_{1}

This theoretical note aims at studying the role of reference points in generating unemployment volatility. For this purpose, I introduce the notion of reference points in a standard Mortensen- Pissarides model. I obtain two results. First, I find that the obtained model is similar to the one found by Pissarides in 2009. Second, I show that the introduction of reference points can increase significantly unemployment volatility through a mechanism à la Hagerdorn and Manovskii.

Economic studies and laboratory experiments clearly show that reference points play a fundamental role in (wage) negotiations (see, within a large literature, [

Moreover, a pervasive challenge in macroeconomics is to understand why the standard Mortensen-Pissarides (hereafter MP) model cannot generate the volatility of the unemployment rate observed in US data. This is the so-called Shimer puzzle. Several solutions have been proposed to solve this puzzle. For example, [

The aim of this theoretical note is to draw a link between reference points and the unemployment volatility puzzle. For this purpose, I consider a simple MP model with exogenous separations, reference points and where the partition of the surplus is no longer derived by a Nash bargaining game. It is determined by a sequential bargaining game where the outcome of this new negotiation process is evaluated relative to a reference point. I then deduce the new wage equation and the new associated job creation. I find that the obtained model is equivalent to the one found by [

Notice finally that this is not the first framework that integrates reference dependence in a MP model. In a recent working paper, [

This note is organized as follows. Section 2 describes the search and matching model with reference points. Section 3 provides a conclusion.

The model considered hereafter is the standard search and matching model with reference points and sequential bargaining.

I follow [

and

with r the risk-free interest rate, z the unemployment benefits, s the separation rate and

and

with c the cost of a vacancy, p the productivity of workers,

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 ^{1}:

with

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. ^{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

This is the familiar “split the difference rule”: if demands are compatible (i.e.

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:

^{1}The comparison with [

^{2}It is possible to consider a general utility function such that

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.

where

[

and the Beveridge curve is identical to the one in Equation (6). Thus, up to a coefficient ^{3}. As in [

To conclude, contrary to [

In this note, I integrate reference dependent preferences in the wage bargaining of the benchmark MP model. In so doing, I study how reference points affect unemployment volatility. I obtain two results. First, I show that reference points act similarly to matching costs in [

H | c | ||
---|---|---|---|

0.000 | 0.356 | 0.98 | 3.66 |

0.050 | 0.277 | 0.98 | 4.12 |

0.100 | 0.199 | 0.98 | 4.71 |

0.150 | 0.120 | 0.98 | 5.51 |

0.200 | 0.044 | 0.99 | 6.62 |

0.219 | 0.015 | 0.99 | 7.17 |

Several extensions can be considered. For example, reference points are introduced (in the present article) as a fixed reduction in utility. This means that there is no loss aversion: the valuation of gains and losses enters symmetrically in the utility function. Therefore, future research should be naturally directed at understanding the effect of reference points that exhibits loss aversion.

I thank the referee for his comments. I also thank Jean Olivier Hairault, Pierrick Clerc, Nicolas Dromel and Antoine Lepetit for their help.