I follow [7] . Let U and W be the asset values of being unemployed and being employed. These asset values are given by:

and

with r the risk-free interest rate, z the unemployment benefits, s the separation rate and the job finding rate. Let V and J be the asset values of a vacancy and a filled job. These asset values are defined as:

and

with c the cost of a vacancy, p the productivity of workers, the wage and the job filling rate. Using Equation (3), Equation (4) and the free entry condition (i.e.), the job creation equation is determined as:

Furthermore, notice that the unemployment rate of the economy is given by the following standard Beveridge curve:

Once the match is made, employer and employee have to negotiate over the partition of the surplus defined as according to a sequential bargaining game. In the first stage of the game, one player is randomly chosen to make a take-it or leave-it offer. The probability for the worker to be drawn is assumed to be while the probability for the firm is. If the offer is accepted by the opponent, the game ends. Conver- sely, if the offer is rejected, the game goes on to the next period where a player is again randomly selected and bargaining begins again. Note that the time interval separating one period from another is. If players disagree forever, their payoffs are equal to zero. If players agree on a partition of the surplus, they enjoy the following utility function used by [8] ¹:

with and where W is the index of the worker such that, F is the index of the firm such that and is the reference point of player i. Equation (7) states that the utility of agents depends

on the deviation of the value of the agreement from the reference point. In line with prospect theory, this means that outcomes are compared to a reference point that splits the agent preferences into gains and losses (i.e. for and for). In particular, the reference points are viewed as commitments. It is as if players simultaneously commit, or announce their will, not to accept a surplus share smaller than. However, contrary to prospect theory and for the sake of simplicity, the valuation of gains and losses are symmetric (i.e. no loss aversion)². Within this environment and noting that employer and employee discount future utilities, the sub-game perfect equilibrium of such a game is:

if and only if. Otherwise (i.e. if), no agreement exists. Solving system (8) for and and letting leads to:

This is the familiar “split the difference rule”: if demands are compatible (i.e.), then an agreement is a situation where each agent gets the utility value of its reference point and the remaining fraction of the surplus according to his bargaining power. Reducing system (9) gives the following new sharing rule:

Using the above sharing rule, the wage satisfies:

Likewise, using Equation (1), the job creation equation and the sharing rule, I obtain:

Plugging Equation (12) in Equation (11) yields:

¹The comparison with [8] stops there since, in [8] , the reference points are endogenous and dynamically changing according to the offers previously made by the players. Also note that reference-dependence distorts the bargaining process by introducing fixed-costs only. It does not distort the matching process. However, one should introduce reference-dependent preferences from the Bellman equations. The results would be exactly the same.

²It is possible to consider a general utility function such that where f could exhibit loss aversion. Nonetheless, I assume a linear utility function in order to show that the [5] model is a particular case of this general function.

Equation (13) shows that the worker’s reference point increases the wage by raising the reservation wage while the firm's reference point decreases the wage by lowering the expected return of the match. Moreover, observe that if reference points are equal (i.e.), I end up with the standard wage equation derived from a generalized Nash bargaining game. Finally, the wage equation can be rewritten as:

where can be viewed as an index measuring the relative importance of the worker’s reference point. Integrating Equation (14) in Equation (5), the job creation equation becomes:

[5] considers a search and matching model with additional matching costs. In this setup, the job creation equation is

and the Beveridge curve is identical to the one in Equation (6). Thus, up to a coefficient in (16), the job creation equation determined by a MP model with reference points is the same as the one determined by a MP model with matching costs. This suggests that these two models generate the same quantitative results. To confirm this intuition, I solve the job creation Equation (15) for the unknown with [5] calibration. I then study the effect of a 1% productivity shock on the model’s unknown by computing the elasticity of the tightness index with respect to productivity and the elasticity of the wage with respect to productivity. Table 1 gives the results for different values of H³. As in [5] , the model generates persistent high wage elasticities and an increase in H raises dramatically the volatility of job creation. Especially, the model is able to reproduce the observed volatility of labor market tightness (i.e.) when. Since wage stickiness does not matter here, the amplification mechanism is driven by the relative role of workers’ reference point. Indeed, for high H, the reference point of the worker is larger than the reference point of the firm. This leads to an increase in the wage set by firms because the reservation wage (or the outside option of the worker) is very high. This lowers the firm’s surplus and so increases the effect of the productivity shock. Namely, the introduction of reference points in a standard MP model can increase the unemployment volatility through a mechanism developed by [4] .

To conclude, contrary to [5] where matching costs are always assumed to be exogenous, it is easy to endogenize reference points in this setting. In this stationary framework, a natural candidate for the worker’s reference point is the partition of the surplus received by a worker in the standard MP model. This surplus is equal to 0.438. Assuming that the firm has no reference point, the reference point of the worker is and so. Using Table 1, one can observe that the volatility is almost matched, meaning that the introduction of endogenous reference points in a standard MP model is a credible solution to solve the Shimer puzzle.