lecture5_103

lecture5_103 - Econ 103C-Lecture 5 Signaling David Sraer...

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Unformatted text preview: Econ 103C-Lecture 5 Signaling David Sraer Berkeley University April 14, 2008 David Sraer (Berkeley University) Econ 103C-Lecture 5 April 14, 2008 1 / 32 A reminder Signaling refers to a situation where the party offering the contract (the Principal) has private information. In that case, the nature of the contract offered / or the nature of some action taken by the Principal can send a signal to the agent about this information. Example: in finance, a firm that choose to issue equity to finance its investment might convey a different signal than a firm that prefers to issue a debt contract! David Sraer (Berkeley University) Econ 103C-Lecture 5 April 14, 2008 2 / 32 Education as a signal We begin with the simplest model of signaling due to Spence (1973) A worker can be of two productivity: either r H or r L with r H > r L . A firm knows that the worker is of productivity r H (resp. r L ) with probability β H (resp. β L , β L + β H = 1). Workers are willing to work for any wage w > 0 and the firm is willing to hire any worker at a wage less than the worker’s expected productivity. A worker of productivity i ∈ { L , H } can get e years of education at a cost c ( e ) = θ i × e before entering the labor market. Key Assumption : θ H < θ L ⇒ the marginal cost of education is lower for high productivity worker (e.g. higher ability)! In this model education does not affect productivity ⇔ it is purely wasteful, society would be better off if all workers selected e = 0! David Sraer (Berkeley University) Econ 103C-Lecture 5 April 14, 2008 3 / 32 The set-up + First best 1 the worker choose his education level, e . 2 the worker apply for a job with the firm and make a take-or-leave it offer to the firm. Assume the worker’s productivity is observable. Then an agent of productivity r i selects e = 0 and makes an offer w = r i ! Obviously, when the productivity is no longer observable, this cannot be an equilibrium, as low productivity worker would also ask for the high wage w = r H ! David Sraer (Berkeley University) Econ 103C-Lecture 5 April 14, 2008 4 / 32 Second-best problem We now assume that productivity is no longer observable. Only the choice of education e is. Consider the second stage of the game. Let e be the level of education selected by an agent in the first stage (we’ll figure out afterward how e was selected). Let β ( θ i | e ) be the firm’s posterior belief that the worker is of productivity r i after observing the level of education e (we’ll figure out afterward how β ( θ i | e ) is determined) Then, we know that the firm is willing to pay the worker its expected productivity, so that the worker will make the following offer: w ( e ) = β ( θ H | e ) r H + β ( θ L | e ) r L , with β ( θ L | e ) + β ( θ H | e ) = 1 Difficulty : the choice of education depends on the firm’s posterior belief about the productivity conditional on observed education = ⇒ loop. . . This loop needs to be consistent!!!...
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lecture5_103 - Econ 103C-Lecture 5 Signaling David Sraer...

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