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concerns that the FDIC’s choice of which assets to sell, retain, or loss-share biases our results.

Next, we use an alternative measure of the costs of resolution of a failed bank. Instead of the cost estimates provided by the FDIC, we can measure the actual premia or discounts offered for assets and deposits of the bank by the winning bidder. Bidders can offer to acquire the assets of the failed bank at a discount, but also to pay a premium for the deposits of the failed bank (both as a percentage of the failed bank’s assets). We take the difference between the discount and the premium to obtain the net discount offered by the bidder on the failed banks’ assets and liabilities. We again control for other bid charac-teristics. Columns (3) and (4) of TableXI, Panel C, show that the results based on this alternative measure are quantitatively very similar, suggesting that the asset discount and deposit premium are primary inputs into FDIC costs.

We also conduct a number of additional robustness tests. We first condition on the efficiency of failed banks. We find that more efficient failed banks had lower resolution costs, but conditioning on failed bank efficiency does not subsume the effect of the capitalization of local potential acquirers. Next, we find that our results obtain when we focus on savings as well as commercial banks, and when we control for the most comprehensive audit level of the failed bank in the year prior to failure. Our results also persist when we limit attention to the largest banks in the sample, although the effects are muted, suggesting that larger banks have fewer “specific” assets. We further examine the opacity of assets. Because data on opacity are only available for a small part of the sample, we obtain quantitatively similar, but noisier, results. We also experiment with several alternative specifications, such as different fixed effects (MSA fixed effects or state × year fixed effects), as well as different definitions for our distance measures and find similar results.

Selling Failed Banks 1781 acquirers relative to the failed bank determine their willingness to pay for a failed bank.

We next show that the capitalization of potential acquirers distorts the allo-cation of failed banks. When banks that would like to acquire a failed bank are themselves poorly capitalized, the allocation of the failed bank is tilted toward acquirers whose characteristics suggest a lower willingness to pay. Our frame-work rationalizes this finding, suggesting that the poor capitalization of some potential acquirers drives a wedge between their willingness and ability to pay for a failed bank, and that this wedge may lead to a misallocation of failed banks. We measure the magnitude of the misallocation using the additional costs incurred by the FDIC. Our is the first paper to study the qualitative and quantitative allocation consequences of failed bank sales.

We interpret our findings within a model of auctions with budget constraints.

However, the evidence provided in this paper connects to several theoretical literatures. Our finding that the wedge between the willingness and ability to pay distorts the allocation of failed banks is consistent with the presence of fires sales in this market (Shleifer and Vishny (1992)). The frictions in the sale of failed banks uncovered in this paper also highlight important aspects of banks’ production function that are posited by existing banking theories.

These theories include those emphasizing the role of soft information (Stein (2002)), banking relationships (Rajan (1992)), and specialized human capital in lending (e.g., the monitoring function (Diamond (1984))). Our results are inconsistent with the view that these aspects of a bank’s production function have declined in importance with innovations in information technologies and the reduction of regulatory constraints. More broadly, our findings suggest that selling failed banks is not frictionless, but rather is associated with certain costs. Policy makers and regulators should weigh these costs against those of other methods of supporting distressed banks.

Our findings have several policy implications. Prior work suggests that not failing a bank may create incentives for risk-shifting and moral hazard that hinder the efficient allocation of capital (Dam and Koetter (2012)). Our paper suggests that policy makers must weigh these costs against those of misal-locating a bank’s assets when selling failed banks. We find that the costs of misallocating the assets of failed banks are largest when the best users of a failed bank’s assets are themselves poorly capitalized. Therefore, a poorly cap-italized banking system not only increases the likelihood of individual bank failure, but also the costs of selling troubled financial institutions. Micropru-dential regulation aimed at minimum capital requirements for banks may thus also have consequences for optimal bank resolution policies.

Initial submission: May 13, 2015; Accepted: August 13, 2015 Editors: Bruno Biais, Michael R. Roberts, and Kenneth J. Singleton

APPENDIX

LEMMA: Suppose(ν,c) and,c), such thatν > v. Let b and b be the corre-sponding bids. Then bb.

Proof: Consider two types with the same capitalization (ν,c) and (ν,c) such that ν > v. Our claim is that the firm with a higher willingness to pay bids more, that is,bb. Suppose not, andb<b. Incentive compatibility requires that each type prefers its equilibrium bid to bidding an alternative amount:

(v−b)G(b)≥(v−b)G(b) (vb)G(b)≥(vb)G(b).

Summing these inequalities, we obtain ν−ν G(b)G

b

≥0.

Because the probability of winning is increasing in bids,G(b)G(b)<0, we

have a contradiction.

LEMMA: A symmetric equilibrium of an auction with unconstrained bidders results in weakly higher expected revenue than the symmetric equilibrium of an auction with the same distribution of willingness to pay but where some bidders are capital constrained.

Proof: Denote the probability that an unconstrained type with willingness to payνwins the auction with capital constrained bidders byFC(v), where

FC v

=

{(ν,c):b(v,c)<b(vc)}

f(v,c)dνdc.

Denote the corresponding probability that a type with willingness to payν wins the auction if no bidders are constrained by FU(v).

In an auction with constrained bidders, the unconstrained bidder outbids all bidders with a lower willingness to pay as well as some bidders with a higher willingness to pay who are constrained. In contrast, when all bidders are unconstrained, the only bidders who bid less than an unconstrained bidder are those with a lower willingness to pay. We thus have

FU v

FC v

.

Our auctions with constrained and unconstrained bidders satisfy condition (A2) in Che and Gale (2006). Thus, by Theorem 1 in Che and Gale (2006), the unconstrained auction yields weakly higher revenues.

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