lec10_with_answers - Econ 138 Financial and Behavioral...

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Econ 138 Financial and Behavioral Economics Lecture 10: I/CF sensitivity and Diversi fi cation Ulrike Malmendier UC Berkeley Tu, February 26, 2008
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Organization Using STATA in the computer lab in Barrow’s Hall (Room 64). (Out- side the lab, there is an announcement that students a letter from the department con fi rming that the undergrad needs to use the lab.) Jenny Cornet sent the list of Econ 138 ID’s over to Jack Burris at SSIL, and he’ll set you all up with drop-in access. Lunches!
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1 Investment-Cash Flow Sensitivity Empirical fact : Internal funds (retained earnings) are a dominant source of fi nancing in all countries. Let’s introduce a variable name for pledgeable income: ρ p H ( R B p ) . Suppose our universe of fi rms have all the same investment project with cost I and returns R or 0 (with probabilities p H or p L and 1 p H or 1 p L ) , but they are heterogeneous in pledgeable income p H ( R B p ) and available cash C .
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Further suppose pledgeable income and C are independently distributed. (Note that, given the identical investment projects across fi rms, this amounts to B and C being independently distributed.) Realistic? Answer : No. Firms with more higher pledgeable income (lower private bene fi ts) may have been able to invest more in the past and are richer today! C distributed G ( C ) , continuous cumulative distribution function with density g ( C ) . Which fi rms receive fi nancing? Answer : Those with p H ( R B p ) I C .
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What is the aggregate investment? (Remember that I , R , p H , p L are identical for all fi rms.) Answer : The aggregate investment among all fi rms with pledgeable in- come ρ is I ( ρ ) (1 G ( I ρ )) I . (Remember that the minimum required cash, C , for a given level of pledge- able income ρ is de fi ned by C = I ρ .) We can also calculate the aggregate investment among the full universe of fi rms. Denote the cumulative distribution of ρ as H ( ρ ) , with a con- tinuous density h ( ρ ) . Then, the aggregate investment among all fi rms is R I ( ρ ) dH ( ρ ) .
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Now consider a small, uniform increase in cash, δC for all fi rms. How does the aggregate investment change? Answer : First note that a uniform increase in cash, δC for all fi rms leads to a shift of the distribution function G ( C ) to the right. The new distribution function, say, e G ( C ) , is de fi ned by e G ( C ) = G ( C δC ) and the new aggregate investment for all fi rms with pledgeable income ρ is e I ( ρ ) (1 e G ( I ρ )) I = (1 G ( I ρ δC )) I. To evaluate the impact of a small, uniform increase in cash, δC for all fi rms, let’s fi rst consider the impact on investment among all fi rms with a
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given pledgeable income ρ, δ e I ( ρ ) δC , using a fi rst-order Taylor expansion.
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