Empirical Methods for Corporate Finance. Identification

Transcription

1 mprcal Methods for Corporate Fnance Identfcaton

2 Causalt Ultmate goal of emprcal research n fnance s to establsh a causal relatonshp between varables.g. What s the mpact of tangblt on leverage?.g. What s the mpact of leverage on product prces? Ths corresponds to a smple «f then» statement Causalt s requred to formall test theores, make predctons and assess polc mplcatons Ths s a bg challenge for corporate fnance research 4/20/2015 2

3 4/20/2015 xample

4 4/20/2015 xample

5 OLS frst The econometrc model Consder a sample of N observatons ver sngle observaton follows 1,...,N x ' u 0 x 1,1 x 2,2... K x, K u where s a (K 1) - dmensonal column vector, x ' s a (K 1) - dmendonal row vector, and u s a scalar called the error term 4/20/2015 5

6 A1: Lneart ' x u and ( u ) 0 The lnear specfcaton s correct Ths often derves from theor and models Ths needs to be tested n practce, how? How to nclude non lneart n a lnear equaton? 4/20/2015 6

7 A2: Independence x N, 1..d (ndependentl and dentcall dstrbuted) The observatons are ndependentl and dentcall dstrbuted In practce, ths assumptons guarantees that the data come from a random sample Frms under analss are taken randoml from the unverse of all frms, and not from a sub sample of specfc frms,.e. large frms 4/20/2015 7

8 A3: xogenet a) u b) u x c) ( u d) cov( x ~ N(0,σ x x (ndependent) ) 0 (mean ndependent), u 2 ) ) 0 (uncorrelated) The explanator varables contan no nformaton about the error term We wll see that ths s dffcult to assume n man corporate fnance contexts! 4/20/2015 8

9 A4: Identfablt rank(x) K 1 N The regressors are not perfectl collnear No varable s a lnear combnaton of the others ver explanator varable adds addtonal nformaton 4/20/2015 9

10 A5: rror varance a) V ( u b) V ( u x x ) ) 2 2 (homoskedastct) g( x ) (condtonal heteroskedastct) a) Homoskedastct means that the varance of the error term s a constant b) condtonal heteroskedastct allows the varance of the error term to depend on the explanator varables,.e. larger error varance for small frms Wh s ths mportant? We wll further dscuss ths pont 4/20/

11 A6: Identfng varaton ' ( x x ) Q XX s postve defnte and fnte All regressors (but the constant) have non zero varance and not too man extreme values OLS requre varaton to dentf potental lnear relatons Use wnsorzaton n practce Remove outlers (1% or 5% n each tal of the varable dstrbuton) that are probabl due to data problem,.e. msreportng 4/20/

12 Issue xogenet s a crtcal assumpton n OLS specfcatons Ths s dffcult to assume n man emprcal contexts Often we have a valoton of exogenet : ( x u ) 0 Wh? There ma exst an (some) unobserved varable that correlates wth the explanator varables (X) and wth the error term (u) Implcatons The estmated coeffcent (β) does not have a causal nterpretaton because t contans (selecton or omtted varables) bas(es) 4/20/

13 Omtted varable representaton Imagne the true (structural) model s gven b x q u wth ( u x, q ) 0 and ( q ) 0 where q s not observed. OLS estmaton wlltreattas an error term x v wth v q u Problem f Cov( x, q ) 0 (x s endogenous) In ths case, we have that ˆ Cov( x, q ) / Var( x )] BIAS Postve bas f 0 and Cov( x, q ) Negatve bas f 0 or Cov( x, q ) 4/20/

14 o hoptals make people healther? Ths s a causal queston (f then queston) Compare the average health status of hosptal vstors and nonvstors (2005 NHS) Health status: 1 (poor) to 5 (excellent)] Results Group Sample sze Mean Health status Std. rror Hosptal 7' No Hosptal 90' (1) (2) 0.72*** (t stat : 58.9) Can we conclude that gong to the hosptal makes people scker? 4/20/

15 o hoptals make people healther? No! People who go to hosptal are probabl less health to begn wth ven after hosptalzaton people who have sought medcal care are not as health, on average, than those who were never hosptalzed Though the ma well be better off than the otherwse would have been Ths s a tpcal selecton problem (or omtted varable) Some non random people (sck) people go to hosptal There s a unobserved varable (health status before hosptalzaton) 4/20/

16 Treatment representaton Thnk of hosptal treatment as a bnar varable ={0,1} and the outcome of nterest, health, denoted b Queston: How s affected b hosptal care? Thought experment: what mght have happen to someone who went to the hosptal f that person had not gone? Two potental outcomes for an ndvdual Potental outcome 1 0 f f s the health status of an ndvdual had he not gone to hosptal 0 s the health status f he went 4/20/

17 Treatment representaton fference 1 between and 0 s the causal effect of gong to the hosptal for ndvdual We cannot measure t because we onl observe one of these two outcomes per person. Unobserved outcome s counterfactual Ths dfference s exactl what we would measure f we could go back n tme and change a person s status The observed outcome could be wrtten n terms of potental outcomes 1 f 1 or 0 ( 1 0 ) 0 f 0 The treatment effect ( 1 0 ) can be dfferent for dfferent people 4/20/

18 Treatment representaton When we compare averages b hosptalzaton status,ths tell us somethng about causalt but not necessarl what we want to know The term s the average causal effect of hosptalzaton on those who were hosptalzed The observed dfference n health status adds a selecton bas gven b Ths term s the dfference n 0 between those who were and those who were not n the hosptal ( s «endogenous») Because sck people are more lkel to seek treatment, the bas s negatve 4/20/ ] 1] 1] 1] 0] 1] ] 1] 1] ] 1] 0 0

19 Random assgnment Random assgnment of overcomes selecton bas because random assgnment makes ndependent of potental outcomes Reconsder the selecton term underrandom assgnment 0 0 1] 0 0] 0 1] 1] 0 Snce outcomes are ndependent of status, we can swap 0 0] and 1] 0 Reconsder the causal term under random assgnment 1] 0 1] 1 0 1] Random assgnment elmnates selecton bas ] 4/20/

20 Regresson representaton In a regresson framework (assume the same treatment for everone for smplct, ρ), we would have Where does ths come from? Consder the potental outcomes So that Selecton bas amounts to correlaton between the error term (η ) and the regressor ( ) 4/20/ )] ( ) ( ) ( ] 0] 1] 1] (when non treated) (when treated) η α η ρ α 0] 1] 0] 1]

21 Thnk n terms of perfect experment.g. What s the effect of collateral on leverage? Nave answer: OLS regresson of leverage on collateral (and other control varables) ndogenet ssue: collateral s chosen b the frm so that t ma be related to the error term n the OLS specfcaton Ideal world (frst best): Take some frms, randoml modf ther collateral value and see how the adjust ther leverage Second best: Look for shocks to collateral value that seem «unrelated» to leverage and see how frms adjust Ths s exactl what IV or dff n dff do (more on that later ) 4/20/

22 Concluson Rarel do we have randomzed experment n fnance We have observatonal studes where non random selecton s a ke concern We cannot rewrte hstor to get counterfactuals, so we need to approxmate for unobserved counterfactuals Goal s to overcome the selecton/ omtted varable bases to make causal statement Hosptals make people healther COs create value for frms Acqustons destro value Frms ssue equt to take advantage of msprced securtes tc. Rest of the class deals wth several potental solutons 4/20/

23 Prevalence? Source: Bowen, Fresard, and Tallard (2015)

24 Prevalence? Source: Bowen, Fresard, and Tallard (2015)

25 conomcs vs CF Source: Bowen, Fresard, and Tallard (2015)

26 dtoral Boards? Source: Bowen, Fresard, and Tallard (2015)

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28 Who does adopt?