Financial Instability as a Collective-Action Problem

Abstract

This paper develops a bounded-rationality model of Minsky's financial instability hypothesis along with related ideas from Keynes and others. It proceeds to link financial instability to game-theoretic representations of collective-action problems. Minsky argues that three types of finance regimes can exist in an economy: 1) hedge finance, whereby lenders and borrowers follow standard conservative financial principles; 2) speculative finance, whereby a borrower's current income sufficient to cover interest payments on loans but insufficient to cover principal payments due on maturation of a loan, and 3) Ponzi finance, whereby a borrower's current income is not sufficient to cover either interest or principal on a loan. With this foundation, he presents two key propositions: i) the finance regime, which consists of portions of each type of finance, influences economic stability, and ii) extended prosperity generates inherent tendencies to move the economy in the direction of more unstable financial regimes. This paper represents Minsky's approach to the business cycle as a collective-action problem. This approach facilitates modeling somewhat elusive elements of Minsky's hypothesis in a relatively tractable fashion. The collective-action model points to critical tipping points in the financial instability argument and strengthens its call for policy action.

Full text

Financial Instability as a Collective-Action Problem
Presented at the 85th Annual Conference of the Western Economic Association International
Portland, OR, June 29 - July 3, 2010.
Revised February 2011
William D. Ferguson
Gertrude B. Austin Professor of Economics
Grinnell College
ferguso1@grinnell.edu
ABSTRACT
This paper develops a bounded-rationality model of Minsky’s financial instability hypothesis
along with related ideas from Keynes and others. It proceeds to link financial instability to
game-theoretic representations of collective-action problems. Minsky argues that three types
of finance regimes can exist in an economy: 1) hedge finance, whereby lenders and borrowers
follow standard conservative financial principles; 2) speculative finance, whereby a borrower’s
current income sufficient to cover interest payments on loans but insufficient to cover principal
payments due on maturation of a loan, and 3) Ponzi finance, whereby a borrower’s current
income is not sufficient to cover either interest or principal on a loan. With this foundation, he
presents two key propositions: i) the finance regime, which consists of portions of each type of
finance, influences economic stability, and ii) extended prosperity generates inherent
tendencies to move the economy in the direction of more unstable financial regimes. This
paper represents Minsky’s approach to the business cycle as a collective-action problem. This
approach facilitates modeling somewhat elusive elements of Minsky’s hypothesis in a relatively
tractable fashion. The collective-action model points to critical tipping points in the financial
instability argument and strengthens its call for policy action.

1
This paper develops a bounded-rationality model of Hyman Minsky’s financial instability
hypothesis along with related ideas from John Maynard Keynes and George Akerlof & Robert
Schiller. It proceeds to link financial instability to game-theoretic representations of collective-
action problems. This approach facilitates modeling somewhat elusive elements of Minsky’s
hypothesis in a relatively tractable fashion. Furthermore, it identifies critical tipping points in the
financial instability argument and strengthens its call for policy action.
Minsky argues that investment in productive assets, physical and human capital, drives
economic development in capitalist economies. The path of such development, however, is
inherently unstable due to the uncertainties that underlie the investment process. Because the
returns on investment materialize only in future periods, investment must be financed—generally
with other people’s money, on the basis of, rather uncertain, expectations concerning future
returns. The willingness of both borrowers and lenders to engage in such financial exchanges
depends upon expectations (1992, 1986). These expectations lend themselves to periods of
instability, generating a financial cycle of booms and busts.
To elaborate slightly, the logic of the financial cycle relies on the mix of three types of
finance. The first is hedge finance, the most conservative form of finance (not to be confused
with hedge funds). Here a borrower’s current income, assuming it continues without growth, is
sufficient to cover both interest and principal payments on any loans. The second is speculative
finance, where a borrower’s current income covers interest payments, but is not sufficient to
cover the principal when the loan comes due. To maintain speculative finance, the borrower’s
income or asset values must increase in the intervening period, or the loan needs to be rolled over
upon maturity. The third is Ponzi finance, where current income does not even cover interest

2
payments. Ponzi finance typically relies on a bet that asset values will increase sufficiently
during the intervening period to avoid default.
Now the expectations that underlie financial decisions form under conditions of deep
uncertainty. Accordingly, they are subject to swings in confidence whereby emerging spells of
rising optimism break, leading to sudden collapse. Expectations, moreover, influence the type of
financial commitments that facilitate investment. A cycle develops whereby gradually rising
confidence leads to progressively riskier mixes of finance types. As expectations rise, the mix of
financial types moves from virtually all hedge finance to growing proportions of speculative and
even Ponzi finance, ultimately becoming unsustainable. A crash follows and the process starts
over again. Because finance underlies investment in real assets, financial instability can spill
over into other important sectors and ultimately to single or multiple economies.
Collective-action problems arise whenever the pursuit of individual self-interest conflicts
with social well-being. Financial instability involves two basic dimensions of collective action
problems: expectational problems, and response problems. Game theoretic representations of
these problems add insight into their nature by specifying socially undesirable outcomes and by
identifying critical tipping points. Furthermore, a collective-action approach highlights the
potential role for policy in ameliorating both types of financial collective-action problems.
Corrective policy should dampen both sides of the swings in financial expectations and also
compensate for corresponding over lending in the upswings and underinvestment after a crash.
The argument of this paper proceeds as follows. We first characterize the nature of the
investment process and relate it to roles of uncertainty and salience in forming expectations. We
then develop a corresponding bounded-rationality expected-returns equation. We proceed to
discuss concepts of borrower’s and lender’s risk, linking them to the three types of finance and

3
(-ω, 0)
(0, 0)
Loan
No
Lender
Invest
No
Firm
Figure 1
(
()
ee
L LF
RR
,
e
F
R
)
then Minsky’s two theorems. On this modeling foundation, we trace the outlines of Minsky’s
financial cycle. We then model the collective-action elements of this process and close with
policy implications.
For Minsky, financing investment involves “exchanges of present for future money
(1992, 2)” on both the supply and demand sides of the market. On the supply side, lenders offer
money (credit) to borrowers in exchange for commitments to pay back more in the future—
principal plus interest. If, however, lenders do not expect sufficient future earnings, they will not
extend the necessary finance. On the demand side, borrowers (firms) use their borrowed cash or
credit to purchase productive assets in the present, hoping to profit in the future.
1
If firms do not
expect future profits, they will neither take out loans nor invest in productive assets. If future
returns on investment projects are high enough, borrowers can both honor their commitments
and make a profit. Exchanges continue. On the other hand, systematic failure of borrowers to
meet commitments threatens the financial solvency of lenders and can thus undermine the
financial system.
On both sides of the financial market, then, expectations concerning future returns
motivate exchange. Figure 1 shows a simple game representation of the investment process. The
lender moves first, deciding between
Loan (L) and No. If the lender
chooses L, the firm decides between
Invest (I) and No. Here the term
()
ee
L LF
RR
shows the lender’s expected
1
Here, Minsky notes that liabilities “determine a time series of prior payment commitments” and assets “generate a
time series of conjectured cash receipts (1992, 2-3).”

4
return as a function of the lender’s expectation of the firm’s return.
e
F
R
shows the firm’s own
expected return; ω represents the (likely small) cost to the lender of designing a contract that is
not accepted. If both expected returns are above zero, the lender will extend the loan and the firm
will invest. Insufficient returns on either side result in no contract.
Expectations concerning future returns on investment projects, however, emerge from
environments of fundamental uncertainty.
2
Such uncertainty is not reducible to a probability
calculus because there is no guarantee that underlying processes are normally distributed (or fit
other commonly used distributions), and in any case the relevant parameters of a pertinent
distribution are simply unknown.
3
Uncertainty here influences both the kind of information one
pays attention to when forming expectations as well as actors’ responses to uncertain
information. Concerning the former, the salience of information determines its incorporation into
expectations. For the latter, the willingness to act, what Keynes calls animal spirits (1936)
determines whether actors actually decide to invest. We address these in order.
Keynes has the following to say on the formation of expectations under uncertainty:
It would be foolish, in forming our expectations, to attach great weight to matters
which are very uncertain. It is reasonable, therefore, to be guided to a
considerable degree by the facts about which we feel somewhat confident, even
though they may be less decisively relevant to the issue than other facts about
which our knowledge is vague and scanty. For this reason, the facts of the existing
situation enter in a sense disproportionately, into formation of long-term
expectations [my italics]. . . our usual practice being to take the existing situation
and to project it into the future, modified only to the extent that we have more or
less definite reasons for expecting a change (148).
2
Keynes had the following to say concerning knowledge of future returns on investment: “The outstanding fact is
the extreme precariousness of the basis of knowledge on which our estimates of prospective yield have to be made.
Our knowledge of the factors which will govern the yield of an investment some years hence is usually very slight
and often negligible. If we speak frankly, we have to admit that our basis of knowledge for estimating the yield ten
years hence of a railway, a copper mine, a textile factory, the goodwill of patent medicine … amounts to little and
sometimes to nothing; or even five years hence (Keynes, 1936, 149).”
3
Complexity theory argues that Gausian probability distributions do not offer an appropriate modeling framework
for complex processes. See for example Miller and Page (2006).

5
In terms of contemporary theory, “the facts of the existing situation,” “even though they may be
less decisively relevant …” emerge as the ones that possess the most salience. Actors pay
“disproportionate” attention to information that they attain easily, that fits existing conceptual
frameworks, and with which they feel comfortable.
4
The active or inactive response of actors to such expectations depends on Keynes’s
notion of animal spirits. Incorporating this concept to explain contemporary financial dynamics,
Akerlof and Schiller define animal spirits: “It refers to our peculiar relationship with ambiguity
or uncertainty. Sometimes we are paralyzed by it. Yet at other times it refreshes and energizes
us, overcoming our fears and indecisions (2008, 4).” Investors may show too much exuberance
on either the up side or the down side of a cycle. We proceed to formalize these ideas as a
foundation for game-theoretic modeling of financial instability.
If we define Keynes’s concept of “existing situation” as reflecting the present and recent
past, we arrive at a general expected return function for investors. Assuming for simplicity that
ee
LF F
RR
so that
ee
LF
RR


and then for simplicity dropping the parameter, we may express a
general Re function that could fit either firms or lenders.
5
In normal times, when changes in
external factors stay within certain bounds, investors form expectations of future returns
,1
e
it
R
using weighted averages across sets of salient returns (R). They do so on two levels: i) over
time: investors weigh returns from the present and recent periods within memory, attaching a
greater weight to the present and most recent returns; ii) within any given period: investors pay
attention to returns from a salient comparison group (Ri). Within Ri, investor i’s own returns
likely carry a relatively large weight. Other salient returns may include those from similar firms
4
On salience, see Kahneman (2003).
5
We could instead call this the firm’s R function and then derive a lender’s function. The key elements of analysis
would not differ as long as the trends in expectations of both groups are relatively highly correlated.

6
(or lenders) and perhaps notable market or economy indicators. These comparisons suffice for
normal times; we emerge with expected return for future period t+1:
,1
e
it
R
, shown on line 1 of
equation 1). On occasion, however, sufficiently large changes in returns from a typically
different (usually external) salient comparison group (
'
t
R
) generate a different expectational
dynamic, moving us to line 2. Thus, we have:
1)
,1
e
it
R
= αRt + βRt-1 + γ Rt-2 . . . + zRt-m , when |
'
t
R
–
'1t
R
| ≤ ε, and
,1
e
it
R
= Φ
'
t
R
+ θ[ βRt-1 + γ Rt-2 . . . + zRt-m] when |
'
t
R
–
'1t
R
| > ε; Φ>θ
Expected returns
,1
e
it
R
signify the expected profits on one’s own productive or financial
investment. Note that the term m (in the final subscript) indicates the number of remembered
time periods considered by the investor, the number of salient periods. For the weights: α > β > γ
. . . > z, indicating higher salience of the present and recent past; α + β + . . ., z = 1.
Now, reflecting Keynes’s “more or less definite reasons for expecting a change,” the first
line of equation 1) holds only when the absolute value of an immediate change in external set R’
falls within some threshold value ε.
6
If and only if |
'
t
R
–
'1t
R
| > ε, the second line applies
(otherwise set R’ is not salient). Here immediate returns on
'
t
R
exert a “disproportionate
influence” on current expectations.
7
Thus, a dramatic event in a previously non-salient firm may
suddenly dominate expectations. For example, many investors probably paid little attention to
returns from Bear Stearns, a firm that had a long history of success, until its near collapse.
Suddenly, their dismal performance influenced expectations worldwide. Accordingly, in line two
weight Φ > θ, indicating that returns from all prior periods from the comparison group for R
6
Variable ε is a critical-mass tipping point in the sense of Schelling (1978). It could represent a value large enough
to displace a punctuated equilibrium as in Young (1996).
7
Internal weights within R’ probably differ from those in R as well.

7
enter less heavily than present returns to those from R’. Equation 1 then represents key features
of financial instability as envisioned by Keynes and Minsky. Moreover, it will illustrate
accompanying collective-action problems.
We could interpret a sufficiently large change in ε as a shift in the underlying confidence
of investors. Akerlof and Schiller (2008) argue that a change in confidence is more than a shift
between two plausible Nash equilibria, more than a shift in focal points in a classical game. To
illustrate, consider the following two-stage bank deposit game from Gibbons (1992, 74-75):
Stage 1: Stage 2:
D2 D2
D1
J D1
In the first period, depositors 1 and 2 (D1 and D2) decide whether to withdraw (W) or keep their
deposit in the bank (K). If both choose K, they move to the second stage where they make the
same decision. We may interpret K as keeping a deposit until maturity or until the bank has
access to other funds. Payoffs have the following relations: R > D > r > D/2. It is straightforward
to see that W is the dominant strategy for the second stage. Using backward induction, we then
replace “next stage” in the first game with the Nash payoff from the second stage (R,R). We
find:
D2
D1
Given the payoff relations, this is a game of assurance, where KK is clearly the better outcome
for both players.
Withdraw
Keep
Withdraw
r, r
D, 2r – D
Keep
2r – D, D
next stage
Withdraw
Keep
Withdraw
R, R
2R – D, D
Keep
D, 2R-D
R, R
Withdraw
Keep
Withdraw
r, r
D, 2r – D
Keep
2r – D, D
R, R

8
One could argue that this assurance game has a likely focal point on strategy combination
KK. For Akerlof and Schiller, however, confidence in finance goes beyond this. Confidence
involves trust (from the Latin root fido). They continue:
The very meaning of trust is that we go beyond the rational. Indeed, the truly trusting
person often discards or discounts certain information. She may not even process the
information that is available to her rationally; even if she has processed it rationally, she
still may not act on it rationally. She acts according to what she trusts to be true
[emphasis in original] (2008, 12).
Interpreting the game in this light, we can argue that during unstable times a collapse in
confidence in the banking system, that is a loss of trust, leads to the sub-optimal WW →(r,r)
outcome. Thus, in the early 1930s the public lost its confidence in the banking system as
customer withdrawals brought on its collapse, ushering in the Great Depression.
8
Relating this
logic to equation 1), a sufficiently large change in salient external returns, |
'
t
R
–
'1t
R
| > ε,
shatters the confidence among investors in the previously reigning expectational regime.
9
A loss
of confidence presents an expectational collective-action problem.
10
Likewise, overconfidence
reflects excessive trust in potentially dangerous financial arrangements. In the recent crisis,
overoptimistic assessments by credit-ratings agencies of various instruments including
collateralized debt obligations generated and reinforced excessive belief in their reliability
(Brunnermeier, 2009). Accordingly, Minsky’s logic suggests that collective-action problems
inhabit both sides of the cycle; more precisely, overconfidence during the upswing sows the
seeds for collapse.
8
For an insightful discussion of historical collapses of confidence, see Kindelberger (1978).
9
Confidence regimes then exhibit the properties of punctuated equilibria.
10
An expectational collective-action problem occurs when expectations held by individuals among members of a
group lead to actions that generate suboptimal outcomes for the group. Using a similar kind of logic, applied to a
somewhat different arena, William Easterly states: “The increasing returns story of poverty traps says that poverty is
a failure of coordination (2002, 168).”

9
Returning now to Minsky’s three types of finance—hedge, speculative and Ponzi—we
specify each precisely. First, we designate the borrower’s commitments to repay the lender in a
specific time period (ct). For a standard loan (or bond) contract, where, for simplicity, we assume
that the principal is paid on the day the loan is due, we may express ct as:
2) cit = Li0rt for periods t = 1, 2. . . . T-1 and
ciT = Li0(1 + rt) for period T when the principal is due.
L0 is the net size of the loan (loan minus any collateral put down) taken out in period t = 0, and rt
is the current interest rate on the loan. Assuming a fixed interest rate (r), over the entire period of
the loan (T periods), we have:
3)
0
1(1 )
T
it it
tc Tc L Tr

  

With this specification, the following three equations illustrate conditions for hedge, speculative
and Ponzi finance respectively:
4) Tyi0 > L0(1+Tr) (Hedge)
5) L0Tr< Tyi0 < L0(1+Tr) (Speculative)
6) Tyi0< L0Tr, (Ponzi)
where yi0 is the borrower’s income in the period the loan is taken out, t = 0; r indicates the (fixed)
rate of interest, and T indicates the number of periods for the loan.
It is easy to see that a risk of default increases as we move from equation 4) to 5) to 6).
For Minsky, a financial regime consists of the relative proportions of the three forms of
finance. With these concepts in mind, Minsky offers two key theorems:
1. The finance regime critically influences the stability of the economy.

10
2. Extended periods of prosperity generate inherent tendencies to move the economy to
unstable finance regimes.
Noting the definitions of speculative and especially Ponzi finance, the intuition behind Theorem
1 should be obvious. Subsequent discussion explains more fully. We can immediately relate
Theorem 2 to equation 1: extended good times increase expected returns. As expected returns
rise, agents on both sides of the financial markets become increasingly willing to engage in
riskier types of finance. In Akerlof and Schiller’s terminology, continued good times generate
excessive confidence, leading to what they call an overheated economy:
The term overheated economy, as we shall use it, refers to a situation in which confidence
has gone beyond normal bounds, in which an increasing fraction of people have lost their
normal economic skepticism about the economic outlook and are ready to believe stories
about a new economic boom (65).
11
Within the normal progression of expectations during extended periods of good times, we then
find periods of overconfidence which generate an expectational collective-action problem
manifested as a move towards risky, unstable finance. A more detailed description of Minsky’s
vision of the cycle with related games will elaborate this point.
The Financial Cycle as a Collective-Action Problem
To reiterate slightly, for Minsky, firms borrow money in order to invest in real assets
(physical investment).
12
Firms undertake such investment only if they expect sufficient future
return. If
,1
e
it
R
, from the first line in equation 1), is high enough (usually > 0 as defined here),
firms put money down in a current period (t0). Such borrowing generates known commitments
(ct from equation 2) that must be paid on schedule. Over this time horizon, the firm will have met
its commitments using actual future revenue, which, however, must be estimated at the point of
11
Note that Akerlof and Schiller do not argue that overheated necessarily implies excessive inflation. The boom of
the 1920s, to which they refer, was not characterized by excessive inflation; nor was the 2004-2008 period.
12
For simplicity, we assume that borrowing takes the form of traditional loans or sales of bonds.

11
the borrowing decision. Since the future is uncertain, the investment decision is essentially a
wager: it balances uncertain expected returns against known future commitments. Borrower i’s
margin of safety at any point in time (MSBt) appears in the following equation:
7) MSBit = yit + LQit – cit,
where yit represents the firm’s income in period t, and LQit is the firm’s liquidity (cash balances)
in t. Following Minsky and using this specification, we define borrower’s risk as the risk that
MSBt < 0 for a long enough period to lead to bankruptcy. Borrower’s risk evolves over time:
firms evaluate it prior to investing and then reevaluate it over the duration of a loan.
Financiers (lenders) occupy the other side of financial exchanges. Financiers extend
credit, money given now, in return for promise to repay principle and interest on a loan,
mortgage, bond, or ownership shares.
13
Minsky defines lender’s risk as the risk posed to lenders
that borrowers will default on repayment. There are two ways of looking at lender’s risk. First,
stressed by Minsky, the lender knows how much repayment is needed to make the loan
worthwhile for periods t1, t2, …, tn. The lender then writes appropriate payment terms into the
contract, specifying the borrower’s commitments cit (from equation 2), subject to market
constraints. The contracted interest rate r reflects the lender’s evaluation of risk of default, again
subject to market constraints. Riskier companies must typically pay higher interest. If the risk
exceeds feasible market interest rates, the loan is not extended. Both sides know the contracted
initial estimate of lender’s risk. Once set in contract, the terms cannot be changed unless and
until a loan is refinanced.
14
13
Note that derivatives repackage combinations of bonds, mortgages, etc. to sell them to second- and third- tier
lenders, as a form of insurance against changes in market value of specific assets. Derivatives complicate the
extension of credit, effectively turning some lenders into borrowers. While offering insurance, they introduce new
sources of instability which still follow and indeed augment the patterns of Minsky’s logic.
14
Market conditions may or may not adjust rt over time depending on the contract.

12
Like borrower’s risk, however, estimates of lender’s risk may change with relevant
conditions over time. Thus, we may express the lender’s margin of safety at a point in time
(MSLt). Assuming that solvent firms always repay their loans, we have:
8) MSLτ =
0
1Bt
tMS tL r




for periods τ = 1…T-1 when interest is paid and
MSLT =
0
1(1 )
T
Bn
tMS L Tr



for period t = T, when principal is repaid. We may then express a dynamic concept of lender’s
risk as the risk that MSLt < 0 for a sufficiently long period for the loan to be in default. Like
borrower’s risk it is subjective and evolving; banks estimate risk upon extending a loan and
periodically adjust their estimates as events influence expectations.
Before proceeding, we define the leverage ratio:
9) LVt = Dt/Vt,
where Dt signifies the total debt of the borrower for period t, and Vt signifies the borrower’s total
value of assets, as in total capitalization for a firm or the present value of all investment projects.
If LVt increases, both borrower’s and lender’s risk increase. This can lead to a higher rate of
interest charged on a loan or a need to refinance at a higher interest rate.
15
On this foundation, we summarize Minsky’s concept of the financial (business) cycle and
relate it to expectational collective-action problems. Minsky’s cycle emerges from evolving
perceptions of borrower’s and lender’s risk and their relations to the availability of finance in an
environment of uncertainty. Over the cycle, extended prosperity leads to higher expected returns,
reducing borrower’s and lender’s perceived risks, increasing the expected benefits of
15
This leads to an upwards sloping supply of capital function (Minsky…)

13
increasingly risky forms of finance. As the proportions of speculative and then Ponzi finance
increase over time, the economy becomes overheated and the financial regime becomes
vulnerable. In order for the economy to function properly, the vast majority of the commitments
shown in equations 2) to 7) must be met on time. Limits to the availability of finance lead to
some major default whereupon expectations reverse, initiating a collapse.
Sometimes the unstable portions of these cycles remain largely within the financial
sector, as the technology stock crash in the late 1990s was in the United States. Other times, such
instability spills over into the entire economy, as in the Asian financial crisis of the late 1990s or
the recent and present global series of interconnected financial crises. In all cases, such
developments present collective-action problems.
The cycle starts with a Hedge finance regime, then progressively introduces speculative
finance and finally Ponzi finance. Here is a stylized description of the steps in Minsky’s cycle.
16
1. End of Recession: caution dominates, few loans, little finance, all hedge. Both numerator
and denominator of LV low, so value is intermediate.
2. Early Expansion: Profits are greater than expected, some relaxation of expectations.
Increase in valuation of firm’s assets puts downward pressure on leverage. Returns
exceed commitments; internal financing available. Plenty of cash. Both risks fall. Some
new investment projects. Hedge finance regime dominates. Borrowers and lenders are
still reasonably cautious.
3. Expansion: Rising demand for investment increases profit opportunities. Several years of
reasonably good returns boost expectations.
17
With more investment and more loans,
commitments increase as does leverage. Speculative finance begins to emerge. There is
some layering of debt in the sense that some debt is rolled over without repayment of
principal. Interest only loans allow for higher leverage. Lenders, whose expectations have
also risen, are willing to engage. Emergence of a potential for instability.
4. Bubble Stage: After more years of good returns, confidence increases disproportionately
and the economy overheats. Speculative finance increases as hedge finance recedes. With
16
I borrow somewhat from the description in Peterson and Estenson (1992,332-340 and 786-794)
17
During the expansion phase, we have what Schelling (1978) calls self-confirming expectations: rising
expectations increase demand for investment, increasing profit opportunities, confirming expectations. Note this is a
positive feedback loop.

14
more layering of debt, sustainable refinance requires higher asset prices. Actual, and
more importantly, anticipated capital gains become a source of borrowing power
(McCulley, 2009b). Ponzi finance begins to emerge when both borrowers and lenders
expect asset values to rise fast enough to enable future payment of both interest and
principal that current income cannot cover.
In the recent financial crisis, high confidence led to increased leverage through the introduction
of multiple short-term financing instruments including, overnight debt financing, subprime
lending, and credit-default swaps. “These new financial products provided the basis for an
illusion of low risk, a misconception that was amplified by the inaccurate analysis of rating
agencies (Yellen, 2009, 2).” At this stage, with speculative and Ponzi finance, borrowers’ ability
to meet contractual commitments concerning repayment of principal and interest relied upon
continuously increasing asset valuations.
18
The economy had entered an Alice-in-Wonderland
phase where it must keep running faster just to stay in place. The boom was not sustainable. One
big event or a series of related big events could shatter expectations. The collapse of Bear
Stearns provided one such event. A few months later Lehman Brothers failed. The boom came to
a halt at what financier Paul McCulley called a “Minsky Moment.”
5. Minsky Moment: The big event occurs. Some large default shatters bubble expectations.
For the present crisis, McCulley identifies the key event as the August 2007 run on
commercial paper. Asset prices drop. Referring to the present crisis, he states:
It all went swimmingly, dampening volatility in a self-reinforcing way, until the
bubbles created by the financial alchemy hit the fundamental wall of housing
affordability. Ultimately, fundamentals do matter! We have a day of reckoning,
the day the balloon comes due, the margin call, the Minsky Moment.
19
Now the cycle slams into reverse.
6. The Rush to Liquidity and the Reverse Journey: Lenders demand higher interest rates and
more collateral for new loans. Where they can, they demand higher interest rates for
existing loans (e.g., variable-rate mortgages). The drop in asset prices immediately
18
“Clearly, the explosion of exotic mortgages—subprime; interest only; pay-option, with negative amortization;
etc.—in recent years have been textbook examples of Minsky’s speculative and Ponzi units (McCulley, 2009b).”
19
McCulley (2009b). For McCulley, three bubbles burst: housing prices, mortgage markets, and “shadow banking”
(investment banks and related).

15
pushes Ponzi loans into default. Trying to stay afloat, borrowers and lenders sell or try to
sell assets, placing additional downward pressure on their prices. At this point,
speculative loans become vulnerable. As more loans enter default, both expectations and
asset prices drop further, pushing the more speculative loans into default. Meanwhile,
rating agencies react by lowering ratings, reducing confidence further. Regulators, noting
danger of default, join in, tightening lending standards. Everyone wants cash, but it is
scarce. Lenders call in loans and demand impossible terms on new loans; borrowers
cancel investment projects. Rapid contraction ensues: the reverse journey (McCulley,
2009b).
The financial crisis may spill over to other sectors and push economies into recession.
Statistically speaking, the problem here is that financial mistakes are not independently
distributed, as risk assessment models assume. Rather they are positively correlated with each
other. Their dynamics, then, exhibit properties of positive rather than negative feedback: errors in
one direction do not induce movement in the opposite direction; instead, they compound each
other. Drops in asset prices in one area or market induce similar drops in related markets via their
reinforcing impacts on rapidly declining expectations.
20
The economy enters its reverse journey.
Concerning the entire cycle, we can represent the movement in financial regimes with
several N-player collective-action games. Suppose there are N investors who, for simplicity, may
engage in one of two types of finance: hedge finance (H) and risky finance (R; a mix of
speculative and Ponzi). Expected payoffs for each depend on the elements in equations 1)-9) as
well as the number who engage in the same activity—hence collective action. An easy way to
model the distinction between H- and R-investors is to give the former longer “memories.” That
is H-investors base expectations upon long time horizons, whereas R-investors attach great
salience to the present and very recent past. Accordingly in equation 1), we set mH >mR.
20
“The financial engineering that was thought to hedge risks probably would have worked beautifully if investors
had faced shocks that were uncorrelated with those of their counterparts. But declines in bond and house prices hit
everyone in the same way, inflicting actual and expected credit losses broadly across the financial system (Yellen,
2009, 2).”

16
q
h
0
-
H(n)t
R(n)t
nt*
0
N
Figure 1
Now we construct a simple N-player evolutionary model to represent the core of the
collective-action problem during the upswing of the cycle. In evolutionary models, players
“inherit” strategies from previous learning experiences, and payoffs reflect the fitness of
strategies.
21
Fitness here indicates players’ propensities to stick with a strategy in the future. In
this context, then, we may interpret fitness as a player’s confidence in her strategy. Now, the
fitness payoff for each type of player reflects the combined influence of expected returns and
safety margins, where the latter is a declining function of the number who engage in risky
finance (n). To see this, note that LVt in equation 9) should be an increasing function of n since
risky investors on either side of the market engage in more loan activity. At least over time, then,
LQt for borrowers in equation 7) should decrease in LVt and thus in n. For two types of
borrowers, hedge and risky finance respectively, we arrive at the following fitness equations:
10) H(n) = κ
,1
eH
it
R
+ MSBH(n) = h – υ(n)
11) R(n) = δ
,1
eR
it
R
+ MSBRt(n) = q –φ(n),
where ∂MSB/∂n < 0 for both types, with |MSBR/∂n| > |∂MSBH/n|: the safety margin for R-finance
decreases more sharply in n than the safety margin for H-finance. Equivalently, φ > υ and scaling
parameters κ and δ indicate the relative importance of the two effects on fitness.
Figure 1 illustrates the model in phase 2 of
Minsky’s cycle. Notice this is an evolutionary
game of chicken, with a mixed-phenotype
equilibrium with n* risky investors. It is
straightforward to show that nt* does not
represent a socially optimal mix of the two
21
Fitness here impacts strategies, not players. Over time, players may adjust their strategies, reflecting adaptive
(procedurally rational) learning.

17
phenotypes at time t (see Appendix). Hence, even from a static point of view—early in the
economic expansion, no less—there are too many risky investors, and society faces a collective-
action problem.
The cycle, of course is a dynamic phenomenon: it evolves over time. As the expansion
progresses, both curves shift upwards, reflecting the impact of prosperity on expected returns.
The R(n) curve, however, shifts up faster, reflecting greater salience R-investors place on present
and very recent returns. As this happens, the relative fitness (confidence in) the R strategy
increases. Extrapolating backwards, at the end of the recession, the R(n) curve may lie entirely
below the H(n) curve, so we would have entirely H-finance. As the boom progresses past stage
2, the R(n) curve continues to shift up faster than H(n) moving nt* further and further to the
right. The magnitude of society’s successive static collective-action problems increases
accordingly.
To illustrate the full magnitude of the collective-action problem, however, we need to
model the financial stability of the system. From equation 1), investor confidence, manifested by
steadily rising expected returns over the upswing, shatters when |
'
t
R
–
'1t
R
| > ε. The economy
crosses this threshold at the “Minsky moment.” Following Minsky, relating the likelihood of
such an event to leverage, we have the following probability function:
12) P(|
'
t
R
–
'1t
R
| > εt) = f(LVt); f’>0.
We now turn to the leverage ratio, beginning with the numerator. Total debt is the sum of debts
from the three types of finance.
13) Dt = DHt + DSt + DPt
Assume that at time period t = τ, somewhere in stage 3, we have the following relations for each
of Minsky’s three types of finance:

18
14) DHτ =
0
1 1 1
{}
H
i it
i t t
yc

  

  
= 0 Hedge Debt
15) DSτ =
00
1 1 1 ,
{}
S
i it
i t t i t
y c LN

  

   
Speculative Debt
16) DPτ =
00
1 1 1 , ,
{}
P
i it t
i t t i t i t
y c LN r


  
  
    
; 0<κ<1 Ponzi Debt
Note that the timing of period t = 0 differs by individual firm. In every period, some firms
receive new loans. Turning to the more aggregated concept of risky investment from Figure 1,
we may show Risk-Debt as:
17) DRτ = DSτ + DPτ
Note that at an earlier point in the cycle, the debts shown in equations 14) to 16) should all be
low. At a later stage both elements of DRt should increase faster than DHt, reflected in Figure 1 by
the more rapid upward shift of the R-Debt curve. Moreover, following Minsky’s logic, this late
in the cycle we expect a rise in the proportion of Ponzi finance within R-Debt. All of these
factors indicate a non-linear rise in Dt as the cycle progresses. For simplicity, assume a standard
exponential form based upon an initial amount of debt:
18) Dt = D0eλt
Using equations 6) and 18), we may express aggregate borrower’s margin of safety as:
19) MSBt = LQt – D0eλt
The aggregate margin of borrower safety equals liquidity minus debt. This equation expresses
the core of financial instability: unless liquidity can continuously increase at increasing rates,
safety margins will vanish. Now, defining yt = Σyit and ct = Σcit, , and using 19), we can express
the rate of growth of debt:
20) dD/dt = d/dt(ct – yt) = λD0et

19
The preceding argument concerning shifts from hedge to speculative to Ponzi finance accords
with this equation: commitments grow faster than income and so debt grows exponentially, again
illustrating financial instability.
Turning to the denominator of leverage ratio, which does not grow exponentially, we
posit a simple valuation function and bias the argument in favor of growth in valuation.
21) Vt =
1
e
t Bt
R MS


With this formulation,
22) dV/dt =
( ) ( )
eB
dR dt dMS dt


Terms θ and ω are parameters. Here
e
dR dt
> 0 until the end of period 4, but equation 19)
indicates that
B
dMS dt
decreases over time (at least after period 1) and eventually must turn
negative. The decrease in
B
dMS dt
indicates that somewhere during the expansion, likely by
period 3, dV/dt <dD/dt, at which point leverage (Dt/Vt) starts to rise. From equation 12), as
leverage rises, the probability of a shock (p(|
'
t
R
–
'1t
R
| > ε)t) increases. Eventually, a large
enough drop in one or more external returns occurs, and the Minsky moment arises. Once
e
dR dt
< 0, dV/dt falls (probably noticeably) below zero as dDt/dt continues to rise. Hence the
rush to liquidity: everyone wants cash, but there is little available.
(A future draft will develop one or more multi-player tipping-point models in order to
illustrate some of these last points.)
A Few Modest and Preliminary Policy Statements
A financial crisis, particularly one like the present, represents a particularly costly form
of market failure. Had the United States been able to avoid the present crisis, GDP would have

20
been higher and unemployment would have been lower by at least several percentage points. The
argument here suggests two related collective-action problems. First, and most important, there
is an expectational collective-action problem: during the boom expectations rise “too much”;
expected returns exceed possible returns. Likewise, during the reverse journey they fall “too
much,” pessimism exceeds that warranted by economic circumstances. Solving this problem
could prevent the second from arising. Second, responses to expectations, aggregated across
individual decisions, lead to instability: an unsustainable rise in leverage on the upside and a
hyper-contractionary rush to liquidity on the downside.
22
In principle, policy can intervene in
either problem. Once the second has kicked in, policy must address both.
A caveat: realistically, policy can achieve only two goals: i) preventing a reverse journey
from turning into a full-scale depression, and ii) dampening, but not eliminating, the swings of
the cycle. Eliminating the cycle is not possible due to multiple factors. Here is a partial list.
Policy instruments are limited, often operating with lags. Policymakers operate with limited data.
Policymakers tend to share in the exuberance of the upswing and likely in the pessimism of the
reverse journey as well. Even if they have reasonably accurate data and are not themselves
swayed by optimism, participants have difficulty distinguishing the early stages of a bubble from
a normal expansion.
The first policy goal is, obviously, the most urgent during times of the reverse journey,
such as the present. Concerning the expectational collective-action problem, we can regard the
policy problem as a multi-player game of assurance. In the reverse journey stage, everyone in the
market thinks that everyone else is pessimistic, and so follow along. Financial markets need
22
“As Minsky’s financial instability hypothesis suggests, when optimism is high and ample funds are available for
investment, investors tend to migrate from the safe hedge end of the Minsky spectrum to the risky speculative and
Ponzi end. Indeed, in the current episode, investors tried to raise returns by increasing leverage and sacrificing
liquidity through short-term—sometimes overnight—debt financing (Yellen, 2009).”

21
some focusing agency to reestablish confidence, particularly concerning extension of credit. To
restore confidence, policy needs to shift the expectations of a critical mass of potential investors
away from deep pessimism (could add diagram). Potential investors need some assurance that
they will not lose money by either extending loans or purchasing productive assets.
There are two straightforward ways for policy to offer the needed assurance, one
monetary and one fiscal. On the monetary side, the central bank needs to act as a “lender of last
resort.” When markets are starved for liquidity, the central bank must provide some.
What is needed is for the government to take the other side of the trade,
effectively becoming the bid side, (1) buying assets, (2) guaranteeing assets, (3)
providing cheap funding for assets, (4) buying bank equity securities (McCulley,
2009a).”
In financial markets these actions can put a break on the downward slide in expectations.
Furthermore, the additional credit likely provides some aggregate demand, dampening the slide
in profits. With Minsky’s dynamics, once investors have noticed that things have stopped
declining, they might cautiously enter stage 1 of the recovery.
On the fiscal side, the government needs to spend money to shore up demand enough so
that private investors in real assets dare to venture into the market and so that potential lenders
can have some assurance they will be repaid. Government expenditure puts a floor on spending
cuts in the downswing; it maintains some cash flow that is not vulnerable to shifts in
expectations (McCulley, 2009a). Note that the aggregate demand impacts of monetary and fiscal
policy also deal with the second kind of collective-problem, investor reactions. If investors see
money flowing into economic activity, they will more likely react by beginning cautiously to
invest and lend.
A somewhat more delicate question concerns the role that policy might play in
dampening the upside of the swing. As the taking-away-the-punch-bowl-at-the-party metaphor

22
suggests, central bankers have long considered this part of their role. Minsky’s theory, however,
suggests more than just contractionary monetary policy to dampen inflation during a boom.
Indeed part of the problem in the recent crisis is that inflation did not really manifest itself;
hence, the monetary authorities felt less need to intervene. This is precisely the kind of problem
that Minsky’s framework suggests: central bankers are susceptible to the same over-confidence
that infects the financial markets.
23
This framework points to rising leverage during the upswing as a key proximate source of
financial instability. Hence, there needs to be some regulation of leverage ratios. The system
established in the 1930s, in response to the Great Depression, created such regulation for the
commercial banking system. Financial innovation over the past 30 years, however, has created
important financial sectors, notably investment banks, that have circumvented such regulation
(McCculley, 2009, Yellen, 2009). In terms of the present model, a sustainable cap on leverage
might hold the probability of failure term (P(|
'
t
R
–
'1t
R
| > εt) in equation 12) to acceptable levels.
The corresponding regulations for commercial banks have appeared to work well. Waves of
recent financial innovation, however, suggest a more difficult problem. Since regulatory changes
are likely to lag behind financial innovation, any given system of regulation will lose at least
some of its effectiveness over time. Hence the best regulators can hope for is periodic revisions
of regulation to dampen the size and impacts of the Minsky cycle.
23
Yellen (2009) and McCulley (2009) both mention this problem.

23
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