Concluding Remarks

In this chapter we have drawn together the component parts introduced in previous chapters and formulated an equilibrium model of search with offer rationing or null offers. In considering an equilibrium model of search we have trodden new ground; the analysis of search equilibria is in its infancy.

The main purpose of this chapter has been to compare and contrast models of search where offer rationing is or is not a feature and to that end we have formulated the simplest models that seem to capture the appropriate notions of vacancy creation. It has been seen that an essential difference implied by the existence of constraints on offer creation is with regard to the uniqueness of employment in equilibrium. In the case of unrationed vacancies employment was technologically determined by our simple matching assumption. Employment was independent of all parameters save those directly affecting the matching process. It is important to note that this conclusion is not robust to different specifications of matching technology, indeed the work of Diamond (1982) and Fissarides (1984) confirms this. However, as assumptions go our assumption was not a bad one. Contacts were seen as being initiated by unemployed searchers so that total contacts were independent of the number of firms in equilibrium. This simplifying restriction on matching processes we feel at least worthy of testing or empirical investigation. In any case, it remains an interesting question

181

whether assumptions that give rise to uniqueness and neutrality in a model with limitless vacancies continue to give these conclusions when offer rationing is allowed.

We have in fact seen an important distinction between rationed and unrationed models. When offer constraint was allowed it has been shown that steady state employment once again depends upon all the parameters of the model. Indeed, we have shown that simplistic partial equilibrium results concerning the effect of increased search costs for example are reversed in an equilibrium setting. Higher search costs imply higher wages, fewer firms, greater

rationing and lower employment. More importantly, however, rationed equilibria are non unique. There exists the possibility that the market can be in equilibrium with high unemployment and wages when exactly the same parameters are consistent with a low unemployment equilibrium. The problem exists because offer constraint determines the wage required to induce participation which in turn partly determines profit and thereby entry incentives. High wages, high unemployment and 'rationed' vacancies can therefore persist as an equilibrium in circumstances where if firms could be induced to enter a low unemployment, zero profit equilibrium is possible.

We believe this non-uniqueness of equilibria is the most

important insight to come out of an equilibrium model of search with null offers. Inefficiencies of Nash wage bargains will exist

whether offers are scarce or effectively infinite, bootstrap

equilibria, however, arise out of the very nature of offer rationing and the feedback on vacancy creation implied by it.

182

From this point of view it should be noted that the simplifying assumptions made in the course of analysis add strength to the results. We deliberately restricted attention to a very simple matching technology which allowed for total matching to be a

linear function of unemployment. If a more general matching function is allowed for it follows that the multiplicity of equilibria

result will be reinforced. Furthermore by introducing worker bargaining into the simple framework discussed here we have established that stable inefficient equilibria exist. These equilibria are inefficient not only with regard to the social optimum but also in comparison with other market outcomes. This distinction is important since social optima may not be obtainable (depending upon the ability to make the appropriate lump sum transfers to keep firms in business) whereas market outcomes are certainly feasible. The existence of the kind of inefficiencies discussed in this chapter offer a rationale for intervention which does not depend upon precise welfare calculations but simply upon the desire to shift the 'natural rate' of unemployment to a more desirable level.

Finally, it should be noted that the equilibrium models discussed here are of the 'vacancy' search kind discussed in chapter 2.

Equilibrium consists of a unique wage offer made by all firms. It is, however, possible to use the techniques discussed here to model search equilibria with wage dispersion. Indeed, the simplified form of the models developed in this chapter makes a model that generates wage dispersion analytically tractable in a way not possible with

the work of Diamond (1982). A necessary condition for wage dispersion is that searchers' reservations differ. Clearly a

183

continuous distribution of reservations (via a dispersion of search costs) cannot easily be handled. However, a two-point discrete distribution can easily be allowed for. Equilibrium may then consist of a proportion of firms paying low wages which only high cost (low reservation) searchers accept whilst the remaining firms make offers that all (high and low cost) searchers find acceptable. It is not to be expected that the efficiency or non uniqueness questions posed by this chapter will significantly differ in these new circumstances. The questions which one may ask concerning such a model are the determinants of the degree of wage dispersion, /gain this issue is left to future work.

184

Chapter 7