Robert H. Strotz (1963), Robert E. Lucas (1967) and John P.Gould (1968), was instrumental. Specifically, instead of the term sI in Jorgenson's equation, the Eisner-Strotz-Lucas-Gould modification was to propose sI + C(I)sI where C(I) is a convex function reflecting marginal adjustment costs. These adjustment costs can be due to "intrinsic" factors (i.e. costs of installation) or "extrinsic" factors (rising supply price). Thus, firms now face the problem:

max V = ・/font>

_{0}^{･ }[p_{t}Y_{t}- s_{t}I_{t}- C(I_{t})s_{t}I_{t}- w_{t}N_{t}] e^{-rt}dt

s.t.

Y

_{t}= F(K_{t}, N_{t})

dK

_{t}/dt = I_{t}- d K_{t}

which, solving via standard dynamic optimization techniques, yields a pair of differential equations:

dq/dt = (r+d )q - (ds/dt)/s - pF

_{K}/s

dK/dt = y (q

_{t}) - d K_{t}

where, if we had explicit terms for C(I) we could solve for the *path*
K(t) and q(t). Thus, the marginal adjustment cost model does not yield an "optimal
capital" level but rather an optimal adjustment path. The q defined in the first
equation is actually James Tobin's "q" (which, in this model, is defined as q = l /s where l is a costate variable
representing the shadow value of capital). Notice that in our net investment equation,
dK/dt, we have the implicit function y (q) - i.e. a Keynesian
"investment" schedule y (q) where y
(1) = 0 and y ｢ > 0.

James Tobin's "q" theory of investment was presented in Brainard
and Tobin (1968) and Tobin (1969). Effectively, Tobin's q theory proposes
that a firm will invest until q = 1 where q is defined as the ratio between the
stock-market valuation of existing real capital assets and its current replacement cost.
In Keynes's (1936: p.135) language, q = V/C where
V is what Keynes defined as present value of the prospective yield of the capital asset
while C is what he defined as the supply price of the capital asset. Consequently, at the
margin, q can be seen as the ratio of the marginal efficiency of investment to the rate of
interest, i.e. q = MEI/r so that the Keynesian investment function can be rewritten as I(q
- 1) where firms invest until q = 1 (or, equivalently, MEI = r). As we can see immediately
from above, this function is captured by y (q). Thus, as other
commentators have noted, the Eisner-Strotz-Lucas-Gould theory of investment with marginal
adjustment costs is formally equivalent to Tobin's "q" theory of investment -
and, of course, logically equivalent to what Abba Lerner
(1944, 1953) had already long proposed. Notice, finally, the main difference between the
adjustment cost story and the Jorgenson one regarding the rate of interest: if r rises, q
falls and consequently investment collapses in the adjustment cost story - just as Keynes
proposed; in Jorgenson, bar the contrivance of *ad hoc* lags, optimal capital stock
falls but investment just "jumps".

**(C) The Liquidity Preference Function**

One of the early items to be tackled was Keynes's money demand function.
Before the *General Theory*, John Hicks (1935)
had explained that money demand ought to be analogous to any exercise of choice by the
consumer - in this case, choice of portfolio holdings, and that therefore the principles
of marginalist economics ought to be applicable to determining optimal money holdings (and
those of other assets). In Hicks's view, the opportunity cost of money was the interest
foregone on other assets. This concept, already insinuated by Keynes in his *Treatise on Money* (1930) was
enshrined in and expanded upon in the "liquidity preference" theory of interest
of Keynes's *General Theory* (1936).

Keynes (1936) designated three motives for holding money: for transactions purposes (to finance regular expenditures); precautionary purposes (to finance unexpected expenditures); and speculative purposes (to hold as an asset). In terms of Keynes' liquidity preference function, money demand was affected by current income and interest rates so:

M

^{d}= L(r, Y)

where r is bond interest rate (an average of rates of returns on illiquid
assets) and Y is income. The basic proposition was that L_{r} < 0 and L_{Y}
> 0 - although a specification more faithful to Keynes's original system would include
expected *and* current interest rates into this function. Keynes originally proposed
that interest would only affect speculative demand - by far, the most controversial of the
three motives. Specifically, the basic problem is that under normal circumstances, money
pays no interest whereas other assets (such as bonds) do. Since bonds are essentially
promises to pay a certain amount of money at a future date (plus interest), then there
seems to be no reason why one should hold money as an "asset" instead.

Keynes's original answer revolved around the issue of expectations. If,
for instance, an agent expects interest rates to rise in the future, then to avoid
expected capital losses, he will hold his wealth in money and await for that rise. Once it
has risen, he can then purchase bonds. The inverse of this analysis applies to an agent
who expects interest rates to fall: she would buy bonds now rather than later. When
interest rates collapse and bond prices rise, she can then sell her bond and make capital
gains. Thus, Keynes treated his agents as "plungers", i.e. in other words, they
will hold *all* of their wealth in money or *all *of their wealth in bonds,
depending upon their expectations of interest rate movements. In other words, in terms of
the speculative demand for money, an agent does *not* have a diversified portfolio.
Consequently, for there to be an "aggregate" portfolio which includes *both*
money and bonds, then there necessarily must be heterogeneity of expectations. It must *not*
be that everyone expects interest rates to increase or else no one will hold bonds and
everyone will try to hold money (notice that Hicks's
(1937) "liquidity trap" would be precisely such a
case). If an agent is willing to hold money, then somebody else must be willing to hold
bonds - and to explain this, Keynes argued, their expectations must differ.

For Neoclassical economists used to arguing on the basis of a single "representative" agents with relatively rational (and thus relatively homogeneous) expectations, Keynes's explanation for the relationship between interest and money demand - via a world of heterogeneous agents with differing (and thus irrational?) expectations - must have sounded like a sour note. Instead, they looked upon Hicks (1935) to offer them a way of maintaining a relationship between money demand and interest without Keynes's "speculative demand".

The first set of propositions was the reformulation of the "*transactions
demand for money*" as an optimization problem by William Baumol (1952) and James Tobin (1956). Specifically, they proposed that people
needed money to undertake transactions (Y), but if they hold too much money, they
sacrifice the opportunity cost of holding bonds (the interest rate r). However, if they do
not hold enough money, they have to convert bonds to money several times over during any
transaction period (n times per period) and thus incur transactions costs (c per
conversion). Thus, suppose that W is the amount an agent converts from bonds to money
every time he converts. Assume he receives some income (Y) over a period and that he
spends all his income, thus must convert it all. Assuming he converts n times, then nW =
Y. Thus, over the period, average money holdings are M = W/2 and average bond holdings are
the remainder, i.e. B = (Y -W)/2. If it costs him c every time, then total transactions
costs are C = cn. Assume, of course, that rB > C so that it is always worthwhile to
hold bonds. The consumer's decision to hold money can be expressed as the solution to the
following optimization problem:

max U = U(Y + rB - C)

s.t.

Y = nW

C = cn

M = W/2

B = (Y-W)/2

rB > C

which, plugging everything in and solving, yields the following:

M* = ﾖ [cY/2r]

which is the famous Baumol-Tobin "square root rule" for the optimal transactions demand for money. Notice, then, that money demand M* is positively related with income and negatively related with the rate of interest on bonds - thus the relationships within the regular money demand function, L(r, Y) can be explained solely via this "transactions" motive.

The *precautionary motive* for holding money was also formalized as
an optimization problem - this time by E.J. Whalen (1966) and M.H. Miller and D. Orr (1966). Their basic point was that
people hold money to finance unexpected purchases. Consequently, these economists decided
to formalize precautionary demand by having net unplanned disbursements be some random
variable (distributed around zero with finite variance). Transactions costs and interest
rates are also included in the story so agents have an incentive not to hold everything in
money (thus interest rates) and not to hold everything in bonds (thus transactions costs).
Following an effectively similar procedure to Baumol-Tobin, we obtain the following:

M* =

^{3ﾖ }[2cs^{2}/r]

a "cube-root" rule which relates precautionary money demand (M*) positively to transactions costs and the variance of net disbursements (uncertainty) and negatively to the rate of interest.

The most celebrated liquidity preference function was the attempt to
formalize the speculative demand for money (as an "asset") by James Tobin in his famous article "Liquidity Preference
as Behavior Towards Risk" (1958). Together with Harry Markowitz (1952), Tobin's (1958) article effectively
launched "modern portfolio theory" and, consequently, much of the rest of modern
finance theory. Tobin's principle was simple:
people are faced with a variety of assets with higher return *and* higher risk than
money. If people are also risk averse, they may still
wish to hold riskless money in spite of the fact that it has zero return. Tobin's more
interesting result was than, in constructing a portfolio that maximizes expected utility,
people will hold *both* bonds and money in their optimal portfolio. This, of course,
is based on the simple principle of diversification.

To see this in a simple scenario, suppose we have two assets, bonds and
money. The return on bonds is merely R_{B} = r + G where r is the interest rate
and G are capital gains. Capital gains on bonds are assumed to be distributed with mean
zero (E(G) = 0) and finite variance (var(G) = s _{G}^{2}).
Thus, the expected return on the bond is merely E(R_{B}) = r. Money is riskless
and returnless, so R_{M} = 0. In the mean-variance (or rather mean-standard
deviation) space, as in Figure 6, we can denote the return-risk positions of a unit of
money at the origin 0 and a unit of the bond at point B.

A "portfolio" consists of a bundle of bonds and money, thus the
"return" on a portfolio, R_{p} is merely a linear combination of the
individual returns (R_{B}, R_{M}) with the weighting parameter a denoting the relative proportion of the portfolio dedicated to the
specific asset, i.e. R_{p} = aR_{B} + (1-a)R_{M} = aR_{B} as R_{M}
= 0. The expected return on the portfolio, thus, is E(R_{p}) = aE(R_{B})
= ar. The "risk" of the portfolio, however, is:

s

_{p}^{2}= E[R_{p}- ar]^{2}= a^{2}s_{G}^{2}

i.e. it is related to the variance of the capital gains. Consequently, we
see that we can write the portfolio weight as a = s_{p}/s_{G}. Thus, the
expected return on the portfolio can be rewritten as follows E(R_{p}) = ar = (r/s_{G})s_{p},
i.e. the expected return on the portfolio is some linear function of its standard
deviation. We can draw this line in Figure 6 (m = E(R_{P}))
and it represents the "opportunity locus", or the various combinations of
portfolio risk and expected return available - the line connecting the origin to point B
with slope r/s_{G}.

Figure 6- Tobin's Portfolio Decision

Notice that once we obtain s_{p}, we
can immediately obtain a by appealing to our old relationship
that a = (1/s_{G})s_{p}. This is shown in Figure 6 in the lower quadrant as the
line extending from the origin with slope (1/s _{G}).
Thus, for any combination of risk and return (m , s_{p}^{2}) in the opportunity locus in the upper
quadrant, we can, bouncing off the line in the lower quadrant, obtain the implied
portfolio allocation decision, a .

All that remains to be determined is the "optimal" portfolio
allocation a *. For this, we need an expected utility function in mean-variance space, i.e.
some U = U(m , s_{p}^{2})
which is positively related to expected return and, by risk aversion, negatively related
to variance. As shown in Figure 6, assuming convexity, continuity and other nice
properties for utility, then maximizing U(m , s_{p}^{2}) subject to the opportunity locus m = (r/s_{G})s_{p},
we obtain the optimal portfolio risk-return combination (m*, s_{p}*) which, bouncing off the locus in the lower quadrant,
yields the optimal portfolio allocation decision a *. Notice
that the optimal decision is at neither extreme - thus, at the optimal portfolio, people
hold *both* money and bonds.

The negative relationship between money holdings and interest rates is easily visualized in Figure 6: simply if r rises, swing the opportunity locus anticlockwise and we obtain a new optimal portfolio allocation - which, assuming the substitution effect dominates, will be higher than the old a* - thus people reallocate their portfolios such that they increase their bond holdings relative to money - thus the interest rates and money demand are negatively related when money is treated as an asset. Thus, risk-aversion, as Tobin (1958) argued, can be a rationalization of the "speculative demand" for money.

**(D) The Transmission Mechanism**

Keynes (1936) had broken the Neoclassical dichotomy between monetary and real phenomenon in a decisive fashion via his liquidity preference theory of interest. However, following developments in integrating various Keynesian relationships with Neoclassical microeconomic logic, the traditional channels by which monetary phenomena (money, bonds, interest, etc.) were "transmitted" to the real economy (output, employment, etc.) were modified and expanded. No longer was it simply that, say, increases in the supply of money led to declines in interest and thus rises in investment. Things could be more complicated and operate through various channels.

As Franco Modigliani (1971) stresses, one of the new avenues of transmission was consumption. The Life Cycle Hypothesis outlined earlier made consumption also a function of interest. How a particular agent's consumption would react in response to, say, a rise in the interest rate, however, depends on the relative power of various effects: the substitution effect implies consumption will fall, the income effect implies it will rise (if a lender) or fall (if a borrower) and the wealth effect implies it will fall. Thus, the standard assumption is that a general consumption function C = C(r, Y) would be negatively related to interest.

The impact of financial factors on investment seemed clear enough by Keynes's MEI rule. However, James Tobin (1969) worked out some more details. Specifically, a rise in the bond interest rate can lead directly to higher cost of capital and thus lower investment (the standard channel). However, the rise in interest rate can lead to lower valuation of current assets - namely, decreasing Tobin's "q" and consequently investment. Furthermore, if firms use capital as collateral on bank loans, lower valuation on the financial markets implies less valuable assets and thus potentially higher borrowing costs. This is similar to some of the discussions on the "credit" channel of monetary transmission particularly pertinent to New Keynesian stories (thus we shall postpone our discussion of this). For an example of the richer relationship between financial factors and output levels, see Olivier Blanchard's (1981) integration of Tobin's q into a simple IS-LM model.

Mention should also be made at this point of the work of Robert Mundell (1962, 1963, 1968) and J.M. Fleming (1962) in extending of the IS-LM apparatus to incorporate a foreign sector, which will be analyzed later. This not only expanded the Keynesian portfolio to include foreign assets, but also incorporated new variables, such as the exchange rates, into the model which have become, in turn, incorporated into standard transmission mechanism.

Finally, one important set of innovations was the enrichment and
integration of the IS and LM constraints. Recall that Keynes
had posited his own dichotomy, dividing the consumption-savings decision of the household
from the simple money-bonds portfolio allocation decision. Lloyd Metzler (1951), J. Gurley and E.S. Shaw (1960),
James Tobin (1961, 1969) and W. Brainard and J.
Tobin (1963, 1968) greatly expanded upon this by increasing the asset menu available to
households to include short-term bonds, long-term bonds, equity, financial intermediaries
and bank loans, foreign assets, currency, etc. in their portfolio decision. In this case,
excess money supply no longer feeds "immediately" and necessarily into excess
demand for bonds, but rather could feed into greater demand for a greater variety of
assets, even implying that *some* categories of interest rates might fall. By
enriching the simple Keynesian portfolio, the transmission mechanism becomes more complex,
but useful insights, for instance about term structure, effects of monetary policy,
crowding out, etc. were obtainable.

Some economists, notably Milton Friedman
(1956) and Sho-Chieh Tsiang (1956, 1966, 1980,
1982) took this a step further and suggested that the IS and LM constraints should be
integrated with each other. Specifically, they disputed the strict "Tobinesque"
separation of the consumption-savings decision from the portfolio allocation decision - a
point of contention that harked back to the Keynes-Robertson-Ohlin
debate of 1937. What Friedman and Tsiang suggested, and was only later taken up by
James Tobin (1982), was that instead of a
multiplier flow constraint (I-S) = 0 being accompanied by a self-contained wealth
constraint, (M^{d} - M^{s}) + (B^{d} - B^{s}) = 0, one
ought to include the "flow terms" of savings (demand for wealth) and investment
(supply of wealth) as potential equilibrators of the portfolio decision. In other words,
they envisaged the following sort of generalized Walras's Law constraint for stock
variables:

(M

^{d}- M^{s}) + (B^{d}- B^{s}) = DW^{d}- DW^{s}

where D W^{d} and D
W^{s} are changes in the demand and supply of wealth respectively. As we can
conceive of savings as a *change* in the demand for wealth and investment as a *change*
in the supply of wealth, then DW^{d} - DW^{s} = S - I and so the new portfolio constraint becomes:

(M

^{d}- M^{s}) + (B^{d}- B^{s}) + (I - S) = 0

where we now have the flow variables of the goods market decision in the portfolio stock constraint. Thus, it is now possible that, say, an increase in money demand does not necessarily imply a reduction in bond supply (as was necessarily implied before) but it can lead to an increase in savings instead. In other words, the portfolio decision spills over into the flow decisions.

Milton Friedman's (1956) transmission mechanism suggested precisely
this kind of integration of flow and stock constraints: excess money supply, he claimed,
might leave bond interest rates unchanged and spill over directly into excess demand for
goods, i.e. M^{d} - M^{s} < 0, B^{d} - B^{s} = 0 and I
- S > 0, and *that* will lead, by the multiplier, to an increase in output - thus
the "money-income" causality debate
that Friedman sparked. In his Nobel lecture, James Tobin
(1982) provided an enriched multi-asset IS-LM model with overlapping stock-flow decisions
precisely of this type.

Back |
Top |
Selected References |