We present evidence on the duration of firm-bank relationships
using a unique panel data set of connections between Oslo Stock
Exchange-listed firms and their banks for the period 1979-1994.
We focus on the determinants of the duration of a relationship
and the causes for ending an existing bank relationship. We find
that duration itself does not greatly influence the likelihood
of ending a relationship: short-lived relationships are as likely
to end as long-lived relationships. We also find firms that maintain
simultaneous multiple-bank relationships are more likely to end
a bank relationship than a single-bank firm and that small, highly-leveraged
"growth" firms are more likely to end a bank relationship
than large, low-leveraged "value" firms.
JEL code: G21, C41
Keywords: banking relationships, hazard models, duration analysis.
We use a panel data set containing annual information on the bank connections for virtually all Oslo Stock Exchange (OSE)-listed companies for the sixteen-year period 1979-1994 to study the duration of bank relationships. The driving motivation behind our study is to shed further light on the notion that (a) banks play a vital role in resolving information asymmetries that hinder some firms from obtaining financing and (b) this role arises through the relationship the bank develops with a firm.
In particular, we focus jointly on the length of bank relationships and the decision a firm takes to end a bank relationship and possibly begin another, an event we term a switch. Recent theoretical papers in banking suggest that the duration of a relationship itself may influence the decision to end the relationship. For instance, the repeated provision of bank services through time may reveal valuable private information about the customer to the bank. In so doing, an established relationship increases the array of contracting possibilities, but also increases the possibility that the bank can use the private information it obtains to "lock in" the customer to the bank. Our data set permits us to directly estimate the dependence of the decision to switch banks on the length of the existing relationship and thus yields a novel approach to examining implications from recent theoretical banking papers.
Moreover, the value to a firm of an existing bank relationship may also vary as a function of the degree of asymmetric information between the firm and the public, the availability of alternative monitoring mechanisms and the need and availability of alternative financing sources. To study these possibilities, we widen our analysis to model the duration of bank relationships as a function of a set of exogenous variables meant to proxy for the services offered by competing banks, the level of uncertainty about firm value, the financing needs of the firm and the existence of alternative monitoring sources.
Petersen and Rajan (1994) and Berger and Udell (1995) also study the importance of the duration of bank relationships. Using the 1988-89 National Survey of Small Business Finances, a large cross-section of data collected by the U.S. Small Business Administration (SBA), Berger and Udell (1995) find that the interest rate charged and collateral pledged on lines of credit is decreasing in the length of a firm's relationship with its bank. Using the same SBA survey, Petersen and Rajan (1994) find no relationship between the average loan interest rate and the length of a firm-bank relationship, but do find that credit is more readily available to firms with longer bank relationships.
Besides having a focus different from the earlier studies, our paper utilizes a new and interesting data set that complements the detailed survey data used in the Berger and Udell (1995) and Petersen and Rajan (1994) papers. For example, we derive our information on bank relationships from a time-series of annual data. This enables us to observe the beginning, end and evolution of many of the existing bank relationships through time, as well as switches by firms from one bank to another. As one "snapshot" in time, the SBA survey data does not account for the dynamic characteristic of the bank relationship. Further, as opposed to a sample of small, mostly family-owned firms as in the SBA survey, the firms in our data set are publicly traded and include both large and small firms with varying levels of ownership concentration. Finally, because it has inherited characteristics of both a European-styled, "bank-denominated" economy and a regulatory framework similar to the United States, the Norwegian banking environment provides a rich experimental setting. Like many European countries, virtually all debt financing to the corporate sector in Norway comes in the form of "inside" debt from financial institutions. In contrast to other European countries, banks are prohibited from owning large equity positions in the companies they do business with. Thus, although our sample firms are publicly traded, they exist in an environment where the primary debt financing source is "inside" bank debt.
When estimating the duration of a firm-bank relationship, we are also careful to recognize that our sample is censored; we are not able to observe the complete history of every relationship. Many of the bank relationships of listed firms begin before 1979 or continue after 1994, censoring our maximum observable relationship duration to sixteen years. Firms also list and delist during the sample period, widening the censoring problem. Not controlling for censoring in the data can severely bias inferences about the length of the relationship. For example, we find that although the average observed firm-bank relationship is seven years, the expected duration of a relationship, after controlling for the presence of censored observations, is at least fifteen years and may be as long as forty years.
Consistent estimation of the duration and likelihood of switching requires an estimator that is robust to the censored sampling distribution. We utilize non-, semi-, and fully-parametric estimators of hazard functions, which describe the likelihood of ending a given bank relationship, conditional on the length of the existing relationship. We also analyze the sensitivity of our results to assumptions about the underlying distribution of durations. To the extent that these estimators have seen little use in the financial literature, our paper introduces a relatively novel methodology and provides evidence on the importance of the use of censored-robust estimators.
When the hazard function is initially estimated using censored-robust, non-parametric techniques, we are unable to detect a dependency between the duration of a bank relationship and the likelihood that the relationship will end. In other words, we find that short-lived bank relationships are as likely to be terminated as long-lived relationships. This observed lack of duration dependence is inconsistent with the idea that firms become "locked in" to bank relationships as the relationship lengthens.
Parametric estimation of the hazard function yields mixed results on duration dependence. A Weibull specification is unable to reject the null hypothesis of no duration dependence in favor of monotonically increasing or decreasing dependence. However, estimation using a distribution that allows for non-monotonic duration dependence provides some evidence that firms are increasingly more likely to end a bank relationship at short durations and increasingly less likely to end a bank relationship at longer durations.
The parametric techniques also allow us to jointly estimate the influence of firm characteristics on the duration of bank relationships. We find that a firm is more likely to end a relationship, or equivalently, the expected length of a bank relationship is shorter, when firms simultaneously maintain a relationship with more than one bank. This finding is consistent with the argument that competing banks lessen the ability for one bank to maintain monopoly power over a firm.
We also find the likelihood of ending a bank relationship is increasing in the growth potential - as proxied by market-to-book-ratios- of the firm and the proportion of firm asset's financed with debt and decreasing in the inflation-adjusted size of the firm. We observe no statistically significant relationship between the level of ownership concentration in the firm and the decision to switch. Taken together, our latter results suggest that it is the firms most in need of bank services and financing - small, high-leverage, high-growth - that maintain the shortest bank relationships and switch most often. To the extent that this reasoning runs counter to the argument for why bank relationships are valuable, our results present a challenge to the theoretical banking literature.
The rest of the paper is organized as follows. Section II provides an overview of the theoretical literature relevant to our investigation. Section III describes the data used in our analysis. Section IV introduces non-parametric techniques for analyzing duration data and presents preliminary results from the non-parametric estimation of hazard functions. Section V continues the empirical analysis by describing the use of the proportional hazard model as a method for studying the influence of exogenous variables on the hazard rate. Section VI concludes.
A distinguishing feature of a bank may be its ability to reduce costly information asymmetries between those seeking financing and those willing to contribute capital. Leland and Pyle (1977), Diamond (1984), Ramakrishnan and Thakor (1984), Fama (1985), and Boyd and Prescott (1986) argue that a bank can monitor and credibly communicate inside information more efficiently than its individual depositors or borrowers. Moreover, a bank can help to reduce the likelihood that a firm will choose poor projects by threatening not to renew future debt contracts (Stiglitz and Weiss, 1983). A firm that establishes a relationship with a bank can thus reduce the uncertainty about future investment projects and obtain debt financing that would otherwise be unavailable or prohibitively expensive.
It is through the progression of a relationship that a bank learns more about a firm's ability to meet future obligations, both through past payment histories and other services offered by the bank (e.g. deposits, clearing and payment services, lines of credit, etc.). Because of its ability to observe a stream of proprietary information, the bank has the potential to extract monopoly rents from its customer. At any point in time, the bank also has the flexibility to influence a firm's investment choice and to deny the firm continued financing in the future. Greenbaum, Kanatas and Venezia (1989), Sharpe (1990) and Boot and Thakor (1994) examine the association between the temporal nature of a firm-bank relationship and the dynamic nature of loan pricing, the availability of credit and the influence of competition.
In Greenbaum, Kanatas and Venezia (1989) one firm can choose in each period to continue its existing lending relationship or pay a fixed cost to search for a competing bank. In equilibrium, the value of the profit function is increasing in the uncertainty about the firm's future ability to pay. A continuing relationship implies a reduction in uncertainty about the payment ability of the firm, making the firm less valuable to the bank and more likely to switch banks.
Sharpe (1990) studies an economy where banks compete for firms of varying unobservable quality requiring financing of two-period projects. Within this environment, a bank has an incentive to lure firms in the first period with below cost loan rates. A privately successful firm with a noisy, but low public signal of success is "captured" by the bank and must pay a high loan rate because the cost of switching banks is too high. The strength of the monopoly power is mitigated by a more accurate public signal of the firm's ability to pay or through the loss of reputation with new customers.
Boot and Thakor (1994) consider an infinite-period contracting framework in which banks require pledged collateral in addition to per-period interest payments. Banks choose the interest rate-collateral combination that dynamically induces the borrower to expend maximal effort towards completing a project, while attempting not to lose the borrower to another bank. Banks offer high interest rate-high collateral contracts in the early part of a relationship to induce optimal effort. Once a firm establishes a successful project, the bank reduces both the interest charges and required collateral on the project.
Rajan (1992) studies an economy where a firm may choose to borrow from a bank ("inside debt") or from a outside source such as the bond market ("arm's-length debt"). The advantage to bank debt arises from the bank's ability to monitor the progress of a firm's project, its discretion in continuing the lending relationship and its ability to influence the effort of the borrower. An arm's-length contract, on the other hand, allows for no intermediate discretion in reallocating resources or changing the contract specifications. Rajan (1992) argues that this rigidity can have a beneficial effect on the borrower's incentive to expend effort on the project.
Rajan (1992) obtains several interesting results from his model. First, a firm should forego arm's-length debt in favor of a long term bank contract when the bank exerts strong bargaining power over the firm. A bank could have strong bargaining power when it has strong influence over suppliers, sits on the board of the firm or when the national economy is denominated by several (possibly government controlled) banks. Second, high quality firms will be more likely to forego a bank relationship in favor of the use of arm's-length debt. Third, the ability for a bank to maintain a relationship through its reputation (Sharpe, 1990) may be eroded since high quality firms are more likely to borrow using arm's-length debt. Fourth, public signals of a firm's ability to pay can increase the likelihood that a firm remains captured by a bank. Finally, multiple bank relationships may reduce the chance that a firm may be informationally captured, but also may lead to excessive monitoring by the banks.
To summarize, the theoretical literature provides a stimulus for the study of firm-bank relationships through time and the likelihood that a firm may switch banks. Greenbaum, Kanatas and Venezia (1989) predict that the likelihood of observing a bank switch is increasing in the duration of the firm-bank relationship, while the models of Sharpe (1990) and Boot and Thakor (1994) imply that the incentive for the firm to switch relationships is decreasing in the duration of the relationship. Sharpe (1990) suggests that the likelihood a firm switches banks increases as public signals of the firms ability to pay increases. Competition, in the form of multiple bank relationships (Sharpe, 1990 and Rajan, 1992) or arm's-length debt (Rajan, 1992) can, by making the costs of switching lower, increase the likelihood of observing a switch. Finally, implicit in the moral hazard models of Boot and Thakor (1994) and Rajan (1992) is the idea that a bank's ability to induce value-maximizing effort may be unnecessary if the firm has internal monitoring mechanisms to effectively steer manager' s efforts.
We obtain annual data on bank relationships of Oslo Stock Exchange (OSE)-listed firms for the years 1979 to 1994 from Kierulf's Handbook, an annual handbook published by Oslo Børs Informasjon AS, a data-publishing subsidiary of the OSE. The handbook contains financial and accounting information on all listed firms, as well as other firm-specific information. In particular, as part of the listing requirement, each firms must report on an annual basis its "primary" bank connections, up to a maximum of four. We identify a firm as switching banks when it drops one of its banks from the survey or replaces one of its banks with a new bank. We define the duration of a relationship to be the number of years we observe a firm maintaining a bank connection.
Table 1 presents an annual overview of the number of firms in our sample along with the number of firms listing, delisting and the number of firms switching. In a given year, our sample on average contains roughly 100 OSE firms, representing 97% of the population of exchange-listed firms. We observe a total of 93 firms switching over the sample period or an average of six per year. The number of switches roughly doubles in the years 1986-1988, a period in which substantial deregulation occurred in both Norwegian financial markets and the Norwegian banking sector. Concurrent with the increase in the number of bank switches during the crisis period was an increase in the number of firms delisting. The number of firms going public increases during the 1983-84 period and later in the early 1990's, roughly matching periods in which the level of the OSE market was high.
Table 2 summarizes some of the characteristics of the bank relationships. The top of Table 2 and Figure 1 provide information on the distribution of the sample firms by the number of bank relationships maintained at a given point in time. A firm is defined as having a multiple bank relationship if the firm maintains more than one simultaneous bank relationship during the sample period. Three quarters of the sample firms maintain only one bank relationship over our sample period, with the proportion increasing in the 1990's. Another 17% of the banks maintain two relationships and seven percent have three banks. By the end of the sample period, very few firms have more than three bank relationships.
In our analysis to follow, we define a sample observation as one firm-bank relationship. The number of firm-bank observations equals the total number of firms in the sample times the number of bank relationships maintained by each firm over the sample period. Our data set contains 401 firm-bank observations.
The middle section of Table 2 categorizes the proportion of 401 firm-bank observations by their observed duration. That is, this section provides a distribution of the length of bank relationships for firms listed on the OSE between 1980 and 1994. The pattern that emerges is interesting. If we only consider the most obvious, end-of-sample censoring, it appears that only a small proportion of relationships (8%) last beyond fifteen years. Furthermore, the median observed relationship lasts six years, a third of the observed relationships do not last past two years and fully 85% of the firms appear to have ended a bank relationship by the tenth year. A first-pass look at the duration data thus seems to suggest that bank relationships are short-lived and that censoring affects only a small proportion of the observations.
The bottom of Table 2 gives a breakdown of the type of banks represented in the sample. The sample firms maintain relationships with 51 different banks. Fourteen of the banks are international banks, 22 are Norwegian commercial banks, while the remaining 15 are Norwegian savings banks.
The pie-charts in Figure 2 provide some insight into the concentration of the relationships within the banking industry, by graphing the proportions of relationships by bank. The charts reveal that, despite the relatively large number of banks represented in the sample, the relationships are concentrated. Most importantly, approximately 75% of the firms maintain a relationship with at least one of Norway's two largest banks, Den norske Bank and Kreditkassen.
The clearest circumstance of censoring is created by the beginning and ending dates of our sample. We cannot observe the entire length of relationships that begin before 1979 (a form of left censoring), nor can we observe the outcome of relationships that continue as of 1994 (a form of right censoring). However, the listing and delisting of firms also represent a form of random censoring, since we are not able to observe a firm's bank relationship when it is not listed on the OSE. A left censored observation is created when a firm lists on the OSE, since the company will typically maintain a bank relationship before it goes public. Right censoring occurs when a firm delists, if the delisting is due to a switch to another exchange or if the firm is taken private again. On the other hand, a delisting due to a merger signals the end to a bank relationship (if the merged firm does not use the original bank), as does a delisting due to liquidation.
Motivated by the theoretical literature on bank relationships, we incorporate firm-specific data that may influence the duration of, and likelihood of ending, a bank relationship. All financial statement and stock price data come from databases maintained by Oslo Børs Informasjon (OBI). Information on equity offerings (both public and private) are obtained from the datasets used by Bøhren, Eckbo and Michalsen (1996) and Bøhren, Eckbo, Michalsen and Smith (1996), while ownership structure information is collected from company annual reports and Kierulf's Handbook.
The five firm-specific variables we use later in our analysis our discussed in the following subsections. We match each set of firm-specific variables to a firm-bank observation using the value of firm-specific variable in the year prior to end of the relationship or end the year prior to censoring. Due to data lost in matching the two data sets, we are left with 263 matched firm-bank observations. Table 3 contains summary statistics and pairwise correlation across the 263 observations for the five firm-specific variables.
Firms with more than one bank relationship may find the cost of ending one bank relationship to be lower. First, the ability for any one bank to "lock in" a customer will be hindered if other banks also maintain valuable private information on the firm. Second, competition between the banks for loan and clearing services may induce the firm to shift all services to one bank and end services with another. The dummy variable MREL takes the value of 1 when a firm maintains a multiple-bank relationship at some point during the sample period and takes the value 0 otherwise.
We may expect that a firm with high ownership concentration will be monitored and disciplined better than a firm with disperse ownership, thus reducing the need for monitoring services from a bank. A highly concentrated firm may also have stronger bargaining power against a bank in negotiating contracts. As a proxy for the concentration of ownership and possible control, we define the variable CONC to be the proportion of a firm's equity owned by the ten largest shareholders.
We use the size of the firm as a proxy for the degree of uncertainty about the value of the firm. We posit that larger firms are more likely to be followed by analysts and appear in newspaper articles in Norway and abroad more often. Furthermore, twenty-two of the largest OSE firms are listed on the New York Stock Exchange (NYSE), London Stock Exchange (LSE) and/or NASDAQ trading systems. Listing on a foreign exchange implies greater dispersion of company results and possibly stricter reporting requirements then the OSE. We define the variable SIZE to be the log of end-of-year market value of equity, deflated by the Norwegian consumer price index (CPI).
As a measure of Tobin's Q, market-to-book ratios can proxy for future growth opportunities available to the firm: a high market-to-book indicates that a firm has strong growth opportunities. If a high growth ("growth") firm is more likely to require financing of its projects than a low growth ("value") firm, then a growth firm will find it more costly to end a relationship with the bank as its financing source. In addition, because much of the value of a growth firm is tied up in unrealized investment opportunities, growth firms may face more adverse selection problems and therefore be more reliant on bank financing vis-à-vis the use of arm's length debt. The market-to-book ratio, labeled Q, is measured as the ratio of the end-of-year market value of equity plus book value of assets divided by the book value of assets.
The last firm-specific variable incorporated in our analysis proxies for the proportion of the firm's assets financed with debt. Given the heavy reliance in Norway on bank debt, a heavily leveraged firm is more dependent on bank financing then a mostly equity-financed firm, possibly making it costlier for the firm to switch banks. We define DEBT to be the ratio of the book value of debt to the sum of the market value of equity plus the book value of debt.
As is evident from Table 3, roughly 60% of the 263 firm-bank observations come from firms with multiple relationships. The ten largest shareholders in the average sample firm owns 68% of the equity in the firm. The average firm has a real market value of equity of $18 million (measured in 1994 dollars), finances 54% of its assets with debt and has a market-to-book value of 1.4. Given the method for constructing the variables, it is not surprising that SIZE, Q and DEBT are highly linearly correlated. To what extent this correlation influences the regression estimates remains an empirical issue.
Duration studies focus on the analysis and modeling of data which involve the passage of time before a particular event occurs. For instance, the study of duration data has been applied in the labor economics literature to the length of strikes, the duration of unemployment, and employment and the time before a pay increase. In our paper, we are interested in studying the length of a bank relationship, or the passage of time before a bank relationship ends. The econometrics of duration analysis has developed primarily to estimate the distribution underlying the duration data, to study the dependence of duration on explanatory variables and to obtain estimators that account for censored observations.
To better understand the analysis of duration data, define T
to be the duration of time that passes before the occurrence of
a certain random event. The passage of time is often referred
to as a spell, while the occurrence itself is often called
a switch. A simple way to describe the behavior of a spell
is through its survivor function, 
,
which yields the probability that the spell duration T lasts
at least to time t (i.e., the survivor function equals
one minus the cumulative distribution function of T).
An alternative way of describing the behavior of a spell is with
a hazard function. The hazard function describes
the likelihood that a switch will occur, conditional on the spell
surviving through time t and is defined by
where
is the density function associated
with the distribution of spells. Neither the survivor nor the
hazard function provide any additional information that could
not be derived directly from
, they are
simply economically interesting ways of examining the distributions
of spell duration.
The hazard function provides a convenient method for summarizing
the relationship between spell length and the likelihood of switching.
When
is increasing in t, the hazard
function is said to exhibit positive duration dependence,
since the probability of ending the spell is increasing in the
spell length. Similarly, negative duration dependence
occurs when
is decreasing in t.
It follows that the case of constant duration dependence
occurs when
. Under constant duration
dependence, no relationship exists between spell length and the
likelihood of switching.
In this section, we introduce a methodology for summarizing and graphically viewing the sample distribution of bank relationship duration. The methodology employed is intuitive and robust to censored observations. Much of the development is taken from Kiefer (1988).
Let 
be the number of bank relationships
with observed duration i and maximum duration j,
where 
, 
corresponds
to the maximum fixed cutoff (fifteen years in our data set) and
. An observed duration of zero (
)
indicates that a firm listed a bank in one year, while both 
and
are
recorded as zero when a firm is listed for only one year. When
, the spell is right censored; one cannot
distinguish whether the spell ended that year or continued in
the unobserved future (
is the number
of censored spells).
Define 
, and 
to be the number spells that have neither been completed nor censored
as of length 
, 
.
A natural, non-parametric estimator for
,
the likelihood that a firm switches banks in the kth year
given that the relationship has lasted k years, is
, (1)
which is the number of switches in year 
divided
by the number of relationships that have survived to length 
.
Note that the estimator
is robust to
right censoring since the denominator in (1) normalizes the number
of switches at length k by the number of uncensored spells
still existing at time k.
We define the estimator of the survivor function to be
, (2) which is the
Kaplan - Meier (1958) or "product-limit" estimator for
the survivor function. An additional benefit of the survivor
function is the ability to construct approximate standard errors
around the estimates
. The approximate
variance of the survivor estimates is:
. (3)
Table 4 and Figure 3 jointly provide a first look at the distribution of the duration of bank relationships through the non-parametric estimation of the survivor function in equation (2).
Both Table 4 and Figure 3 indicate that adjusting for censored observations in the data drastically changes the estimated shape of the survivor function. For instance, the censored-robust estimated median bank relationship is fifteen years, more than double the length implied by directly observing the data over the fifteen year period. Furthermore, when no adjustment is made for censoring, the survivor function decreases at a quick rate. The estimated likelihood of surviving beyond five years is 54% and the estimated chance of surviving past fifteen years is 11%. In contrast, the robust estimator for the survivor function implies that 85% of the relationships will last beyond five years and that 63% of the relationships continue after fifteen years.
Table 4 and Figure 3 also provides some insight into the importance of duration dependence in the non-parametrically estimated hazard function. The heavy-dashed line plots the implied censored-robust estimate for a survivor function calculated under the restriction that the likelihood of ending a bank relationship is independent of the duration of the relationship. The two light-dashed lines plot approximate 95% confidence intervals around the restricted estimate. The difference between the restricted and unrestricted estimates is small and lies everywhere within the 95% confidence bands, suggesting that the likelihood of ending a bank relationship is not influenced by the duration of the relationship.
To separately examine their influence of on the conditional likelihood of switching banks, Figure 4 plots pairwise cohort comparisons of survivor functions for each of our five independent variables. In Figure 4a, we plot the cohort of single-bank relationships against the plot of multiple-bank relationships. To construct each of the cohorts in Figures 4b-e, we arrange the data from highest to lowest and split the sample roughly in half to form a "high" and "low" cohort. For each of the figures, we also plot 95% confidence bands around the "low" estimates to gauge the statistical differences in the two categories. Several interesting patterns emerge from the plots.
First, the plots in Figure 4a suggest that firms with multiple bank relationships are more likely to end a given bank relationship than firms with single bank relationships. This result holds uniformly across all intervals of time, with the difference in the rate of ending a relationship increasing toward duration of ten years. For example, the likelihood of a multiple-bank relationship continuing after fifteen years is 55%, compared with 80% for single-bank relationships.
Second, small market value firms are more likely to end a bank relationship than large firms, with the difference in the switching probabilities being most pronounced for intermediate duration (4 to 9 years). In fact, Figure 4b suggests that both size cohorts exhibit non-monotonic duration dependence. For larger firms, the likelihood of ending a bank relationship decreases for intermediate duration, relative to both short (< less than 4 years) and long duration (> 9 years). For smaller firms, the probability of ending a bank relationship increases over the intermediate duration. Measured at the longer duration, no statistically significant difference exists in the survival rate of large versus small firms.
Third, no difference is apparent in the survival rates of the high and low cohorts measured for ownership concentration and market-to-book ratios. Plots of the cohorts lie very near each other, with the large cohort plot lying well within the confidence bands of the plot of the low cohort.
Fourth, Figure 4e shows high debt firms to be more likely to end a bank relationship than a low debt firm for duration out to 12 years, where upon the two cohorts become statistically indistinguishable.
Conclusions regarding the influence of the independent variables in Figure 4 may be misleading since they do not control for common variation among the independent variables. In the next section, we turn to estimating the hazard function within a multiple regression framework. This framework enables us to quantify estimates of duration dependence and allows us to jointly estimate the influence of the independent variables on the conditional likelihood of ending a bank relationship.
In this section, we introduce semi-parametric and parametric techniques for studying the influence of explanatory variables on the duration of the banking relationship within the context of a proportional hazard model. The proportional hazard model assumes that the hazard rate function can be written
, (4)
where X is a set of explanatory variables,
is a vector of unknown parameters associated with the explanatory
variables,
is a baseline hazard function
and
is a non-negative function.
Estimation using the proportional hazard model typically requires
specification of functional forms of
and
.
For example, we could begin by choosing a function that describes
the shape of the baseline hazard
. Define
the integrated baseline hazard to be
and let
. Kiefer (1988) shows that, in
the absence of censored observations, the proportional hazard
model can be written as a log-linear regression:
, (5)
where
follows an extreme value distribution
(Johnson and Kotz, 1970). An appealing feature of equation (5)
is that the coefficients
have the usual
least squares interpretation of reflecting the partial influence
of each of the variables in X on the conditional likelihood
of ending a spell.
The shape of the distribution of spell lengths arises from
the specification of the baseline hazard
.
Two commonly-used specifications are the Weibull and the
exponential. The hazard and integrated hazard functions
for the Weibull distribution are:
,
. (6)
The Weibull distribution allows for duration dependence. When
,
distribution exhibits positive duration dependence, while
implies negative duration dependence. The exponential is nested
in the Weibull as the case
and represents
the testable restriction that the likelihood of switching is independent
of the duration of the spell.
Substitution of the expression for the integrated hazard function
(6) into equation (5) indicates that estimating a Weibull hazard
model is analogous to a linear regression of the log of duration,
scaled by
, on the set of variables in
X plus an intercept, with the coefficient on the intercept
representing an estimate of
. Depending
on whether the value is greater than or less than one, the scaling
factor
either "speeds up" or
"slows down" log duration time. In the exponential
case, equation (5) reduces directly to a linear regression of
log duration on X.
The Weibull model restricts duration dependence to be monotonic over spell lengths. Figures 3 and 4 suggest the likelihood of ending a bank relationship may increase and then decrease over the observed duration. The log-logistic distribution, which allows for non-monotonic duration dependence, has the following hazard and integrated hazard functions:
,
. (7)
When
in the log-logistic specification,
the likelihood of ending a spell first increases, then decreases
with duration. When
the hazard function
decreases monotonically with duration. A drawback to the log-logistic
distribution is that constant duration dependence is not
included as a special case.
We use all three parametric specifications (exponential, Weibull, log-logistic) of the baseline hazard to examine the influence of duration and firm characteristics on the likelihood of ending a bank relationship. We also consider one model that does not require specification of a specific baseline hazard.
The Cox (1972) partial likelihood model can be used to
estimate the parameters in
without specifying
.
Let 
represent an ordering of the duration
from lowest to highest. The conditional likelihood that spell
j ends after length tj is given by
(8)
under the proportional hazard specification (4). Intuitively, the partial likelihood function estimates the contribution of the jth observation to the likelihood that the spell ends at length j.
Since the partial likelihood model assumes no specific form for the baseline hazard, it is sometimes referred to as a "semi-parametric" model and benefits from not being susceptible to biases induced by specifying an incorrect hazard function.
Accounting for the presence of (right) censored observations can
be accomplished using techniques standard in the literature on
limited dependent variable analysis. Let
represent the density function defined over duration and note
that 
. Estimation of the proportional
hazard model in the presence on censored data can be accomplished
by maximizing the log-likelihood function
:
,
or,
. (9)
where dk takes on the value of zero if the kth observation is censored and one if the duration is fully observed.
The interpretation of equation (9) is intuitively straightforward.
When the kth observation is uncensored, it is used in
the estimation of the density component of (9), 
.
When the kth observation is censored, we utilize
the information that the this observation has survived to time
t to estimate the survivor function
.
In the next section, we report the results from using the parametric
and semi-parametric specifications, adjusted for censoring, to
estimate the influence of duration and our firm characteristics
on the likelihood of ending a bank relationship.
We first examine the results of multiple regression estimates
of the conditional likelihood of ending a bank relationship using
alternative specifications for the baseline hazard. For each
specification, the MLE system defined by equations (5) and the
censored-robust (9) is estimated using LIMDEP. LIMDEP defines
the likelihood function in terms of the transformed variable,
, where heuristically
is substituted into equations (6) and (7) in order to estimate
the hazard function. Table 5 reports the slope estimates
and baseline hazard parameters
and
for the exponential, Weibull and log-logistic distributions using
all five explanatory variables.
The
is the estimate of the hazard function
at the mean values of X. The conditional likelihood of
ending a bank relationship in a given year, evaluated at the mean
value of the explanatory variables, ranges between 2.6% (exponential)
and 4.7% (log-logistic). The median length of a relationship
is estimated to be between 26.7 years (exponential) and 21.4 years
(log-logistic).
Given the estimate of its standard error (0.178), we cannot reject
the hypothesis that the Weibull estimate,
,
is equal to one. Moreover, a likelihood ratio test statistic
using the difference between the log-likelihood values of the
Weibull and exponential cannot reject the exponential distribution
as a null model. This suggests that when we restrict the baseline
hazard to exhibit monotonic duration dependence, we cannot reject
the hypothesis of constant duration dependence.
Under the log-logistic specification, however, the estimate of
is statistically greater than one (t-value
= 2.29), implying that the likelihood of ending a bank relationship
first increases in the duration of the bank relationship and then
decreases in the duration.
Independent of the baseline hazard specification, an interesting
and consistent pattern emerges in the estimates of
.
If we use a size of 5% as a measure of statistical significance,
then firms are more likely to end a bank relationship when
they maintain more than one bank relationship, are relatively
small and when their market-to-book values are high. Firms with
relatively high debt levels also appear to be more likely to switch
banks, although the statistical significance of the relationship
is weaker (significant at the 10% level). The concentration of
ownership appears to exert no influence on the likelihood of switching
banks.
Noting that
, we can also interpret the
influence of the explanatory variables in terms of their influence
on the expected duration of the relationship. For example, the
estimate of the intercept (-3.682) in the exponential model implies
that the expected length of a bank relationship is
years, when all values of X are zero. The estimate
then implies that multiple-bank relationships are expected to
last only
years. Similarly, 
from the exponential implies that a 1% increase in the market-to-book
ratio of a firm reduces the firm's expected duration of a bank
relationship by three years. Likewise, the expected duration
of a relationship increases in the inflation-adjusted size of
the firm and decreases in the proportion of debt held by the firm.
In Table 6, we use the semi-parametric, Cox (1972) partial likelihood model to check the robustness of the distributional assumptions made above. We also explore the sensitivity of our results to the adjustment for censoring and to various combinations of the explanatory variables.
The first line (Model 1) in Table 6 contains the full-scale, censored robust estimates of the influence of the explanatory variables on the proportional hazard function. With the exception of the DEBT variable, the magnitude and significance of estimates are similar to the estimates in Table 5, suggesting that the results are not dependent on the specification of the baseline hazard. Multiple-bank relationships and high Tobin's Q tend to reduce the duration of a bank relationship, while large firms tend to maintain longer bank relationships. Both the sign and magnitude of the DEBT variable indicates that the proportion of debt held by a firm does not influence the duration of the bank relationship in the partial likelihood model.
Model 2 is estimated assuming that no censoring occurs, or that all relationships end with the last observed year of the firm-bank relationship. When the model does not account for censoring, inflation-adjusted size remains as a statistically and economically important explanatory variable. Otherwise, the slope estimates are very sensitive to the adjustment. For example, the number of bank relationships is no longer important in estimating the hazard function, nor is the Tobin's Q variable. Thus, as in the non-parametric estimation, not accounting for censoring in the data biases the conclusions of the multiple regression model.
Models 3-6 examine the relative influence of combinations of the explanatory variables, by excluding some of the variables from (censored-robust) estimation. Interestingly, the influence of the multiple bank dummy is diminished when it is the only variable in the regression (Model 3): the point estimate drops from 0.759 to 0.487 and is no longer significant at the 5% level. The value of the log-likelihood statistic (27.22) strongly rejects the null hypothesis that the excluded variables are unimportant in estimation. The estimates in Model 4 suggest that ownership concentration adds no statistical explanatory power to the model. The value of the likelihood ratio test statistic comparing models 3 and 4 is 2.54, which is less than the 5% (one degree of freedom) critical value of 3.84. Adding the inflation-adjusted size variable to the multiple-bank relationship variable (Model 5) adds a much greater degree of explanatory power. The increase in the value of the likelihood ratio statistic comparing Model 5 to Model 3 is 20.2, which is far out in the right tail of chi-squared distribution. A likelihood ratio test comparing Models 5 and 1 indicates that the joint contribution of the ownership concentration, Tobin's Q and proportion-of-debt variables are marginally significant: the value of the statistic is 7.42 with an implied p-value of 0.06.
Overall, we find that the likelihood of ending a bank relationship is not strongly related to its duration. For instance, we cannot reject constant duration dependence using either non-parametric methods or parametric specifications in which the null of constant duration dependence can be tested. This result does not support the intuition suggested by asymmetric information models in which a bank customer becomes "locked-in" to the relationship. Nor does the result necessarily support the idea that firms will be more likely to leave the bank as the relationship lengthens.
The log-logistic specification provides a potential mitigating explanation for the results on duration dependence. A log-logistic distribution allows for duration dependence to be non-monotonic over different spell lengths, a feature not allowed by the Weibull specification. Estimates based on the log-logistic distribution are able to reject the null hypothesis of decreasing duration dependence in favor of a distribution that first decreases in duration and then increases. This relationship suggests the possibility that firms find it beneficial to search for the "right" bank in the early years of a relationship and then become locked in later in the relationship.
The estimated relationship between the likelihood of ending a bank relationship (or alternatively the duration of the relationship) and the explanatory variables is more stable: we find the likelihood of ending a bank relationship to be increasing (duration of relationship to be decreasing) in a firm's market-to-book ratio, when the firm maintains more than one bank relationship and to a lesser degree, in the proportion of the firm's assets financed by debt. We also find a strong relationship between the firm's real size, as measured by the inflation-adjusted log market value of equity, and the length of a relationship: larger firm's are less likely to switch banks than smaller firms. Moreover, we find no statistical relationship between the duration of the bank relationship and the level of ownership concentration in the firm.
The observation that multiple-bank firms are more likely to end a bank relationship is consistent with the information-based arguments that multiple bank relationships will decrease the value of private information to any one bank, reducing the ability for any one bank to lock in a customer. The results are also consistent with the notion that multiple-bank customers find it less costly to credibly communicate their value to the public, decreasing the value of holding any one bank relationship.
Our results, however, present a puzzle if we accept that the other explanatory variables served their intended use as proxies that indicate: (1) the level of firm uncertainty, (2) the overall need for financing and (3) the need for bank monitoring.
For instance, we would expect that larger firms would be more likely to have a higher switch rate (and shorter relationship duration), if there is less uncertainty about firm value in large firms and if large firms have a greater array of financing alternatives. Larger firms are less likely to be locked-in by a bank when exposure by analysts, regulators and journalists reveals more information about the firm. For the same reason, a large firm should have greater access to competitive alternatives to bank financing.
High growth firms, other things equal, should be more dependent on bank financing to fund investment opportunities. Moreover, growth firms may be riskier and more susceptible to information problems, since a larger portion of firm value is related to projects not yet realized (Martin, 1996). Thus it is also puzzling that we find that high growth firms are more likely to switch banks if higher risk, growth firms are more likely to be locked in to a bank relationship by information asymmetries with the public. A similar argument holds for firms with high debt financing. A high-debt financed firm within the bank-denominated Norwegian economy should find it costlier to leave a particular bank relationship, if banks maintain monopoly power.
Contrary to the implications from the information-based literature, our results suggest that firms that are in most need of bank financing maintain relatively shorter relationships and are more likely to end a bank relationship than firms where bank financing may be of a secondary need.
Many of the most interesting theories arising from the theoretical banking literature focus on the potential for a bank to mitigate information asymmetries that hinder firms from obtaining valuable financing. An appealing aspect of this literature comes from the idea that both banks and firms gain from their ongoing relationship. Firms which can only credibly communicate valuations at a large cost, gain from a bank's ability to dynamically improve a financing contract once the bank has privately observed the payment ability of the firm. The bank stands to gain from the relationship if it can "lock in" the firm as a customer and extract monopoly rents because of the information it learns about the firm.
The extent to which these theories have been explored empirically is limited. Petersen and Rajan (1994) and Berger and Udell (1995) study the importance of the duration of bank relationships and find somewhat conflicting results. Berger and Udell (1995) find that the interest rate charged and collateral pledged on lines of credit is decreasing in the length of a firm's relationship with its bank and Petersen and Rajan (1994) find that credit is more readily available to firms with longer bank relationships. Both papers argue that the favorable contracts terms to older customers arise through the shared benefits of relationship. On the other hand, Petersen and Rajan (1994) find no relationship between the average loan interest rate and the length of a firm-bank relationship.
Using a new time-series data set based on the bank connections of OSE-listed firms over the period 1979-1994, we explore the importance of bank relationships by studying the determinants of their duration and termination. We first explore the dependency between the length of a bank relationship and the decision to terminate the relationship and find no strong link between the two. This result is important by itself since the relationship-theories typically suggest a link between the duration of the relationship and the contracting possibilities available to the firm. We also explore firm characteristics that may influence the likelihood of ending a bank relationship. We find that the probability of ending a relationship increases when firms maintain more than one bank relationship and as a firm's Tobin Q and debt financing increases. Firms are less likely to end a bank relationship as they become larger.
Our results appear to run counter to the theories that suggest that banks have an ability to lock in customers which have more difficulty in communicating private valuations, already rely on bank financing or which are more likely to require financing in the future. On the contrary, we find that small, highly-leveraged growth firms are more likely to end a bank relationship than large, low debt "value" firms. Moreover, the concentration of ownership in a firm - a proxy for both alternative monitoring abilities and bargaining power - does not appear to influence the decision to end a bank relationship. These results may suggest that the selection of bank services is competitive enough to induce those most needing bank financing to "shop around".
Drawing too many conclusions from our study would be unwarranted, since our data set suffers from a number of shortcomings. First, we are unable to observe the reason for the termination of a firm-bank relationship. In this paper, we have implicitly assumed that any termination is initiated by the firm. It is likely that a bank could also terminate a relationship. A possible avenue for future research would investigate the sensitivity of observed bank switches to changes in the banking environment or to bank characteristics rather than firm characteristics. We are also unable to observe information specific to the contract between each firm and their bank: we can only observe that a relationship exists. Therefore, our study lacks an analysis of the influence of the cross-sectional variation that is sure to exist in the debt contracts held by the firm.
Berger, A. N. and G. F. Udell, 1995, Relationship lending and lines of credit in small firm finance, Journal of Business 68, 351-381.
Bhattacharya, S. and A. V. Thakor, 1993, Contemporary banking theory, Journal of Financial Intermediation 3, 2-50.
Billett, M. T., M. J. Flannery and J. Garfinkel, 1995, The effect of lender identity on a borrowing firm's equity return, Journal of Finance 50, 699-718.
Blackwell, N. R. and A. M. Santomero, 1982, Bank credit rationing and customer relation, Journal of Monetary Economics 9, 121-129.
Boot, A. W. A. and A. V. Thakor, 1994, Moral hazard and secured lending in an infinitely repeated credit market game, International Economic Review 35, 899-920.
Borio, C. E. V., 1990, Leverage and financing of non-financial companies: an international perspective, Bank for International Settlements Economic Papers 27.
Bøhren, Ø., B. E. Eckbo and D. Michalsen, 1996, Why underwrite equity offerings? Some new evidence, working paper, Norwegian School of Management and Stockholm School of Economics.
Bøhren, Ø., B. E. Eckbo, D. Michalsen and D. C. Smith, 1996, Corporate dividend policy in Norway, working paper, Norwegian School of Management.
Cox, D., 1972, Regression models and life tables, Journal of the Royal Statistical Society B 24, 187-201.
Diamond, D. W., 1984, Financial intermediation and delegated monitoring, Review of Economic Studies 51, 393-414.
Diamond, D. W., 1991, Monitoring and reputation: the choice between bank loans and directly placed debt, Journal of Political Economy 99, 688-721.
Eckbo, B. E., V. Maksimovic and J. Williams, 1990, Consistent estimation of cross-sectional studies in event studies, Review of Financial Studies 3, 343-365.
Fama, E. F., 1985, What's different about banks?, Journal of Monetary Economics 15, 29-39.
Greenbaum, S. I., G. Kanatas and I. Venezia, 1989, Equilibrium loan price under the bank-client relationship, Journal of Banking and Finance 13, 221-235.
Gritz, R. M., 1993, The impact of training on the frequency and duration of employment, Journal of Econometrics 57, 21-51.
Hodgman, D. R., 1961, The deposit relationship and commercial bank investment behavior, Review of Economics and Statistics, August, 257-261.
Jaggia, S. and P. K. Trivedi, 1994, Joint and separate score tests for state dependence and unobserved heterogeneity, Journal of Econometrics 60, 273-291.
James, C., 1987, Some evidence on the uniqueness of bank loans, Journal of Financial Economics 19, 217-35.
Johnson, N. and S. Kotz, 1970, Distributions in statistics: continuous univariate distributions, Vol.1, Wiley.
Kaen, F.R., and D. Michalsen, 1995, The effects of the Norwegian banking crisis on Norwegian bank and non-bank stocks, working paper, Norwegian School of Management.
Kane, E. J. and B. G. Malkiel, 1965, Bank portfolio allocation, deposit variability, and the availability doctrine, Quarterly Journal of Economics 79, 257-261.
Kaplan, E. L and P. Meier, 1958, Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481.
Kiefer, N. M., 1988, Economic duration data and hazard functions, Journal of Economic Literature 26, 646-679.
Klemperer, P. D., 1987, Markets with consumer switching costs, Quarterly Journal of Economics 102, 375-394.
Lancaster, T.,1979, Econometric methods for the duration of unemployment, Econometrica 47, 939-956.
Lummer, S. I. and J. J. McConnell, 1989, Further evidence on the bank lending process and the capital market response to bank loan agreements, Journal of Financial Economics 25, 99-122.
Martin, K. J., 1996, The method of payment in corporate acquisitions, investment opportunities and management ownership, Journal of Finance.
McCall, B. P., 1994, Specification diagnostics for duration models: A martingale approach, Journal of Econometrics 60, 293-312.
Nilsen, R., 1995, Markedet for risikokapital, in, Vale, B., ed., Norske finansmarkeder, norsk penge- og valutapolitikk, Norges Banks Skriftserie 23, 104-109.
Nilssen, T., 1992, Two kinds of consumer switching costs, RAND Journal of Economics 23, 579-589.
Nordal, I. A., and M. Nærland, 1995, Financial institutions in 1994, Bank of Norway Economic Bulletin 1, 69-97.
Petersen, M. A and R. G. Rajan, 1994, The benefits of lending relationships: Evidence from small business data, Journal of Finance 49, 3-37.
Petersen, M. A. and R. G. Rajan, 1995, The effect of credit market competition on lending relationships, Quarterly Journal of Economics, 487-443.
Rajan, R. G., 1992, Insiders and outsiders: The choice between informed and arm's-length debt, Journal of Finance 47, 1367-1400.
Ramakrishnan, R. T. S. and A. V. Thakor, 1984, Information reliability and a theory of financial intermediation, Review of Economic Studies 51, 415-432.
Roosa, R. V. , 1951, Interest rates and the central bank, money trade and economic growth: In honor of John Henry Williams (Macmillan, New York), 270-295.
Sueyoshi, G. T., 1992, Seminon parametric proportional hazards estimation of competing risk models with time-varying covariates, Journal of Econometrics 51, 25-58.
Sharpe, S. A., 1990, Asymmetric information, bank lending and implicit contracts: A stylized model of customer relationships, Journal of Finance 55, 1069-1087.
Shockley, R. and A. V. Thakor, 1993, Information content of commitments to lend in the future: Theory and evidence on the gains from relationship banking, working paper, Indiana University.
Slovin, M. B., M. E. Sushka and J. A. Polonchek, 1993, The value of bank durability: borrowers as bank stakeholders, Journal of Finance 48, 247-66.
Statistical Yearbook of Norway 1996, Statistics Norway, Oslo.
Stiglitz, J. and A. Weiss, 1983, Incentive effects of termination: applications to credit and labor markets, American Economic Review 73, 1069-1087.
Thakor, A.V., 1995, Financial intermediation and the market for credit, in: Jarrow, R., Handbooks in OR and MS 9, 1073-1103.
Wilson, P. F., 1993, The pricing of loans in a bank-borrower relationship, Working Paper, Indiana University.
Wood, J. H., 1975, Commercial bank loan and investment behavior,
Wiley, New York.
| Barclays Bank Plc., London | Midland Bank Mees Pierson N.V. |
| Bergens Skillingsbank | Morgan Guaranty Trust Co., NY or London |
| Bergen Bank A/S | National Westminster Bank |
| Brumunddal Ringsaker Sparebanken | Norges Hypotekinstitutt |
| Buskerudbanken A/S | Oslo-Banken |
| Bøndernes Bank A/S | Ringsaker Sparebanken |
| Chase Manhattan Bank, London or NY | Rogalandsbanken A/S |
| Chemical Bank, London, Oslo or NY | Royal Bank of Canada, London |
| Citibank | Sparebanken ABC |
| Credit Lyonnaise | Sparebanken Hedemark |
| Den norske Bank A/S | Sparebanken Midt-Norge |
| Den norske Creditbank A/S | Sparebanken Nord-Norge |
| Fellesbanken A/S | Sparebanken NOR |
| Finansbanken A/S | Sparebanken Oslo Akershus |
| First National Bank of Commerce, NY | Sparebanken Sør |
| Forretningsbanken A/S | Sparebanken Vest |
| Fokus Bank A/S | Sparebanken Vestfold |
| Gjensidige Bank | Sparebanken Østlandet |
| Hambros Bank Ltd., London | SR-Bank |
| Handelsbanken | Sunnmørsbanken A/S |
| Kreditkassen | Sørlandsbanken A/S |
| Landsbanken A/S | Sør-Varanger Sparebanken |
| Lazard Brothers & Co. Ltd., London | Telemarksbanken A/S |
| Manufacturers and Traders Trust Co., NY | Texas Commerce Bancshares, Houston |
| Manufacturers Hanover Corporation, NY | Trondhjems og Strindens Sparebanken |
| Meldal Sparebanken | Vestfoldbanken |
| Merging banks | into | Year |
| Den norske Creditbank A/S | Den norske Bank A/S | 1990 |
| Bergen Bank A/S | Den norske Bank A/S | 1990 |
| Buskerudbanken | Fokus Bank | 1987 |
| Bøndernes Bank | Fokus Bank | 1987 |
| Forretningsbanken | Fokus Bank | 1987 |
| Vestlandsbanken | Fokus Bank | 1987 |
| Rogalandsbanken | Fokus Bank | 1991 |
| Sørlandsbanken | Kreditkassen | 1990 |
| Sunmørsbanken | Kreditkassen | 1990 |
| Sparebanken ABC | Sparebanken NOR | 1990 |
| Sparebanken Vestfold | Sparebanken NOR | 1990 |
| Sparebanken Østlandet | Sparebanken NOR | 1990 |
| Texas Commerce Bancshares | Chemical NY Corporation | 1987 |
| Chemical NY Corporation | Chemical Banking Corporation | 1991 |
| Manufacturers Hanover Corporation | Chemical Banking Corporation | 1991 |
For each estimator of the integrated hazard function 
and for each duration 
, 
,
there exists an integrated hazard function 
with constant duration dependence, for which the hazard rate is
constant and equal to
,
and a survivor function equal to
.
The approximate variance of this survivor function 
with constant duration dependence is
,
for 
and 
and for 
and 
.
Hence this specification of the variance takes into consideration
the number of observations and the degree of censoring underlying
the original survivor function, 
.
To test the null of constant duration dependence against the
alternative of negative duration dependence in period 
at
5% level of significance, check
.
Notes. The third column lists the number of firms
in the sample listed for the first time on the OSE. The fourth
column lists the number of firms in the sample listed for the
last time on the OSE. Notice that firms can switch more than
one bank, hence the total number of relationships ending in each
year is at least as high as the number in the fifth column in
the table.
| Proportion of firms with multiple relationships | |
| One Bank | |
| Two Banks | |
| Three Banks | |
| Four Banks | |
| Number of relationships for each firm | |
| Mean | |
| Median | |
| Total Number of Firm Observations | |
| Proportion of Observations Censored | |
| Distribution of Observed Duration of Relationships, by Year | |
| < 1 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
| 11 | |
| 12 | |
| 13 | |
| 14 | |
| 15 | |
| Duration of Observed Relationships, in Years | |
| Mean | |
| Median | |
| Number of Banks in the Sample, by Type | |
| Domestic - Commercial | |
| Domestic - Savings | |
| International | |
| Total | |
| Banks involved in mergers | |
Notes. Number of observations: 263. MREL takes the value of 1 when a firm maintains a multiple-bank relationship at some point during the sample period and takes the value 0 otherwise. CONC is the proportion of a firm's equity owned by the ten largest shareholders. SIZE is the log of end-of-year market value of equity, deflated by the Norwegian CPI. Q is the ratio of the end-of-year market value of equity plus book value of assets divided by the book value of assets. DEBT is the ratio of the book value of debt to the sum of the market value of equity plus the book value of debt.
| |||||
Notes. Number of observations: 263.
 |
 |  | |||||||||
|
|
|
|
|
|
|
|
|
| ||
|
|
|
|
|
|
|
|
| |||
|
|
|
|
|
|
|
|
| |||
Notes. Number of observations: 263. MREL takes the value of 1 when a firm maintains a multiple-bank relationship at some point during the sample period and takes the value 0 otherwise. CONC is the proportion of a firm's equity owned by the ten largest shareholders. SIZE is the log of end-of-year market value of equity, deflated by the Norwegian CPI. Q is the ratio of the end-of-year market value of equity plus book value of assets divided by the book value of assets. DEBT is the ratio of the book value of debt to the sum of the market value of equity plus the book value of debt. All estimates are adjusted for censoring. Coefficients are listed on the first row in each cell and standard errors are reported below between parentheses. The last column lists the log of the likelihood L() and the log likelihood ratio test statistic between parentheses. Based on the log likelihood ratio test statistic, -2log(L(weibull)/L(expo)), which is asymptotically 2(1), H0: =1 cannot be rejected in the Weibull model. *** Significant at 1%, ** significant at 5%, * significant at 10%. ªª Significantly different from one at a 5% level.
|
|
|
|
| |||
|
|
|
|
| |||
|
| ||||||
|
|
| |||||
|
|
| |||||
|
|
| |||||
Notes. Number of observations: 263. MREL takes the value of 1 when a firm maintains a multiple-bank relationship at some point during the sample period and takes the value 0 otherwise. CONC is the proportion of a firm's equity owned by the ten largest shareholders. SIZE is the log of end-of-year market value of equity, deflated by the Norwegian CPI. Q is the ratio of the end-of-year market value of equity plus book value of assets divided by the book value of assets. DEBT is the ratio of the book value of debt to the sum of the market value of equity plus the book value of debt. The estimates in model 2 are not adjusted for censoring. The estimates in model 1 and 3 to 6 are adjusted for censoring. Coefficients are listed on the first row in each cell and standard errors are reported below between parentheses. The last column lists the log of the likelihood L() and the log likelihood ratio test statistic between parentheses. The latter statistic is -2log(L(1)/L(i)), asymptotically 2(n) , with i=3,..., 6, and n=4 if i=3 and n=3 otherwise. *** Significant at 1%, ** significant at 5%, * significant at 10%.
Proportion of the firms in the sample having one to four relationships.
| MREL | ||
| CONC | ||
| SIZE | ||
| Q | ||
| DEBT | ||
Notes. Number of observations: 263. The bold solid
line represents the survivor function of the "low" group
of firms, the other solid line represents the survivor function
of the "high" group. The dashed lines represent a band
of 2 standard deviations around the survivor function of the "low"
group. The stratification sheme for MREL has 107 observations
in the "low" group. These firms have only one relationship.
The cut-off levels in the other stratification shemes are chosen
in order to approximately divide the sample in two equally sized
groups: there are 132 observations with CONC lower than 0.7, 126
observations with SIZE lower than 7.5, 156 observations with DEBT
lower than 0.6, and 135 observations with Q lower than 1.25. ***
Significant at 1%, ** significant at 5%, * significant at 10%.