Transcript University of Auckland Economics 776 Experimental Economics

Economics 776
Experimental Economics
First Semester 2007
Topic 7: Market Experiments
Assoc. Prof. Ananish Chaudhuri
Department of Economics
University of Auckland
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Market Experiments
• The aim here is
– to understand the equilibration process in
markets
• what causes faster/slower convergence to
equilibrium
– Examine efficienty properties of different
market institutions
• We will focus on two of these
– Competitive Markets
– Posted Offer Markets
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Group of subjects randomly divided into two
subgroups
– Buyers
– Sellers
• Each buyer receives a card containing a
number, known only to that buyer, which
represents his valuation for the good
• Each seller receives a card containing a number,
known only to the seller, which represents his
minimum acceptable price
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The buyer’s willingness to pay numbers
and the sellers willingness to accept
numbers generate the market demand and
supply curves
• Buyer and sellers can buy/sell only one
unit of a fictitious good during one market
period – lasting 5 – 10 minutes
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• As soon as a contract is accepted, the
contract price is recorded together with
the minimum supply price of the seller
and the maximum demand price for the
buyer
• This sets the stage to study price
behaviour under a particular set of
demand and supply functions
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$2.00
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Q=6
An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Trades are feasible in the shaded area
below the demand and above the supply
curve
• Given these demand and supply curves,
competitive price theory asserts that there
will be a tendency for price-quantity
equilibrium to occur at the intersection of
the two curves
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• But there is no guarantee that the equilibrium
defined by the intersection of these sets will
prevail
• The mere fact that these demand supply
schedules exist in the background of a market
does not guarantee that any meaningful
relationship exists between those schedules and
what is observed in the market they are
presumed to represent
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Thus in Figure 1 the $3.20 buyer can buy
from the $3.20 seller, the $3.00 buyer from
the $3.00 seller without violating any
restrictions imposed on buyers and sellers
• These experiments conform in several
important ways to many kinds of real
markets such as a commodity or stock
exchanges
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• In those markets, each individual is likely to be ignorant
of the reservation prices of other buyers and sellers
• The only way one can learn about those things is by
studying the bids and asks that are tendered and
whether or not they are accepted
• One important difference is that in the experimental
markets the demand and supply curves are held
constant over a period of time while real markets are
likely to be continually subjected to changing demand
and supply conditions
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The most striking general characteristic
of most of these markets is the
remarkable tendency for exchange
prices to approach the predicted
equilibrium
• Over time the variations in exchange
prices tend to decline
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Compute coefficient of convergence () as
the ratio of the standard deviation of
exchange prices (0) to the predicted
equilibrium price P0 expressed as a
percentage, i.e.  = 100*(0/ P0)
•  provides a measure of the variation of
the exchange prices relative to the
predicted equilibrium price
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• If we now look at markets 2 and 3 then we
can see that the equilibrium price and
quantity are approximately the same for
both these markets
• The significant difference in the design of
these two markets is the supply and
demand curves for market 2 are relatively
flat while those for market 3 are steeper
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The Walrasian hypothesis states that
– the rate of increase in the exchange price is an
increasing function of the excess demand at that
price
• Thus we would expect prices to converge to
equilibrium much more quickly in market 2
compared to market 3
• Convergence to the equilibrium is quicker and
much less erratic in market 2 than in market 3
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• In market 4 the supply curve is infinitely
elastic (horizontal) with the same minimum
acceptable price of $3.10 for each seller
• According to the Walrasian hypothesis this
market should converge rapidly towards
the equilibrium since there is considerable
excess supply at prices slightly above the
equilibrium
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Decrease in Demand
Demand DD
Demand D’D’
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• However while the market does converge
relatively quickly but it converges to a
price that is above the equilibrium price
• Furthermore in market 4B which
introduces a reduction in demand from DD
to D’D’, we do not see any change in the
equilibrium price
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The prices approach the equilibrium from
above since prices below the equilibrium is
not an option in this market
• These results suggest that convergence to
equilibrium may depend not only on the
intersection of demand and supply
schedules but also one their shapes
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The lack of convergence in market 4 leads
to the hypothesis that this might have to
do with the relative size of the consumer
and producer surpluses
• The tentative hypothesis is that the actual
price will be above the equilibrium price by
an amount which depends how much
larger the CS is compared to the PS
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• In market 3 CS > PS and while prices do
converge they do so slowly and usually
from above
• Next we look at market 7 which does the
reverse of what market 4 did
• Here producer surplus is much larger than
consumer surplus
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• It is clear that convergence is slow and
occurs from below
• Thus it appears clear that the relative
magnitude of consumer and producer
surpluses affects the speed of
convergence to equilibrium
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Market 5 looks at convergence when there
are shifts in demand and supply
• Again prices seem to converge quickly
following a shock
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Increase in demand and reduction in supply – higher eqlbm. P and27Q
An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Market 6 looks at whether the presence of
intra-marginal buyers and sellers near the
equilibrium affect that equilibrium
• Here the demand curve falls continuously
in one-unit steps while the supply curve
becomes perfectly inelastic at a price of $4
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Reduction in demand after period 4
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The tentative hypothesis is that the large rent
enjoyed by the marginal seller with still larger
rents for the intra-marginal sellers may affect
convergence to equilibrium
• Again the conjecture regarding the effect of a
divergence between consumer and producer
surplus on the approach to equilibrium is
confirmed
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Convergence is slow and from below
• But the presence of intra-marginal sellers
who enjoy large rents do not prevent
convergence to equilibrium
• Convergence happens even with a
downward shirt in the demand curve
following period 4
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Market 8 introduces a change in the institution
with only sellers permitted to enunciate offers
• Buyers are passive and can only accept or reject
the sellers asks but cannot make bids
• This market simulates a posted-offer
institution which we will study in greater detail
shortly
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Both buyers and
Sellers make offers
Only sellers make offers
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Out of all the different markets considered here
market 8 shows the clearest lack of convergence
towards equilibrium
• Allowing only sellers to put in asks has a
distinctly disturbing effect on the equilibrating
process
• Also it appears that this institution operates
to the benefit of buyers at the expense of
sellers
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• These results suggest that there must be a stochastic
difference equation which “best” represents the
convergence to equilibrium
pt  pt 1  pt  f [ x1 ( pt ), x2 ( pt )...]  t
• where the arguments “x” reflect characteristics of the
experimental supply and demand curves and the
bargaining characteristics of the different groups
• f(0) = 0 and  is an error term with zero mean
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Four specific forms of this difference
equation are studied
• These are
– Walrasian
– Excess rent
– Modified Walrasian
– Modified excess rent
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Walrasian:
pt  01  11 x1t
• where xit is the excess demand prevailing
at price pt at which the t-th transaction
occurred
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Excess rent:
pt   02   22 x2t
• where x2t is the algebraic area between
the demand and supply curves and
extends from the equilibrium price down to
the price of the t-th transaction
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Modified Walrasian:
pt   03  13 x1t   33 x3t
• where xit is the excess demand prevailing at
price pt at which the t-th transaction occurred
• where x3t = A0t – B0t, the algebraic difference
between the equilibrium consumer surplus and
producer surplus
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Modified excess rent:
pt  04  24 x2t  34 x3t
• where x2t is the algebraic area between the demand and
supply curves and extends from the equilibrium price
down to the price of the t-th transaction
• where x3t = A0t – B0t, the algebraic difference between the
equilibrium consumer surplus and producer surplus
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Regression results provide support for both the
Walrasian hypothesis as well as the excess rent
hypothesis
• In discriminating between these two one can look at (1)
their ability to predict zero price change in equilibrium
and (2) the standard errors of those predictions
• By and large using a number of non-parametric tests the
evidence favours the excess rent hypothesis
42
An Experimental Study of Competitive
Market Behavior - Smith (1962)
• The excess rent hypothesis would seem to have some
plausibility from the individual decision-making point of
view
• Once a contract price has been struck, each trader
compares that price to his reservation price – the
difference being a “profit” or rent which is achievable
• And to present a degree of bargaining resistance in the
auction process which is greater the smaller is this rent
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An Experimental Study of Competitive
Market Behavior - Smith (1962)
• Thus if equilibrium buyer’s rent exceeds seller’s rent, any
early tendency for contract prices to remain above
equilibrium (and balance the rents achieved on both
sides) might be expected to break down as it becomes
evident that the “paper” rents at those prices might be
unattainable by all of the sellers
• This argument suggests that the propensity of sellers to
reduce their offers when the price is above the
equilibrium is related to their attempts to obtain some –
even if it is a “small” amount - rent rather than to a direct
influence of excess supply
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CONCLUSIONS: An Experimental Study of
Competitive Market Behavior - Smith (1962)
• Even where numbers are “small” there are
strong tendencies for a supply and demand
competitive equilibrium to be attained as long as
there is no collusion and bids and asks are
publicly announced
• Changes in the conditions of demand and
supply cause changes in the volume of
transactions per period and the price. These
changes correspond reasonably well with the
predictions of price theory
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CONCLUSIONS: An Experimental Study of
Competitive Market Behavior - Smith (1962)
• Markets where only sellers can make price
quotations exhibit weaker equilibrating
tendencies than markets where both buyers and
sellers can make price quotations
• The excess rent hypothesis seems to be a better
predictor of the mechanism of market
adjustment rather than the Walrasian hypothesis
which relates the adjustment process to the
magnitude of excess demand/excess supply
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Effect of Market Organization on
Competitive Equilibrium – Smith (1964)
• Smith (1962) suggested that a “posted
offer” market where only sellers can make
price quotations and buyers can either
accept or reject those quotations does not
equilibrate as easily as markets where
both buyers and sellers can make price
quotations
• Smith (1964) looks at this in greater depth
47
Effect of Market Organization on
Competitive Equilibrium – Smith (1964)
• Three different institutions
• Rs – sellers are permitted to make offers; buyers
are free to accept offers but cannot make bids
• RSB – both buyers and sellers are free to make
price quotations
• RB – buyers are permitted to make bids; sellers
are free to accept bids but cannot make offers
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• In each session there are an equal
number of buyers and sellers
• Given the underlying demand and supply
curves the equilibrium consumer and
producer surplus are equal
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• No support for the hypothesis that the
initial prices are the highest in Rs
• However the data upholds a general
hypothesis that across all periods
PtS < PtSB < PtB
• That is the ordering relationship holds for
all periods
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• The third hypothesis about the ordering of
equilibrium prices – E(PS) < E(PSB) < E(PB)
– is also borne out
• As is the hypothesis regarding the speed
of convergence
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Ketcham, Smith and Williams (1984)
• Compares performance of a “posted offer”
institution compared to a “double auction”
• Previous research that we have looked at
suggests that double auction markets exhibit two
important characteristics
– Rapid convergence of prices to the competitive
equilibrium
– Highly efficient allocations
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Ketcham, Smith and Williams (1984)
• Subjects have up to 5 units to buy/sell in
each period
• For each unit, the buyer (seller) has a
marginal valuation (cost)
• These valuations/costs yield the aggregate
market demand and supply curves
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Ketcham, Smith and Williams (1984)
• The double auction incorporates
– a “bid-ask spread reduction rule”
– A “rank queue”
• Subjects earn 10 cent commission on
each trade in Design 1 but not in Design 2
– Provides an incentive to engage in trade at
low profit
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Design 1 - Ketcham, Smith and
Williams (1984)
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Design 2 - Ketcham, Smith and
Williams (1984)
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Ketcham, Smith and Williams (1984)
• In Design 1 the competitive equilibrium is also a
Nash Equilibrium in the double auction institution
but not in the posted offer institution
• This is because in the latter case there are
opportunities for individual sellers to deviate
from the competitive equilibrium price
• This is turn has some implications for the
quantity supplied in equilibrium
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Ketcham, Smith and Williams (1984)
• In Design 2, each seller has a constant
cost and subjects do not get a commission
• The market structure in Design 2 is a
variation of a triopoly wher the highest cost
seller is cut out of the market above the
CE price
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Ketcham, Smith and Williams (1984)
• In Design 2, given the underlying
parameters there are two possible prices
that the system can converge towards
since several prices clear the market in
this case
• The equilibrium price is taken as the
midpoint of that set and labelled PC
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Ketcham, Smith and Williams (1984)
• Alternatively the market might approach a
“limit price” equilibrium where the highest
cost seller is just excluded from the market
– This price is labelled PL
– With constant costs, this limit price will
equal the unit cost of the highest cost
seller
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Ketcham, Smith and Williams (1984)
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Double
Auction
Posted
Offer
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Ketcham, Smith and Williams (1984)
•
The authors look at three measures of
convergence
1. The asymptotic root mean square error (RMSE)
deviation in contract prices from the CE price
2. The mean error (ME) deviation in contract prices
from the CE price
3. Efficiency in any period t
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RMSE
• Let r(t) be the RMSE of contract prices in period t
i.e.
• Then the asymptotic RMSE is given by
•
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Mean error deviation
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Ketcham, Smith and Williams (1984)
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Ketcham, Smith and Williams (1984)
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P = 0 if DA, 1 if PO
D = 1 if Design 1, 2 if Design 2
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Ketcham, Smith and Williams (1984)
• Subject experience reduces RMSE and
ME and increases Efficiency
• No strong impact of market institution
(whether DA or PO) on RMSE but ME is
higher with PO while Efficiency is lower
with PO
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Signalling and Tacit Collusion
• In DA the signalling opportunities are the same
for buyers and sellers (if information is public)
• The opportunity cost of signalling is insignificant
• Consequently signalling occurs frequently but
there is little evidence that this leads to collusive
outcomes on either side of the market
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Signalling and Tacit Collusion
• In PO only sellers can signal
• This might favour tacit collusion among
them to coordinate and increase prices
• Since a posted price cannot be revoked,
the opportunity cost of posting “high”
prices in foregone sales
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Signalling and Tacit Collusion
• This reduces the incentive of the individual seller
to signal and may promote “free riding” – each
seller wants the others to signal
• Signalling is quite common in PO markets
• In Figure 5 note the repeated attempts by one or
more sellers to signal a price increase with high
unaccepted price offers
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Ketcham, Smith and Williams (1984)
• In Design 2 the presence of a third seller
with constant cost at PL increases the
opportunity for tacit collusion
• If prices are at or below this price then this
seller typically engages in price signalling
by raising her posted offer
• By doing so this seller has nothing to lose
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Ketcham, Smith and Williams (1984)
• Given that cost information is private the
other two sellers do not know that this
action is costless to the third seller
• This is shown in Figure 9 where the
highest cost seller engaged in price
signalling in period 10 – 12, 15 – 19, 21 –
23 and 25
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Ketcham, Smith and Williams (1984)
• Findings suggest that prices tend to be higher and
efficiency lower in PO markets compared to DA markets
• This institutional effects interact with other design
parameters such as subject experience
• Subject experience increases both efficiency and speed
of convergence towards the competitive price
• Price signalling and tacit collusion is common in the PO
institution
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