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Federal Reserve Bank of Chicago

Bank Imputed Interest Rates:
Unbiased Estimates of Offered Rates?
Evren Ors and Tara Rice

WP 2006-26

Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?

Evren Ors
Finance & Economics Department
HEC School of Management
78351 Jouy-en-Josas, France
+33.1.39.67.71.23
ors@hec.fr
and
Tara Rice
Economic Research
Federal Reserve Bank of Chicago
230 South LaSalle Street
Chicago, Illinois, USA
312-322-5274
trice@frbchi.org
November 2006

Abstract
We examine whether “imputed” interest rates obtained from bank financial statements are unbiased
estimates of “offered” interest rates that the same banks report in surveys. We find evidence of a
statistically significant amount of bias. However, the statistical bias that we document does not appear to
be economically significant. When used as dependent variables in regression analysis, imputed rates and
offered rates lead to the same policy conclusions. Our work has important methodological implications
for empirical research that examines the product market competition among depository institutions.
Key words: deposit rates, transactional rates, imputed prices, product market, competition
JEL codes: G21, L11
The views presented here are those of the authors and do not necessarily reflect the views of the Federal
Reserve Bank of Chicago or the Federal Reserve System. We are thankful for comments and suggestions
made by Robert DeYoung, Bill Marcum, session participants at the 2006 WEA Meetings, and the seminar
participants at the Federal Reserve Bank of Chicago, the Federal Deposit Insurance Corporation, George
Washington University, and the Board of Governors of the Federal Reserve System.

Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?
1. Introduction
Analysis of product market competition in the banking and finance literature (and more generally,
in the industrial organization literature) has critical public policy implications. It aids antitrust analysis,
for example, in determining whether proposed bank mergers will adversely affect consumers through
increased market concentration. The theory models on which this analysis is based refer to prices that the
banking firm offers to its customers given the structure of the market it faces. Likewise, the empirical
literature examines the statistical relationship between the banking product prices and market
concentration. This line of research uses deposit and loan interest rates as dependent or explanatory
variables. Those prices are, however, a topic of contention. Prices are difficult to measure and in the
banking research, as is the case in most fields of economic research, transaction prices are difficult to
obtain. The alternative is to impute prices, that is, to calculate prices by taking the ratio of interest
expenses (revenue) to the stock of deposits (loans).

However, imputed prices, which incorporate

measurement error, may incorporate bias that affects the results of empirical analyses.
In this paper, we examine whether “imputed” (calculated) interest rates are suitable estimates of
“offered” (transaction) interest rates using a set of U.S. banks for which both rates are observable. What
we term as “offered” rates are those explicitly stated by banks in surveys, and we assume that the offered
rates are indeed the “true” interest rates to which the theory models refer.1 Many researchers, however,
rely on interest rates that are imputed from the financial statements because offered rates are either only
observable for a limited sample of banks or simply not observable. Even when observed, offered rates
may not be readily accessible because they are collected through surveys that are either confidential or
sold by private data providers.2 This contrasts with imputed interest rates which are calculated using

1
2

We discuss whether such an assumption is warranted later in the paper.
In the U.S., interest rate survey data collected by the Federal Reserve System, such as the Monthly Survey of
Selected Deposits or the Survey of the Terms of Lending, remain confidential. Access is limited to economists
working for one of the federal banking regulators. Data from private data providers, such as the Bank Rate
Monitor, are available at a non-trivial cost.

information provided in the financial statements. While financial statements, and as a result, imputed
interest rates, are available at no cost for the population of U.S. banks, these constructed variables may
involve significant measurement error that could lead to systematic bias. Whether such bias exists and, if
it exists, whether it affects empirical model estimates are questions that have not been systematically
explored.3 In this paper, our goal is to determine whether using imputed rather than offered interest rates
leads to any statistically and economically significant bias. We focus on deposit accounts, rather than
loans, because the former have more standard product characteristics than the latter.4
Our work has important methodological implications for large strands of empirical research on
depository financial institutions. Our results provide evidence of statistically significant bias: the raw
imputed deposit rates are not particularly good estimates of the stated interest rates that banks offer to
their customers. However, the observed bias decreases when imputed rates are winsorized or truncated,
with the truncation being more effective than the winsorization. Once the imputed rate data have been
truncated, they become more suitable estimates of the offered rates. Moreover, the observed statistical
bias is not economically significant. We show that the coefficient estimates obtained when either imputed
or offered rates are used as dependent variables have the same sign, same order of magnitude and the
same order of statistical significance. The important implication of our work is that, when properly
adjusted for measurement error, imputed interest rates lead to the same policy conclusions as offered
rates. The paper proceeds as follows: section 2 presents the data, section 3 provides a short survey of the
relevant literature, section 4 presents our empirical analysis, and section 5 concludes.

3
4

Hannan and Prager (1999) touch on this in their work. We discuss their paper below.
Loans are significantly more heterogeneous intermediation products than deposits. This holds true even for more
standardized lending contracts, such as mortgages. Although it is possible to observe and control for some of the
price and non-price loan characteristics in the loan survey data that are available (such as the Survey of the Terms
of Lending), it is not possible to create imputed rates for homogeneous loan categories using Call Reports due to
lack of detail at the product level. Moreover, loans’ differing maturities make it difficult to compare imputed loan
rates with lending rates offered to customers.

2. Data on Offered Rates and Imputed Rates
We combine data from three different sources. Imputed deposit interest rates are calculated using
data from the Consolidated Reports of Condition and Income (the Call Reports), the publicly available
quarterly financial statements that all U.S. commercial banks file with their federal regulators. We impute
rates for three types of deposit accounts for which information is available in the Call Reports: Negotiable
Order of Withdrawal (NOW) accounts, Money Market Deposit Accounts (MMDA), and passbook
savings accounts. NOW accounts, first introduced in 1980, are interest paying withdrawal-upon-demand
checking accounts with minimum balance requirements. MMDA accounts, first introduced in 1982 by
banks to compete with the Money Market Mutual Funds, pay higher interest rates than NOW accounts but
have more restrictive check-writing privileges and higher minimum balance requirements than NOW
accounts.5 Passbook savings accounts are traditional household saving instruments without check-writing
privileges.6
The imputed rates are calculated for each of the three account types by dividing the quarterly
interest expense in the Call Reports by the stock of deposits for that quarter. It should be noted that the
Call Report deposit expense items do not include any other fees or expenses related to deposit account
management.7 We use two measures of quarterly imputed rates. The first of these is based on the latest
stock of deposits of the corresponding account type at the current quarter’s end, and the second is based
on the average of deposits over the quarter.8

The survey offered rates are stated as simple (non-

Prior to the introduction of NOW and MMDA accounts, checking accounts did not pay explicit interest in the U.S.
By 1984, the start of our sample period, both types of accounts were among the standard banking products.
6
We exclude certificates of deposits (CDs) and negotiable certificates of deposits (NCDs), which are non-checkable
savings accounts with specific maturities, from our analysis. Although interest rates on these instruments are
included in the MSSD survey, there are no corresponding interest expense items in the Call Reports that are
detailed enough to impute maturity-specific CD rates.
7
Our focus, similar to most of the empirical banking literature, is on explicit interest rates. Implicit rates paid on
deposits (in the form of service flows, such as the number checks or transfers allowed per month) and fees that
depositors are charged are excluded from our analysis. Note that, since we match imputed rates that we calculate
for a particular bank with the offered rates by the same institution, differences in implicit interests or fees charged
across banks do not affect our analysis.
8
The stock of deposits is stated in Schedule RC-E of the Call Reports and the quarterly average is reported in
Schedule RC-K of the Call Reports.

compounded) annual percentage rates. To make the quarterly imputed rates comparable with the annual
offered rates, we multiply the quarterly imputed rate by four to obtain a simple annual rate.9
NOW, MMDA and savings account interest rates offered by banks are collected from the Federal
Reserve System’s Monthly Survey of Selected Deposits (MSSD), available to us starting with January
1987. The MSSD stopped collecting offered interest rate information in September 1994 and was
discontinued in 1997.10 The survey respondents were asked to provide the most commonly offered
interest rate on the largest volume of deposits per deposit type during the last week of each month.11 The
MSSD provided offered-rate data at the bank rather than at the bank and market (or branch) level.
Because the MSSD data sampling frequency is higher than the reporting frequency of the Call Reports,
we use two alternative measures: the survey rates from the last month of the quarter and the average of
monthly survey rates for the quarter.
We also collect market structure variables from the Federal Deposit Insurance Corporation’s
(FDIC) annual Summary of Deposits datasets, and market level personal income data from the Bureau of
Economic Analysis’ Regional Economic Information database.
An additional survey data set is currently available to researchers, the Bank Rate Monitor (BRM)
data. The BRM is a survey provided by a private data vendor that collects bank and market level data on
a weekly basis. Due, however, to substantial reporting issues which render these deposit prices
incomparable with Call Report imputed prices, we do not use the BRM data. The primary issue is that the
BRM Survey asks participating banks to provide the rates for the banks’ “lowest minimum to open” noninterest checking account and “lowest minimum to open and earn interest” checking account. Thus, the
9

Note that the resulting imputed rate is based on interest paid, which is compounded interest. Since the Call
Reports do not include any information regarding the frequency of the compounding periods (which varies across
banks from monthly to semi-annual) we do not make any further adjustments to imputed rates. As it will be seen
below, despite this error, our imputed rates slightly underestimate the offered survey rates.
10
Until end of June 1989, MSSD collected the most commonly offered rate per account type. Starting with July
1989, MSSD surveys collected more detailed NOW and MMDA information that accounted for the possibility that
the bank may offer higher rates for larger maintained-balances. For consistency in our data series, we filtered
these data to collect only the most commonly observed offered rate per account type. Samples available to us end
in September 1994, because after that date MSSD started to collect interest expense information, instead of interest
rate information.
11
Arguably, offered interest rate per number of accounts is a better definition for “most common” than one based on
the dollar volume of deposits, but MSSD opts for the latter rather than the former.

rates stated in the BRM data are effectively the lowest rates offered by banks, not the most-commonly
cited rates (the mode) as in the MSSD data or the imputed average interest rate paid by the bank (the
mean) obtained from the Call Report data.

Moreover, BRM does not provide information on the

percentage of deposits that earn the lowest rates, nor information on rates paid to accounts with greater
deposit balances. As a result, we cannot infer the mean or the mode of the rate distribution from BRM
data. In summary, as no additional information on the distribution of the BRM deposit rates is available
that would allow researchers to infer the central tendencies of the surveyed rates, we conclude that the use
of BRM data in analysis would provide ambiguous results.12

3. Literature Survey
Given the methodological focus of this paper, we confine our literature survey to the studies,
namely the Structure Conduct Performance (SCP) tests, that have examined the relationship between local
market concentration and deposit interest rates where either the offered or the imputed interest rates have
been used as dependent variables. In section 4.3, we test whether using imputed versus offered rates in
tests of market concentration and deposit rates leads to economically different results. The SCP paradigm
implies a relationship between market concentration and firm conduct (in terms of profit or performance);
such that noncompetitive behavior in more concentrated markets results in a positive (negative)
relationship between market concentration and profitability (deposit prices).
While early studies examined the relationship between market concentration (as measured by the
Hirschman Herfindahl Index) and profitability, Berger and Hannan (1989) was the first to test the pricemarket concentration relationship using MSSD offered rates rather than testing the profit-concentration
relationship. The authors’ results strongly support the SCP hypothesis when MMDA, NOW and short12

We examined the BRM surveyed NOW and MMDA rates between January 1998 and December 2000 and
compared them with the corresponding imputed rates obtained from the Call Reports. For the said period, BRM
rates were significantly lower than the corresponding imputed rate. For NOW accounts mean (median) BRM rate
was 1.23% (1.01%) compared to mean (median) Call Report imputed rate of 2.56% (1.64%) for the same banks over
the same period. For MMDA accounts BRM rate mean was 2.29% (median 2.25%) compared to 3.14% (3.14%) for
imputed rates.

term CD rates are used as measure of deposit account prices. Most of the studies that followed using the
MSSD data confirm this negative relationship between deposit rates and market concentration (Calem and
Carlino (1991), Berger and Hannan (1991)), though not without exceptions (for example, Jackson
(1992)). Other studies using MSSD data examine how banks change the rates they offer depositors
(Neumark and Sharpe (1992)), and whether the relationship between market concentration and deposit
rates holds when concentration changes due to mergers (Prager and Hannan (1998)) or bank branching
restrictions (Calem and Nakamura (1998)). A recent study by Brewer and Jackson (2004) considers the
effects of including bank-specific risk variables (which capture nonperforming loans, capital and the
interest-rate sensitivity of assets and liabilities) in the SCP analysis.
Another set of studies use imputed deposit rates obtained from the Call Report data (Heitfield and
Prager (2002), Rosen (2003), Dick (2002), Hannan and Prager (2004) and Hannan and Prager (2006)) and
find results generally consistent with studies using the MSSD data. These more recent studies contribute
to the literature by testing additional aspects of the SCP paradigm. Rosen (2003), for example, examines
whether the size distribution of banks in a market (in addition to market concentration) affects the deposit
rates. Heitfield and Prager (1998) test the price-concentration relationship using alternative measures of
markets (defined at the Metropolitan Statistical Area or MSA and state-level) and find that while local
market concentration measures are useful, broader concentration measures are also appropriate. Several
of the studies comment on the advantage of using the imputed Call Report prices given the extended time
period for which these data are available (e.g., Rosen (2003), Heitfield and Prager (1998)).13
What differs among these studies is the particular interest rate that is found to have the strongest
relationship (in terms of statistical significance), and the economic implications of the results. Berger and
Hannan (1989) find that MMDA rates are 25 to 100 basis points less in the most concentrated markets
than in the least concentrated markets. They find similar results for NOW and savings account rates, but
13

To date, only a few studies to date have used the Bank Rate Monitor data, partly due to its inaccessibility to
researchers and academics until recently. These studies, however, have not been direct tests of the SCP hypothesis.
Radecki (1998) and Heitfield (1999) examine the appropriate size of the ‘local-market’; Rosen (2002) presents a
model of price setting in the presence of heterogeneous customers; and Kiser (2003) studies whether conditions in
the bank loan market affect the pricing of retail deposits.

not for longer-term CD rates. Calem and Carlino (1991) use MMDA and short-term CD rates (3 and 6
months) and find similar results, though they do not interpret the economic effects of their findings.
Berger and Hannan (1991) focus solely on MMDA rates and find an asymmetric relationship between
rate increases and decreases: a 29 basis point decrease in the rate of market treasuries leads to 62 percent
probability that a bank will reduce its MMDA rate. The same increase in market rates leads to a 39
percent probability that a bank will increase its MMDA rate.
Neumark and Sharpe (1992) use MMDA and 6 month CD rates and find that the rates, on
average, drop 60 basis points between the least to most concentrated markets. Rosen (2003) includes
MMDA and NOW accounts also, and finds a small 4 to 7 basis point change in rates with a one standard
deviation change in the market concentration. He attributes a larger change in deposit rates to market size
than market concentration. Brewer and Jackson (2004) find that the magnitude of the relationship
between deposit rates and market concentration decreases by 50 percent when bank-specific risk variables
are included in the SCP analysis.
In summary, most studies use MMDA or NOW accounts, find strong statistical significance using
MMDA accounts, less so using NOW accounts and find vastly different economic implications for the
results. What is not evident is whether the different economic results found using different rates depend
on the additional elements included in later studies (i.e., market size, megamergers) or the dataset and
specific rates used. We examine this issue in tests of the SCP hypothesis below.
The only study that examines whether using MSSD offered rates versus Call Report imputed rates
may lead to different inferences is Prager and Hannan (1999). In an earlier paper, Prager and Hannan
(1998), the authors used MSSD offered rates and found that substantial horizontal mergers lead to
statistically significant decreases in NOW and MMDA rates (24 and 32 basis point decreases,
respectively).

When revisiting this evidence using Call Report imputed rates (which results in

significantly larger samples), Prager and Hannan (1999) find that large horizontal mergers have no effect
on NOW and MMDA accounts, whereas such mergers lead to a small decrease in savings account rates (9

basis points).14 Prager and Hannan (1999) then investigate whether this discrepancy is due to the data
source upon which each study relies. They repeat their analysis for a subsample of banks for which both
offered and imputed rates are available, and find that coefficient estimates differ significantly depending
on whether monthly MSSD offered rates or quarterly Call Report imputed rates are used. The authors
note that the coefficient estimates have the same sign but they do not necessarily have the same statistical
significance. Further, the authors find that the coefficients of correlation between offered and imputed
series range between 0.731 and 0.933 for NOW accounts and 0.515 and 0.689 for MMDA accounts. The
authors conclude Call Report imputed prices are “noisy” and “should be used with caution.”
Our study differs from theirs in a number of dimensions. First, the Prager and Hannan (1999)
analysis is limited to a comparison of the coefficient estimates of their model when offered or imputed
rates are used as dependent variables. In contrast, we provide formal tests of the bias analyzing the
direction and the size of the potential bias. Second, we discuss the reasons why the observed difference
may exist in the two series. Third, Prager and Hannan (1999) use all of the monthly survey interest rate
observations and the quarterly imputed series that are available to them when estimating their empirical
model. In contrast, throughout our analysis we include only those banks that have both available offered
and imputed interest rates. Our approach allows us to compare the differences in standard errors while
the estimates are based on the same exact number of observations for the same banks in the same
quarters.
Finally, a number of studies examine the effects that the presence of multimarket (i.e., larger,
regional or national banks) may have on local market competition, specifically the impact on small singlemarket banks (community or rural banks). Cohen and Mazzeo (forthcoming) assess competition among
financial institutions in rural markets by differentiating among different types institutions (single-market
banks, multimarket banks and thrifts).

The authors find that heterogeneous institution types affect

competition and profitability and conclude that analysis of market concentration should address this
differentiation. Berger, Dick, Goldberg, and White (forthcoming) find similar results. These authors
14

Savings accounts were not analyzed in Prager and Hannan (1998).

examine how competition from large, multimarket banks affects the performance of small, single-market
banks in the same markets and how that competition changed over time. The authors find that technical
progress enabled large multimarket banks to compete more effectively against small single-market banks
in the 1990s. This finding did not hold with large banks that remained in a single market. Results of
these studies provide strong support for conducting robustness checks on a sample of single-market
banks, rather than examining both multimarket and single market banks together.

4. Empirical Analysis
We conduct three sets of tests to examine whether imputed deposit rates are representative of the
deposit rates that banks offer to customers. First, we examine the distributions for the imputed and
offered rates for different types of deposit accounts. Second, we test the null hypothesis that imputed
interest rates are unbiased estimates of rates that banks offer by regressing offered deposit rates on their
imputed counterparts in cross-sectional OLS regressions.

In this step, we also examine whether

winsorizing or truncating helps reduce any statistical bias that may exist. Finally, to examine whether
observed statistical differences have any impact on empirical estimations, we estimate separate SCP
regressions where the dependent variable is first the offered deposit rate and then the imputed deposit
rate.

4.1 Alternative measures of imputed and offered rates
The MSSD is a monthly survey. Thus, we use the offered rates from last survey of the quarter
(where R_MSSD_END denotes the MSSD rate at the quarter’s end) and an average of the monthly
surveyed deposit rates during the quarter (R_MSSD_AVE, where AVE denotes quarterly average of the
MSSD rate). Included in our MSSD dataset are offered interest rates from 1987 to 1994 for three types of
accounts: NOW, MMDA and savings accounts.
The two Call Report imputed rates that we use in our analysis are (1) the ratio of the end-ofquarter deposit expense (for each account type) divided by the end-of-quarter stock of deposits for the

corresponding account type and quarter (R_CR_END) and (2) the ratio of the end-of-quarter deposit
expense (for each account type) divided by the average stock of deposits over the quarter (R_CR_AVE).

4.2. Descriptive Statistics and Univariate Tests
In Table 1 Panel A we provide detailed distribution information on all of the interest rate series
that we use in our analysis. The imputed rates obtained from the Call Report contain extreme outliers.
Maxima and minima presented in Panel 1A. MSSD survey rates also contain interest rates that are too
small or too high, suggesting that the survey data, too, contain outliers.
One method to minimize the effect of such extreme observations on the empirical analysis is to
winsorize the variable in question by assigning the tail observations to a specified percentile of the data.
We assign the observed values below the 1st and above 99th (5th and 95th) percentiles of the distribution, to
the values of the 1st and 99th (5th and 95th) percentiles, respectively. Alternatively, one could truncate the
series by dropping observations that are lower or higher than a given threshold at either end of the
distribution. Each of these methods, however, has its weaknesses. While both methods preserve the
central tendency of the distribution for the variable in question, truncation throws out valuable
observations whereas winsorization assigns arbitrary values to observations that fall outside of the set
threshold.
Panel 1A suggests that the large discrepancies observed in the tails of the distributions between
R_MSSD and R_CR series are attenuated when we move to the 5th and 95th percentiles of series’
distributions. The 25th, 50th and 75th quartile observations show relatively smaller differences. We,
therefore, work with data series that are winsorized or truncated at 1st–99th or 5th–95th percentiles. The
tests that we conduct provide guidance whether winsorize or truncate and at what level. While higher
levels of winsorization or truncation are certainly possible, we do not consider them here as it would lead
to the loss of valuable data points and are unlikely to be adopted by researchers.
In Panel 1B, we test the statistical significance of the observed differences that we observe in
Panel 1A for selected pairs of survey and imputed rate series that are winsorized at the 1st–99th percentiles

of their distributions (first three columns of Panel 1B) or truncated at the 5th–95th percentiles (last three
columns). The t-tests of the equality of the means are rejected in all of the cases at the 1 percent level
(except for the truncated savings account rates rejected at the 5 percent level). The equality of the
variances (the variance ratio test) is also rejected at the one percent level for all six pairs of series that we
examine. The rank-order correlations range between 0.51 to 0.89, and are the lowest for savings account
series and the highest for the NOW account series. These results suggest that, even though the survey and
imputed rate series that we examine are highly positively correlated, they may incorporate important
differences that might lead to imputed rates being biased estimates of survey rates.
The results of Table 1 provide evidence of statistically significant differences between the offered
rates obtained from MSSD data and the corresponding imputed rates obtained from the Call Report data
(for the same set of banks in the same quarters).
There are a number of reasons why the imputed rates would not be good estimates of the offered
rates. The imputed rates, a ratio of the interest expense and the stock of deposits, are affected by error in
either component. Such errors include data entry errors, rounding issues, and reporting errors which may
distort the imputed rate. Data entry errors are uncommon, but do exist. Such errors include: entries with
an incorrect number of zeros, and general typos (reporting the wrong numbers or putting them in the
wrong item number). All dollar amounts entered into the Call Reports are rounded to the nearest $1,000.
Thus, rounding issues are of greater concern for smaller banks which may end up having less accurate
imputed rates. A number of reporting errors are likely to affect either the interest expense or the stock of
deposits reported by banks. In reporting the interest expense, for example, banks are instructed to deduct
from gross interest expense any penalties for early withdrawals or portions of such penalties that represent
the forfeiture of interest accrued or paid to the date of withdrawal. This accounting requirement would
reduce the amount of net interest expense reported by any bank that had early withdrawals.

Next, we investigate to what degree researchers of financial institutions should consider
winsorization or truncation of imputed rates obtained from bank financial statements. Following this, we
examine whether these observed differences generate biases of which researchers should be aware.

4.3. Winsorization versus Truncation of the Offered and Imputed Deposit Rates
These outliers, attributed to reporting errors, rounding errors, and mismeasurement, are
substantial. Specifically, the MSSD-based MMDA offered rates range between 0.01% and 15.48%,
whereas the corresponding raw imputed rates range between –60.53% and 216.05%. Similar outliers are
observed for all of the offered and imputed deposit rate series in our samples.
To examine the effects of different levels of winsorization and truncation, we regress the
winsorized (truncated) offered rate series on winsorized (truncated) imputed rate series with the same
level of winsorization or truncation:

R_MSSD i, t = α + β R_CR i, t + ε i,t ,

(1)

where R_MSSDi,t is the offered rate collected from the MSSD survey, and R_CRi,t is the corresponding
Call Report imputed interest rate. We use 1st-99th and 5th-95th percentile thresholds when winsorizing or
truncating. In regression (1), if imputed rates are unbiased estimates of the offered rates, the null
hypothesis requires that α=0 and β=1.15
The OLS regression estimates of equation (1) for NOW accounts are presented in Table 2.16
The left-hand-side of Table 2 presents results using the quarter-end rate for the survey data
(R_MSSD_CR) and imputed rates based on the stock of NOW accounts at the end of the quarter
(R_CR_END). The null hypothesis (H0: α=0 and β=1) is rejected in Table 2. The F-test results are
provided at the bottom of the table. When using the imputed rates winsorized at the 1st-99th percentile of

ˆ
ˆ
their distribution, we obtain estimates of α =0.0135 and β =0.6594. Truncating at the same threshold
15

This null hypothesis is in fact a joint-hypothesis since it presumes that offered transaction rates are the “true”
interest rates in which researchers are interested.
16
We repeat the analysis using MMDA and savings account rates, but to conserve space, we do not to report these
results.

ˆ
ˆ
level, we obtain estimates of α =0.0094 and β =0.7644. Moving the threshold to the 5th-95th percentiles
ˆ
ˆ
and winsorizing the series yields α =0.0064 and β =0.8473, whereas truncating at the latter level yields
ˆ
ˆ
α =0.0040 and β =0.9183. The regression R2s systematically increase from 0.6333 to 0.8088. These
results indicate that truncation at the higher threshold (5th-95th percentiles of the imputed rate distribution)
provides a better fit than the other options tested. However, the null hypothesis of no bias (H0: α=0 and
β=1) is rejected for all four regressions.
In the right-hand side of Table 2, we repeat the above analysis by regressing the average of rates
surveyed in a given quarter (R_MSSD_AVE) on imputed rates that were calculated based on the average
stock of deposits during the same quarter (R_CR_AVE). The results show that the bias is reduced in all
of the regressions when compared with their counterparts on the left-hand side of Table 2.

The

ˆ
ˆ
coefficient estimates for the series winsorized at the 1st-99th percentiles are now α =0.0073 and β =0.8343
with an R2 of 0.7895. The coefficient estimates for the series truncated at the 5th-95th percentiles are

ˆ
ˆ
ˆ
ˆ
α =0.0026 and β =0.9627 with an R2 of 0.8857. Despite a lower α and a higher β , the null hypothesis
of no bias is still rejected in all of the regressions.
We conclude that survey rates and imputed rates truncated at the 5th and 95th percentiles of their
distribution show the least amount of statistical bias. In the next section, we repeat this analysis and
check the robustness of our results for rates on other account types.

4.4. Robustness Checks
In this section, we examine first whether the results observed for NOW accounts in Table 2 also
hold for MMDA and savings accounts. We find that they do not. Columns 1 and 2 of Panel 3A repeat
columns 4 and 8 of Table 2, respectively, for NOW accounts, while columns 3 and 4 of Panel 3A present

the results for MMDA accounts.17 A sharp increase in the bias appears with regard to the MMDA rates
results. As column 3 shows, regressing R_MSSD_END on R_CR_END for MMDA accounts yields

ˆ
ˆ
ˆ
ˆ
α =0.0280 and β =0.4863 with an R2 of 0.3408 (compared to α =0.0038 and β =0.9244 and an R2 of
0.8107 for the comparable NOW account rates in the first column). Regressing R_MSSD_AVE on

ˆ
ˆ
R_CR_AVE (column 4) yields α =0.0227 and β =0.5832 with an R2 of 0.4622. The observed bias is
ˆ
ˆ
higher yet in the case of savings account rates (column 6); where α =0.0325, β =0.3689 and R2=0.2964.
Not surprisingly, the null hypothesis of no bias is strongly rejected in all of the cases in Panel 3A. When
we repeat our bias regressions with the interest rate variables winsorized or truncated at 1st and 99th
percentiles, we find larger bias (we do not report these results to conserve space).
Given the discrepancy in the bias tests between the NOW accounts versus the MMDA and
savings accounts, we examine whether the observed differences hold in different subsamples.
Specifically, we explore whether these discrepancies hold across (i) multimarket versus single-market
banks (which may potentially explain the observed differences if NOW account rates have less dispersion
than the MMDA or savings account rates for multimarket banks) and (ii) urban (MSA) versus rural banks.
The results presented in panels 3B and 3C show that the results observed in Panel 3A for the overall
sample also hold for the above-mentioned subsamples. NOW account rates show the least amount of
bias.
In Panel 3B, we re-estimate regression (1) for multimarket and single-market banks with the
series that show the least amount of bias (rates based on averages truncated at the 5th and 95th percentiles).
The results for multimarket banks are very similar to those for single-market banks. For example,

ˆ
multimarket bank NOW account rates (column 1 of Panel 3B) yield estimates of α =0.0024

The number of observations for the NOW account regressions differs slightly between Tables 2 and 3. We restrict
the regressions in Table 3 (for all account types) to contain observations for which the end of quarter rates and
average of the quarter rates are available for each bank. This allows better comparison of the bias inherent in either
end or average rates for each account type.

ˆ
and β =0.9752, with R2=0.8755.

The single-market bank NOW account rates (column 4) yield

ˆ
ˆ
α =0.0027, β =0.9599 and R2=0.8982. Similar results hold for the MSSD and savings account rates.
We also examine whether the bias differs between urban (MSA) versus rural banks, two
subsamples that researchers typically examine separately due to the differences in these markets’
characteristics. In results presented in Panel 3C, we observe that the amount of bias (always statistically
significant) remains about the same for banks operating in these two different types of markets for NOW
and MMDA accounts. In the case of savings accounts, the bias for rates reported by urban banks is larger
than the bias associated with the rates reported by rural banks.
These results suggest that there are no major discrepancies in the way imputed rates relate to
survey rates when one compares the multi- versus single-market banks or urban versus rural banks.
However, the bias is statistically significant for all rates considered in the different subsamples that we
examined. What holds across these tests is that the observed bias is the smallest for NOW accounts,
much larger for MMDAs, and even larger for savings accounts.
A number of reasons exist as to why the observed bias may differ across account types. The
larger biases observed for MMDA and savings accounts may be due to the fact that banks are more likely
to offer rate schedules tiered by deposit amount for MMDA and savings accounts than for NOW
accounts. If so, then the offered schedules for MMDA and savings accounts would incorporate more
dispersion than those for NOW accounts and mode of the distribution collected by the MSSD may be less
representative of the distribution of rates for MMDA and savings accounts than it is for NOW accounts.
Another possible source of discrepancy is the minimum amount that is required for the payment
of interest. Banks typically impose such minimum thresholds, and these are likely to be higher for
MMDA and savings accounts than they are for NOW accounts. If so, MMDA and savings accounts may
carry proportionally larger number of accounts that carry non-interest earning balances because they fell
below the interest-earning threshold required by the bank.

Despite these data errors and issues, the existence of statistical bias need not result in
economically different inferences when imputed rates are used instead of offered rates. We test this
conjecture next.

4.5. Imputed Deposit Rates versus Offered Deposit Rates in SCP Analysis
In this section, we compare the results of deposit price-market concentration regressions to
determine whether using imputed interest rates instead of the offered interest rates leads to different
conclusions in studies of the relationship between market concentration and prices (or tests of the SCP
Hypothesis). While the scope of this test is limited to a specific case, it is relevant because deposit price
information has been commonly used in SCP analysis. We conduct regressions based on equation (2)
below and present the results in Table 4:
T

R i, t = a + b1 HHI i ,t + b2 MSAi ,t + b3 HHI i ,t × MSAi ,t + b4 PIPCi ,t + ∑ ct Dt + ei ,t ,

(2)

t =1

where Ri,t is the deposit-account specific offered or imputed interest rate (R_MSSD or R_CR,
respectively), HHI is the Herfindahl-Hirshman Index of market concentration (calculated for each market
once a year due to the availability of Summary of Deposits data), MSA is dummy variable that equals 1
for metropolitan markets and 0 otherwise, and PIPC is the personal income per capita in the market in
question (in constant beginning-of-sample-period dollars, scaled by $10,000).

Deposit markets are

defined as the largest of a county, a Metropolitan Statistical Area (MSA) or a Consolidated-MSA
(CMSA). We interact the HHI variable with the MSA “dummy” to capture the potential differences in
market concentration that may prevail in rural and urban markets. This interaction captures the marginal
effect of an increase in concentration given that market concentration tends to be higher in rural markets
(DeYoung, Goldberg and White, 1999). Finally, we account for time variation in deposit rates by
including time “dummy” variables (Dt) for each quarter except the first.
We first present the results using the series that exhibited the highest amount of bias in Table 2,
the offered rates from the last survey of the quarter (R_MSSD_END) and the corresponding imputed rate

(R_CR_END), both winsorized at the 1st and 99th percentiles of their distributions. The results of the SCP
regressions using the MSSD data are presented in Panel 4A. The coefficient estimate for HHI is –0.0033
(statistically significant at the 1 percent level) when the NOW account offered rate (R_MSSD_END) is
used as the dependent variable. This result is consistent with previous studies. When the NOW account
imputed rate (R_CR_END) is used, however, the coefficient for HHI (–0.0035) has the expected sign, but
is not statistically significant.

The HHI interacted with MSA is positive and statistically significant in

two of the offered rate regressions (the NOW account and savings account rates), but is not significant in
any of the three imputed rate regressions. A positive sign on the HHI*MSA coefficient suggests that an
increase in market concentration in urban (MSA) markets results in marginally lower deposit rates than in
a non-MSA market.
While the coefficient estimates are similar, the standard errors are larger when Call Report
imputed rates are used as the dependent variable. Indeed, all of the standard errors in column 2 (where
R_CR_END is the dependent variable) are larger than their counterparts in column 1 (where
R_MSSD_END is the dependent variable). This is not surprising, as the Call Report rates (the R_CR)
presumably incorporate larger measurement error; and hence larger standard errors. Importantly, the
measurement error in the dependent variable does not lead to a bias or inconsistent estimates but to less
efficient estimates.
The results for the MMDA accounts (columns 3 and 4) and savings accounts (columns 5 and 6)
are similar; we find variation in the coefficient estimates between offered (R_MSSD) and imputed
(R_CR) rates, with the standard errors being larger in the case of the latter. The coefficient on HHI is not
statistically significant for regressions using MMDA rates.
Results of SCP regressions for the series that exhibit the least amount of bias are presented in
Panel B of Table 4. This panel contains the average of rates surveyed over the quarter (R_MSSD_AVE)
versus imputed rates based on average deposits during the quarter (R_CR_AVE) and truncated at the 5th
and 95th percentiles of their distributions. In general, the results using the two data sets are more similar
in this panel than in Panel A. The coefficient estimates and standard errors are comparable between the

offered and imputed rates, and, consequentially, the signs and statistical significance of the coefficients
would, in all cases but one, lead to like policy conclusions. A quick comparison of the two panels of
Table 4 yields the following observations: First, in Panel 4B the discrepancy across coefficient estimates
in columns 1 and 2 is much smaller, as are the standard deviations for the coefficient estimates. For
example, in column 1 the coefficient estimate for HHI is equal to –0.0019 (with a standard error of
0.0013), in column 2 the corresponding coefficient estimate is –0.0012 (with a standard error of 0.0014).
Again, neither of these coefficients is statistically significant. As in Panel A, the observed discrepancies
for the same coefficient estimates are larger in the other columns as MMDA and savings account rate
series exhibit larger biases.

Even in those cases, however, the coefficient estimates in the SCP

regressions for offered and imputed rates are similar and exhibit the same signs and significance levels;
the coefficient on HHI is not significant in any of the regressions, but the coefficient on HHI*MSA is
statistically significant in the regressions using the NOW imputed or offered rates. We find one notable
difference in this set of regressions: HHI*MSA is significant in the regression using the savings account
offered rate, but not the savings account imputed rate.
Based on these results, we recommend that researchers use the imputed series based on the
average stock of deposits during the quarter and truncate the obtained variable at the 5th and 95th
percentiles of its distribution.

This choice would lead to coefficient estimates that are qualitatively

similar to those that obtained from survey data, with the caveat that the former would have larger standard
errors due to measurement error.18
As Prager and Hannan (1999) note, imputed interest rates are noisy estimates of offered
(transaction) deposit rates. However, our work shows the importance of truncation and suggests that the
18

While these findings and conclusions seemingly contradict Prager and Hannan (1999), a number of discrepancies
between the Prager and Hannan (1999) study and our study exist. First, Prager and Hannan (1999) estimate a model
of price changes that compares pre- and post-merger prices whereas we estimate a SCP model in the price levels.
Second, Prager and Hannan (1999) estimate the same model using monthly MSSD offered rates and quarterly Call
Report imputed rates for the same time horizons. Thus the offered rate regressions would have a higher number of
observations, and hence lower standard errors, than the regressions in which quarterly Call Report imputed rates are
used. Conversely, our comparisons of offered versus imputed rates use the same number of observations in each of
these regressions.

coefficient estimates obtained using the imputed rates (properly constructed and truncated) leads to
analogous policy conclusions.

5. Summary and Conclusions
In this paper, we provide a systematic analysis of the bias that imputed interest rates may
introduce when used as estimates of offered interest rates. Our results provide strong evidence of
statistical bias. Imputed interest rates tend to underestimate the true interest rates offered to customers for
the same account type at the same bank. We further examine whether this observed bias leads to
economically different results in analyses that researchers conduct. Reassuringly, we find that this is not
the case; typically the coefficient estimates have the same signs, same levels of statistical significance,
and are of the same order of magnitude irrespective of whether imputed or offered rates are used. This
suggests that imputed rates are suitable estimates of offered (transaction) rates when conducting empirical
research. An important implication of our research is that empirical analyses of bank price data need not
remain limited to survey data as imputed rates from the Call Reports are available for the population of
U.S. banks.

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Table 1. Summary Statistics and Univariate Tests
Panel A presents distributional information on Monthly Survey of Selected Deposits (MSSD) survey rates and Call Report (CR) imputed rates. END
refers to MSSD series based on the last survey of quarter and CR series based on the stock of deposits at the end of the same quarter. AVE refers to
MSSD series based on the average of surveyed rates during the quarter and CR series based on the average stock of deposits during the quarter. Panel
B presents tests of equality of the means (t-test with H0: meanX – meanY = 0), tests of equality of the variances (F-test with H0: varX ÷ varY = 1). And
rank-order correlations (ρ) for selected pairs of series from Panel A. * and ** denote statistical significance at the 5% and 1% levels, respectively.

R_MSSD_END
R_CR_END

N
14,445
14,445

Minimum
0.0001
–0.8296

1st
percentile
0.0120
0.0098

R_MSSD_AVE
R_CR_AVE

14,445
14,445

0.0014
–1.9801

0.0122
0.0097

0.0161
0.0155

0.0285
0.0273

0.0470
0.0443

0.0509
0.0499

0.0548
0.0570

0.0608
0.0782

0.1528
1.0000

R_MSSD_END
R_CR_END

8,339
8,339

0.0350
–0.0771

0.0450
0.0245

0.0495
0.0466

0.0525
0.0534

0.0550
0.0576

0.0600
0.0635

0.0710
0.0747

0.0800
0.0975

0.1150
1.3333

R_MSSD_AVE
R_CR_AVE

8,339
8,339

0.0350
–0.0967

0.0460
0.0262

0.0494
0.0479

0.0525
0.0533

0.0553
0.0570

0.0600
0.0629

0.0708
0.0741

0.0794
0.0925

0.1050
1.7770

R_MSSD_END
R_CR_END

8,442
8,442

0.0400
–0.8703

0.0425
0.0223

0.0450
0.0415

0.0500
0.0485

0.0510
0.0512

0.0550
0.0547

0.0575
0.0691

0.0737
0.1157

0.0895
0.4727

R_MSSD_AVE
R_CR_AVE

8,442
8,442

0.0386
–0.8387

0.0425
0.0224

0.0450
0.0431

0.0500
0.0492

0.0516
0.0514

0.0550
0.0549

0.0576
0.0690

0.0733
0.1186

0.0892
1.1104

Panel 1A
NOW
Accounts

MMDA

Savings
Accounts

1987Q21994Q2

1987Q11991Q2

Panel 1B

NOW
Accounts
MMDA
Savings
Accounts

5th
percentile
0.0151
0.0155

25th
percentile
0.0275
0.0275

Rates Winsorized at 1st & 99th Percentiles
Mean
Standard Deviation
Rank-order correlation (ρ)
Mean
Standard Deviation
Rank-order correlation (ρ)
Mean
Standard Deviation
Rank-order correlation (ρ)

R_MSSD_END
0.0404
0.0134

R_CR_END
0.0408
0.0161

0.0571
0.0068

0.0588
0.0099

0.0520
0.0044

0.0527
0.0113

tests
–2.44
0.69
0.82
–13.02
0.47
0.59
–5.63
0.15
0.51

Median
0.0470
0.0439

75th
percentile
0.0505
0.0502

95th
percentile
0.0550
0.0617

99th
percentile
0.0608
0.1027

Maximum
0.1548
1.3333

Rates Truncated at 5th & 95th Percentiles
**
**
**
**
**
**
**
**
**

R_MSSD_AVE
0.0408
0.0118

R_CR_AVE
0.0396
0.0115

0.0562
0.0046

0.0574
0.0053

0.0515
0.0027

0.0514
0.0040

tests
7.94
1.05
0.89
–13.64
0.74
0.69
–1.80
0.46
0.64

**
**
**
**
**
**
*
**
**

Table 2. Winsorize or Truncate the Deposit Rates?
This table presents the results of the following OLS regression for unbalanced panels of U.S. commercial banks:

R_MSSD i, t = α + β R_CR i, t + ε i,t

(1)

The dependent variable is the interest rate that the bank has most commonly offered for NOW accounts and reported in the last survey of the quarter.
The explanatory variable is the imputed interest rate for NOW accounts obtained from the Call Reports for the same bank in the same quarter. All
equations are estimated using OLS with Huber-White standard errors (reported in parentheses below coefficient estimates) for clustering across
banks. F-statistics are reported for the joint-null hypothesis that α=0 and β=1. * and ** denote significance at the 5% and 1% levels, respectively.
NOW Account Rates

Constant

0.0135
(0.0009)

R_CR
winsorized at 1%

0.6594
(0.0244)

0.7644
(0.0212)

R_CR
truncated at 1%

0.8473
(0.0112)

R_CR
winsorized at 5%

Bank-quarter obs.
Number of banks
R2
Regression F-stat

14,446
735
0.6333
731.4

95.1

13,912
730
0.7175
1296.5

99.8

105.7

14,446
735
0.7760
5680.7

12,564
720
0.8088
14702.3

14,973
737
0.7895
4007.8

R_MSSD
truncated at 5%
0.0026
(0.0003)

0.9627
(0.0057)

72.9

**
**
**

95.3

12,751
721
0.8857
28312.8

0.0044
(0.0004)

0.9158
(0.0084)
0.9183
(0.0076)

118.9

R_CR
truncated at 5%
H 0: α = 0 & β = 1

R_MSSD
winsorized at 5%

0.0044
(0.0003)

0.9083
(0.0087)

0.0040
(0.0003)

0.0073
(0.0005)
0.8343
(0.0132)

0.0064
(0.0005)

R_MSSD
truncated at 1%

R_MSSD
winsorized at 1%

0.0094
(0.0008)

R_MSSD_AVE i, t = α + β R_CR_AVE i, t + ε i,t

R_MSSD
truncated at 5%

R_MSSD
winsorized at 5%

R_MSSD
truncated at 1%

R_MSSD
winsorized at 1%

R_MSSD_END i, t = α + β R_CR_END i, t + ε i,t

105.0

14,393
735
0.8542
10981.0

88.9

14,973
737
0.8528
12015.4

Table 3. Tests of Statistical Bias
This table presents the results of the following OLS regression for unbalanced panels of U.S. commercial banks:

R_MSSD i, t = α + β R_CR i, t + ε i,t

(1)

The dependent variable is the interest rate that the bank has most commonly offered for a particular type of deposit account. We use either the rate
from the last survey of the quarter or the average of rates in all surveys of the quarter. The explanatory variable is the imputed interest rate obtained
from the Call Reports. We use either the stock of deposits as reported at the end of the quarter or the average stock of deposits through the quarter (as
reported in Schedule K of Call Reports). All imputed rates are truncated at 5% of either side of their distributions. All equations are estimated using
ordinary least squares (OLS) with Huber-White standard errors for clustering across banks. F-statistics are reported for the joint-null hypothesis that
α=0 and β=1. T-statistics appear in parentheses. * and ** denote significance at the 5% and 1% levels, respectively.
(all rates truncated at 5th & 95th percentile of their distributions)

Constant

0.0038
(0.0003)

R_CR_END

0.9244
(0.0077)

# of bank-quarter obs.
# of banks
R2
Regression F-stat

**
**

0.9641
(0.0058)

97.1

462.2

11,967
714
0.8858
27475.3

6,646
619
0.3408
828.0

R_CR_AVE
H0: α=0 & β=1

0.0280
(0.0009)
0.4863
(0.0169)

0.0026
(0.0003)

68.3
11,967
714
0.8107
14509.2

Savings Accounts

0.0336
(0.0011)

0.3490
(0.0205)

0.0227
(0.0011)

R_MSSD_AVE

R_MSSD_END

MMDA

R_MSSD_AVE

R_MSSD_END

NOW Accounts

R_MSSD_AVE

Panel 3A

230.4

511.2

6,646
619
0.4622
884.5

6,914
614
0.2655
289.8

255.0

6,914
614
0.2964
173.2

0.3689
(0.0280)

0.5832
(0.0196)

0.0325
(0.0015)

Table 3. Tests of Statistical Bias (continued)
Multimarket Banks vs. Single-Market Banks

R_MSSD_AVE i, t = α + β R_CR_AVE i, t + ε i,t

Panel 3B

(all rates are truncated at the 5th & 95th percentile of their distributions)
Multimarket Banks
Constant
R_CR_AVE
H0: α=0 & β=1
# of bank-quarter obs.
# of banks
R2
Regression F-stat

NOW
0.0024
(0.0004)

MMDA
0.0271
(0.0022)

Savings
Accounts
0.0363
(0.0018)

Single-Market Banks
Savings
NOW
MMDA
Accounts
0.0027 **
0.0282 **
0.0392
(0.0004)
(0.0023)
(0.0028)

0.9756
(0.0087)

0.5049
(0.0379)

0.2901
(0.0346)

0.9599
(0.0086)

0.4901
(0.0408)

0.2470
(0.0534)

55.4

112.9

210.0

41.1

87.5

100.9

3,537
322
0.3940
177.8

3,574
318
0.2255
70.1

4,563
348
0.8982
12441.7

2,746
290
0.4010
144.4

2,861
284
0.1848
21.4

6,265
394
0.8755
12538.5

Urban (MSA) vs. Rural Market Banks

R_MSSD_AVE i, t = α + β R_CR_AVE i, t + ε i,t

Panel 3C

(all rates are truncated at the 5th & 95th percentile of their distributions)

Constant
R_CR_AVE
H0: α=0 & β=1
# of bank-quarter obs.
# of banks
R2
Regression F-stat

Urban (MSA) Market Banks
Savings
NOW
MMDA
Accounts
0.0024 **
0.0275 **
0.0383
(0.0003)
(0.0018)
(0.0018)

Rural Market Banks
Savings
NOW
MMDA
Accounts
0.0030 **
0.0287 **
0.0303
(0.0007)
(0.0038)
(0.0029)

0.9712
(0.0068)

0.5002
(0.0307)

0.2565
(0.0344)

0.9509
(0.0156)

0.4737
(0.0678)

0.4159
(0.0572)

83.4

163.3

236.8

13.4

33.8

53.5

5,325
479
0.3926
264.6

5,441
474
0.1929
55.7

1,688
106
0.8657
3736.0

958
90
0.4113
48.8

994
88
0.3241
52.9

9,140
558
0.8880
20449.2

Table 4. Imputed Vs. Offered Rates in Structure Conduct Performance Analysis
T

R i, t = a + b1 HHI i ,t + b2 MSAi ,t + b3 HHI i ,t × MSAi ,t + b4 PIPCi ,t + ∑ ct Dt + ei ,t

(2)

t =1

The dependent variable is either (i) the MSSD offered interest rate (R_MSSD) or (ii) the Call Report imputed rate (R_CR). HHI is the HerfindahlHirshman Index of market concentration. MSA is a “dummy” variable for metropolitan markets. PIPC is the personal income per capita (in constantbeginning-of-sample-year dollars). OLS regressions control for clustering at the bank level using Huber-White standard errors. T-statistics appear in
parentheses below the estimated coefficients. * and ** denote statistical significance at the 5% and 1% levels, respectively.
Panel 4A

MSSD Offered Rates versus CR Imputed Rates in SCP Regressions
(all rates winsorized at 1st & 99th percentile of their distributions)

Constant

0.0250
(0.0016)

0.0225
(0.0025)

HHI

–0.0033
(0.0015)

–0.0035
(0.0027)

MSA

–0.0020
(0.0009)

–0.0035
(0.0016)

HHI×MSA

–0.0067
(0.0028)

PIPC (in $10,000)
Quarter dummies
# of bank-quarter obs.
# of banks
R2
Regression F-stat

0.0508
(0.0014)

0.0553
(0.0016)

0.0482
(0.0014)

R_CR_END

R_MSSD_END

Savings Accounts
R_CR_END

R_MSSD_END

MMDA
R_CR_END

R_MSSD_END

NOW

0.0458
(0.0031)

–0.0018
(0.0024)

–0.0015
(0.0026)

–0.0003
(0.0015)

0.0041
(0.0048)

–0.0014
(0.0013)

–0.0007
(0.0015)

–0.0002
(0.0008)

0.0002
(0.0019)

–0.0042
(0.0045)

–0.0020
(0.0038)

–0.0034
(0.0047)

–0.0065
(0.0025)

–0.0087
(0.0061)

–0.0008
(0.0005)

0.0002
(0.0008)

0.0030
(0.0007)

0.0017
(0.0009)

0.0015
(0.0005)

0.0013
(0.0009)

yes
10,956
589
0.8609
406.2

yes
10,956
589
0.6213
268.0

yes
6,348
511
0.2553
50.2

yes
6,348
511
0.1742
61.8

yes
6,343
511
0.0641
10.8

yes
6,343
511
0.0268
18.3

Table 4. Imputed Vs. Offered Rates in Structure Conduct Performance Analysis (continued)
The dependent variable is either (i) the MSSD offered interest rate (R_MSSD) or (ii) the Call Report imputed rate (R_CR). HHI is the HerfindahlHirshman Index of market concentration. MSA is a “dummy” variable for metropolitan markets. PIPC is the personal income per capita (in constantbeginning-of-sample-year dollars). OLS regressions control for clustering at the bank level using Huber-White standard errors. T-statistics appear in
parentheses below the estimated coefficients. * and ** denote statistical significance at the 5% and 1% levels, respectively.
Panel 4B

MSSD Offered Rates versus CR Imputed Rates in SCP Regressions
(all rates truncated at 5th & 95th percentile of their distributions)

Constant

0.0255
(0.0013)

HHI

–0.0019
(0.0013)

MSA

–0.0017
(0.0008)

HHI×MSA

–0.0057
(0.0024)

PIPC (in $10,000)

–0.0003
(0.0005)

–0.0001
(0.0005)

0.0021
(0.0005)

yes
9,763
579
0.8800
414.9

yes
9,763
579
0.8215
372.3

yes
5,746
514
0.2671
39.9

Quarter “dummies”
# of bank-quarter obs.
# of banks
R2
Regression F-stat

0.0250
(0.0015)

0.0476
(0.0013)

0.0486
(0.0014)

0.0496
(0.0010)

R_CR_AVE

R_MSSD_AVE

Savings Accounts
R_CR_AVE

R_MSSD_AVE

MMDA
R_CR_AVE

R_MSSD_AVE

NOW

0.0500
(0.0012)

–0.0012
(0.0014)

0.0005
(0.0021)

0.0008
(0.0020)

–0.0004
(0.0015)

–0.0009
(0.0015)

–0.0018
(0.0009)

–0.0001
(0.0009)

0.0002
(0.0009)

–0.0002
(0.0007)

–0.0011
(0.0008)

–0.0066
(0.0025)

–0.0029
(0.0030)

–0.0031
(0.0031)

–0.0053
(0.0021)

0.0017
(0.0005)
yes
5,746
514
0.2607
53.7

–0.0042
(0.0026)

0.0006
(0.0004)

0.0007
(0.0005)

yes
5,887
503
0.0626
7.7

yes
5,887
503
0.0354
6.9

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Full text of Working Papers (Federal Reserve Bank of Chicago) : Bank Imputed Interest Rates : Unbiased Estimates of Offered Rates?, Working Paper 2006-26

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