# Money Creation in a Random-Matching Model of Money

Open Access

- Graduate Program:
- Economics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- July 17, 2002
- Committee Members:
- Gustavo Ventura, Committee Member
- Neil Wallace, Committee Chair
- James Schuyler Jordan, Committee Member
- Dmitry Dolgopyat, Committee Member

- Keywords:
- inflation
- optimal allocations
- random-matching models
- Friedman rule
- optimal monetary policy

- Abstract:
- 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 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.