The Moorish Wanderer

Thesis Working Paper n°2

Posted in Dismal Economics, Read & Heard by Zouhair ABH on January 11, 2011

Description of the Monetary Policy as a bargaining process between two players:

a. Players features: The Central Bank (CB) and a representative private firm (PF) bargain for a pair are respectively were i(e) and Y(e) the equilibrium interest rate and output.

Each player has specific preference utility function, where the bank seeks to stabilize output via interest rate (in optimal settings, it would systematically set up interest rates so as to maximize potential output). We assume for the time being that the central bank does not take into account inflation directly into its computations (inflation is captured by the potential output). Central Bank’s preferences are captured by an altered version of the Taylor Equation such:

The Private firm, on the other hand, has a preference for high output and low interest rates, which means that its utility function is such:

This is due to the fact that the firm prefers low interest rates for valuation purposes and investment cost. High output generates higher profits and higher levels of cash flows (leading to higher valuation again).

It can be inferred from these preferences that both players have contradicting interests (and in facts the Firm does not take into account the potential output) and so the bargaining model is an attempt to seek an equilibrium.

b. Game: The game is a mapping

 

Where :

 

 

 

 

The bargaining is a standard Rubinstein-Osborne model, where the set of agreement pairs is described as follows:

 

The game starts with the Central Bank announcing a pair . The firm has the choice of accepting the pair or rejecting it. If it accepts it, the game is over, and the economy produces Y(e) at an interest rate i(e).

If it rejects the Bank’s proposal, then the game moves to stage 2, whereby it’s the firm’s turn to propose a pair

The bank has in turn the choice of settling for it, or moves to stage 3, and proposes another pair,

and so on and so forth. We assume that the actions take in a finite time set T, but at each period t, the proposed set from one player or the other is such:

This can be explained as the ‘price of disagreement’. For the central bank, it is damaging its policy-making credibility, or because danger of inflation, when not dealt with at the time, compels the bank to be more stringent in pushing for scheduled higher interest rates and lower output target (and by computation, a negative output gap). As for the firm, the punitive discount rate can be explained either by the uncertainty risk or because of the future negative effects non controlled inflation has on its valuation or profits.

The assumptions described in Osborne & Rubinstein on the extensive form hold: each player has a continuum of choices over the pair (i,Y). For this game to lead to a subgame perfect equilibrium, the following properties are to be verified:

1/Disagreement is the worst outcome: that can be easily verified with the punitive time factor: at every node of bargaining, the worst outcome is to reject the offer, as the utility derived from the next stage is lower than the previous one.

2/ Desirability for a particular outcome is embedded in both players’ preferences as described earlier on

3/ Time is valuable, and is also verified with the punitive discount factor δ.

4/ Continuity: the assumption of continuity needs to be discussed. As specified before, both players have defined intervals respectvely for interest rates and output. The series are therefore bounded but also converge to equilibrium state because it is the

most desirable at every node of the bargaining process:

 

 

 

5/ Stability is also defined by the effect of discount time factor.

6/ Increasing loss to delay: the discount factor also fulfils the condition.

This game has therefore a perfect subgame equilibrium. That means, at every node of the game, the reached equilibrium is part of the larger game, and because utility out of a Nash agreement is higher at stage t-1 compared to stage t, both parties have every incentive to agree right from the start. Next piece is dealing with the requirements the Central Bank has to meet in order to be credible in its decision/announcement.

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