Local Bank Financial Constraints and Firm Access to External Finance

happens with probability p (j+1) w (1-p w ) N-(j+1) . The last term of the sum represents the number ofpotential combinations of j banks that may participate out of N-1 potential candidates.Finally, the cutoff η w * is determined by the value of η that makes the expected profit ofparticipation in (A2) equal to zero. This participation threshold is the same for all banks giventhe symmetry assumptions made so far. Substituting η w * into (A1) gives an implicit expressionfor the probability of participation:⎡ ⎡= ⎢ ⎢∑ − 1w⎢⎣⎣ j=0 1+j⎤1 ⎛ N −1⎞⎤w⎥⎥⎝ j ⎠⎦⎥⎦N 1j+N −( j+1)p Pr η < A p ( 1−p ) ⎜ ⎟(A3)wwThe probability of participation p w is an increasing function of wave size A w , which isconsistent with the positive correlation between wave size and number of participating banksobserved in the data.The model can be modified to allow the probability of participation to vary across banks. Iassume that the resources in a wave are distributed according to the actual formula used toallocate program resources (II-3). Each bank receives a fraction of the resources available in thewave that is proportional to the ratio of their score points (Zregion -i , Zsize -i ) relative to the sum ofthe scores of all participating banks. Each bank will now have a different participationthreshold, η iw *, and a different probability of participation, p iw . The expression for the expectedprofits of bank i of participating in wave w can be summarized as:E( πiw) = AwG( Zregioniw, Zsizeiw,Zregion− iw,Zsize−iw) −η(A3)iwThe function G(.) is the expression for the expected fraction of resources in a wave assigned tobank i. It is the equivalent of the sum term in (A2) but it is now a function of bank i’s regionand size scores, and the rest of the potential participant bank’s region and size scores. The keyfeature of this function is that it is increasing in the point scores of bank i. Thus, banks with a40