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lecture17 - Economics 202A Lecture Outline November 15-20...

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Economics 202A Lecture Outline, November 15-20, 2007 (version 1.1) Maurice Obstfeld The main point of the model we’ll study today is to show how agency costs of investment can be mitigated by a larger decision-maker stake in projects. Thus, more plentiful internal funds can spur investment and, conversely, sharp reductions in decision-maker wealth can cause investment to collapse. Idea of the Bernanke-Gertler ( QJE; February 1990 ) model To set the stage, start with a setting much more simple than that of Bernanke-Gertler (BG). A risk-neutral investor or entrepreneur with total real wealth w (observable by outsiders) faces a world capital market in which the gross interest rate on loans is (the given constant) r . There are two time periods; investment takes place in the °rst and consumption in the second. A project requires the input of 1 unit of output on date 1 and has a date 2 payo± of R with probability p and of 0 with probability 1 ° p . Importantly, p is the entrepreneur’s private knowledge. An entrepreneur can undertake at most one project, and has the option of instead investing his or her wealth at the gross risk-free rate r < R . The cumulative distribution function for p within the population of entrepreneurs is H ( p ). Assume tentatively that an entrepreneur with wealth w can borrow 1 ° w at the world interest rate r: Lenders can observe the investment outcome and compel repayment up to the limit of the borrower’s resources. For which values of p will entrepreneurs choose to invest in their risky projects? If there were no nonnegativity constraint on consumption, the cuto± value of p would be where the expected returns to risky and riskless investment coincide: p [ R ° r (1 ° w )] ° (1 ° p ) r (1 ° w ) = rw: The solution is p ° fb = r=R; 1
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which, you can con°rm, gives an e²cient amount of investment. But con- sumption cannot be negative. An entrepreneur whose investment goes sour can only repay 0 in period 2, so that the problem he or she solves in period 1 has a cuto± probability given by p [ R ° r (1 ° w )] = rw; with solution p ° = rw R ° r (1 ° w ) ± r R : (The last inequality is strict if w < 1.) Notice that unless w = 1 (so the en- trepreneur bears the entire risk of the project), p ° < p ° fb . Too many projects will be undertaken relative to the e²cient benchmark. There is a classic problem of adverse selection, because \bad" borrowers who know they have low p will borrow and invest. They have a small chance of a big win, but default at the lender’s expense if the investment fails. Notice that the lower is w , the investor stake, the greater is the incentive to gamble on high-risk projects (d p ° = d w > 0). Furthermore, rational lenders, anticipating the behavior above, would never lend at the interest rate r: Instead, they o±er a loan contract designed in the expectation that the borrower will default if the project fails. The equi- librium loan contract is simple (and is equivalent to an equity contract in this simple setting). A borrower undertaking a risky project repays R (1 ° w ) if the project is successful and 0 otherwise (i.e., there is a default).
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