# Money creation in a random-matching model of money

Abstract (Summary)

I study the effects of lump-sum money creation against the background of the
random-matching model of Trejos-Wright (1995) and Shi (1995). That model is interesting
for the study of money creation because, alongside with the usual harmful
internal margin effects, money creation has beneficial external margin effects. Positive
money creation shifts the distribution of money towards the average holdings,
thus increasing the frequency of trades in meetings. Molico (1997) demonstrates
numerically that beneficial effects are possible in that model. However, Molico
assumes a particular bargaining rule, take-it-or-leave-it offers by consumers. That
bargaining rule is known to cause too much production in some meetings. Because
lump-sum money creation tends to reduce production in meetings with binding
producer participation constraints, the beneficial effects he finds may come from
offsetting the effects of that bargaining rule. Instead of working with any particular
bargaining rule, I consider optima over all implementable outcomes.
In order to keep the optimization problem manageable while enlarging the set
of outcomes in that way, I have to make some other compromises. I assume that
money is indivisible and that there is a bound on individual holdings - sometimes
a low bound but one that always exceeds unity. However, I do permit randomization,
which enlarges the set of trades and, thereby, the possible distribution
effects. Given randomization, there are two main ways to define the set of implementable
outcomes: either ex ante (allowing people to commit to randomization)
or ex post (requiring that people go along with each element in the support of the
randomization scheme).
Essay 1.“Another Example in which Lump-Sum Money Creation is Beneficial.”
(Joint with Neil Wallace.) We assume a two-unit upper bound on money holdings
and adopt ex post individual rationality as the notion of implementability. The
policy is a probabilistic version of the standard helicopter drops followed by proportional
reduction in individual holdings. For all discount factors greater than a
critical value, we show analytically that the ex ante optimum involves creation of
money. This is done by finding the best outcome subject to no money creation
and by showing that some creation can improve that outcome. Our results for
a two-unit bound on holdings are indicative for what can happen with all higher
bounds.
Essay 2. “Optimal Money Creation in a Random-Matching Model with Ex post
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Individual Rationality.” Although Essay 1 accomplishes the goal of showing that
money creation can be helpful, it does not describe the optima. I study the same
model (while letting the bound on money holdings be arbitrary) where I do two
things. First, I show that, under a mild restriction on the set of implementable
outcomes, conditional on the amount of money transferred in a meeting there
is no randomization over output, a property I call degeneracy. This degeneracy
result facilitates the exploration of the trade-off between harmful and beneficial
effects of money creation by way of examples. I compute optimal allocations for
examples with a two-unit bound on holdings. These examples are consistent with
the conjecture that the optima do not have take-it-or-leave-it offers by consumers
in all meetings — the bargaining rule imposed by Molico.
Essay 3. “Money Creation and Optimal Pairwise Core Allocations in a Matching
Model.” Here I adopt the ex ante pairwise core notion of implementability.
In contrast to what happens using the ex post IR notion, now the optimum, even
with no money creation, involves binding participation constraints. Therefore, the
proof technique of Essay 1 is not applicable. Moreover, it is difficult to get any
analytical results. Therefore, I compute numerical examples. In no examples is
money creation optimal.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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