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14.06: Section HandoutTA: Jose TessadaApril 8, 2005Today we will cover the basic idea of the model introduced by Bernanke andGertler in their paper in the AER, 19891.SummaryThis paper introduces a friction (or imperfection) in the financial market intoan otherwise “relatively standard” neoclassical model. This friction arises becauseheterogeneous entrepreneurs (investors) have private information and the financialcontract then incorporates additional characteristics that guarantee the entrepreneursactually reveal the private information. The new addition to the model will give ussome very interesting insights about investment and will also shed light on somepersistence and amplification mechanisms.An important part of the paper is devoted to the analysis of the microfoundationsof the problem. I will skip that discussion here, and will focus mostly on the macro-economic implications of the imperfections in the financial markets. In particular, themodel will provide us with a simple rationale for financial constraints on the firmsand the sensitivity of firm level investment to the availability of internal funds.I will first describe the model and it assumptions. Then we will see how the no-friction (flexible) equilibrium looks like, and finally we will b e able to compare theequilibrium when there is an imperfection in the financial market.The ModelBernanke and Gertler (1989)’s model is a relatively standard neoclassical modelof investment. The feature that will allow the authors to introduce a twist later isthe fact that the production of capital has an stochastic output.The main ingredients of the model are:• This is an infinite horizon, overlapping generations model (OLG).21Bernanke and Gertler (1989).2The main intuition behind the results in this model can still be explained without making explicitreference to this part; but this does not mean that it is not an important element for the particularsolution presented in the paper.1• There are two types of agents: lenders and entrepreneurs. There is a fraction ηof entrepreneurs. Every agent owns an initial stock of wealth.There are two differences: first, lenders are risk averse and entrepreneurs havelinear preferences; second, entrepreneurs are the only ones that can start a“project”.• There are two goods: capital (k) and output (final) good. Capital can betransformed into output good within the same period, in particular,yt=eθtf (kt)whereeθ will play the role of a demand shock in the market for capital.Capital can be produced with output goods, but its production takes one period.Production is such that entrepreneurs need to invest an amount ω of the outputgood today and will have a return κ in the next period, which is stochastic;assume for simplicity that κ takes only two values: κHand κL, with κH> κL.Entrepreneurs will differ in their abilities, which will be reflected in the amountthey need to invest in the first period. In this way, entrepreneurs can be indexedaccording to ω, with a lower ω for a more productive entrepreneur.• Agents have also access to a third technology, an storage technology, whereagents get a payment r in the next period for each unit of the output good they“invest” today.Equilibrium without FrictionsI will not provide a thorough revision of the microeconomics of the problem, butinstead I will explain the intuition behind the solution.The storage technology is very useful as it provides a constant alternative return toall investors. Think of the problem a lender faces, she has two options, she can eitherinvest her wealth in the storage technology or she can lend it to an entrepreneur(s)who will use it to create capital.3Of course, she will choose the second alternativeif and only if the expected return is higher than r.4Heterogeneity kicks in here,because there will be a marginal entrepreneur ω such that the expected return on hisproject is exactly r. There is one more detail left in here, entrepreneurs have projectsthat require investment in output goo ds and give a return in capital goods, so theprofitability of the projects also depends on the expected (as of time t) price of capitalin t + 1, bqt+1. in fact, a higher expected price makes additional projects profitableand so ω is an increasing function of bqt+1, thus kt+1is an increasing function of bqt+1.3The model feature perfect competition, so we can think of a single lender as facing a constantreturn rate.4The authors assume that lenders and borrowers are risk-neutral in the second period, so we canfocus on expected returns.2Figure 1: Equilibrium without Frictions.Producers of the final good need capital for production. Under the assumptionof perfect competition in the market for capital goo ds, demand is implicitly given bythe first order condition of the firms:bqt+1=eθtf0(kt) . (1)Equation (1) determines a downward sloping curve, which we will call DD curve.Both curves determine the equilibrium in period t, see Figure 1.5Equilibrium with FrictionsWe now relax an assumption that was implicit in the previous section. The returnto the investment in capital goods is stochastic, but we haven’t made a bid deal outof it. In fact, we have implicitly assumed that the lenders know the realization of thisstochastic process: the actual value of κ is observed by all the agents. Let us relaxthat assumption now and work under the assumption that κ is private info to theentrepreneur. Does this change anything?Yes! The contract in the previous case specified a fixed payment in the nextperiod. Suppose that we keep the same contract in this case and the entrepreneurgets the high realization κH. Given that he is the only one observing the realizationhe can cheat and say that the actual return was κL. For some entrepreneurs it will be5The equilibrium in period t is defined in terms of variables in t +1 because of the “time-to-build”assumption.3optimal to do so, either because they are not very productive or because they werenot very wealthy in t and borrowed more.6The authors assume that the lenders have access to a monitoring technology thatreveals the actual realization of κ to everyone but it has a cost γ units of the capitalgood.7It can be shown then that the optimal contract sp ecifies a probability p > 0of monitoring if the entrepreneur reports κL, while there is no monitoring if κHis re-ported. The main element in this case is the fact that the contract has the “net worthproperty”, that expected agency


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MIT 14 06 - Study Notes

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