The Determinants of Bank Mergers: A Revealed Preference Analysis∗

Oktay Akkus†, J. Anthony Cookson‡and Ali Hortaçsu§

March 20, 2015

Abstract

We provide new estimates of merger value creation by exploiting revealed preferences ofmerging banks within a matching market framework. We find that merger value arises fromcost efficiencies in overlapping markets, relaxing of regulation, and network effects exhibitedby the acquirer-target matching. Beyond our findings, the revealed preference method hasnotable advantages that warrant its application beyond the bank merger market. Notably,we show the method outperforms reduced form alternatives out of sample, enables sensiblecounterfactual experiments, and that it can be used to evaluate private-to-private mergers,which have been understudied due to lack of stock market data.

∗The authors gratefully acknowledge helpful feedback from participants at the 2014 Conference on Financial Economics and Accountingat Georgia State University. The paper has also benefited from insightful comments and careful criticism from David Becher, NathalieMoyen, Mattias Nilsson, and Marco Qin.

†Bates White Economic Consulting‡University of Colorado at Boulder - Leeds School of Business. Corresponding author. tony.cookson@colorado.edu.§University of Chicago - Department of Economics.

Introduction

Understanding merger value creation is critically important for the shareholder value at stake, but also because how

merger value is created has important implications for the nature of competition and consumer well-being (e.g.,

see Bernile and Lyandres, 2010). Unfortunately, the vast majority of mergers involve at least one private company,

making it difficult to estimate value creation using changes in stock market value around merger announcements

(Bayazitova et al., 2012). This limitation of stock market evidence is especially pronounced in industries where

private firms play an important role (e.g., banking, supermarkets, restaurants).

To overcome this difficulty, we develop a novel approach to estimate merger value creation that can be applied

even for private-to-private mergers because it relies on the choices of the merging firms directly, rather than stock

market responses to the merger announcement.1 We use the structure of a two-sided matching market to identify

outside options for each firm (e.g., see Becker, 1973; Roth and Sotomayor, 1990), and use characteristics of these

outside options in comparison to the actual merger choices to structurally estimate merger value creation. Our

approach has three notable advantages relative to reduced form methods that utilize stock market information.

First, our method is easily applied to evaluate mergers with private targets or acquirers because it does not rely

on stock market information. Second, our structural estimation accounts explicitly for the endogenous matching

process by which acquirers match with targets, which is an important source of endogeneity in determining which

characteristics matter for merger synergies. Finally, our structural analysis allows for counterfactuals, which are

difficult using reduced form methods.

We highlight each of these advantages in an empirical analysis of the bank merger market, employing compre-

hensive merger-level data from 1995 until 2005 in our study of the determinants of bank merger value. The choice

to study bank mergers is natural because it is straightforward to define the scope of the matching market within a

narrowly-defined industry such as banking. This is especially true during our sample time frame (1995-2005), the

decade following the elimination of cross-state branching restrictions (Riegle-Neal Interstate Banking and Branch-

ing Efficiency Act 1994).2 We use this cross-state standardization of merger regulations to motivate our treatment

1Using a method that is similar in spirit, Devos et al. (2009) use Value Line forecasts of cash flows to produce an estimate of mergervalue that is linked directly to the underlying fundamentals of the firm. By comparison to their method, our technique does not requireanalyst coverage, or any assumption about the validity of the forecasts. In place of an assumption that the forecasts are reliable, we maintainthe assumption that each firm in the merger market reveals a consistent set of preferences by their choice of merger.

2The 1994 Riegle-Neal Interstate Banking and Branching Efficiency Act effectively standardized the state-by-state deregulation inbranching rules that had been taking place over the previous two decades. After the Riegle-Neal Act, the U.S. banking industry con-solidated considerably, in large part due to the merger wave we study. Specifically, the total number of banking institutions in the UnitedStates declined from 10,416 to 7,582 in the decade following Riegle-Neal (FDIC Summary of Deposits, 1995 – 2005). For a completehistorical account of this deregulation process as well as a comprehensive empirical analysis of its determinants, see Kroszner and Strahan(1999).

1

of mergers in the U.S. banking industry as a national merger market that takes place each year.

In our empirical analysis, we recover a structural merger value function that accounts explicitly for the endoge-

nous matching process, and thus, can be used for causal inference. We use our approach to study how features

of the acquirer and the target institutions affect the value of the bank merger. According to industry sources, an

important reason for banks to merge during our sample was to capitalize on economies of scale. As a 1998 article

in the San Francisco Chronicle noted, “A bigger bank can acquire customers more cheaply by marketing on a na-

tional scale, and can reduce risk by diversifying geographically” (Marshall, 1998). In a two-sided matching market,

these factors suggest that large banks derive more value from larger target banks, which would generate a positive

assortative match in bank size (Becker, 1973). Our framework accounts for this cost advantage of large banks by

including terms in the match value function that capture the interaction between the size of the acquirer and target

banks.

Our main specification quantifies the effect on merger value of cost efficiencies of various types (e.g., merging

to a more efficient scale and capturing economies of scope in nearby markets), as well as merger value derived

from additional market power. Our structural approach accounts for these explanations by defining a merger value

function that explicitly depends on market concentration and the overlap between acquirer and target markets. We

also include measures of performance and valuation of the target banks to evaluate how target performance relates

to value creation (Maksimovic and Phillips, 2001). In effect, this specification allows us to distinguish whether the

merger value we recover arises from choices motivated by synergies of different types. The revealed preference

method allows the data and the pattern of mergers to speak directly to which of these explanations is consistent

with merger decisions and merger value creation.

Throughout our empirical exercise, we find that the mergers we study were primarily motivated by efficiencies,

cost reductions or reducing inefficiencies from previous regulations, and that market concentration (measured by a

Herfindahl index) also contributes positively to the value of the merger. On the other hand, we find little evidence

that mergers were motivated by high (or low) performing target banks. Consistent with an efficiency rationale for

value creation, we find that merger value is greater when there is a greater overlap between acquirer and target

markets, and that these gains are greater for mergers between banks regulated by the same agency before the

merger. These effects likely represent efficiencies rather than market power because we also control for market

concentration in the target’s markets in these specifications. The magnitude of these efficiency effects on merger

value are sensible, amounting to nearly the annual administrative cost of operating a single bank branch (Radecki

et al., 1996). These efficiencies may arise from the ability of the combined bank to pool fixed operating expenses

2

such as advertising and ATM networks across the acquirer and target banks.3

Our work also sheds light on the effects of banking deregulation by studying mergers in the post-Riegle-Neal

banking industry. Early work on banking deregulation focused on how deregulation affects aggregate measures of

economic activity such as state per capita income growth and its volatility (Strahan, 2003). More recent work has

turned to study deregulation’s competitive effects on small-firm finance and innovation (Rice and Strahan, 2010;

Cornaggia et al., 2013). We deepen existing work on the outcomes of banking competition by studying the value of

bank mergers at the merger level. When we aggregate to the entire banking industry, we estimate significant value

generated from the increased merger activity during our post-Riegle-Neal sample, a new and novel quantitative

indication that the prohibition of banking and branching across state lines was costly.

In addition, we also include other features of banking regulation in our specifications for the merger value

function. In particular, we allow the merger value function to depend on whether the acquirer and target have

different banking charters, and thus, report to different regulatory agencies before the merger. By including this

information in the merger value function, we recover the implicit costs of diverse chartering regulations from the

pattern of mergers. In this way, our results speak to the effects of inconsistent regulators, and are complementary

to the evidence presented by Agarwal et al. (2014). In a counterfactual exercise, we find that value generated

by mergers would be 20 to 50 percent higher per year if all banks were of the same charter type. This result

suggests that there are significant frictions in the bank merger market imposed by regulation.4 Once we rescale our

estimates by the fraction of banks that merge in a typical year, our counterfactual-estimated cost of bank chartering

regulation equals 1 to 2.5 percent of the value of the entire banking industry. This cost estimate reflects both

implicit and explicit costs as revealed by choices of the merging firms, and is of the same magnitude as explicit

annual supervisory costs (Whalen, 2010).

Because our approach uses the matching equilibrium explicitly in a structural model, the estimated match value

function we obtain can be used to predict bank mergers, even after the policy environment changes. A structural

approach like ours is particularly useful because matching market equilibria are sensitive to small perturbations in

payoffs and changes in the policy environment. In these cases, structural estimates can be used to more reliably

predict merger outcomes than analogous reduced form approaches. Indeed, the predictive strength of our structural

3Viewed from the perspective of the banking literature, these findings provide an external check on previous work that evaluated marketpower versus branching efficiency motives for bank mergers using stock market evidence (Rhoades, 1994; Seims, 1996). Notably, theexisting literature documents a takeover premium for acquired firms as in the broader merger literature (Rhoades, 1994; Eckbo, 2009),mergers do not appear to lead to significant changes to market concentration, and that there appears to be an efficiency motive for mergersbetween banks with significant overlap in markets (Seims, 1996).

4These frictions reduce value generated in the bank merger market because we find that – on balance – the mergers in our sample generatevalue. If the mergers that were obstructed by the frictions were value destroying, the regulatory frictions could actually increase value.

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method is borne out in the data. We compare the one-year-ahead predictive accuracy of our structural method to a

reduced form predictive regression that uses a binary logit and the predictors that make up our match value function.

We find that our revealed preference method dramatically outperforms standard predictive regressions, allowing us

to more reliably predict mergers one year ahead than a binary logit approach. Our method represents such a

dramatic improvement over reduced form predictive regressions partly because reduced form methods without

proper instruments are subject to endogenous matching. Our technique explicitly accounts for the endogenous

matching process, therby providing a more reliable basis for predicting mergers.5

The fact that we maintain the assumption that managers maximize firm value highlights a limitation of using

our revealed preference methodology. By relying on the choices of managers to identify what determines merger

value, the revealed preference method recovers the value created from the standpoint of managers, not necessarily

shareholders. Thus, whenever agency conflicts are important, revealed preference estimates of value creation are

a poor substitute for event study estimates, which more directly recover value created for shareholders. This

limitation is important to keep in mind when applying our methodology to study shareholder value or fundamental

synergies. Nonetheless, using our structural merger value function to estimate merger value creation, we estimate

an annual average of 6.02 percent of mergers that destroy value from the standpoint of the merged entity. Although

our estimates are based on the choices of managers, our magnitudes are similar to recent estimates of merger

synergies from the shareholder’s persective (Bayazitova et al., 2012).

Beyond being consistent with recent stock market evidence on merger synergies, several advantages of the

revealed preference method are important to emphasize. First, because it does not rely on stock market data, our

revealed preference method can be applied to mergers between two private entities when mergers and characteris-

tics data for private-to-private mergers are available, expanding the potential scope of analysis and inference. In a

similar vein, other authors have expressed interest in relaxing the dependence of merger value creation measures

on stock market data. Maksimovic and Phillips (2001) suggest an alternative method for evaluating the value of

mergers that does not rely on stock market information, by using productivity measures. More recently, Devos et al.

(2009) produced estimates of merger synergies from Value Line forecasts, which depend more directly on funda-

mental value creation. Our method shares the advantage of these methods without requiring a reliable measurement

5Although our method requires relatively few assumptions, a notable assumption we employ to apply our model to the bank mergerssetting is that the bank merger market is national immediately after the Riegle-Neal Act passed. This assumption is not literally true becausesome states lagged in their official adoption of the law’s provisions (see Johnson and Rice, 2008). We address this concern about thevalidity of our assumption and robustness of our method by estimating the match value function in each year of the sample. The predictiveaccuracy of our structural method outperforms the baseline binary logit predictive accuracy in every year of our sample (even in earlieryears), suggesting that to the extent the assumption is violated, the advantages of our structural method outweigh the costs. Appendix B.1presents and reports this exercise.

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of productivity or coverage by Value Line. Second, our structural model accounts for endogenous merger selection

directly, which enhances confidence that the characteristics that drive merger values actually drive merger values,

rather than a byproduct of the merger selection process. Finally, our structural method allows for counterfactual

exercises that are robust to changes in the policy environment. This feature of our structural exercise enables a

more accurate forecast of merger activity than alternative methods to predict mergers.

More broadly, our approach relates to recent work by Gorbenko and Malenko (2014) who estimate merger

valuations by explicitly modeling each merger as an independent auction using observed takeover bids. In con-

trast, our equilibrium-based approach implies that takeover bids are not independent, but are linked across targets

because each acquirer in the same merger market can bid on the same set of targets. We infer merger value by

the choices forgone by successful bidders, and as a result, our method does not require observation of successful

and unsuccessful bids by acquirers. This is an attractive feature of our setting when high bids by strong potential

acquirers discourage bidding from potential acquirers with slightly lower valuations, or when few formal bids are

solicited from strongest potential acquirers.

Our work also relates to a growing literature in industrial organization that employs revealed preference meth-

ods (e.g., Aguirregabiria et al., 2012). Notably, Chen and Song (2013) apply the Fox (2010a) estimator to the

matching between banks and firms, and find evidence of a positive assortative match between banks and firms.

To the extent that firms’ linkages with target banks are persistent, we should expect that these characteristics of

bank-firm matching would be relevant to acquirer-target bank matching, which is our focus. Indeed, that larger

targets likely have larger firms as clients is one reason to expect that acquirer and target banks mergers will also

exhibit the positive assortative match we document here.

More generally, our paper contributes to an increasingly-important segment of the empirical finance literature

that explicitly addresses endogeneity in financial markets research (Roberts and Whited, 2012). In the last decade,

structural approaches have yielded new insight into a wide variety of topics in finance, including debt dynamics,

corporate cash holdings, and the role of venture capital firms (Sorensen, 2007; Hennessy and Whited, 2005; Boileau

and Moyen, 2009). Relative to existing structural work in finance, our paper employs relatively few assumptions

to recover a structural value function. As a result, our method is conceptually straightfoward, and similar methods

to ours should find fruitful application to address important questions in financial economics.

The remainder of the paper is structured as follows. Section 1 presents our revealed preference method, and

uses Monte Carlo experiments to evaluate the estimator’s small sample properties. Section 2 describes the data and

basic summary statistics. Section 3 motivates and describes the form of our specifications. Section 4 is a discussion

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of the main results on value creation and the determinants of value creation. Section 5 discusses in-sample and

out-of-sample performance, compares to relevant alternatives, and presents a counterfactual simulation. Section 6

concludes.

1 The Revealed Preference Model

When analyzing merger value, it is instructive to observe that each acquirer deliberates among a number of viable

alternative targets, and each target considers viable offers from a number of alternative acquirers. In practice, targets

often entertain multiple takeover bids at the same time (e.g., see Bhagat et al., 2005), but these offers need not be

explicit to matter for the merger market decisions of targets and acquirers. Through this equilibrium channel, the

values of feasible alternative matches - both implicit and explicit offers - provide a lower bound for the value of each

realized merger. Our revealed preference approach formalizes this intuition by explicitly using the characteristics

of each bank’s alternative matches together with the observed acquirer-target transfers to estimate the value of the

mergers that do occur.

In our model of bank mergers as a two-sided matching game (Roth and Sotomayor, 1990), the merged acquirer-

target pair realizes a joint match value, which is split using an equilibrium transfer from the acquirer to the target.

Each bank matches with the bank on the other side of the market that maximizes its individual payoff. In equilib-

rium, matched banks receive a higher payoff from the observed match partners than they could get from counter-

factual partners.

In the model, we construct many possible counterfactual matches to each observed match within a matching

market, yielding many inequalities in the structural match value for each observed match. Given these inequalities

and a parametric form for the match value function, we choose the parameter vector that maximizes the fraction

of inequalities that hold. This is the maximum score estimator, which Fox (2010a) proved to be consistent for

matching games given a rank order condition (as in Manski (1975; 1985)).6 Building on Fox(2007; 2010a; 2010b),7

we develop a maximum score estimator that incorporates acquirer-target transfer data. Transfer data allow the

maximum score estimator to produce estimates on an interpretable scale, which is advantageous for understanding

6Fox (2010a) made separate consistency arguments for one large matching market and many independent matching markets. In the U.S.bank mergers setting for our sample time frame, we have 11 distinct matching markets, one for each year. We view each annual matchingmarket as a large matching market in the sense of Fox (2010a)’s one matching market asymptotic result, and the fact that we observe mergersfor multiple years allows us to estimate the match value function with even greater precision. Nevertheless, our year-by-year results relymore explicitly on the assumption of a large matching market that meets each year.

7The maximum score estimator proposed by Fox (2007) does not use data on transfers. The fact that the estimator works when transferdata are not available is an advantage if no data on transfers are available, which is true in many matching contexts.

6

the determinants of merger value creation.8

1.1 Matching Model

For a total number of My matches in matching market y, we denote acquirers by b = 1, ...,My and targets by

t = 1, ...,My. We assume there is one national merger market per year and markets in different years are independent

of one another. The merged pair (b, t) realizes a post-merger value f (b, t), which is the summation of the individual

payoffs to the acquirer and target, f (b, t) =Vb (b, t)+Vt (b, t).

The payoff to the acquirer Vb (b, t) is the post-merger value minus the acquisition price pbt paid to the target,

f (b, t)− pbt . The target’s payoff Vt (b, t) equals the acquisition price pbt . Each acquirer b maximizes Vb (b, t)

across targets. Each target t maximizes Vt (b, t) across acquirers. In the matching equilibrium, every bank derives

higher value from the observed acquirer-target match than from any counterfactual match. This revealed-preference

insight gives inequalities that we use in our estimation. For example, if acquirer b is matched with target t while

target t ′ could have been acquired by acquirer b, we infer that b derives more value from being matched with t than

with t ′, which gives the condition:

Vb (b, t) ≥ Vb(b, t ′

)f (b, t)− pbt ≥ f

(b, t ′

)− pbt ′ (1)

The transfer from acquirer b to target t ′ pbt ′ is not available from data on observed matches, but in equilibrium,

each target t receives an offer that is the same across acquirers. For acquirer b to acquire target t, the offer pbt

from acquirer b must be weakly greater than the offer pb′t from a competing acquirer b′. Acquirer b’s equilibrium

offer will not be strictly greater than the alternative because higher offer prices reduce acquirer b’s payoff. Hence,

pbt ′ = pb′t ′ and the inequality in (1). The same logic applies to acquirer b′, yielding the inequalities:

f (b, t)− f(b, t ′

)≥ pbt − pb′t ′ (2)

f(b′, t ′

)− f

(b′, t

)≥ pb′t ′− pbt (3)

The inequalities have a natural interpretation. For example, (2) means that the extra value that acquirer b derives

8In addition, we demonstrate that for parameters that are identified using the without-transfers estimator of Fox (2010a), our estimator ismore precise. We also demonstrate that our method identifies parameters that cannot be identified without transfer data, e.g., the sensitivityof the match value function to a change in some characteristic of the target bank.

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acquiring target t rather than target t ′ exceeds the extra expense of acquiring target t rather than target t ′. Equations

(2) and (3) are useful if we have data on transfer amounts, but these data are often unavailable. In the absence of

transfer data, we can add these inequalities to obtain a single inequality that does not rely on data from transfers:

f (b, t)+ f(b′, t ′

)≥ f

(b′, t

)+ f

(b, t ′

)(4)

This inequality implies that the total value from any two observed matches exceeds the total value from two

counterfactual matches constructed by exchanging partners.

1.2 Estimation of the Matching Model

Let εbt be a match-specific error that affects the value to acquirer b matching with target t. Then, acquirers and

targets match to one another according to the match value function F (b, t)= f (b, t)+εbt . As each acquirer can only

acquire one target, the acquirer’s choice among targets is a discrete choice. As a simple semiparametric technique

to estimate this discrete choice, we turn to maximum score estimation.9 Fox (2010a) developed a maximum score

estimator that makes use of inequality (4). Specifically, given a parametric form for the match value function

f (b, t|β ), one can estimate the parameter vector β by maximizing:

Q(β ) =Y

∑y=1

My−1

∑b=1

My

∑b′=b+1

1[

f (b, t|β )+ f(b′, t ′|β

)≥ f

(b′, t|β

)+ f

(b, t ′|β

)](5)

over the parameter space for β . For a given value of the parameter vector β̃ , Q(

β̃

)is the number of times

the inequality (4) is satisfied. The maximum score estimator β̂ , therefore, maximizes the number of times that this

inequality holds among the set of inequalities considered.10

Although attractive in its simplicity, the maximum score estimator based on (4) does not make use of transfer

data, which may significantly improve the performance of the estimator. Moreover, acquirer-specific or target-

9If we assume that the match-specific errors εbt are distributed iid Type 1 extreme value, the model reduces to the familiar multinomiallogit model. A significant weakness to the multinomial logit approach is that imposes a restrictive set of substitution patterns, for example,the red-bus blue-bus problem (McFadden, 1974; Debreu, 1960). An acquirer should be more likely to substitute between similar targets, yetthe multinomial logit model does not easily allow for this type of substitution. We explicitly contrast the performance of the multinomiallogit to our maximum score technique in Appendix (A.2). The appendix also considers another alternative, one-sided matching. In bothcases, our two-sided matching method that uses maximum score estimation is preferable.

10Fox demonstrates that one need not consider all possible inequalities to obtain a consistent estimator, but merely form a large subsetof all possible inequalities. Fox (2010a) shows that the maximum score estimator β̂ is consistent if the model satisfies a rank orderproperty (as in Manksi (1975; 1985)) for matching games – i.e., the inequality in equation (4) implies P [b acquires t and b′ acquires t ′] ≥P [b acquires t ′ and b′ acquires t]. In addition to providing intuition for conditions under which the maximum score estimator should beused, this strong version of the rank order property is used in the identification arguments given by Fox (2010b).

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specific attributes cancel out when we adding the inequalities (2) and (3) together to obtain (4). Therefore, any

parameters that measure the sensitivity of the match value function to target-specific attributes cannot be identified

with maximum score estimation based solely on without-transfers information.11

Both to improve the precision of the estimator and to identify the effect of target-specific attributes, we develop

a related estimator that uses transfer data, which we call the with-transfer estimator (WT1). We call the maximum

score estimator based on equation (4) the no-transfer-data (NTD) estimator.12

For the same pairwise comparisons used to form the objective function for the NTD estimator, the WT1 estima-

tor imposes the inequalities (2) and (3) simultaneously. If both (2) and (3) hold, (4) holds as well, but the converse

is not true. The WT1 estimator maximizes the objective function:

Qtr (β ) =Y

∑y=1

My−1

∑b=1

My

∑b′=b+1

1[

f (b, t|β )− f(b, t ′|β

)≥ pbt − pb′t ′ ∧ f

(b′, t ′|β

)− f

(b′, t|β

)≥ pb′t ′ − pbt

](6)

In the appendix, we perform a series of Monte Carlo exercises to evaluate the properties of the with-transfers

estimator (WT1), finding that our with-transfers estimator performs well relative to a number of notable alterna-

tives.13 Relative to the without-transfers estimator of Fox (2007), we confirm two main advantages: (1) transfers

data allow for much greater precision in estimating determinants of merger value creation, and (2) the with-transfers

estimator can identify parameters that are otherwise unidentified without data on transfers - namely, target-specific

determinants of merger value creation.

1.3 Interpretation of Estimated Merger Values

It is important to clarify the interpretation of estimated merger values from our framework. Because we rely heavily

on manager choices to infer merger value creation, our approach recovers the value created from the standpoint of

the managers of the firm. Given this, if the managers maximize shareholder value, revealed preference estimates of

merger value creation are a good substitute for stock market estimates. On the other hand, when agency problems

11This point only applies to target-specific attributes. The sensitivity of match value to acquirer-specific attributes is unidentified in thisrevealed preference model. This is straightforward to see in equations (2) and (3). For example, the difference on the left hand side of (2)refers to the same acquirer, and thus, anything characteristic in the value function that is acquirer specific is differenced out of the revealedpreference inequalities.

12We have also considered an alternative with-transfers estimator (WT2) that imposes inequalities (2) and (3) separately, but this estimatordoes not perform as well in the Monte Carlo experiments as WT1. In the appendix, we also describe a quadratic loss specification wheredifferences between target and acquirer are penalized, and a cross-attribute specification in which asset× branches interactions are allowed.

13In addition, the appendix reports a comparison of the with-transfers estimator to a multinomial logit specification along the lines ofMcFadden (1974), and find that our structural method has greater precision. We also relax the assumption that mergers occur in a matchingmarket with two sides (acquirers and targets) in favor of a weaker assumption that each bank that merged could be on either side of themerger market. Our method based on two-sided matching exhibits strikingly similar performance as this one-sided matching model.

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between managers and shareholders are important (e.g., empire building motives), manager-centric values from a

revealed preference approach will correspond less well with changes in shareholder wealth.

In addition, even if there are no agency conflicts between shareholders and managers, greater cross-ownership

of acquirer and target firms by institutional investors (as is studied by Matvos and Ostrovsky, 2008) reduces the

cost of large acquirer-to-target transfers from the standpoint of shareholders. In this context, managers who well

represent the preferences of their institutional shareholders view transfers as less costly than they appear from the

standpoint of our methodology. In our methodology, a merger that occurs despite a high transfer price is inferred to

have high synergy. As such, mergers with a high degree of cross-ownership will tend to have greater merger values

inferred from revealed preference. These high estimated merger values arise because of synergies in who owns the

firms, not necessarily because of fundamental synergies in the underlying firms.

With these caveats in mind, our revealed preference method is an effective method to use when studying the

motives of managers to undertake corporate decisions, but to the extent that there are agency conflicts, future

research should be cautious in applying the insights from revealed preference to the value created for shareholders

or to fundamental synergies. On the other hand, our revealed preference estimates of merger value creation are

manager-centric, which implies that they may be more appropriate for recovering merger synergies that are more

salient to managers than to shareholders.

2 Description of Data

2.1 Merger-Deal Data

We study the matching market for banks using comprehensive bank merger and attribute data from SNL Financial.

The data span all bank mergers in the United States between 1995 and 2005 and provide information about acquirer

and target banks at the merger-deal level. For the date at which the acquisition is announced, the data provide the

asset holdings (Ab and At) and number of branches (Bb and Bt) for both acquirer and target bank. We also observe

the market value of the transfer (pbt) from the acquirer bank to the target bank upon merging.

SNL Financial’s database also provides data on several performance measures of acquirer and target banks.

These performance measures are the efficiency ratio (non-interest expense / (net interest income + other income))

and the loan loss reserve coverage ratio (loan loss reserves / nonperforming loans).14 As the information on these

14The data also contain the price to book ratio (stock price/ book value) of target bank at the time of merger as long as the bank is apublicly traded company. Restricting the sample of mergers to those where the target is publicly traded leaves too few observations to obtainreliable estimates.

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performance measures is not available for every merger deal in our sample, we employ these measures in auxiliary

specifications that serve to check the robustness of our main findings, and also to speak directly to managerial

motives to merge. In addition, we also construct a measure of deal value at the merger-deal level to use as the

equilibrium transfer pbt in our with-transfers estimator.15 Figure 1 portrays the distribution of deal values in our

sample in a density plot of logged deal values. From the figure, the distribution of logged deal values is well-

behaved and symmetric.

2.2 Bank and Branch Attribute Data

The FDIC Summary of Deposits Banking Database gives the deposit holdings as of June 30th of each year and the

location – specifically, Metropolitan Statistical Area (MSA) and state – for each branch of each banking institution

in the United States from 1995 to 2005. Table 1 presents summary evidence on the merger-induced consolidation

in the banking industry. From 1995 to 2005, the number of banking institutions declined from 10,416 to 7,582

while the average number of branches per bank increased from 7.81 to 12.50. The consolidation is not merely

taking place among a few large banks, as is indicated by trimmed mean of branches per bank, which has increased

by nearly 50 percent over this period.

The Summary of Deposits Database also provides information on the regulatory agency responsible for over-

seeing each bank, which depends on the bank’s charter. Banks can adopt either a national charter or a state charter.

If the bank has a national charter, it is regulated federally16 and it must become a member of the Federal Reserve,

which adds an additional layer of audits in exchange for the liquidity provided by being a member of the Federal

Reserve system. Additionally, the FDIC serves as a back-up regulator to all banks with national charters. If the

bank has a state charter, the state regulatory agency is responsible for audits and the FDIC is the primary federal

regulatory.17 A number of mergers in our sample took place between acquirer and target banks with different

charter types. To empirically assess the importance of this regulatory friction, we construct an indicator variable

samecharterbt , which equals one if the acquirer and target have the same type of charter.

At the MSA level, we construct the market share of each banking institution using its fraction of total deposit

15We measure deal value as aggregate price paid for the equity of the entity sold in the transaction, as of the event in question. Whereavailable, deal value is calculated as the number of fully diluted shares outstanding, less the number of shares excluded from the transaction,multiplied by the deal value per share, less the number of "in the money" options/warrants/stock appreciation rights times the weightedaverage strike price of the options/warrants/stock appreciation rights. Deal value excludes debt assumed and employee retention pools.

16Depending on the type of institution during our sample time frame, one of two federal regulatory agencies may be responsible forregulating a bank with a national charter: the Office of Thrift Supervision (OTS), which regulates savings banks and savings and loansassociations; The Office of the Comptroller of the Currency (OCC), which regulates national banks.

17State-chartered banks can also become members of the Federal Reserve system, but in practice, most state-chartered banks do not. Thissuggests that there is a tradeoff between the benefits provided by the Federal Reserve and the auditing requirements.

11

holdings in the MSA. Using these market shares, we calculate this MSA-level Herfindahl Hirschman Index (HHI)

before and after each merger, which allows us to assess whether a merger meets the criteria for additional scrutiny

under the U.S. Antitrust Guidelines (HHI > 1800 and ∆HHI > 200). We compute each MSA’s HHI by taking the

sum of squared market shares. Using this information, we construct a merger-deal level covariate HHIviolatebt ,

which equals the fraction of target t MSAs for which a merger with acquirer b would lead to Antitrust scrutiny

under the Department of Justice’s Merger Guidelines.

Finally, for acquirer and target branches within MSAs, the FDIC geography identifiers allow us to construct a

merger-deal level covariate overlapbt , which equals the fraction of overlapping MSA markets for the acquirer and

target banks. We construct this variable for each potential merger and estimate its contribution to the match value

function.

3 Estimation

3.1 Determinants of Match Value

During our sample period (1995-2005), bank mergers were potentially motivated by some combination of effi-

ciencies,18 merging to acquire and exploit market power, and acquiring better performing branches to improve the

bank’s overall performance.19 Together with our data on institution size and performance (see Section 2.1 for de-

tails on performance measures), we estimate how efficiencies and market power separately affect the bank merger

match value function. A number of these determinants of bank merger value are target-specific. Thus, the ability

of the with-transfers estimator to identify target-specific determinants of merger value is important.

After the 1994 Riegle-Neal Act, mergers were often motivated by creating national banking networks that are

less sensitive to local economic shocks, and more valuable to consumers. To this end, there are obvious advantages

to banking with a bank with a wider geographic footprint, as Anil Kashyap noted in 1998, “If you are a BofA

customer, you won’t have to pay transaction fees at ATM machines since there’ll be one in every city you go to”

18Using data from the pre-Riegle-Neal era, Kroszner and Strahan (1999) demonstrate that new banking technologies for both deposit-taking and lending increased the geographic scale of banking. Our sample time frame (1995 – 2005) occurs during a period of rapidinnovation in Internet technology, which increases the efficient scale of banking beyond the ATM and credit history technologies describedby Kroszner and Strahan (1999). Thus, economies of scale are as relevant for bank mergers in our time period as they were for the geographicscale of banking in Kroszner and Strahan (1999).

19At the time of our sample, industry experts pointed to efficiencies (or reductions in inefficiencies) from cross-state mergers, and deem-phasized the role of market power as a motivator for merging (Marshall, 1998). Nevertheless, we consider this hypothesis by includingmarket power terms in the match value function. In a 1998 newsletter to the Federalist Society (Financial Services & E-Commerce Newslet-ter - Volume 2, Issue 2, Summer 1998), James Rockett makes the point that the purported merger mania after the Riegle-Neal Act was - inpart - motivated by achieving better stock market performance and improving balance sheets. To the extent that our measures of financialperformance of targets and acquirers, we can assess whether these were primary motivators.

12

(Marshall, 1998). As an alternative to opening new branches, mergers are an effective way for a bank to achieve

a large, national banking network. We account for this large-banking-network motivation to merge by including

interactions between target and acquirer banking attributes (assets and branches) in our specification of the match

value function.

A merger between two banking institutions will also generate cost efficiencies (or inefficiencies) unrelated to

the size of the network of branches. If economies of scale are easier to capture in banking markets familiar to the

acquiring bank, the match value between an acquirer bank and a target bank will tend to increase with the fraction of

overlapping markets (captured by overlapbt). On the other hand, Aguirregabiria et al. (2012) document significant

potential to diversify geographic risk post-Riegle-Neal by expanding into new markets. Thus, the effect of overlap

on bank merger value will tend to be negative to the extent geographic diversification of risk is an important motive

for bank mergers. Thus, the ex ante relationship between overlapbt and match value is an empirical question that

speaks to whether geographic risk or economizing on local efficiencies is more important.

To address the extent to which the degree of market concentration increases merger match value, we include

the average HHI of the target bank’s markets as a component of our match value function. Moreover, to the degree

that antitrust regulation tempers this incentive to merge, we also include the fraction of target markets that would

warrant antitrust scrutiny (HHIViolatebt) in our match value specifications. In the middle of this merger wave,

however, industry experts did not consider market power to be an important explanation for the large number of

mergers during our sample period.20 Nevertheless, including these terms in the match value function allows us to

assess the market concentration hypothesis directly.

3.2 Functional Form for the Match Value Function

To use the maximum-score estimator, we specify a parametric form for the value of a match between target t and

acquirer b.21 For the match-value function, we follow existing empirical work on matching markets (e.g., Fox 2007

and Chen and Song 2013), and evaluate the degree and direction of assortative matching using interactions between

acquirer and target attributes. Exploiting the ability of our estimator to identify non-interacted parameters, we also

20“Most experts believe a merger between two huge banks operating in different parts of the country – such as NationsBank and BofA –is unlikely to harm consumers by reducing competition, unlike a consolidation of banks in one local market” (Marshall, 1998).

21As different specifications for this functional form focus on different features of the matching between acquirer and target, we evaluatethe robustness of our conclusions to several related specifications for the match value function in the maximum-score estimation in AppendixA.

13

extend the specification to include target-specific attributes:

F (b, t) = β1WbWt + γ′1Xt + γ

′2Xbt + εbt (7)

where Wb is an attribute of acquirer b and Wt is the same attribute for target t, Xt contains target-specific covariates,

Xbt is a vector of match-specific covariates and εbt is an unobserved match-specific error term that we assume is

independent across matches in our data set. We estimate several variations on this basic specification, adding to

the match function in (7) interaction terms for additional attributes. Using the transfers data with our with-transfers

estimator allows us to identify γ1 , which is unidentified in the without-transfers estimator.

3.3 Subsampling Confidence Intervals

We generate point estimates by running the differential evolution optimization routine from 20 different starting

points and selecting the coefficient vector that yields the highest value for the maximum score objective function.22

For valid inference, we generate the confidence intervals using the subsampling procedure described by Politis and

Romano (1992) and Delgado et al. (2001) to approximate the sampling distribution. For the entire data set, we set

the subsample size to be 500 – approximately 1/3 to 1/4 of the total sample size. Of all samples of size ns = 500

drawn from the original data set (N observations), we select at random 100 of these samples for use in constructing

the confidence bounds.

For each of the S = 100 subsamples, we compute the parameter vector that maximizes the objective function in

(6). Call the estimate from the sth subsample β̂s and the estimate from the original full sample β̂ f ull . The approxi-

mate sampling distribution for our parameter vector can be computed by calculating β̃s =(ns

N

) 13(

β̂s− β̂ f ull

)+ β̂ f ull

for each subsample. This procedure accounts for the 3√

N convergence of the maximum score estimator (Politis and

Romano, 1992; Delgado et al., 2001). We take the 2.5th percentile and the 97.5th percentile of this empirical

sampling distribution to compute 95 percent confidence intervals for all of our estimates.

22(Fox, 2007) argues that the maximum score estimator is consistent if we randomly sample a sufficiently large number of inequalities toimpose rather than the full number of inequalities (which is often intractably large). Relying on this insight, for each specification we run in

this paper, we sample 40 acquirer-target pairs from each year and form the(

402

)inequalities implied by their matching.

14

4 Main Findings

This section presents the results from estimatingseveral specifications of the match value function in order to better

understand the determinants of value creation in the merger market. The most robust determinants of merger value

creation are lower regulatory frictions, cost efficiencies from overlapping markets, and network effects exemplified

in the assortative matching between acquirers and targets.

4.1 Bank Size, Market Concentration, and Overlap of Markets

Table 2 presents results from estimating the revealed preference model with merger value function given by equa-

tion (7). In every specification in Table 2, the coefficient estimates on the interactions between acquirer and target

assets (branches) are positive and statistically significant.23 This finding suggests that large acquirer banks tend

to match with larger target banks, and that this pattern of matching is revealed to be valuable by the pattern of

potential mergers that did not occur. For example, the estimate on the interactive term in column (2) implies that

a 10 percent increase in the number of acquirer branches is associated with a $408,000 increase in the effect of

an additional target branch on merger match value. This interactive effect remains significant whether or not the

match value function includes target assets and the interactive term between acquirer and target assets. Although

the magnitudes vary across specifications, the interpretation in the context of the observed match is that the match-

ing equilibrium exhibits a strong positive assortative match on both branches and assets, a finding that is consistent

with the conventional understanding that mergers during this time period (1995 to 2005) were motivated by taking

advantage of large national networks.

Across specifications in Table 2, the estimates for the own effect of target assets and branches is negative across

specifications, and these own effects tend to be statistically significant. This finding together with the consistently

significant interactive effects suggests that a larger number of assets and branches in the target bank contributes

positively to the match value, but not independently of the size of the acquirer bank. Taken together, the result

suggest that a network of branches and customers is more valuable on average as the size of the network grows,

suggesting that an acquirer with many branches and customers would derive disproportionately more value from

a large target, ceteris paribus. On the other hand, there is a cost to managing more assets and branches. This

cost shows up in the coefficient estimates on target attributes, which are consistently negative and statistically

significant.

23We take statistical significance to mean that the 95 percent confidence interval from subsampling does not contain zero.

15

In the final two columns of Table 2, the positive and significant estimates for overlapbt suggest that banks

derive significantly more match value if the acquirer and target have more overlapping markets. Relative to having

no overlap in MSA markets, the estimate in column (4) implies that an acquirer and target with complete over-

lap in MSA markets will realize a nearly $1 million ($967,440) increase in the merger match value. Because our

specifications account for market concentration, this finding suggests that the merging banks can realize operating

efficiencies better when the target and acquirer banks have branches in the same MSA. The magnitude of this es-

timate is sensible given previous estimates to operate a bank branch. In a different context, Radecki et al. (1996)

estimate that the total costs of operating a branch are around $1.4 million annually with indirect costs (e.g., ad-

vertising, and computing systems) amounting to half of that. Given this estimate holds constant the number of

branches as another predictor in the match value function, these efficiencies more likely represent cost savings on

indirect costs like advertising that can be spread across multiple branches than cost savings from branch closures.

To the role of market concentration, the positive estimate on target bank’s average HHI suggests that greater

market concentration increases the match value, consistent with greater market concentration allowing the com-

bined bank to extract additional profit. On the other hand, having a higher fraction of MSA-level markets that

would justify antitrust scrutiny (i.e., greater HHI Violation Fraction) does not seem to either detract from the match

value nor add to it. As column (5) demonstrates, this finding on insensitivity of the match value function to the

HHI violation fraction is robust to controlling for the target bank’s average HHI. Taken together with the results on

assortative match and overlapping markets, the results from these specifications indicate that both efficiency and

market power rationales to merge create value for the merger.

4.2 The Role of Pre-Merger Target Performance

We also allow the match value function to depend on performance measures of targets: the efficiency ratio (nonin-

terest expense/ income) and the loan loss reserve coverage ratio (loan loss reserves/ nonperforming loans).24 We

include these performance measures to assess the importance of efficiency and distress in merger value creation.

Given existing work on agency and merger activity, this is a natural line of inquiry. Although merger value could

depend on the target’s operational performance for efficiency reasons (e.g., see Maksimovic and Phillips (2001)),

the performance characteristics of targets could proxy for agency frictions in the acquirer, and thus be related to

merger value creation through that channel.

24These measures are available from SNL Financial, but not for the same set of banks. As such, including all measures at once reducesthe number of observations in the specification to the point where identification is questionable. Thus, we evaluate the contribution of eachof these categories in isolation of the other.

16

In Table 3, we report specifications for merger value that include these measures of performance, and across

specifications, there is not a significant relationship between merger value and pre-merger target performance.

Nonetheless, the qualitative findings of Section 4.1 remain true regarding assortative matching and overlap of mar-

kets. These matching and branching efficiency motives to merge appear to be robust, while performance measures

do not appear to systematically affect merger value. Thus, it appears that the consolidation of banking institutions

during our sample reflects the relaxation of regulation and efficiency motives (e.g., assortative matching and greater

geographic overlap of markets).

4.3 The Role of Bank Regulation

We now use our model to quantify the implicit costs of bank chartering through frictions in the bank merger market.

To evaluate these implicit costs, we allow the merger value function to depend on a dummy variable samecharterbt

that equals one if the acquirer and target have the same type of charter, and thus, are regulated by the same regulator.

We also include an interaction between samecharterbt and overlapbt . The interactive effect is reasonable if having

different charters complicates dealings with multiple types of regulators, especially if the regulation impacts the

cost efficiencies realized in overlapping markets. Agarwal et al. (2014) study a similar regulatory friction in the

context of small state chartered banks that are audited on a rotational basis, finding there are costs to adjusting

to different types of regulators. Agarwal et al. (2014) document costs of inconsistent regulators in the context of

rotational regulation, suggesting in that context that window dressing for the regulator can be costly because it leads

to artificial variability in operations. In the merger context, we evaluate whether there are implicit costs of having

to adapt to a new regulatory regime that are reflected by the choices of the merging banks.

Table 4 presents evidence on the role of bank charter type in determining merger value creation. When we

include the samecharterbt dummy variable, the coefficient estimate is large and positive, but not statistically sig-

nificant. The estimate implies an increase in merger match value of $158,450 on average if the target and acquirer

banks have the same charter. When we include the interaction of this dummy variable with the percentage of over-

lapping markets, the coefficient is large and statistically significant. This finding suggests that the match between

banking charters is more important for geographically overlapping banks. More concretely, for a target and ac-

quirer whose MSA markets completely overlap, having the same charter increases match value by $743,000, and

this increase is statistically significant. More generally, this finding suggests that a match between bank charters

can contribute to the value of the merger by avoiding these regulatory frictions, especially as a bank has branches

in more markets, and thus, greater overlap with potential targets.

17

4.4 Evidence on Merger Value Creation

The fitted values from our merger value function provide merger-specific estimates for value creation from the per-

spective of the merging banks. Thus, subject to the caveat that our measure of merger value is from the perspective

of the firm’s managers, this section takes our estimated merger value function to reflect underlying shareholder

value.25 As evidence on the degree to which unmeasured characteristics (e.g., agency frictions) destroy merger

value, Table 5 presents summary statistics on the fraction of mergers that we compute to have negative merger

value. On average, only 6.02 percent of mergers in a given year yield negative match value, and in every year of

the sample, the lost value from these mergers is less than one percent of overall merger value creation. These es-

timates indirectly yield insight into scope for value-reducing agency problems in the merger market. For example,

if a merger appears to reduce value according to our measure – accounting for cost efficiencies, market power, or

network-enhancing benefits – this could indicate a manager-shareholder agency problem (e.g., see Harford et al.

(2012)).

Our revealed preference estimate of merger synergies may either overstate or understate the true fraction of

value of synergies. On one hand, this measure could overlook some value destroying mergers in which the transfer

appears less costly to the merging firms because of significant overlap in ownership of acquirer and target (Matvos

and Ostrovsky, 2008).26 On the other hand, our specification for merger value creation may not capture some

types of merger-specific synergies. To the extent these synergies are unmeasured and enhance the profitability of

mergers that look unprofitable according to our measures, our revealed preference method will tend to understate

the frequency of value destroying mergers because it will classify some of these mergers as negative value when

they create value for unmeasured reasons. The fact that these estimates of value destruction in mergers are close

to recent estimates using stock market evidence provides additional confidence in the validity of these estimates

(Bayazitova et al., 2012).

25In addition, Appendix B.2 presents an analysis of acquirer-specific value, which nets out the transfer from the overall value created.The fraction of mergers that destroy acquirer-specific value is greater than is discussed in the main text, but is not strikingly greater (fractionof value destroying mergers rises to 6.93 percent instead of 6.02 percent).

26Despite this being an important consideration, there is less concern arising from potential cross-ownership for mergers that involveprivate banks (the typical case) because these kinds of mergers have less cross-ownership. The number of merger observation drops by 22percent ( 1484−1158

1484 ) when requiring the acquirer to be publicly traded. Targets are even more likely to be privately held, with about half ofthe sample of targets being private.

18

5 Robustness and Extensions

5.1 In-Sample Performance of Merger Value Function

Our framework allows us to compute a number of measures that allow us to evaluate the in-sample performance

of the revealed preference method. To evaluate our revealed preference model, we benchmark against the optimal

computed match as we did in evaluating the extent of merger value creation in the bank merger sample. We compute

five measures of fit for our merger value function: (i) the fraction of mergers for which the realized match has the

highest computed match value (Highest Value), (ii) the fraction of mergers for which the realized match is the same

as the optimal pattern of mergers (Same Match), (iii) the average percentile rank of the observed matched target in

the rank-order list of acquirers (Avg. Rank), (iv) the correlation coefficient between the actual deal values and the

equilibrium transfers computed from the linear programming problem in (8) (Price ρ), (v) the fraction of realized

merger value relative to the merger value created in the solution to the linear programming problem in (8) (% of

Optimal Value). Greater values for each of these measures implies better performance of the estimated merger

value function in sample.

For each year in our sample, Table 6 summarizes these measures of performance. Same Match ranges from

0.118 to 0.355, but it is relatively stable across years with an average of 0.261. Contrast Same Match with the

Highest Value (a naive measure of fit), which ranges from 0.03 to 0.27 during our sample time frame, and averages

0.13. The Highest Value fraction is lower for in-sample predictions because some targets would generate the highest

value for multiple acquirers, but this is not possible in equilibrium. Our equilibrium measure of fit (Same Match)

accounts for this, and as a result, the model correctly predicts observed matches where the acquirer-target match

does not generate the highest value for the acquirer (but where that acquirer’s highest value target is assigned to

another acquirer who values the target more highly), as is indicated by the greater success rate of Same Match.

Using average rank in the acquirer’s rank order list, we observe a measured Avg. Rank ranging from 0.70 to

0.84 across years, with an average of 0.79 . Thus, when the estimated match value is not precisely at the top for the

observed match, it is very often near the top of match values. By this measure, the fit of the model appears to be

quite good. The advantage of an out-of-equilibrium measure of fit like Avg. Rank is that it is easy to compute, but

their disadvantage is that it does not account for the effect of small perturbations in value on the matching market

equilibrium.

Given the closer link to the underlying equilibrium of Same Match, one way to evaluate the relative validity

of these out-of-equilibrium measures of fit is to compute their correlation across years with Same Match. The

19

correlation between the Highest Value and Same Match is only 0.209 while the correlation between Avg. Rank and

Same Match is greater at 0.396 . On this basis, we may prefer Avg. Rank to Highest Value for in-sample measures

of it.

In our fourth assessment of the performance of the estimates from the revealed preference model, we compute

the correlation between the actual transfer amounts to the equilibrium transfer prices from the dual of the linear

programming problem. Regardless of the year considered, the high correlation between actual transfer amounts and

the transfers from the linear programming problem, ranging from 0.715 to 0.996 indicates that our model replicate

the transfer amounts quite well.

Finally, we contrast the observed set of mergers with this computed optimal pattern of mergers by computing

the total match value under the observed equilibrium and compare it to the total match value in the solution to the

linear programming problem. The implied value of mergers for the observed matching is meaningful, ranging from

$93 million in 2002 to $1.96 billion in 2004. By this metric, the actual mergers produce 72.1 to 97.1 percent of the

optimum of the linear programming problem with an average of 85.0 percent. This small scope (15 percent) for the

amount of value destroyed is a conservative estimate of the amount of value left on the table from agency issues

and optimization error because the optimal solution to the linear program may overfit the particular characteristics

of the sample while the realized mergers may account for merger-specific synergies that, in reality, create value.

From this standpoint, the merger value function we estimate fits quite well.

5.2 Comparison to Binary Logit Regression

Another way to assess our revealed preference method is to compare its predictive accuracy to the performance of

a binary logit regression that uses the same set of regressors. To implement the binary logit regression, we need

to construct a data set of counterfactual and observed mergers with all of the information we used in our revealed

preference model. On this data set, we use binary logistic regression to predict whether an acquirer-target pair

was an observed merger using the features of our match value specification as the right hand side of the logistic

regression.

We use the fitted values from the logistic regression to predict which target the acquirer will acquire. For each

acquirer, the target with the largest fitted value is predicted to merge with the acquirer. Using this rule, we find that

logistic regression performs dramatically worse than our revealed preference method. As the fraction of successful

predictions in Table 7 indicate, binary logistic regression successfully predicts slightly greater than one percent of

observed mergers, as compared to a yearly average of 26 percent using our reduced form method (see Table 6).

20

We attribute the significantly-better performance of our method to the fact that we explicitly take into account the

nature of equilibrium in the bank merger market. Not only does this provide our method with an improved ability

to relate our estimates to economic theory, the comparison to predictive logistic regression suggests that we achieve

significant gains in predictive accuracy.

5.3 Out-of-Sample Fit and Predicting Mergers

A notable extension of our framework is to estimate a merger value function and use it predict mergers that will

subsequently take place. The year-by-year estimates suggest that we could estimate the merger value function using

observed and counterfactual mergers from year T −1, then roll forward our estimated merger value function to date

T to predict the mergers that are most likely to take place.

With an estimated match value function, we can evaluate the match value for realized mergers as well as for

counterfactual mergers (a hypothetical merger between the acquirer and another target). To evaluate the ability of

the model to predict mergers, we estimate the match value using the estimates from the previous year, and then

assess the model fit using the measures of fit we discussed in the previous section.

Table 8 summarizes our ability to predict mergers out of sample. As expected, the Same Match column indicates

that our ability to predict mergers out of sample is worse than the in-sample fit. Specifically, the average fraction

of correct predictions across years is 0.032. This fraction of correct predictions as well as the drop off in out-of-

sample predictability is comparable27 with other recent work on the ability to predict mergers in and out of sample

(Cremers et al., 2009). In addition, the correlation of the prices from the dual of the linear programming problem

with actual prices remains high (ranging from 0.625 to 0.997). That is, the model appears to predict the pattern of

transfers better than the identity of the participants.

Table 8 also illustrates why it is unwise to use non-equilibrium measures of fit (Highest Value and Avg. Rank)

in the two-sided matching setting. Using the Highest Value fraction and Avg. Rank as our measures of fit, the

out-of-sample fit appears to be on par with the in-sample fit. Nevertheless, these measures do not account for the

fact that small perturbations in the payoffs can lead to large changes in the observed match. Even if the differences

in match value do not reorder the preference ordering for each particular acquirer, they can change the intensity of

preference, and this can change the allocation. Our equilibrium measure of fit accounts for this kind of reordering,

and hence, it is more realistic about the out-of-sample validity of the model.

27For example, Cremers et al. (2009) construct a takeover factor, which together with the market factor, exhibits a cross-sectional R2 of0.1339. When the authors consider out-of-sample predictions similar to what we do in this section, their R2 drops to 0.0403.

21

5.4 Counterfactual Evidence

As we saw in our bank charter specifications, an important aspect of the bank merger market is the match between

type of banking regulation that applies to target and acquirer banks. Our specifications in Table 4 implied that

acquirer and target banks with the same type of charter experience a premium in their match value. This premium

reflects a cost of multiple types of bank charters. In this section, we report the findings from a counterfactual

simulation where we impose that all banks have the same charter. Our findings suggest a sizable cost of the dual

chartering system, which manifests itself in fewer mergers between banks of different chartering types.

Table 9 reports the results from our counterfactual simulation. Relative to the baseline where banks may have

different charters (and hence different regulatory agencies), the number of acquirer-target pairs that go unmatched

declines slightly, and the total match value is significantly larger when there is no distinction between the charter

types, typically a 20 to 50 percent increase in the total estimated match value of bank mergers for any given year.

Despite its large magnitude relative to banks that merge in a particular year, our estimated magnitude of 20 to

50 percent of the match value reflects a much smaller fraction of the banking industry as a whole. We observed

approximately 200 mergers per year relative to a total number of banks from 7,000-10,000.28 Rescaling our esti-

mate by the fraction of banks that merge in a typical year in our sample, our counterfactual-estimated cost of bank

chartering regulation equals 1 to 2.5 percent of the value of the entire banking industry. To put this estimate in

context, 1 to 2.5 percent is slightly larger, but on the same order as the annual supervisory fee paid by national

banks. For example, see calculations in Whalen (2010), Table 1, which report that supervisory fees for national

banks average $21,000 for a bank with $25 million in assets, and $48,000 for a bank with $100 million in assets.

In percentage terms, this amounts to approximately 0.5 percent to nearly 1 percent.

The implied effect reflects direct costs of additional regulation and the costs imposed by compliance with

diverse chartering rules, as well as foregone opportunities when these costs stand in the way of a merger between

a state bank and a national bank. Consider the example of a state acquirer bank and a national target bank with

branches in multiple states. The potential merger may be advantageous due to an otherwise large overlap of markets

and similarity of assets and branches, but the national bank has branches in another state. In this case, the state

bank must decide whether it will learn and comply with federal charter regulations (either for the acquired branches

or for the bank as a whole), or if upon acquisition of the national bank, it will divest of holdings in other states in

order to bring the entire bank under the original state charter. In either case, this is a significant friction in the bank

28For this calculation, take 400 merging banks from 200 mergers, and use 8000 banks as the size of the overall industry.

22

merger market.

6 Conclusion

In the context of bank mergers, this paper develops a novel technique to estimate merger value creation without

relying on stock market information. We do so by exploiting the features of a matching market equilibrium between

acquirer and target banks. The fact that our approach does not rely on stock market information to recover estimates

of value creation is particularly advantageous when at least one of the parties involved with the merger is private.

When we evaluate the determinants of merger value creation, bank mergers appear to be motivated by branching

efficiency and competitive concerns, rather than pre-merger performance of the target or the threat of antitrust

regulation.

Despite its simplicity, our method is useful for predicting mergers. We obtain a structural estimate of the

match value function that allows us to forecast the value of potential bank mergers based on characteristics of the

target and acquirer bank. Our analysis shows how to use the revealed preference methodology to forecast which

mergers will occur. In our sample of bank mergers, we find that the revealed preference method outperforms

relevant alternatives (e.g., binary logit) partly because reduced form analysis without proper instruments is subject

to endogenous matching, while our structural method explicitly accounts for matching endogeneity.

Consistent with recent work by Agarwal et al. (2014), our specifications suggest that significant implicit costs

are imposed on banks through regulation. The fact that banks with national charters are subject to different regula-

tory procedures than banks with state charters imposes a friction in the bank merger market that prevents mergers

between banks of different charter types. From our counterfactual exercise, we estimate that the cost of bank char-

tering regulation amounts to 20 to 50 percent of the value created by bank mergers in a typical year. Rescaled by

the number of banks that merge in a given year, this amounts to a cost of chartering regulation of 1 to 2.5 percent

of the value of the banking industry. The regulatory friction from dual chartering is costly because the mergers

it prevents are value creating, on average. In settings where mergers are value destroying, similar frictions in the

merger market could be beneficial, rather than harmful, because they would prevent value destroying mergers at

the margin.

This paper is part of an emerging literature that uses the structure of matching markets and networks in research

on financial markets (Sorensen, 2007; Akkus et al., 2013; Chen and Song, 2013; Ahern and Harford, 2014). As

matching processes are ubiquitous in financial markets and endogeneity frequently confounds finance research

23

(Roberts and Whited, 2012), we expect techniques that leverage the structure of matching in financial markets will

play an increasingly important role in finance research going forward.

24

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27

Tables and Figures

Figure 1: Distribution of Deal Values in the Bank Merger Sample

Note: This plot portrays the distribution of logged deal values in the sample of observed mergers. Deal value is defined as aggregate price

paid for the equity of the Entity Sold in the transaction, as of the event in question. Where available, Deal Value is calculated as the number

of fully diluted shares outstanding, less the number of shares excluded from the transaction, multiplied by the deal value per share, less the

number of "in the money" options/warrants/stock appreciation rights times the weighted average strike price of the options/warrants/stock

appreciation rights. Deal Value excludes debt assumed and employee retention pools.

Table 1: Consolidation in the U.S. Banking Industry (1994 to 2006)

Year Num. Banks Avg. Branches Tr. Avg. Branches max1994 10416 7.81 2.71 20241995 9825 8.24 2.81 20281996 9422 8.64 2.91 20521997 9110 9.01 3.03 26431998 8744 9.53 3.14 31321999 8449 9.98 3.24 45792000 8324 10.27 3.33 45102001 8175 10.53 3.43 43292002 8031 10.78 3.54 43342003 7877 11.15 3.66 42962004 7756 11.58 3.74 58352005 7644 12.04 3.83 59142006 7582 12.50 3.94 5789

Source: FDIC Summary of Deposits Database. Trimmed averages are computed by dropping the top and bottom deciles and computing the

mean.

28

Table 2: Maximum Score Estimates of Match Value Function

(1) (2) (3) (4) (5)Assetst −360.36∗∗ −211.02∗∗ −2.33∗∗ −392.33∗∗

(-443.09, -225.19) (-395.02, -126.96) (-82.92, -0.92) (-725.27, -99.00)log(Assetsb)×Assetst 47.88∗∗ 24.84∗∗ 0.30∗∗ 151.12∗∗

(29.32, 59.88) (15.02, 48.69) (0.13, 9.98) (91.28, 375.88)Branchest −32.71∗∗ −151.29∗∗ -7.94 -7.11

(-44.27, -25.21) (-389.08, -111.15 ) (-121.00, 33.37) (-83.60, 3.55)log(Branchesb)×Branchest 40.80∗∗ 644.79∗∗ 13.86∗∗ 10.04∗∗

(28.45, 44.60) (372.68, 811.83) (5.53, 137.94) (5.56, 67.57)MSA Overlap 967.44∗∗ 1210.45∗∗

(729.42, 984.44) (1098.15, 1397.11)HHI Violation Fraction 366.91 463.97

(-200.73, 761.48) (-440.10, 1146.41)Target HHI 0.15∗∗

(0.05, 0.42)Number of Observations 1484 1484 1484 1484 1484Percent of Ineq. 0.43 0.37 0.44 0.78 0.79

Note: ∗∗ indicates significance at the five percent level, i.e., 95 percent confidence interval does not contain 0. This table presents estimates of the match

value function F(b, t) = β ′Xbt + εbt using maximum score estimation. Subsampling-based 95 percent confidence intervals in parentheses. Point estimates

are generated by running the differential evolution optimization routine using R’s DEoptim package (Mullen et al. 2011) For differential evolution, we use

100 population members, scaling parameter 0.5 and we employ the classical differential evolution strategy (strategy =1). For point estimates, we run the

optimization routine for 20 different starting points (seeds) and select the run that achieves the largest value of the objective function. For confidence intervals,

we use the subsampling procedure described in Politis and Romano (1992). We set the subsample size to be 500 (approximately 1/3 to 1/4 the total sample

size) and randomly generate 100 replications of the routine to obtain confidence bounds.

29

Table 3: Maximum Score Estimates of Match Value Function with Performance Measures

(1) (2) (3) (4)Assetst −318.25∗∗ −2.07∗∗ -371.12 −1.43∗∗

(-441.91, -203.95) (-312.79, -0.67) (-456.99, 231.99) (-241.62, -0.16)log(Assetsb)×Assetst 41.97∗∗ 0.28∗∗ 48.20∗∗ 0.17∗∗

(26.98, 59.82) (0.09, 41.17) (29.99, 58.91) (0.03, 29.61)Branchest -312.00 -1.79 -265.30 2.76

(-442.11, 377.21) (-241.74, 500.10) (-415.28, 521.83) (-166.48, 411.50)log(Branchesb)×Branchest 73.23 0.75 58.97 0.02

(-97.77, 134.66) (-159.91, 140.23) (-134.86, 286.71) (-70.79, 59.97)Efficiency Ratio Target -5.80 4.26

(-62.07, 10.20) (-46.86, 22.21)LLR Ratio Target 1.72 -0.03

(-2.45, 6.00) (-1.58, 1.04)MSA Overlap 757.89∗∗ 886.86∗∗

(335.91, 933.89) (655.64, 958.27)HHI Violation Fraction 933.42 411.92

(-42.09, 943.88) (-169.98, 757.19)Number of Observations 1269 1269 765 765Percent of Ineq. 0.39 0.78 0.38 0.81

Note: ∗∗ indicates significance at the five percent level, i.e., 95 percent confidence interval does not contain 0. This table presents estimates of the match

value function F(b, t) = β ′Xbt + εbt using maximum score estimation. Subsampling-based 95 percent confidence intervals in parentheses. Point estimates

are generated by running the differential evolution optimization routine using R’s DEoptim package (Mullen et al. 2011) For differential evolution, we use

100 population members, scaling parameter 0.5 and we employ the classical differential evolution strategy (strategy =1). For point estimates, we run the

optimization routine for 20 different starting points (seeds) and select the run that achieves the largest value of the objective function. For confidence intervals,

we use the subsampling procedure described in Politis and Romano (1992). We set the subsample size to be 500 (approximately 1/3 to 1/4 the total sample

size) and randomly generate 100 replications of the routine to obtain confidence bounds. These specifications were also estimated with acquirer-specific

efficiency ratio and LLR ratio, which are not reported here due to being unidentified. In separate Monte Carlo exercises, we show that the revealed preference

method performs well on identified parameters (e.g., interaction terms and target-specific terms) when the value function also includes unidentified terms.

Table 4: Estimates of the Match Value Function using Bank Chartering Information

(1) (2)MSA Overlap 934.98∗∗ 878.21∗∗

(700.21, 976.72) (661.52, 957.71)Same Charter 158.45 37.60

(-85.41, 331.96) (-211.71, 306.30)(Same Charter)×(MSA Overlap) 743.28∗∗

(117.42, 901.26)Number of Observations 1484 1484Pct. of Inqualities 0.75 0.75

Note: ∗∗ indicates significance at the five percent level, i.e., 95 percent confidence interval does not contain 0. This table presents estimatesof the match value function F(b, t) = β ′Xbt + εbt using maximum score estimation. Subsampling-based 95 percent confidence intervals inparentheses. As in Table 5, the specifications in this table include (but do not report for the sake of brevity) own-effects and interactionsfor assets and branches as well as HHI Violation Fraction. Point estimates are generated by running the differential evolution optimizationroutine using R’s DEoptim package (Mullen et al. 2011) For differential evolution, we use 100 population members, scaling parameter0.5 and we employ the classical differential evolution strategy (strategy =1). For point estimates, we run the optimization routine for 20different starting points (seeds) and select the run that achieves the largest value of the objective function. For confidence intervals, we usethe subsampling procedure described in Politis and Romano (1992). We set the subsample size to be 500 (approximately 1/3 to 1/4 the totalsample size) and randomly generate 100 replications of the routine to obtain confidence bounds.

30

Table 5: Evaluating the Extent and Impact of Value Destroying Mergers

Year # Mergers % Value Destroying % Unmatched in Optimum Match Value % of Value Lost1995 168 5.95% 4.17% 190.445 0.27%1996 146 4.79% 3.42% 356.079 0.30%1997 152 4.61% 3.29% 189.349 0.38%1998 221 5.88% 1.81% 549.745 0.21%1999 158 6.96% 1.90% 264.840 0.21%2000 109 2.75% 1.83% 210.457 0.13%2001 121 8.26% 4.13% 326.746 0.43%2002 93 5.38% 3.23% 93.517 0.24%2003 95 6.32% 2.11% 122.004 0.27%2004 120 8.33% 2.50% 1957.699 0.07%2005 101 6.93% 3.96% 114.253 0.98%

Note: Match value measured in millions of dollars is the sum across mergers in that year of the estimated match value for merged acquirer-

target pairs. % Value Destroying is the fraction of mergers with negative merger value creation. % of Value Lost is the total (negative)

merger value of these value destroying mergers divided by the overall match value. Unmatched acquirers and targets occur in the solution to

the linear programming problem if mergers involving these acquirers and targets would be value destroying under the re-computed optimal

configuration of mergers.

Table 6: Year-by-Year Measures of Fit

Year # Mergers Same Match Highest Value Avg Rank Price ρ % of Optimal Value1995 168 0.274 0.15 0.81 0.947 84.41996 146 0.171 0.03 0.74 0.996 88.41997 152 0.237 0.12 0.72 0.945 83.21998 221 0.118 0.10 0.73 0.994 86.51999 158 0.241 0.18 0.81 0.994 72.12000 109 0.303 0.06 0.70 0.941 85.02001 121 0.331 0.12 0.78 0.981 84.02002 93 0.355 0.19 0.82 0.792 83.32003 95 0.253 0.27 0.84 0.984 85.82004 120 0.283 0.17 0.79 0.988 97.12005 101 0.307 0.04 0.79 0.715 85.4

Note: "Same Match" is the fraction of acquirers that are matched to the same target in the optimal pattern of mergers, "Highest Value" is

the fraction of acquirers whose realized target produces the highest match value of any possible target, "Price ρ" is the correlation between

the equilibrium transfers and the transfers implied by the equilibrium solution. "Highest Value" equals the fraction of matches where the

observed match had the highest estimated match value for the acquirer among all counterfactual mergers, and "Avg Rank" equals the average

percentile of match value for the observed match relative to all counterfactual matches. % of Optimal Value is the percentage of merger

value that the observed mergers create relative to the merger value created in the solution to the linear programming problem.

31

Table 7: Comparison of Predictive Accuracy with Binary Logistic Regression

Year # Mergers Revealed Preference Binary Logistic1995 168 0.274 0.0061996 146 0.171 0.0141997 152 0.237 0.0071998 221 0.118 0.0141999 158 0.241 0.0192000 109 0.303 0.0092001 121 0.331 0.0332002 93 0.355 0.0112003 95 0.253 0.0212004 120 0.283 0.0082005 101 0.307 0.010

Note: The Revealed Preference column indicates the fraction of successful predictions using revealed preference method to estimate match

value for each acquirer-target pair, and then using those estimated match values to solve for the matching market equilibrium. The Binary

Logistic column indicates the fraction of successful predictions using the maximum fitted value from a logistic regression (with the same

set of predictors as enters into the match value function) for each acquirer as the prediction of the acquirer-target match.

Table 8: Predicting Mergers One Year in Advance

Year Same Match Highest Value Avg Rank Unmatched # Observed Mergers Price ρ

1996 0.089 0.16 0.78 28 146 0.9951997 0.092 0.07 0.77 28 152 0.9391998 0.041 0.05 0.69 82 221 0.9881999 0.013 0.12 0.77 79 158 0.9972000 0.018 0.15 0.78 44 109 0.9412001 0.025 0.06 0.70 81 121 0.9792002 0.011 0.17 0.78 16 93 0.6252003 0.000 0.21 0.84 18 95 0.9942004 0.025 0.17 0.79 47 120 0.9892005 0.010 0.15 0.79 69 101 0.916

Note: The estimated match values are obtained by running the maximum score estimator the previous year’s sample of merger deals. Tocompute the "Same Match" fraction, compute the matching equilibrium assuming these estimated match values, and calculuate the fractionof matches that are the same as observed. Based on this matching equilibrium, "Unmatched" is the number of acquirers-targets that arenot assigned to one another, and "Price ρ" is the correlation between the equilibrium transfers and the transfers implied by the equilibriumsolution. As for non-equilibrium measures, "Highest Value" equals the fraction of matches where the observed match had the highestestimated match value for the acquirer among all counterfactual mergers, and "Avg Rank" equals the average percentile of match value forthe observed match relative to all counterfactual matches. Because the estimated match values are computed for the year ahead, computingmatch value and % of optimal value makes less sense than in the in-sample case.

32

Table 9: The Effect of Eliminating Dual Bank Chartering Regulation on Bank Merger Match Value

Year # Observed Mergers Same Match Not Matched Match Value ($ millions) % Increase in Match Value1995 168 0.232 6 294.825 54.81996 146 0.205 4 443.008 24.41997 152 0.270 1 272.677 44.01998 221 0.113 2 677.061 23.11999 158 0.215 2 359.794 35.92000 109 0.330 1 277.520 31.92001 121 0.355 3 398.945 22.12002 93 0.516 3 152.552 63.12003 95 0.316 1 187.534 53.72004 120 0.342 2 2028.748 3.62005 101 0.347 3 176.175 54.2

Note: Match value is the sum across mergers in that year of the estimated match value for merged acquirer-target pairs assuming thoseacquirers and targets have the same bank charter. Unmatched acquirers and targets occur in the solution to the linear programming problemif mergers involving these acquirers and targets would be value destroying.

33

A Supporting Derivations and Alternative Specifications

This appendix presents a number of alternative specifications and assumptions to the revealed preference model wepresent in the main text, and contrasts the use and viability with our preferred specification.

A.1 Basic Monte Carlo Evidence on Maximum Score Estimators

Our with-transfer estimators are similar in spirit to the NTD estimator, but the addition of transfer data can signifi-cantly improve the performance of maximum score estimation. We demonstrate this advantage in two Monte Carloexperiments. Our findings are broadly similar to those found in Fox and Bajari (2013), which replicated many ofthe results found in an earlier draft of our paper.

We employ Monte Carlo experiments rather than formal derivations because Manski (1975)’s rank order con-dition is not guaranteed to hold if there is an unobserved component of the match value function, even if thisunobserved component is independently and identically distributed. This is not a feature unique to our setting asit is true for the NTD estimator that Fox (2010a) develops. In the case of our with-transfers-data estimators, wehave another reason to present Monte Carlo exercises; namely, we do not offer an analogous rank order propertythat guarantees consistency for the estimators that use transfer data.29 Nevertheless, as our Monte Carlo exercisesdemonstrate, the maximum score estimators – especially, the estimators that use transfer data – have a number ofstrengths relative to alternative techniques.

A.1.1 Data Generating Process

We simulate data on acquirer and target attributes and use a match value function with a known functional form togenerate match values for each possible acquirer-target pair. Consistent with the previous section, we add an iidmatch-specific error to each match value. As proposed by Shapley and Shubik (1971), we solve the social planner’sproblem to determine the equilibrium one-to-one matching function m(b, t):

maxm(b,t)

My

∑b=1

My

∑t=1

m(b, t)F (b, t) (8)

subject to non-negativity constraints 0≤m(b, t) for all b and t, and the constraint that each agent may have at mostone match, ∑t m(b, t) ≤ 1 for all b and ∑b m(b, t) ≤ 1. for all t. The solution to this linear programming problemgives m(b, t) = 1 if acquirer b and target t are matched and m(b, t) = 0 if they are unmatched.30 We solve thedual to this linear programming problem to obtain the equilibrium acquisition prices. For target t, the equilibriumacquisition price pt = pbt equals the shadow price on the constraint that the target t may be acquired by at most oneacquirer.

With the implied matches, we form a data set that includes only matched acquirers and targets, their attributesand the acquisition prices implied by solving the dual to the social planner’s problem. We solve numerically to findthe global maximum of (5) for the without-transfers estimator and (6) for the with-transfers estimator.31

29In our inequalities, the choice of acquirer b to acquire target t depends not only on the match values f (b, t) and f (b, t ′), but also onboth equilibrium transfer amounts pbt and pb′t ′ . Because the choice probabilities depend directly on continuous equilibrium prices in ourwith-transfers-data setting, it is much more difficult to write down a rank order condition that depends solely on primitives. For this reason,our argument for the desirability of our with-transfers-data estimators relies heavily on the Monte Carlo evidence.

30Shapley and Shubik (1971) proved that we can solve the general problem, which allows for fractional matchings, without loss ofgenerality. The optimal solution to this problem will not involve fractional matches.

31Specifically, we employ a classical differential evolution algorithm. Differential evolution is an attractive optimization technique whenthe objective function is not well behaved (i.e., not differentiable and potentially having many local optima) and when the objective functionis costly to compute, as it is here (Storn and Price, 1997). For each replication in the Monte Carlo exercise, we give the differentialoptimization routine a parameter search space of [0,50] for each estimated parameter.

34

A.1.2 Performance of Estimators on an Interactive Model

Our first Monte Carlo experiment compares the with-transfer estimators to the NTD estimator if acquirers andtargets use the matching function F (b, t) = AbAt + β1BbBt + εbt where the match-specific error εbt ∼ N (0,σ).For the Monte Carlo experiments, we set β1 = 1.5. In this functional form, (Ai,Bi) is a vector of attributes (for

either target t or acquirer b) that is jointly distributed as a multivariate normal random vector(

AiBi

)with mean

µ =(

1010

)and variance-covariance matrix

[1 0.25

0.25 1

]. Attributes for acquirers are distributed independently

of attributes for targets prior to solving for the optimal matching and equilibrium transfers.The bias and root mean squared error (RMSE) based on the 100 replications of estimator for σ ∈ {1,5,20} are

presented in Table 10, which confirms that the maximum score estimators that employ transfers data have muchbetter properties than the NTD estimator that does not exploit transfers data - lower bias32 and RMSE regardless ofthe amount of unobserved variability considered. When the error standard deviation is large, the without-transfersestimator has unsatisfactorily high bias and RMSE. This Monte Carlo experiment suggests that in this situation,the with-transfers estimators will have lower bias and RMSE and that we should impose the two inequalitiessimultaneously for better performance.

A.1.3 Performance of Estimators on a Model with a non-interacted term

Our second Monte Carlo experiment compares the with-transfer estimators to the no-transfer-data estimator ifacquirers and targets use the matching function F (b, t) = β0AbAt +β1BbBt +β2Ct + εbt where the match-specificerror εbt ∼ N (0,σ). For the Monte Carlo experiments, we set β0 = 1, β1 = 1.5 and β2 = 2. In this functional form,(Ai,Bi) is a vector of attributes with the same distribution as the first Monte Carlo experiment and Ct is an attributeof the target firm that is distributed normally with a mean of 10 and a standard deviation of 1.

For each estimator and each standard deviation of the error term σ ∈ {5,20}, we perform 100 replications.The bias and root mean squared error based on the 100 replications of NTD and WT1 are presented in Table 11.33

In addition to estimating the model with the non-interacted term using the with-transfers estimators, we produceestimates from a mis-specified model using the NTD estimator. We do this because, for this matching function, theinequalities for the NTD estimator given in equation (4) do not allow us to identify β2 because adding equations(2) and (3) together trivially differences out the β2Ct term.34

As in the first Monte Carlo experiment, the with-transfers estimator is more precise than the without-transfersestimator. In this case, the maximum score estimator produces estimates tightly clustered around the true parametervalues for all three coefficients, exhibiting low median bias in both the low variance and high variance cases.Moreover, the estimator appears to be well-identified.35 In addition to added precision, the Table 11 results indicatethat the with-transfers estimator is able to identify parameters on non-interacted terms (in this case, β2) whereas

32The differential evolution optimization technique always obtains a solution, even if the parameter vector is unidentified. In the uniden-tified case, the parameter estimate is a random draw from the parameter search space. In our Monte Carlo exercise, we allow the algorithmto search over [0,50] while the true parameter value is 1.5. As a result, unidentified parameters in our technique tend to return values near25, the middle of the parameter search interval, which results in bias in the Monte Carlo exercise. In practice, unidentified parameters willalso exhibit bias because (almost surely) the researcher-chosen parameter space will not be centered on the true parameter value.

33In unreported specifications, we also performed this Monte Carlo exercise for the WT2 estimator. Similar to the first Monte Carloexercise, WT2 had worse properties than WT1. Thus, for brevity, we omit the WT2 results from Table 11.

34In unreported Monte Carlo exercises, we ran the NTD estimator in an attempt to recover the unidentified β2 parameter. In this uniden-tified case, the optimization routine will randomly select a number from the parameter space. This process has expected value 25. Thus, ina Monte Carlo exercise where a parameter is unidentified, both bias toward 25 and high RMSE confirm the parameter being unidentified. Inother unreported Monte Carlo exercises, we ran a version of our with-transfers estimators where β0 was restricted to be 1, which facilitateda direct comparison between the NTD and the with-transfers estimator. These results are available upon request.

35This is especially true in the low variance case. In the high variance case, the estimator to go awry for several runs of the MonteCarlo exercise, inflating the bias and RMSE. With skewed outcomes like this, the median bias results are a more reliable estimate of typicalperformance.

35

the without-transfers estimator is unidentified in this case.

A.2 Monte Carlo Evidence for Alternative Estimators

In addition to comparing our with-transfer data estimator to Fox (2010a)’s no-transfer-data estimator, we com-pare our preferred method to two additional alternative estimation techniques: multinomial logit estimation of thematching market, and maximum score estimation in a one-sided matching market.

A.2.1 Multinomial Logit

To estimate the match value function using a multinomial logit, we must assume the error term εbt is distributediid Type 1 Extreme Value (T1EV). Both assumptions about εbt – the T1EV distributional assumption and theassumption of independence across acquirer-target pairs – are restrictive. Nevertheless, the multinomial logit modelis widely understood and applied in other contexts, and thus, it serves as a useful baseline for our maximum scoreestimator. For this reason, we compare our with-transfers matching estimator to the multinomial logit using thefirst Monte Carlo experiment from Section A.1.

Table 12(a) presents the results from 100 replications of the multinomial logit alongside the comparable resultsfrom the with-transfers estimator. In all cases (σ = {1,5,20}), the maximum score estimator exhibits similar biasand lower RMSE. These results confirm that the maximum score approach, which accounts for endogeneity byexplicitly modeling the matching market, performs better than the standard multinomial logit.

A.2.2 One-sided Matching

Our maximum score estimators assume that acquirers and targets are two distinct groups to obtain the set of es-timating inequalities for maximum score estimation, but this assumption is unrealistic as well. In a real worldmerger market, an acquirer could become a target if equilibrium transfers change. Using revealed preference andthe fact that each target can become an acquirer and each acquirer can become a target, we derive two additionalinequalities for each comparison of an observed match to a counterfactual match.36

f (b, t)− pbt ≥ f(b,b′

)−(

f(b′, t ′

)− pb′t ′

)pbt ≥ f

(t, t ′

)− pb′t ′

These inequalities can be combined with the inequalities in equations (2) and (3) to form the basis of anothermaximum score estimator. This estimator, the one-sided matching maximum score estimator, maximizes the ob-jective function:

Qtr (β ) = ∑Yy=1 ∑

My−1b=1 ∑

Myb′=b+1 1

[f (b, t|β )− f

(b, t ′|β

)≥ pbt − pb′t ′

∧ f(b′, t ′|β

)− f

(b′, t|β

)≥ pb′t ′ − pbt (9)

∧ f (b, t|β )− pbt ≥ f(b,b′|β

)−(

f(b′, t ′|β

)− pb′t

)∧pbt + pb′t ′ ≥ f

(t, t ′|β

)]In Table 12(b), we present results from a Monte Carlo experiment where the underlying matching market is

based on one-sided matching with the same match value function as the first Monte Carlo experiment.37 In this

36For the first inequality, consider the acquirer of one pair b trying to acquire the acquirer of another pair b′. For this switch to be optimalfor b′, the price p̃ must be at least f (b′, t ′)− pb′t ′ . Hence, to rationalize the observed matching for b, the equilibrium payoff must exceedf (b,b′)− p̃, which gives the first inequality. The second inequality corresponds to the counterfactual of target t trying to acquire target t ′.

37Sticking with two-sided matching, we also evaluated in unreported Monte Carlo exercises an alternative with-transfer-data estimator,WT2, which imposes the two-sided matching revealed preference inqualities independently of one another. Imposing these inequalities

36

case, the maximum score estimator based on two-sided matching (maximizing (6)) performs as well the estimatorbased on one-sided matching (maximizing (9)). In fact, the two-sided matching estimator performs slightly better.These Monte Carlo results suggest that the primary benefit of the maximum score estimator comes from usingdata on transfers in the matching market (inequalities (2) and (3)), and that the distinction between one-sided andtwo-sided does not improve precision of the estimator.

A.2.3 Empirically Assessing Without-Transfers and One-sided Matching Estimators

Table 13 demonstrates how the without-transfers estimator compares with the with-transfers estimator. As thewithout-transfers estimator cannot identify the scale of the match value function, we normalize the coefficient onthe assets interaction to be one. In contrast, the with-transfers estimator imposes the scale of the transfer amount onthe match value function, and as a result, the estimates from with-transfers estimation are not directly comparableto the without-transfer estimator. Aside from the coefficient estimate on the branches estimation when we controlfor MSA overlap and HHI violation, the sign pattern is the same across the two estimators.

The fact that the with-transfers estimator is on a naturally interpretable scale is a significant advantage tousing transfer data. Additionally, the with-transfers estimator can identify non-interactive terms, which allows usto analyze a wider array of matching functions. For example, we may want to control for the size of the targetbanking institution. Our estimator with transfer data allows us to include target-specific controls while the without-transfers estimator does not. For this reason, we focus the remainder of the paper on results from the more preciseand interpretable with-transfers estimator.

We also run the basic multiplicative specifications using the maximum score estimator based on one-sidedmatching discussed in Section A.2.2.38 Table 14 presents these results, which are qualitatively similar to the resultswe find using the assumption that the merger market is two-sided (see Tables 2, 3 and 4 in the main text). Namely,the results suggest that the interaction between acquirer and target assets and the interaction between acquirer andtarget branches are robust features of the match value function, but in a horse race between the two (column 3),the asset interaction is more important. The finding that the asset interaction is more robust is also a feature of theless-computationally-demanding two-sided matching technique.

The fact that the one-sided matching assumption does not lead to important differences in the estimation resultssuggests that the assumption that there are two distinct groups on either side of the market is not violated in away that perversely affects the results. For this reason and because the two-sided maximum score estimator isappreciably easier to implement, our main specifications rely on the two-sided with transfers estimator.

A.3 Alternative Specifications for the Match Value Function

The multiplicative specification for the match value function in the main text follows much of the literature onmatching markets in that we consider interactions between attributes of each side of the market as components ofthe match value function. Here, we also consider two alternatives to the match value function discussed in the maintext: (1) a quadratic loss match value function, and (2) a cross-attribute interactive match value function.

A match value function with a quadratic functional form penalizes differences between acquirer and targetattributes:

simultaneously yields better RMSE.38Another alternative we assessed in Section A.2.1 is the multinomial logit model. This setting is a computationally difficult one in which

to apply the multinomial logit framework for a couple of reasons. First, the choice set is large for each acquirer who chooses among all ofthe alternative targets for that given year. This choice set is on the order of 200 targets for any given year, which makes applying a simplemultinomial logit estimator a difficult problem. We could reduce the computational difficulty by using a subset of the true choices (formultinomial logit, McFadden (1978) proved that this technique is consistent) as Fox (2007) suggests to do with maximum score estimation.Second, the choice set of acquirers from one year does not overlap with the choice set of acquirers from another year, and the number oftargets changes from year to year. For this reason, canned packages do not accommodate this estimation problem well. Taking these twofactors together, the standard multinomial logit is actually more difficult to apply than our preferred maximum score estimator.

37

F (b, t) = β0 +β1 (Wb−Wt)2 + γ

′1Xt + γ

′2Xbt + εbt (10)

This quadratic functional form allows the researcher to estimate the degree to which acquirer banks place apremium on similarity. For β1 < 0, the match value function implies a penalty to match value to merging witha bank on the other side of the market that is too different. In the context of bank mergers, it is difficult torationalize similarity in the number of branches or the amount of assets as a motive for merging. Hence, we focusour discussion of the empirical results on the multiplicative specification in equations (7).39

As the large-banking-network motivation to merge suggests, interactions between target and acquirer bankattributes can be important. As an alternative to the specification in the main text, an acquirer bank with an ab-normally large amount of assets relative to branches may demand having more branch locations to service thecustomers who hold those assets. Thus, such an acquirer would derive considerably more value from target bankswith a large number of branches. For this reason, we also estimate a matching function that interacts target andacquirer attributes across attributes (i.e., target assets with acquirer branches). To consider these interactive effects,we also estimate the cross-attribute specification:

F (b, t) = β1Wb,1Wt,2 +β2Wb,2Wt,1 + γ′1Xt + γ

′2Xbt + εbt (11)

Table 15 reports the maximum score estimates from the cross-attribute specifications in equation (11). Inparticular, these specifications allow the match value to depend on the interaction between acquirer branches andtarget assets, rather than the same-attribute interactions reported in Tables 2 through 4. Cross-interaction termsallow us to investigate the extent to which mergers are motivated by the match of acquirer branches to targetassets, or the match between acquirer assets and target branches. If the number of branches represents the lendinginfrastructure of the bank and bank assets are loanable funds, the match between branches at one institution andassets at another could play an important role in determining merger value.

Based on the estimates in Table 15, the interaction between acquirer branches and target assets enters positivelyand significantly into the match value function, and matters more to the match value than the interaction betweentarget branches and acquirer assets. Given the context, this finding suggests that bank mergers in our sample weremotivated by acquirers with excess lending opportunities who seek targets with excess loanable funds.

B Extensions and Robustness Checks

This appendix presents two supplemental tests beyond what is conveyed in the main text: (1) a year-by-year analysisto alleviate the concern that the bank merger market did not immediately become national after the Riegle-NealAct, but gradually became national due to some late-adopting states, and (2) an analysis of acquirer-specific valuecreation rather than value creation from the standpoint of the combined enttity.

B.1 Year-by-Year Results

Although the revealed preference method makes relatively few assumptions, we make a notable simplifying as-sumption to adapt the estimator to the bank mergers setting; we assume the bank merger market becomes national

39In unreported specifications, we estimate this quadratic match value function, and find that the penalty term for assets is negative andstatistically significant. In the context of our findings, this result derives from the fact that there is a positive relationship between acquirerand target assets and branches in the bank merger market equilibrium. It is possible that these specifications pick up on the similarity ofbanks in terms of number of business lines, but more similar to the tradition established in previous work in empirical matching, we find itmore plausible that the underlying mechanism driving bank merger value is a multiplicative interaction between acquirer and target bankingnetworks rather than matching on similarity of attributes.

38

immediately following the Riegle-Neal Act. In reality, the act was implemented on a staggered basis at the statelevel after the immediate passage of the act, and thus, the bank merger market was not completely national untilaround 2000 (Johnson and Rice, 2008). The scope of the merger market is important for the revealed preferenceestimator because it defines which mergers comprise the set of outside options to the realized set of mergers. Ifsome of these were not feasible because of delayed adoption of the law, it could affect the estimates.

To evaluate this concern, we estimate the merger value function separately for each year in our sample, andexamine the time series of the effects we estimate. For this exercise, we estimate two specifications for the mergervalue function: (1) the specification in Table 2 with overlap and market concentration regulation variables, and (2)the specification in Table 4 with chartering information included. For both specifications, we present in Figure 2 thetime series plots of the estimated coefficients for log(Assetsb)×Assetst , overlapbt , and samecharterbt×overlapbt .Although there is time series variation in these estimates, the effects we estimate are remarkably consistent in signand estimated magnitude.

We summarize the year-by-year estimates’ persistence and sign in Table 17, which computes the time-seriesmean for each coefficient estimate, as well as the standard error of the time series mean.40 The estimates are ofsimilar magnitude and signficance as the main specifications. As in earlier specifications, Table 17 highlights threerobust features of our setting: (i) a positive assortative match on bank size as measured by assets, (ii) a significantpositive effect of having overlapping markets on merger value creation, and (iii) an important role of regulation,especially in taking advantage of the value of having overlapping markets.

B.2 Acquirer-Specific Value Creation

Our matching model allows us to decompose value destroying mergers into two types: (a) mergers that destroyvalue when an acquirer had a positive value target available, and (b) mergers by acquirers that would destroyvalue regardless of the target. To conduct this decomposition, we estimate the match value function using (7),and compute the structural match value for each acquirer-target pair, both for actual matches and for acquirer-target pairs that did not merge with one another, but with another bank in the same year. Using these structuralmerger values, we solve the linear programming problem in equation (8) for the equilibrium one-to-one match, theequilibrium transfer amounts, and the match value produced in equilibrium. If an acquirer goes unmatched in thesolution to the linear programming problem, none of the remaining feasible targets would generate positive matchvalue, and thus, the acquirer would partake in a value-destroying merger regardless of the target.

As is indicated in Table 5, this fraction of value destroying acquirers ranges from 1.81 percent (1998) to 4.17percent (1995), with a cross-year average of 2.94 percent. This estimate indicates a small scope for value-destroyingacquirers, on an order of magnitude that is consistent with recent findings by Bayazitova et al. (2012). We now turnto developing a number of in-sample and out-of-sample assessments of the performance of our estimates.

When we generate estimated acquirer-specific merger values by subtracting the transfer amount (essentiallyapplying equation (1)), we speak more directly to the merger as a corporate decision made by the acquirer. Becausethe only difference between acquirer-specific merger value and our principal measure is the transfer amount, thisdecomposition allows us to evaluate whether accounting for the possibility of an overpayment by the acquirerwould lead to much higher frequencies of value destroying mergers.

The Observed Mergers columns of Table 18 present estimates of the fraction of mergers that destroy acquirervalue and the overall acquirer value generated from these mergers. In comparison to the same estimates for themerged entity, the fraction of mergers that destroy acquirer value is remarkably similar to the fraction of mergersthat destroy value to the merged entity. The annual average across years for the fraction of value destroyingmergers is 6.91 percent. That is, overpayment by the acquirer can rationalize an additional 0.89 percent of mergersthat destroy value beyond what we observed in Table 5.

40Although our annual regressions are not OLS, this is an approach very similar to Fama and MacBeth (1973), which is an approach thatassumes that the sampling error in the coefficient estimates is independently distributed across years.

39

To evaluate whether the value creation measures we construct automatically lead to value creation, we considera counterfactual exercise in which acquirers randomly merge with targets in the same matching market. TheRandom Mergers columns of Table 18 present the results from this counterfactual exercise. As the table indicates,random mergers destroy value more frequently than not, and often generate negative acquirer value in aggregate.The fact that this is not true in the observed sample of mergers indicates that there is great value for acquirers tochoose sensible targets, which our method uncovers.

C Appendix Tables

Table 10: Monte Carlo Results, maximum score estimation of β1 (100 replications)

without-transfers (NTD) with-transfers (WT1) with-transfers (WT2)σ Bias RMSE σ Bias RMSE σ Bias RMSE1 0.032 0.485 1 0.007 0.018 1 0.001 0.0235 0.503 1.541 5 0.011 0.046 5 0.014 0.04620 6.399 14.349 20 0.127 0.200 20 0.618 4.778

Note: The estimates in this table were produced by maximizing the objective function (5) for NTD, (6) for with-transfers (WT1) and (??)

for with-transfers (WT2) using R’s differential evolution routine (package: DEoptim by Mullen et al., 2011). In the differential evolution

method, we set the number of population members to be 50, the scaling factor to be 0.5, the optimization window for the parameter space

[0,50] and used the classical DE strategy (strategy = 1). The true standard deviation of the observable portion of the match value function

AbAt +1.5BbBt is 28.15.

Table 11: Monte Carlo Results, maximum score estimation of interaction term β1 and non-interaction term β2 (100replications)

(a) Without-Transfers Estimator (NTD)

σ Bias β0 RMSE β0 Bias β1 RMSE β1 Bias β2 RMSE β2

5 (n) (n) 0.434 1.389 (ni) (ni)20 (n) (n) 4.012 11.256 (ni) (ni)

(b) With-Transfers Estimator (WT1)

σ Bias β0 RMSE β0 Bias β1 RMSE β1 Bias β2 RMSE β2

5 0.043 0.210 0.045 0.264 1.152 5.34220 1.500 5.539 1.782 6.304 5.978 12.475

(c) With-Transfers Median Bias Results

σ Median Bias β0 Median Bias β1 Median Bias β2

5 0.013 0.009 0.02420 0.186 0.165 1.713

Note: In the without-transfers panel, (n) indicates that the coefficient was normalized for identification purposes, while (ni) indicates that

the coefficient is not theoretically identified. The estimates in this table were produced by maximizing the objective function (5) for NTD, for

with-transfers (WT1) using R’s differential evolution routine (Mullen et al., 2011). In the differential evolution method, we set the number

of population members to be 50, the scaling factor to be 0.5, the optimization window for the parameter space [0,50]× [0,50] and used the

classical DE strategy (strategy = 1). The true standard deviation of the observed portion of the match value function is 28.59.

40

Table 12: Monte Carlo Results, Comparing With-Transfers Estimator to Alternative Methods

(a) Comparison to Multinomial Logit (100 replications)

with-transfers (WT1) Multinomial Logitσ Bias RMSE σ Bias RMSE1 0.007 0.018 1 0.242 0.4325 0.011 0.046 5 0.141 1.049

20 0.127 0.200 20 0.124 1.232

(b) Comparison to One-Sided Matching Model (100 replications)

one-sided matching estimator two-sided matching estimatorσ Bias RMSE σ Bias RMSE1 0.265 0.365 1 0.253 0.3565 0.355 0.433 5 0.262 0.36820 0.683 0.741 20 0.377 0.513

Note: The multinomial logit estimates were produced using maximum likelihood estimation (R’s maxLik package). The estimates for

one-sided matching were produced by maximizing the objective function (9), and the two-sided with-transfers estimates in this table were

produced by maximizing (6) using R’s differential evolution routine (package: DEoptim by Mullen et al., 2011). For both methods, the scale

is normalized by setting the coefficient on the interaction term AbAt to be 1. In the differential evolution method, we set the number of

population members to be 50, the scaling factor to be 0.5, the optimization window for the parameter space [0,50] and used the classical

DE strategy (strategy = 1). The true standard deviation of the observed portion of the match value value function AbAt +1.5BbBt is 28.15.

Table 13: Maximum Score Estimates of Match Value Function (with-transfers versus without-transfers)

(1) (2) (3) (4)log(Ab)At 1 1 0.02 0.02

(normalized) (normalized) (-7.33, 0.03) (-0.06, 0.03)log(Bb)Bt 14.53 -6.18 0.84 1.29

(6.02, 48.56) (-16.66, 3.37) (0.62, 646.32) (0.54, 7.24)MSA Overlap 975.94 654.61

(871.89, 990.29) (520.83, 882.23)HHI Violation Dummy 249.18 171.77

(-515.77, 723.57) (-508.77, 688.71)Number of Observations 1484 1484 1484 1484

Percent of Ineq. 0.75 0.95 0.20 0.74

Note: Columns (1) and (2) use the without-transfers maximum score estimator while Columns (3) and (4) are the corresponding specifi-

cations using our with-transfers maximum score estimator. 95 percent confidence intervals in parentheses. Point estimates are generated

by running the differential evolution optimization routine using R’s DEoptim package (Mullen et al. 2011) For differential evolution, we

use 100 population members, scaling parameter 0.5 and we employ the classical differential evolution strategy (strategy =1). For point

estimates, we run the optimization routine for 20 different starting points (seeds) and select the run that achieves the largest value of the ob-

jective function. For confidence intervals, we use the subsampling procedure described in Politis and Romano (1992). We set the subsample

size to be 500 (approximately 1/3 to 1/4 the total sample size) and randomly generate 100 replications of the routine to obtain confidence

bounds.

41

Table 14: Maximum Score Estimation of the Match Value Function (one-sided matching)

(1) (2) (3)At -761.83 -843.54

(-860.29, -255.48) (-927.19, -436.31)log(Ab)At 102.43 111.54

(34.55, 113.22) (58.16, 125.18)Bt -663.47 666.20

(-876.87, -419.85) (-448.43, 759.46)log(Bb)Bt 197.93 -236.02

(127.61, 243.18) (-262.09, 145.56)Number of Observations 1484 1484 1484

Percent of Ineq. 0.29 0.28 0.28

Note: 95 percent confidence intervals in parentheses. Point estimates are generated by running the differential evolution optimization routine using R’s

DEoptim package (Mullen et al. 2011) For differential evolution, we use 100 population members, scaling parameter 0.5 and we employ the classical

differential evolution strategy (strategy =1). For point estimates, we run the optimization routine for 20 different starting points (seeds) and select the run that

achieves the largest value of the objective function. For confidence intervals, we use the subsampling procedure described in Politis and Romano (1992). We

set the subsample size to be 500 (approximately 1/3 to 1/4 the total sample size) and randomly generate 100 replications of the routine to obtain confidence

bounds.

Table 15: Cross-Attribute Specifications of the Merger Match Value Function

(1) (2)At 196.18 -140.52

(83.04, 245.06) (-302.67, 301.66)Bt -6.36 -31.56

(-25.27, 125.23) (-332.38, 51.17)AbBt -42.41 -21.23

(-161.00, 722.70) (3.37, 745.12)BbAt 669.61 941.86

(472.42, 941.43) (40.53, 969.80)MSA Overlap 835.86

(536.96, 973.70)HHI Violation Fraction 648.64

(156.30, 898.26)Target HHI 0.00

(-0.03, 0.09)Number of Observations 1484 1484

Percent of Ineq. 0.38 0.80

Note: In these specifications, At , Ab, Bt , and Bb are scaled to have mean zero and standard deviation one. 95 percent confidence intervals in parentheses. Point

estimates are generated by running the differential evolution optimization routine using R’s DEoptim package (Mullen et al. 2011) For differential evolution,

we use 100 population members, scaling parameter 0.5 and we employ the classical differential evolution strategy (strategy =1). For point estimates, we run

the optimization routine for 20 different starting points (seeds) and select the run that achieves the largest value of the objective function. For confidence

intervals, we use the subsampling procedure described in Politis and Romano (1992). We set the subsample size to be 500 (approximately 1/3 to 1/4 the total

sample size) and randomly generate 100 replications of the routine to obtain confidence bounds.

42

Table 16: Year-by-Year Maximum Score Estimates of Merger Value Function

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005At -32.51 11.46 -37.29 -36.29 -16.22 -94.64 -24.88 -18.02 -17.26 -26.56 -0.54

log(Ab)At 4.84 -1.73 6.37 4.07 2.05 11.30 3.67 2.20 2.09 3.30 0.20Bt -41.90 -350.33 -1.90 -102.53 -29.90 -126.04 12.37 253.44 64.62 32.86 -59.18

log(Bb)Bt -14.57 112.42 -36.57 31.66 -9.16 -1.93 -3.28 -51.32 -5.17 -11.16 13.11MSA Overlap 882.96 863.58 756.03 964.11 944.07 601.12 667.12 996.31 778.76 970.19 974.55

HHI Violate -77.96 104.76 -52.04 -28.13 -629.68 297.22 -531.91 -80.24 525.34 -700.69 -272.49Percent of Ineq. 0.68 0.71 0.60 0.79 0.78 0.53 0.66 0.87 0.81 0.75 0.83

# of Observed Mergers 168 146 152 221 158 109 121 93 95 120 101

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005At -12.98 -22.77 -151.37 -53.63 -2.25 -66.27 6.43 -7.58 -33.04 -3.33 -9.18

log(Ab)At 1.91 2.33 18.75 7.09 0.78 7.08 -1.17 0.91 4.06 0.37 1.31Bt -305.04 -439.29 746.71 -297.67 -240.22 -799.45 -163.75 93.73 -78.87 -233.55 53.74

log(Bb)Bt 34.29 178.10 -177.51 59.89 26.78 176.63 83.45 -12.42 41.27 54.49 -19.07MSA Overlap 987.74 705.71 914.54 812.63 954.18 803.20 670.95 788.70 700.07 684.55 984.29

HHI Violate 880.55 492.05 296.90 26.84 -502.43 78.37 -484.33 -655.36 -924.83 -467.82 628.12Same Charter -719.91 13.74 -222.02 -607.33 -250.39 924.67 -151.97 -233.28 -273.25 -481.89 -85.72

(Same Charter)*(MSA Overlap) 636.47 980.69 463.34 999.75 621.54 120.32 831.79 453.27 874.67 820.17 468.25Percent of Ineq. 0.82 0.68 0.57 0.81 0.73 0.54 0.65 0.86 0.89 0.81 0.87

# of Observed Mergers 168 146 152 221 158 109 121 93 95 120 101

Figure 2: Time Series of Year-by-Year Estimated Effects on Match Value for Selected Variables

Note: Each panel plots a time series of coefficient estimates from estimating of the match value function for each year in the sample. Panels

labeled (1) correspond to a specification for the mergervalue function that does not include bank chartering information, while Panels labeled

(2) include an indicator for whether the acquirer and target have the same type of chater, as well as an interaction of this indicator with the

degree of overlap of the acquirer and target markets.

43

Table 17: Time Series Average of Yearly Estimates of the Match Value Function

(1) (2)Assetst −26.61∗∗∗ −32.36∗∗

(8.13) (13.70)log(Assetsb)×Assetst 3.49∗∗∗ 3.94∗∗

(1.02) (1.68)Branchest −31.68 −151.24

(44.10) (115.86)log(Branchesb)×Branchest 2.19 40.54

(12.86) (29.23)MSA Overlap 854.44∗∗∗ 818.78∗∗∗

(40.85) (37.10)HHI Violation −131.44 -57.45

(114.65) (177.39)Same Charter -189.76

(129.68)(Same Charter)×(MSA Overlap) 660.93∗∗∗

(81.52)Average # of Mergers 134.91 134.91Number of Years 11 11Average Percent of Ineq. 0.7282 0.7482

Note: ∗∗∗, ∗∗, and ∗ indicate significance at the one, five, and ten percent level. Each estimate in this table is a time series mean of yearly

estimates of the match value function F(b, t) = β ′Xbt + εbt, which were produced using maximum score estimation. The standard error of

the time series mean is reported in parentheses.

Table 18: Evaluating the Extent and Impact of Value Destroying Mergers: Acquirer-Specific Value

Observed Mergers Random MergersYear # Mergers % Value Destroying Acquirer Value % Value Destroying Acquirer Value1995 168 5.95% 182.626 57.38% 7.5711996 146 5.48% 325.781 60.76% -23.9641997 152 4.61% 175.360 56.17% 0.8041998 221 6.79% 484.082 58.47% -26.2581999 158 8.86% 227.131 64.06% -19.4152000 109 3.67% 197.034 55.52% 15.7102001 121 9.92% 301.769 66.63% -24.1512002 93 7.53% 88.417 67.01% 0.0702003 95 6.32% 112.321 69.95% 7.1192004 120 10.00% 1802.261 64.06% -46.4962005 101 6.93% 106.779 63.75% -0.653

Note: Acquirer value measured in millions of dollars is the sum across mergers in that year of the estimated acquirer value. % Value

Destroying is the fraction of mergers with negative merger value creation.

44