Bank Collapse and Depression

The banking panics of the nineteenth century
and the Great Depression of the 1930s are widely viewed as failures of our economic
system. Moreover, such events are far from unique to U.S. monetary history. However, a fully satisfactory explanation for these events has not been provided. Although no fully satisfactory explanation for banking panics and depression has emerged, existing theory gives guidance in searching for one. One natural place to look for an explanation for failure of our economic system is known failures in the economic model of Walrasian equilibrium. Paul Samuelson introduced a failure to Walrasian equilibrium in his pure consumption-loans model. He showed that
with overlapping generations of finite-lived individuals in a model with no last period, the Walrasian equilibrium need not be Pareto optimal. Moreover, he introduced the concept of a negative net worth entity, the "social contrivance" of fiat (unbacked) money, the use of which makes everyone better off and yields Pareto optimality. We might, then, model recurrent banking panics and depression as recurrent and once-and-for-all collapse of a fiat money system, respectively. It can be demonstrated that such collapse of a fiat money system can generate reduced production and employment.

There are, however, several problems with modeling banking panics and depression as collapses of a fiat money system. First, one must determine what events precipitate a collapse of a fiat money system and why. The collapse of a negative net worth entity causes a net loss, and therefore is something economic agents seek to avoid. Second, the fiat money model has the property that with reinstitution of a fiat money system, the economy revives instantly and completely. The introduction of a negative net worth entity generates excess profits and i entered into at once. However, during the Great Depression deposit insurance and additional bank regulations were introduced, actions that might have reinstituted banks' role as providers of fiat money. Unfortunately, the economy remained depressed. Last, very generally, fiat money is a solution to the capital overaccumulation problem of the competitive economy. In models more elaborate than Samuelson's, fiat money has value because its existence keeps the economy from accumulating too much capital. This suggests that the collapse of a fiat money system causes a period of overaccumulation of capital. It seems wrong to treat the banking panics and Great Depression as periods of high demand for investment.

The above remarks suggest that one look for a model with the "social contrivance'' of a positive net worth entity that solves a capital underaccumulation problem. Cass and Yaari in an elaboration of Samuelson's model, briefly introduce just such a positive net worth entity.' The possibility of such an entity arises in a model of overlapping generations of finite-lived individuals with no first period. This entity has just the symmetric properties one would expect. Because it is a positive net worth entity, economic agents gain from its collapse, they lose from initiating it, and if constrained to reinstitute it following a collapse, they do so to the smallest extent possible. Lastly, collapse of the net worth entity causes a drop in the demand for investment.

All the above facts stem from a basic observation on the positive net worth entity. In Samuelson's model, given that otherwise there will be no fiat money in the future, it is Pareto improving to introduce fiat money and maintain it for all time. Symmetrically, in a model with the positive net worth entity, it is Pareto superior that there will have always been this entity than that it will have never existed. Now we turn to a simple model on the positive net worth "social contrivance." Naturally, to get simplicity one must trade off realism. Therefore we then turn to elaborations of the model that, hopefully, clarify its implications for the real world.