Measuring Matching Using Reported Revenues and Expenses
November, 2016
Sudipta Basu*
William M. Cready**
Wonsun Paek***
Abstract
Dichev and Tang (2008) provide initial evidence on the degree to which expenses are appropriately
matched with revenues in the population of larger Compustat covered firms. They approach the
issue from the perspective that expenses are advanced to produce revenues. Conceptually, however,
matching is defined as the identification of expenses attributable to recognized revenues. That is,
expense recognition depends on revenue recognition, rather than revenues being derived from
expenses. In this analysis, we revisit the core questions considered in Dichev and Tang regarding
matching efficacy over time as well as matching’s relations with earnings variability and
persistence employing measures consistent with this conceptual notion that expense is matched to
revenue. Our alternative measures portray a somewhat different picture than that conveyed by the
primary measure employed by Dichev and Tang. Our analysis indicates that a sizable decline in
matching has taken place since the turn of the century. The decline in this period for their measure
is comparatively modest. We also find only limited evidence of a decline in matching prior to the
turn of the century, while their metric suggests that matching declined substantially between 1980
and 1994. We also find that, in the cross-section, matching is negatively rather than positively
related to earnings persistence. Finally, our analysis indicates that prior to the early 1980s,
expenses are, on average, commonly over-matched to revenues.
Keywords
Matching principle, Expense Recognition, Earnings Variability, Persistence.
JEL Classification
G10, M4
* Professor of Accounting and Johnson Senior Research Fellow, Fox School of Business, Temple
University. [email protected]
**Adolf Enthoven Professor of Accounting, Jindal School of Management, University of Texas at Dallas.
[email protected]
*** Professor of Accounting, Sungkyunkwan University. [email protected]
Measuring Matching Using Reported Revenues and Expenses
1. Introduction
Matching and revenue realization are central to the income statement perspective of
financial reporting. The matching principle recommends that the costs associated with the
generation of revenues should be recognized as expenses in the same period that the revenues are
recognized. Consequently, better matching should result in more accurate measures of profitability
and thereby improve earnings quality. However, a recent analysis by Dichev and Tang (2008)
estimates that matching has declined substantially during 1964 to 2003 and that this decline is
closely related to the general decline in accounting earnings quality over much of this same time
period (Collins et al. 1997 and Francis and Schipper 1999). We revisit these inferences by studying
how to best measure matching using total expense and revenue data. In particular, we argue that
matching measures should be consistent with the core principle that expenses are matched to
recognized revenues, an approach that we show is substantively different from the Dichev and
Tang (DT henceforth) perspective that matching reflects “entities that continually advance
expenses hoping to reap revenues and earnings” (p. 1427).
We identify two specific measures of matching consistent with the conceptual perspective
that expense recognition depends upon revenue recognition. The first measure is the percentage of
contemporaneous expense that is determined by contemporaneous revenue (MEXP%). We
estimate MEXP% by regressing expense on revenue, then using the estimated coefficient on
revenue to determine the amount of revenue-based expense being recognized. In the terminology
of DT, this measure directly reflects the degree to which expenses are not “scattered” to other
1
periods.1 The second measure is the variation in expense that is explained by lead and lagged
revenues incremental to the variation explained by contemporaneous revenues (MISM). This
measure directly targets mismatching by evaluating the degree to which variables that should not
explain expense under perfect matching (i.e., lead and lag revenue) do explain it. Using these
measures, we revisit the core issues considered in DT: (1) The degree to which matching has
changed over time; and, (2) the relation between matching and two core earnings properties—
earnings variability and earnings persistence.
Our measures are consistent with the general conclusion in DT that matching is worse in
recent years than it was 40 years ago. In particular, for the typical firm around 98% of expense is
matched to revenue at the start of our sample period (1964-1973) while less than 91% of expense
is matched to revenue at the end of the period (2004-2013). However, our analysis suggests that
much of this decline is a very recent phenomenon. There is no reliable indication of a decline in
MEXP% prior to 2000. MISM, on the other hand, does increase over most of the time period
examined, with the sharpest rise occurring in the 1990s. In contrast, the primary measure employed
in DT, the coefficient on expense in a regression of revenue on it supplemented by lead and lag
expense, declines considerably between 1980 and 1994 but does not decline any further afterwards.
Such a difference in timing underscores that it matters how one measures matching. It also raises
questions about how closely one should connect changes in matching with the broad decline in
earnings quality taking place over this same general time period since the existing evidence (e.g.
Collins et al. 1997 and Francis and Schipper 1999) suggests that this decline began well before the
1
Alternatively, if expense recognition is entirely unrelated to revenues then the estimated coefficient on revenues
should be 0 meaning that this percentage will also be 0 and this will hold irrespective of how little or how much
variation is present in either expense or revenue.
2
turn of the century, which is before the earliest indication of the emergence of a broad decline in
matching based on our MEXP% measure.
Interestingly, we also find that median MEXP% values often exceed 100% early in our
sample period. That is, the amount of expense recognized as a linear function of revenue exceeds
the amount of expenses being recognized in total. Such values reflect over-matching of expenses
to revenues. For example, if a firm recognizes bad debt expense as 3% of revenue when the correct
level should be 2% of revenue then the expense is being over-matched with revenue. Nominally,
such over-recognition indicates higher matching. Substantively, however, such over-matching
reflects poor rather than high quality matching. Consequently, our evidence indicates that over the
past 50 years, the financial reporting environment has moved from a regime typified by the overmatching of expenses to revenues to one dominated by under-matching.
In the cross-section, we find that MEXP% is negatively related to earnings variability while
MISM is positively related to earnings variability over our entire sample time period (1964-2013).
There is no evidence that these relations change in any systematic fashion over this period. Hence,
consistent with the analyses provided in DT, matching is inversely related with earnings
variability. However, we do not find evidence that matching is positively related with earnings
persistence. In fact, MEXP% reduces and MISM increases earnings persistence. A possible
explanation for this unexpected relation is that matching is more easily achieved with respect to
transitory revenue events relative to permanent or persistent revenue events. That is, it seems likely
that the costs associated with period-specific revenues are also more likely to be period-specific,
and hence, easily matched to revenues in that same period.
3
2. Relevant Literature
While matching has long played a central role in conceptual frameworks for financial
reporting, particularly with respect to how one determines the expense component of periodic
income (e.g. Paton and Littleton 1940), prior to DT it had not been addressed empirically in a
comprehensive manner. The DT analysis focuses on “poor matching,” which is the difference
between recognized expense and (unobservable) perfectly matched expense. The paper argues that
as the level of “poor matching” increases: (1) the correlation between revenues and expenses
decreases; (2) the volatility of earnings increases; and (3) the persistence of earnings decreases.2
While we consider these three relations in our analysis, the subsequent literature largely focuses
on DT’s approaches to assess how “poor matching” introduces error into the correlation between
revenues and expenses. And, while DT report analyses of the correlation between revenue and
expense, their primary approach to assessing the impact of “poor matching” is based on annual
cross-sectional regressions of revenues on lead, lag, and contemporaneous expense as follows:
Revenuei,t = b0 + b1Expensei,t-1 + b2Expensei,t + b3Expensei,t+1 + ei,t
(1),
where revenue is annual revenue for firm i in year t and expense is the annual expense in year t.
DT argue that the magnitude of b2 in (1) declines with “poor matching” and suggest that the
coefficients on the lead and lag expense terms in (1) increase with “poor matching.” They
2
In a largely descriptive exercise, Table 4 of DT presents over time changes in the levels of earnings, expense, and
revenue volatilities, focusing on how earnings volatility has increased substantially while expense and revenue
volatility has not. As, covariance between expense and revenue is the reconciling metric between earnings
variability and the variability of its components (expense and revenue), this analysis implicitly addresses covariance
change. Covariance and covariance change is also the central driver of the MEXP% based analyses presented in this
paper. However, MEXP% explicitly captures covariance changes making it much more amenable to rigorous
empirical analysis, which is not possible with the comparative evaluations presented in DT. (An added challenge
here is that the high level of the covariance between revenue and expenses means that comparatively small shifts in
expense or revenue volatility that are not offset by a change in covariance have sizable relative impacts on earnings
volatility. In particular, based on the Table 4 values reported in DT, a 10% increase in the variance of either revenue
or expenses—which is roughly what happens between the first and last year of the DT analysis—if not offset by a
covariance shift, would increase residual income variation by well over 100%.)
4
document that the coefficient on current expenses has declined considerably over time while the
coefficient on lagged expenses has increased. They interpret these coefficient shifts as indicating
that a substantial decline in matching occurred between 1967 and 2003.
Donelson, Jennings, and McInnis (2011) employ the DT equation (1) approach to assess
the underlying factors that contributed to the decline in matching documented in DT. Decomposing
the estimated coefficients, they show that the decline in matching documented in DT is largely
attributable to a marked increase in the frequency and magnitudes of special items from 1967 to
2005. They argue that this increase in special items is driven by increasing economic uncertainty,
which suggests that the DT decline in matching is mostly attributable to a rise in the sorts of
economic conditions that produce costs that are difficult to match ex ante with revenues, rather
than to any substantive shift in financial reporting standards.3 Relatedly, Srivastava (2014) finds
that due to their being more intangible-intensive, newer firms exhibit lower levels of matching
because most of their costs are expensed immediately, thereby reducing the overall level of
matching of the Compustat population.
He and Shan (2016) use the DT measure to assess matching over time across 42 countries.
They find that matching has declined worldwide from 1991 to 2010. They also find that matching
varies across countries on many dimensions. However, they do not find any evidence of a
connection between matching and IFRS adoptions. Bushman, Lerman and Zhang (2016) employ
the adjusted R2 from (1) as a more direct measure of the random error component of expense
recognition to measure matching. They do not find evidence of an incremental relation, above and
Basu (1997) argues that asset write-downs frequently arise from over-estimation of assets’ useful lives, which
causes mismatching with revenues generated by the asset. As opposed to this conditional conservatism,
unconditional conservatism such as immediate expensing of R&D and advertising effectively underestimates assets’
useful lives, so that some expenditures are not correctly matched to future revenues they help generate.
3
5
beyond a shared trend, between matching and the association between cash flows and accruals,
which they show declines markedly between 1964 and 2014.4
Instead of directly measuring expense as a function of revenue, Prakash and Sinha (2013)
evaluate matching in the context of deferred revenue by examining profit margins. They find that
profit margins are lower in periods when deferred revenues increase and higher in periods when
they decrease. This pattern is consistent with the expenses on deferred revenue being recognized
before the revenue is recognized. Like our MEXP% measure, they employ estimated linear
equation parameters to evaluate matching efficacy. And, as is seen in the next section, profit
margin poses a challenge for such parameter-based perspectives. In the case of Prakash and Sinha,
the analysis implicitly assumes that profit margins based on correctly matched expenses are similar
for deferred and non-deferred revenue items. In the case of MEXP%, we rescale the estimated
parameter to remove the impact of profit margin variation.
3. Measuring Matching
3.1 Conceptual Matching
In devising our approaches to measuring matching, we begin with the conceptual notion
that revenues are first recognized by period and then expenses are matched to these recognized
revenues. At a linear level, this perspective suggests the following equation:
Expensei,t = b0 + b1*Revenuesi,t
(2)
However, the above expression is over simplistic since it assumes that b0 and b1 are constant across
firms and over time. That is, it implies a financial reporting process that operates with universal
4
Dechow (1994) argues that revenue recognition and matching cause recognition of accrual revenues and expenses
to adjust operating cash flows and induce a contemporaneous negative correlation between accruals and cash flows.
6
constants b0 and b1. Financial reporting policy and application, however, is far more idiosyncratic.
That is, b0 and b1 vary across firms and vary within firms over time. Hence, a more accurate linear
equation starting point is:
Expensei,t = b0i,t + b1i,t*Revenuesi,t
(2a)
While it accurately captures matching as a product of the financial reporting process, (2a) is not
useful empirically absent restrictions on b0 and b1. That is, for estimation purposes b0 and b1 must
be restricted to be the same across firms or over time or across both firms and over time. Such
restrictions, however, move the empirical design away from the conceptually rich idiosyncratic
notion of expense recognition reflected in (2a) and toward the more sterile notion of expense
recognition reflected in (2).
Importantly, however, (2a) is not entirely distinct from (2). Indeed, the two equations can
be more directly linked by replacing b0i,t and b1i,t in (2a) with their averages (cross-sectional, timeseries or pooled) as follows:
Expensei,t = b0 + b1*Revenuesi,t + ei,t
(2b)
where bolding indicates that the item is an (weighted) average value of a parameter. (2b), unlike
(2a) but like (2), is empirically estimable. But crucially it also introduces error. Rearranging (2b)
to solve for this error gives:
ei,t = b0i,t - b0 + (b1i,t – b1)*Revenuei,t
(3)
That is, a portion of the residual error arising in estimations following the general form of (2b) is
due to suppressed variation in idiosyncratic parameter values.5 Hence, the implications of the error
5
The conceptually expected variation in coefficient parameter values here differentiates this setting from other
similar conceptualizations of relations among financial performance variables such as those between accruals and
cash flows found in Dechow and Dichev (2002). In their analysis, the independent variable parameter values should
be the same both across firms and over time. Unlike the matching setting, there is no conceptual reason in their
analysis for parameter values to vary over time or across firms.
7
term magnitude in (2b) based estimations are inherently ambiguous. Empirically, the random
“scattering” of expenses to periods in a manner totally unrelated with revenues (i.e., poor
matching) will increase this error term. But, the amount of idiosyncratic variation in b0 and b1
also increases it. And such variation certainly does not reflect poor matching. Indeed, it reflects
good matching in that it is a product of expense recognition that is accurately capturing
idiosyncratic performance differences across firms and within firms over time. Consequently, the
level of residual error from (2b) estimations as well as measures derived or impacted by it such as
the regression R-square and the correlation coefficient between revenue and expense are highly
problematic candidates for measuring matching and changes in matching.
3.2 Parameter Based Estimates of Matching
Alternatively, estimations of (2b) can provide unbiased measures of the average values of
b0 and b1. And, these two parameters do say something about matching. Specifically, the level of
b0 reflects the amount of expense that is impacting income in the period that is unconnected with
current revenue. When b0 is high the level of unmatched expense is high. When it is low the level
of unmatched expense is low. Similarly, b1 reflects the level of expenses that are being matched
to revenues as a percentage of revenues. So, when b1 is high, more expense is being matched to
each dollar of revenue. In our analysis we focus on b1 as a reasonable starting point for measuring
matching. The preceding interpretations of b0 and, in particular b1 do, however, depend on one
additional factor—profit margin. In general, higher profit margins reflect lower expense. And,
ceteris paribus, if expenses are lower, then b1 and b0, which are both measures of matching, will
also be lower. Hence, profit margin represents a crucial confounding factor when employing either
of these measures to evaluate matching. We address this problem by expressing b1 as a percentage
8
of expense rather than using its native percentage of revenue scale. That is, we measure the
percentage of expense recognized as a linear function of contemporaneous revenue for a firm as:
MEXP% = b1(Average Revenue/Average Expense)
.
Our empirical analysis employs firm-specific time-series regressions estimated over ten-year
windows. So, for our purposes average revenue and average expense are determined over the same
ten-year windows used to produce the estimated value of b1.
While MEXP% is a highly intuitive and straightforward measure, it is not without
drawbacks. In particular, while it declines with under-recognition of correctly matched expense
(or, in the terminology of DT, the scattering of expenses to other periods), it increases with overrecognition of expense as a function of revenue. Such over-matching can happen when a firm
inflates the correctly matched expense in the interests of being conservative. For instance, suppose
a firm routinely determines bad debt expenses as 3% of sales when such expenses are only
expected to be 2% of sales. The 3% number is conservative because it is an over-accrual of
expense. But it also (artificially) increases the amount of expense recognized as a linear function
of revenue. 6 Consequently, this measure is better interpreted as reflecting the degree to which
correctly matched expenses are not being scattered to other time periods that is offset by the degree
to which expenses are being over-matched to revenues.
3.3 Measuring Mismatching
As an alternative to focusing on how much expense is being matched to revenues, our
second measure addresses the level of mismatching of expenses that is occurring. That is, instead
6
Importantly, over-recognition of expense in a period does not in and of itself lead to over-matching. The overrecognition must be tied to the magnitude of current period revenues as well.
9
of focusing on how well matching works, one can instead identify specific situations where
matching is unambiguously not working. The lead and lag expense terms in equation (1), as
developed by DT, reflect this perspective. They focus on the lead and, in particular, the lag sales
coefficients as measures of mismatching. In fact, DT identify the lag coefficient as reflecting
accounting conservatism in that it connects lagged expense with current revenues. 7 More
generally, such coefficients reflect expenses from other periods that are associated with current
period revenues. Hence, they are expenses that are arguably being recognized in the wrong time
period. There are, however, two significant drawbacks to the DT approach. First, at a conceptual
level matching dictates that expense, not revenue, is the appropriate dependent variable. Expenses
are determined based on (depend upon) recognized revenues in a period. Second, as we will
elaborate on below, it is actually far from clear that coefficient magnitudes here are the best route
for assessing mismatching in this context.
We introduce mismatching estimation into (2b) by supplementing the current revenue
variable with one period lead and lag revenue variables as follows:
Expensei,t = h0 + h1*Revenuesi,t-1 + h2*Revenuesi,t + h3*Revenuesi,t+1 + ei,t
(4),
where bolding again indicates that the estimated coefficient is an average value. In this form, h1
and h3 represent how (on average) revenues in adjacent periods uniquely explain expenses in
period t incremental to the explanatory power of period t revenues. What is far less clear, however,
is how to appropriately interpret the estimated coefficient values in (4) in terms of what they are
saying about matching efficacy or lack thereof. Consider, as a general example, h1. It reflects the
change in period t expense associated with a marginal (or unexpected given revenues in t and t+1)
7
Lee (2012) explores some of the estimation properties of the DT lagged revenue estimator. He also suggests that a
more natural measure is the coefficient on lagged revenues in a regression of expense on lag, contemporaneous, and
lead revenue. One view of the measures we present here is that they build on Lee’s perspectives of measuring
matching and conservatism.
10
unit change in period t-1 revenues holding period t and t+1 revenues constant. Consequently, the
overall level of mismatched expense depends as much on the magnitude of this incremental change
in revenue as it does on the magnitude of h1. That is, even if h1 is large its impact may be quite
small if the associated incremental revenue changes are expected to be comparatively tiny. A
related concern stems from the possibility that expenses are over-matched to revenue as discussed
in the prior section. Such over-matching necessarily leads to reversals/offsets in other periods. So,
if such a reversal occurs in the next period then h1 is decreased (and h2 is increased as is seen in
the prior section). Or, if expenses are being deferred in t based on (correctly anticipated) period
t+1 revenues (essentially a reversal in advance) then h3 is decreased. These sorts of over-matching
activities lead to lower rather than higher h1 and h2 values.8
Given the difficulties in clearly interpreting the implications of the coefficients in (4) as
measures of overall mismatching magnitude, we focus instead on the total amount of expense that
is explained by the introduction of the adjacent period revenue terms. That is, we examine the
reduction in residual error obtained by supplementing (2b) with the lag revenue variable as
follows:
MISM =
MSE (2b) - MSE(4)
where MSE(2b) is the mean squared error from estimating model (2b) on a given set of data and
MSE(4) is the mean squared error from estimating model 4 over this same set of data.
A particular advantage of MISM is that it reflects mismatching attributable to scattering of
expenses as well as over-recognition of expenses. In particular, while scattering manifests itself in
8
It is even possible that (short term) over-matching is the dominant effect, in which case h1 will be negative. And,
in fact, we do observe negative h1 values in some years in our empirical analyses. (The negative values for the lead
expense coefficient reported in some years by DT is also broadly consistent with this effect, although the precise
interpretation of their coefficients is clouded by its disconnection from the idea that under conceptual matching
expenses are appropriately modeled as a function of revenues).
11
the form of positive adjacent period revenue coefficients, over-recognition manifests itself in the
form of negative adjacent period revenue coefficients, the impact on MSE (4) is not dependent on
coefficient signs. MISM’s limitation, however, is that it only addresses mismatching effects that
arise in or are reconciled in immediately adjacent time periods.
3.4 Dichev and Tang Reverse Regression Measure
At this point it is relevant to revisit the DT equation (1) matching measure—the coefficient
on contemporaneous expense in a regression of lead, lag, and contemporaneous expense on
revenue. In evaluating this measure, it is particularly important to recognize that it is inconsistent
with the core matching principle that expenses are matched to revenues since it places expense(s)
in the independent variable position. Consequently, from a conceptual matching perspective it is
better understood as a reverse regression approach in which matching is measured based on d2
from the following regression of revenues on expenses:
Revenuet = d0 + d1 (Expenset-1 + et-1) + d2 (Expenset + et) + d3 (Expenset+1 + et+1) (5)
As the conceptual matching roles of the lead and lag expense terms in this regression are rather
unclear and their inclusion clouds the core reverse regression properties of the approach, we focus
instead on the simpler regression of revenues on contemporaneous expenses (e.g. Sivakumar and
Waymire, 2003) where expenses are measured with error (due to mismatching). That is:
Revenuesi,t
= g0 + g1*(Expensei,t + ei,t)
(6).
As noted in Dichev and Tang, measurement error in expense, ei,t, biases g1 toward zero. Hence, in
the reverse regression specification, the magnitude of the coefficient on estimated expense declines
as random variation in expense (poor matching) increases.
12
The key drawback to the Dichev and Tang approach is seen when we rearrange (6) to
correspond with the conceptual notion that that matching drives the dependence of expenses on
revenues, not revenues on expenses:
Expensesi,t
= -g0/g1 + (1/g1 )*(Revenuei,t + ei,t)
(6a).
This rearrangement shows that higher (lower) estimated g1 values imply that expenses are less
(more) determined by revenues. That is, apart from measurement error, g1 is inversely related to
the degree to which expenses are being matched to revenues which in turn suggests that the
evidence that g1 declines over time reported in Dichev and Tang can actually be interpreted as
implying that matching has improved over time. So, absent adopting the counterintuitive
assumption that changes in matching impact the level of random error without affecting the level
of expenses being matched to revenues, the implications of this metric for matching are inherently
ambiguous.
4. Empirical Analyses
Our empirical analysis focuses on two error-based measures along the lines proposed by
DT and the two measures of matching/non-matching developed in the previous section—MEXP%
and MISM. The two DT-based measures are: DMSE—the direct regression mean squared error,
which corresponds to the mean squared error from estimations of equation (2b); and, DTM—the
primary DT matching measure, which is the estimated coefficient on contemporaneous expense
from equation (5). The analysis is conducted in two stages. In the first stage, we investigate the
behavior over time of these measures. In the second, we explore the degree to which crosssectional variation in matching is related to earnings persistence and earnings variability.
13
Both analyses use rolling ten-year windows of pooled annual firm-level data. Consistent
with DT, revenue and expenses for a firm in these rolling pools are scaled by the book value of the
firm’s assets. We follow Francis et al. (2004) and estimate the above matching measures for each
firm in each rolling window. We restrict the sample of firms to the 500 largest non-financial firms
listed on Compustat in the start year of each rolling window. We exclude firms for which revenue
or expense data are unavailable in any of the subsequent nine years. The first rolling window we
examine ends in 1973 (start year of 1964), while the last window ends in 2013. Hence, we have
forty-one rolling ten-year windows in total and every tenth window is non-overlapping.
Two of the four matching measures we examine (MEXP% and DTM) are based on
regression parameter values that follow directly from equations (1b) and (5) from the prior section.
We estimate these parameters by firm in a given window using OLS regression. The two mean
squared error based measures, DMSE and MISM, rely on (MSE) calculated as
Sum of Squared Errorsi,wt/(ni,w - p).
where sum of squared errors is the sum of the squared residuals from the firm-specific regression
of interest, ni,w is the number of observations for firm i in rolling window w, and p is the number
of parameters estimated in the associated regression specification (p is 2 for estimations of
equation (2b) and 4 for estimations of equation (4)). Since MSE declines as explanatory power
increases, lower values of MISM indicate that adjacent period revenues have greater explanatory
power for current period expense (i.e., worse matching).
Table 1 reports descriptive statistics for the primary variables employed in our analyses.
As expected, revenues at 87.2% of asset value, on average, slightly exceed expenses at 82.7% of
asset value. The four matching measures (Winsorized at the 2% and 98% levels) all exhibit
comparatively high degrees of variability, reflecting the short time series used in estimating them.
14
DMSE averages 1.111, but its median is only 0.195, indicating that it is highly skewed. The
average of the DTM metric of 0.975 is similar to the 0.957 average for 1967-2003 determined
using ten year averages of the yearly cross-sectional estimation estimates reported in Table 3 of
DT. The median measure of 1.016, however, is slightly higher than the mean. MEXP% averages
97.2% (median is 99%) which indicates that, on average, 97.2% of a firm’s expenses are matched
to revenues via the estimated coefficient on revenue or, equivalently, that only 2.8% of firm
expenses are not matched to revenues. 9 MISM averages 0.140 indicating that adjacent period
revenues are explaining some portion of current period expense. Median MISM, however, is only
0.005 suggesting that the high mean value for MISM is attributable to a small subset of firms.10
In addition to the four primary measures, Table 1 reports values for three more matching
metrics: D_SALES, LGREV, and LDREV (also Winsorized at the 2% and 98% levels). D_SALES
is, as expected, smaller than MEXP% as it expresses expense recognition as a percentage of
revenues instead of a percentage of expenses. Mean and median LDREV are positive, indicating
that expenses are generally being recognized in advance of associated revenues more than they are
being deferred in anticipation of future revenues. In contrast, mean LGREV is negative while its
median is zero. Hence, on average higher values of LGREV lower next period expenses. One
explanation for this relation is that expenses are being over-recognized as a function of revenue in
the current period leading to a reversal of such over-recognized expenses in the next period.
Table 2 reports means of within-window correlations among the four primary matching
measures. DMSE is negatively associated with DTM and MEXP%, consistent with a positive
9
These percentages reflect how much expense is being matched to revenues, they do not necessarily speak to
whether these expenses are being correctly matched to revenues.
10
In general, all of the results we report in the subsequent analysis of the over-time patterns in these matching
measures are robust to using rolling window medians rather than means. The one exception is the analyses of
MISM. While MISM medians exhibit the same sorts of patterns as their means, differences in MISM medians across
windows generally lack significance.
15
relation between unexplained variation in expenses and the values of these two metrics. The 34.7%
value for MEXP%, however, is much higher than the 15.8% level obtained for DTM. Moreover,
DTM is negatively correlated with MEXP%, which is consistent with the reverse regression
interpretation of its value. That is, DTM declines as the magnitude of the underlying direct relation
between expense as a function of revenue increases. DTM is also positively correlated with MISM.
Collectively, these relations indicate that DTM is the least consistently aligned matching measure.
4.1 Matching Over Time Analysis
Figures 1 through 5 present graphs of the mean value of the four matching measures we
consider by (rolling window-end) year as well as rolling-window values for D_SALES, which is
the underlying driver for the MEXP% measure. As these are rather short time-series estimations
they are prone to extreme outcomes. Hence, we focus on cross-sectional mean values within rolling
windows after Winsorizing at 2% and 98%. We take these means as reflective of expense
recognition exhibited by the typical firm in each rolling window period.
All five graphs are consistent with matching having declined between 1965 and 2013. They
differ considerably, however, in terms of when this decline manifests itself. Figure 1 suggests that
DMSE was relatively constant until around 1980 (as these are end-years of ten year windows the
reported point estimates reflect the average effect over the ten years ending with the last year in
each rolling period). DMSE then increases fairly steadily through the end of the sample period.
Interestingly, by the end of the time period its value is around five times its pre-1980 value. The
16
DMSE graph also exhibits a sharp spike in 2009. This spike is consistent with a sharp decline in
matching taking place in, and immediately after, the financial crisis year.11
Figure 2 presents the graph of the DTM metric and it suggests a rather different pattern
than what we see in Figure 1 and the figures that follow. DTM declines over the first half of the
sample period, exhibiting a particularly sharp drop in the years before 1992. It then oscillates
around its 1992 levels in the following years, rising from 1993 to 2000, declining from 2001 to
2009, and then rising from 2010 forward. If we adopt the DT interpretation of this metric (i.e., that
it is primarily capturing random error in expense recognition), then these patterns suggest that a
sharp decline in matching occurred between the mid-1970s and the early 1990s, but this decline
was partially reversed over the later 1990s only to reverse again in the 2000s.12
In contrast to DTM, the D_SALES and MEXP% graphs presented in Figures 3 and 4
indicate that matching was rather stable in the earliest time periods, but then worsens sharply at
the end of the sample period. Interestingly, in the 1975-1982 period, MEXP% exceeds 100%. That
is, in the time periods covered by these rolling windows (roughly 1970 to 1982) expenses are
apparently being over-matched to revenues. Such “too high” values can be evidence of poor
matching. And, they likely partially account for the decline in the DTM measure seen in Figure 2
for this time period. However, this effect is somewhat mechanical. Ceteris paribus, the DTM
measure moves inversely with D_SALES (which is the primary driver of MEXP%). Consequently,
11
The spike does not persist beyond 2010 due in large part to the exit of firms exhibiting extreme values in 20082010. If we limit the sample to only those firms still present in 2011, the spike largely disappears.
12
The pairwise correlation between the values for our measure and the ten year averages of the annual crosssectional DTM estimates reported in Table 3 of Dichev and Tang (2008) is 0.913. Hence, our alternative approach to
generating the DTM coefficient is not the source of the difference in pattern between DTM and the other matching
metrics we examine.
17
while DTM declines when D_SALES values rise it also increases when D_SALES values fall, but
falling D_SALES values typically imply deterioration, not improvement, in matching.13
The Figure 5 graph of MISM, like D_INT and D_SALES, shows no large decline in
matching (or, equivalently, increase in mismatching of expenses to adjacent period revenues) in
the initial time period of the study. However, MISM increases steadily thereafter. Relative to the
patterns exhibited by D_SALES and MEXP%, this increase begins earlier, in the early 1990s, and
peaks in 2009, before declining somewhat at the very end of the sample period.14 The 2009 extreme
peak, however, reflects that the financial crisis increased the level of expenses unexplained by
concurrent revenue, and that this increase was accompanied by an increase in the degree to which
adjacent period revenues explain expenses.
Table 3 presents a more formal evaluation of the over-time patterns in the various matching
metrics. We base this evaluation on the five non-overlapping windows that span our 1964-2013
time period. Hence, the first window covers 1964-1973 while the final window covers 2004-2013.
Panel A of Table 3 reports the mean values for DMSE, DTM, MEXP% and MISM in each window.
Not surprisingly, these values reflect the same general patterns seen in the figures. DMSE increases
uniformly over the five windows, DTM declines sharply in the 1984-1993 window where it is also
lowest, MEXP% declines sharply in the 2004-2013 window, while MISM, like DMSE, increases
over the five windows, particularly so in the final two windows relative to the earlier windows.
Panels B through E of the table report t-statistics of differences in means between rolling
windows for each of the four matching measures. Differences are determined as earlier window
means deducted from later means. For DMSE, reported in Panel B, all of these differences are
13
In fact, a likely contributing explanation for the absence of a more sizable decline in the DTM measure in the final
portion of the sample period is the decline in D_SALES taking place in this same period.
14
Median values for MISM actually decline until the late 1990s before rising substantially over the final 15 years.
18
positive and significant at the 0.05 level consistent with the rising trend in DMSE seen in Figure
1 and Panel A. For DTM, reported in Panel C, the t-statistics for the differences between the means
in the first two windows (1964-1973 and 1974-1983) and the final three windows are quite high,
ranging from -9.05 to -12.90, indicating that the drop in DTM seen in Figure 2 after 1983 is highly
significant. However, the difference in DMSE between the 1984-1993 and 1994-2003 windows is
positive and significant, suggesting that matching recovered during 1994-2003. For MEXP%,
reported in Panel D, the only significant differences are for the 2004-2013 window, where the tstatistics range between -3.91, for the difference with the 1994-2003 time period, and -5.57, for
the difference with the 1974-1983 time period. These differences support the picture presented in
Figure 4 that MEXP% remains relatively stable until the turn of the century before deteriorating.
For MISM, reported in Panel E, the t-statistics for the differences between the last two windows
and each of the first three windows range from 2.05 to 4.60. These results confirm the statistical
significance of the increase in MISM that takes place in the final twenty years covered by Figure
5. However, the differences between the 1984-1993 mean and the earlier 1964-1973 and 19741983 means are significant as well (t-statistics of 3.40 and 2.84) indicating that MISM actually
starts rising before 1984.
4.2 Firm Compustat Age and Matching
Srivastava (2014) finds that much of the temporal change in measures of accounting
quality, including DTM, between 1970 and 2009 is attributable to changes in the set of firms for
which such measures are estimated. In particular, when the sample is restricted to older established
firms, observed declines in earnings quality are far less pronounced. We examine the robustness
of the Table 3 results to this firm age effect by restricting the sample in each of the five non19
overlapping windows employed in Table 3 to only those firms in a window that are listed on
Compustat prior to 1974. Table 4 presents our analysis of these restricted samples. Panel A reports
mean values for these restricted samples while panels B through E report t-statistics for mean
differences by matching metric.
In this restricted sample, consistent with Srivastava, the decline in DTM is smaller relative
to the decline observed in the overall sample. DTM falls to 0.946 in the 2004-2013 period, as
compared to the 0.907 value reported in Table 3 for this same period. Similarly, MEXP% declines
to 93.7% as compared to 90.9% in the full sample. However, the increases in DMSE and MISM
are actually slightly higher for this sample. DMSE increases to 2.125 in the 2004-2013 period as
opposed to 2.051 for this same period in the full sample, while MISM increases to 0.219 in the
2004-2013 period as opposed to its full sample value of 0.197.
In the Panels B to E examinations of changes over time in matching, the results are broadly
consistent with those reported in Table 3. In terms of the significant differences identified in Table
3, the only comparable differences that lack significance for the restricted sample examined in
Table 4 are: (1) DMSE (Panel B) in the 1994-2003 period as compared with the 1984-1993 period;
(2) DTM (Panel C) in the 2004-2013 period as compared with the 1994-2003 period; (3) MISM
(Panel E) in the 1994-2003 and 2004-2014 periods as compared with the 1984-1993 time period.
Among these statistically insignificant differences, only the failure to find significant increases in
MISM after 1983 represents a potentially substantive departure from the Table 3 overall sample
results. Specifically, these results are consistent with the increase in MISM occurring largely prior
to 1993 while the Table 3 analysis suggests that it continues to increase until 2003. However,
inspection of the actual estimated MISM values in Panel A casts considerable doubt on such an
interpretation. The 2004-2013 MISM value is 0.219, which is nearly double the 0.118 value
20
reported for the 1984-1993 window. Hence, loss in power due to declining sample size seems a
more plausible explanation for these insignificant MISM differences in Table 4.
4.3 Variation Attributable to Coefficient Restrictions
In section 3.2, we discuss how suppressed idiosyncratic parameter variation in empirical
estimations of the degree to which contemporaneous revenues explain expense on average
confounds the interpretation of DMSE and DMSE-related measures. While it is impossible to
fully assess the impact of such suppressed variation on DMSE, it is possible to obtain some insights
about the likely severity of this issue by evaluating how much DMSE changes as we move from a
model where parameter estimates are more restricted to one where they are less restricted. We
conduct such an assessment by comparing the error levels based on our firm-specific estimations
with the errors that arise when we estimate equation (1b) using a single pooled regression for each
rolling window. That is, we restrict all firms in a rolling window to have the same slope and
intercept.15 On a firm-by-firm basis, we then determine the average of the squared errors (ASEi,wt)
based on these commonly determined slope and intercept values. DIFSEi,nt, the difference between
ASEi,wt and MSE(1b)I,wt, reflects the amount of error introduced at the firm level when individually
estimated firm parameters are replaced with these pooled cross-sectional based estimators.
Panel A of Table 5 reports median values for DIFSE for the five non-overlapping ten-year
windows in our sample. DIFSE more than doubles between 1964-1973 and 2004-2013, rising from
0.973 to 2.053. The t-statistic for this difference, reported in panel B, is 3.93. Hence, restricting
coefficients to their pooled cross-sectional values introduces increasing amounts of error into the
15
We also conducted the analysis using annual cross-sectional regressions rather than pooling observations across
years, which is the approach employed in DT. The median error levels for these annual regressions differed very
little from those for the pooled regression. Hence, we only report values for the pooled specification here.
21
overall pooled estimations of expense on revenue during 1964-2013. Moreover, such error is
purely the result of imposing a counterfactual restriction on the model parameters and so cannot
be viewed as evidencing poor matching. Indeed, it may well reflect good matching since we should
expect such cross-sectional variation when firms perform differently.
An alternative approach to measuring the error effect of restricting parameters to their
cross-sectional pooled levels is to scale the error by the total amount of error that can possibly be
explained. We do this by dividing DIFSE by ASE to determine the percentage of ASE that is
attributable to the parameter restriction. These values are also reported in Panel A of Table 5 and
range from a low of 46.4% during 1994-2003 to a high of 69.2% during 1964-1973. The
magnitudes of these percentages suggest that parameter restriction contributes substantially to the
residual error in pure cross-sectional estimations such as those employed in DT. However, unlike
DIFSE, the values of these percentages do not rise over time. Indeed, the 2004-2013 value of
55.7% is significantly (0.05 level) lower than the 1964-1973 and 1974-1983 values of 69.2% and
62.8%. So, while parameter variation is increasingly important in absolute terms, its relative
contribution to the overall level of error has fallen in more recent years. And, a decline in matching
quality is a plausible candidate explanation for such a decline.
4.4 Lead and Lag Revenue Coefficients
While the lead and lag revenue coefficients (LDREV and LGREV) from (3) are
problematic as measures of overall matching magnitude or efficacy, they are not without interest
in terms of describing some of the underlying factors that are contributing to how well matching
is working in a given time period or firm. Positive LGREV and LDREV values are broadly
consistent with under-matching in that they identify the expenses recognized in the current period
22
that are clearly attributable to other periods. In contrast, negative LGREV and LDREV values
indicate that expenses in the current period are moving inversely with adjacent period revenues.
That is, expenses are being shifted out of the current period and into adjacent periods. While one
mechanism by which such inverse relations can arise, particularly with respect to LGREV, is overmatching, negative LGREV and LDREV coefficients do not necessarily imply over-matching. For
example, an expense recognition function of the form:
Expense = K - c1*Revt+1 - c2*Revt-1
(7)
where K is a positive constant, c1> 0, and c2>0, gives rise to negative LGREV and LDREV values
but has no implications for the relation between period t revenue and expense. Here, the expense
reductions associated with lead and lag revenue are pulled from the constant term K. That is, higher
values of c1 and c2 cause K to be higher (to cover them). Alternatively, if we replace K with c*Revt
in (7) then the value of c must increase to cover them (which is over-matching).
Figure 6 presents the mean values for the firm-specific estimates of the LDREV and
LGREV coefficient estimates by year. LGREV is negative for the first several rolling windows
(i.e., the 1964-1974 period), but then turns positive increasing in value through the next several
years, peaking in 1982. It then falls back below zero again in 1987, where it remains for the rest
of the sample period. The shifting back and forth between positive and negative values suggests
that both under-matching and contrarian expense shifting are co-occurring with direct shifting
dominating in the early years and contrarian shifting become a major factor in more recent years.
LDREV, on the other hand, is positive for every rolling window year except 2012.
Table 6 presents more formal analyses of median LDREV and LGREV for the five nonoverlapping ten-year windows in our analysis. Panel A reports means as well as the percentage of
the annual estimates that are positive for each of the five windows. LDREV is, on average, positive
23
in all five windows. It is significant at the 0.05 level in all but the 2004-2013 window. It is positive
more often than it is negative in all windows, but the highest percentage positive value is only
57.6%, which occurs during 1964-1973. So, a substantial minority of firms exhibit negative
LDREV values. LGREV is negative in all windows except 1974-1983, when it is positive
(significant at the 0.05 level). The negative values in the last three windows are all statistically
significant (0.05 level). These values are all consistent with the shifts in LGREV observed in
Figure 6. Panels B and C report t-statistics for the differences in rolling window means for LDREV
(Panel B) and LGREV (Panel C). For LDREV the only significant (0.05 level) differences are that
the 1984-1993 mean of 0.042 exceeds the 1974-1983 mean of 0.017 as well as the 2004-2013
mean of 0.006. For LGREV the 1974-1983 mean of 0.010 is greater than all of the other window
means (all of which are negative).
4.5 Cross-Sectional Analyses
In this section, we examine the relations between earnings variability, earnings persistence
and matching in the cross-section. DT propose that earnings variability and persistence both
decline as matching efficacy declines. Both of these observations stem from the notion that poor
matching adds noise to earnings by spreading out costs. We examine these two relations using our
alternative measures of mismatching: MEXP% and MISM. We do not consider DMSE as its
validity depends on parameter variation not playing a confounding role as a design-induced source
of error, and there is no plausible way to completely control for such variation in the cross-section.
And, we know from Table 5 that such variation is a major source of error the size of which
increases over time. DMSE is also arguably a tautological metric, since it measures the variability
of the expense component of earnings. We do not consider DTM because it is conceptually
24
problematic, and empirically it seems out of step with the other matching measures.
Finally, we also consider the cross-sectional relevance of the LDREV and LGREV
estimates from equation 4 for earnings variability and persistence. Since the implications of these
two parameters differ substantively depending on their sign we consider their positive and negative
values separately. Hence, we split the set of LDREV estimates into two variables:
(1) LDREV+, which equals LDREV when LDREV > 0, and is 0 otherwise; and,
(2) LDREV-, which equals LDREV when LDREV< 0, and is 0 otherwise.
We perform a similar division of the LGREV estimates as well to generate LGREV+ and LGREV-.
We examine both earnings variability (Evar) and earnings persistence (Persist) using
regression estimations of the following linear form:
Evari,rt or Persisti,rt
= d0 + d1 Mj,rt + Σj dj controlsi,j,rt + ei,rt
(8)
M represents a given firm-specific measure of matching. In the LDREV and LGREV versions of
this model they enter in pairs. For example, in the case of LDREV, we replace d1M in (8) with d1a
LDREV+ and d1b LDREV-. We employ decile ranks of all variables in estimating equation (8) where
the ranking is done within rolling windows.16 Consequently, explained variation in the model is
due entirely to cross-sectional within-year variation and not to economy-wide trends or
commonalities in the earnings quality or matching measures we examine.17
The set of control variables employed in some of our estimations of (8) are: (i) log(bp),
defined as the natural logarithm of book-to-price ratio of equity (CEQ/CSHO*PRCC_F), to control
for underlying risk or future investment opportunity (Smith and Watts 1992; Fama and French
1992); (ii) log(mv), defined as the natural logarithm of equity market value (CSHO*PRCC_F), to
16
LDREV and LGREV are divided based on coefficient sign after ranking.
The ten-year time-series regressions we employ are, in particular, quite noisy. Hence, it is important to avoid
overweighting extreme observations associated with them, as such observations are almost certainly due to noise. As
an alternative to decile ranks, we also trimmed the data as a means of eliminating such extreme observations. The
trimmed results are broadly consistent with those reported based on decile ranks.
17
25
control for firm size in market value (Fama and French 1992); (iii) log(assets), defined as the
natural logarithm of total assets (AT), to control for firm size in book value (Dechow and Dichev
2002; Francis et al. 2004); (iv) σ(sale), defined as the standard deviation of total sales (SALE) for
the rolling ten-year period, to control for operating volatility (Dechow and Dichev 2002; Francis
et al. 2004); and (v) log(ocycle), defined as the natural logarithm of operating cycle, i.e., months
in accounts receivable plus months in inventory ((RECT/SALE) + (INVT/COGS)), to control for
credit and collection policy (Dechow, 1994; Dechow and Dichev 2002; Francis et al. 2004).
4.5.1 Earnings Variability
Table 7 presents estimations of equation (8) for earnings variability, both without (Panel
A) and with (Panel B) control variables. Estimates are provided for each rolling window and for
the five windows pooled together. In the Panel A estimations, MEXP% exhibits a consistent
significant negative relation with earnings variability while MISM exhibits a consistent significant
positive relation with earnings variability. Hence, consistent with DT, earnings variability is
inversely associated with matching efficacy as captured by MEXP% and MISM. These core
relations differ little across windows. For MEXP% the estimated coefficients vary between -0.392
during 2004-2013 and -0.580 during 1974-1983. For MISM they vary between 0.134 during 20042013 and 0.254 during 1974-1983. Introduction of control variables (Panel B) has minimal impact
on the Panel A MEXP% and MISM relations. Estimated magnitudes shrink somewhat, but remain
significant at the 0.05 level or better in all cases except MISM during 2004-2013.
The LDREV and LGREV relations are also of some interest here. Positive LDREV values
are positively associated with earnings variability in the pooled overall estimation (significant at
the 0.05 level), but negative values are negatively associated with variability (also significant at
the 0.05 level). These divergent directional effects indicate that as the magnitude of the LDREV
26
coefficient increases in absolute terms earnings variability also increases. In the case of LGREV,
however, the estimated relation is negative regardless of the sign of LGREV (both coefficients are
significant at the 0.05 level). So, as LGREV increases, earnings variability decreases
unconditionally. However, the inclusion of control variables raises the LGREV+ coefficient from
-0.062 to -0.007, which lacks statistical significance. Hence, decreasing the absolute magnitude of
negative LDREV coefficients (i.e., moving them toward 0) is associated with lower earnings
variability, which is consistent with near 0 LDREV values reflecting low levels of mismatching.
But, increasing them beyond 0 has little impact on variability or possibly even decreases it further.
A possible explanation for this latter relation stems for the fact that positive LDREV coefficients
reflect recognition of expense in advance of the associated revenue. If the objective of such
advanced expense recognition is to smooth earnings, then higher positive side LDREV values may
reflect such smoothing, which by design decreases earnings variability.
4.5.2 Earnings Persistence
Table 8 presents estimations of equation 8 for earnings persistence. The MEXP% and
MISM relations here are rather surprising. In the overall estimations, MEXP% is negatively
associated with earnings persistence and MISM is positively associated with it. That is, matching
efficacy is negatively, not positively, associated with the level of earnings persistence exhibited
by firms in the cross-section. A possible explanation for these unexpected relations is that
persistence also depends on the frequency with which firms experience one-time or short-lived
earnings shocks. The short-lived nature of such shocks seems likely to inhibit the ability of firms
to shift expenses associated with them to other time periods giving rise to lower levels of MISM
and higher levels of MEXP%. Hence, MISM is lower and MEXP% is higher in high transitory
27
shock (low inherent persistence) firms and lower in low transitory shock (high inherent
persistence) firms.
The LGREV and LDREV relations with persistence are also of interest here. The reported
coefficients are negative in all windows in both panels, and significant (0.05 level) in most
windows. Hence, higher values of LGREV and LDREV, irrespective of sign, are associated with
lower earnings persistence. Interestingly, this general unconditional relation implies that firms with
highly negative values of LGREV (or LDREV) exhibit higher levels of earnings persistence than
firms with near 0 values. Over-matching of expense, in particular, is a plausible explanation for
this. Consider a firm that experiences a purely transitory revenue shock of T in a period where the
appropriately matched expenses for this revenue is a*T, but the firm actually recognizes expenses
of (a+k)*T leading to a reversal of k*T in the next period. If k>0 (i.e., there is over-matching) then
the transitory one period income of (1-a)*T is now spread over two periods with (1-a-k)*T
recognized in the first period and k*T recognized in the second. That is, over-matching causes
transitory single period earnings shocks to positively persist into the subsequent period.
5. Conclusion
As a fundamental principle, matching aims to appropriately assess the cost of recognized
revenue in a period as a measure of current period performance (e.g. Dichev, 2008; Basu and
Waymire 2010). Hence, it is a core concept for any substantive notion of the profitability of firm’s
transactions and is a financial reporting attribute of considerable empirical interest. Existing
archival empirical evidence on matching, however, is limited. Moreover, much of the existent
evidence relies on measures developed in Dichev and Tang (2008) that are derived from the
perspective that matching involves the advancing of expenditures to generate revenues. That is,
28
that expense recognition precedes revenue recognition. Conceptually, however, matching is the
recognition of expenses associated with recognized revenues. That is, expense recognition follows,
rather than precedes, revenue recognition. We examine whether this distinction matters by
revisiting the DT study using measures consistent with the conceptual perspective that expenses
are matched to revenues as opposed to revenues being matched to expenses. More generally, our
study provides a more conceptually grounded empirical perspective of matching efficacy over the
past fifty years as well as how matching efficacy is related to core earnings attributes.
Our primary comprehensive measure of overall matching efficacy is the percentage of a
firm’s expense that, on average, is directly attributable to revenue based on how the firm’s
expenses and revenues covary over time. This measure is remarkably high, averaging 97.2%
during 1964 to 2013. And, through the year 2000 it does not deviate greatly from this average. In
fact, its value is 97.9% in the opening period of our analysis (1964-1973) and its value for the tenyear period ending in 2000 is 98.7%. After 2000, however, it declines markedly, reaching a nadir
of 88.6% in the ten-year period ending in 2009 (the primary financial crisis year). And, it is only
90.9% in the final time period we study (the ten years ending in 2013). In contrast, the primary
over-time matching measure in DT suggests that matching declined markedly during the 1980s
and early 1990s. Its level in 2013 of 0.907 is actually slightly higher than the low of 0.891 it reaches
for the ten-year period ending in 1994. These values suggest that matching efficacy is little changed
since 1994.
Our second measure of matching addresses the amount of mismatching attributable to
adjacent period revenues. It is a partial measure in that it does not capture mismatching to nonadjacent periods. Consistent with the percentage of matched expense measure, it indicates that
29
mismatching is higher in the closing years of our analysis relative to earlier years. It is also
particularly high in the financial crisis time period.
Our analysis also identifies the over-matching of expenses to revenues as a key factor in
understanding matching. Over-matching is the recognition of a greater amount of expense than
appropriate as a function of revenues. And, during 1975-1982, over-matching plays a dominant
role in expense recognition as the percentage of expense being recognized based on revenue
actually exceeds 100%. In fact, if 100% is taken as a benchmark level that one should expect to
observe under perfect matching, then the 1975-2000 time period reflects a shift from a period
where expense recognition is barely dominated by over-matching to one where expense
recognition is barely dominated by under-matching. Over-matching is also a factor in the positive
cross-sectional relation between mismatching and earnings persistence. Over-matching spreads
earnings shocks into other periods through expense reversals, thereby enhancing (in appearance)
their permanence.
Finally, we employ our measures to evaluate how earnings variability and earnings
persistence vary with our measure of matching and our measure of mismatching in the crosssection. Consistent with Dichev and Tang as well as underlying theory, we find that earnings
variability moves inversely with the percentage of expense attributable to revenue and increases
with mismatching. However, we do not find the expected positive linkage between percentage of
expense attributable to revenue and earnings persistence or the expected negative relation between
earnings persistence and mismatching. Over-matching, as discussed in the prior paragraph is one
possible explanation for not finding these relations. Another is that the persistence exhibited by
revenue shocks is directly connected to how difficult it is to match expenses to such shocks. Hence,
30
high persistence shocks give rise to lower matching simply because it is more difficult to
appropriately match expenses to such shocks.
31
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33
Table 1
Descriptive Statistics
Variables
Revenue
Expense
Matching Measures
DMSE
DTM
MEXP%
MISM
Other Measures
D_SALES
LDREV
LGREV
Evar
Persist
Mean
Std. Dev.
Median
Maximum
Minimum
0.873
0.828
0.594
0.585
0.773
0.724
3.507
3.427
0.073
0.058
1.020
0.976
97.2%
0.136
3.221
0.246
19.0%
0.770
0.193
1.017
99.0%
0.005
72.312
1.568
173.3%
15.906
0.000
-0.181
-18.1%
-2.083
0.902
0.025
-0.015
0.161
0.180
0.182
0.931
0.011
0.000
1.386
1.023
0.596
-0.027
-0.833
-1.136
0.026
0.402
0.027
0.362
0.018
0.420
0.337
1.808
0.001
-0.558
Revenue
is annual revenue (SALE) divided by average assets (AT).
Expense
is annual expense, excluding extraordinary items (SALE-IB) divided by average
assets (AT).
DMSE
is the mean squared error (x 103) from regressing expense on contemporaneous
revenue. Regressions are firm-specific time-series, estimated over 10-year rolling
windows.
DTM
is the coefficient on contemporaneous expense from regressing revenue on lead,
lag, and contemporaneous expense. Regressions are firm-specific time-series,
estimated over 10-year rolling windows.
D_SALES
is the coefficient on revenue from regressing expense on contemporaneous
revenue. Regressions are firm-specific time-series, estimated over 10-year rolling
windows.
MEXP%
is D_SALES*Average(Revenue/Expense) where Revenue/Expense is averaged
over the 10 years of data used to estimate D_SALES.
MISM
is the mean squared error (x103) from regressing expense on contemporaneous
revenue less the mean squared error (x103) from regressing expense on lead, lag,
and contemporaneous revenue. Both regressions are firm-specific time-series,
estimated over 10-year rolling windows.
34
LDREV
is the coefficient on lead revenue in regressions of expense on lead, lag, and
contemporaneous revenue. Regressions are firm specific time-series, estimated
over 10-year rolling windows.
LGREV
is the coefficient on lead revenue in regressions of expense on lead, lag, and
contemporaneous revenue. Regressions are firm specific time-series, estimated
over 10-year rolling windows.
Evar
is the standard deviation of a firm’s income before extraordinary items (IB),
determined for 10-year rolling windows.
Persist
is the persistence of earnings before extraordinary items (IB), measured as the
coefficient on income before extraordinary items estimates from firm-specific
temporal regressions of IB on the lag of IB. Income is divided by average assets
(AT).
35
Table 2
Correlations Among Matching Measures: 1964-2013
Variables
DMSE
DTM
MEXP%
DTM (p-value)
-0.158 (<.0001)
MEXP% (p-value)
-0.349 (<.0001)
-0.280 (<.0001)
MISM (p-value)
0.195 (<.0001)
0.040 (<.0015)
-0.032 (<.0018)
Variable definitions are provided in Table 1. Reported correlations are averages of rolling 10year window Spearman correlations. P-values are based on these average values.
36
Table 3
Matching in the 1964 to 2013 Time Period
Panel A: Mean Values For Every 10th Rolling Window
Matching Measures
1964-1973
1974-1983
1984-1993
Window
Window
Window
DMSE
0.180
0.384
0.943
1994-2003
Window
1.484
2004-2013
Window
2.051
DTM
1.080
1.063
0.895
0.943
0.907
MEXP%
97.9%
98.8%
98.2%
97.0%
90.9%
MISM
0.034
0.043
0.097
0.229
0.197
Panel B: t-statistics for Cross-Window Mean Differences in DMSE
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
5.39
8.48
8.84
1974-1983
5.84
7.28
1984-1993
3.15
1994-2003
Panel C: t-statistics for Cross-Window Mean Differences in DTM
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
-1.78
-12.98
-10.25
1974-1983
-11.88
-9.05
1984-1993
2.88
1994-2003
Panel D: t-statistics for Cross-Window Differences in MEXP%
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
1.04
0.25
-0.88
1974-1983
-0.56
-1.72
1984-1993
-0.97
1994-2003
37
2004-2013
8.48
7.48
4.67
2.14
2004-2013
-11.14
-10.10
0.63
-2.04
2004-2013
-4.93
-5.57
-4.67
-3.91
Panel E: t-statistics for Cross-Window Differences in MISM
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
1.15
3.40
4.86
1974-1983
2.84
4.60
1984-1993
3.04
1994-2003
2004-2013
3.54
3.32
2.05
-0.53
This table reports measures reflecting how well expenses are matched to revenues over ten-year
periods. Panel A reports mean firm-level values for the four primary matching measures we
consider based on firm-specific time-series regressions conducted over the specified ten-year
window. Measure definitions are provided in Table 1. The sample of firms for each window
consists of the 500 largest non-financial firms at the start of the window with available data for
the entire 10-year period. Panels B through E of the table reports t-statistics for between-window
comparisons (Baseline window less deducted window) of the means of each of the four matching
measures. Significant t-statistics (0.05 level) are bolded.
38
Table 4
Mean Values of Matching Measures for Firms with Pre-1974 Compustat Start Dates
Panel A. MEANS
Matching Measure
DMSE
DTM
MEXP%
MISM
N
1964-1973
Window
1974-1983
Window
1984-1993
Window
1994-2003
Window
2004-2013
Window
0.180
1.080
97.9%
0.034
500
0.384
1.064
98.5%
0.044
485
1.058
0.901
97.9%
0.118
380
1.135
0.959
98.6%
0.140
323
2.125
0.946
93.7%
0.219
194
Panel B: t-statistics for Cross-Window Mean Differences in DMSE
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
5.33
7.97
6.55
1974-1983
5.86
5.02
1984-1993
0.42
1994-2003
Panel C: t-statistics for Cross-Window Mean Differences for DTM
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
-1.62
-11.06
-8.41
1974-1983
-10.12
-7.34
1984-1993
2.99
1994-2003
Panel D: t-statistics for Cross-Window Mean Differences for MEXP%
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
0.77
-0.06
0.63
1974-1983
-0.62
0.06
1984-1993
0.57
1994-2003
39
2004-2013
4.90
4.37
2.59
2.34
2004-2013
-6.40
-5.66
1.84
-0.54
2004-2013
-2.50
-2.88
-2.24
-2.68
Panel E: t-statistics for Cross Window Mean Differences for MISM
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1.25
1964-1973
3.72
2.70
1974-1983
3.23
2.43
0.49
1984-1993
1994-2003
2004-2013
2.12
2.00
1.13
0.83
This table reports measures reflecting how well expenses are matched to revenues over ten-year
periods for those firms in each period that are listed on Compustat prior to 1974. Panel A reports
mean firm level values for the four primary matching measures we consider based on firmspecific time-series regressions conducted over the specified ten-year window. Measure
definitions are provided in Table 1. The initial sample of firms for each window consists of the
500 largest non-financial firms at the start of the window with available data for the entire 10year period. Panels B through E of the table reports t-statistics for between window comparisons
(Baseline window less deducted window) of the means each of the four matching measures.
Significant t-statistics (0.05 level) are bolded.
40
Table 5
Residual Error Variation Attributable to Imposing Common Regression Parameter Values in the
Cross-section.
Panel A: Mean Values For Every 10th Rolling Window
Matching Measure
1964-1973
1974-1983
1984-1993
1994-2003 2004-2013
Window
Window
Window
Window
Window
DIFSE
0.973
1.047
1.114
1.678
2.053
DIFSE/ASE
0.692
0.628
0.581
0.464
0.557
Panel B: t-statistics for Cross-Window Mean Differences for DIFSE
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
0.49
0.52
3.30
1974-1983
0.25
2.93
1984-1993
1.81
1994-2003
Panel C: t-statistics for Cross-Window Mean Differences for DIFSE/ASE
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
-5.17
-10.84
-3.10
1974-1983
-7.50
-2.11
1984-1993
-5.15
1994-2003
2004-2013
3.93
3.65
2.63
1.19
2004-2013
-6.36
-3.23
-1.06
4.12
This table reports mean values for DIFSE and DIFSE/ASE where ASE is a firm’s average
residual squared error (x103) from a regression of expense on revenue that is estimated using
pooled cross-sectional data (from all 500 firms over all 10 years in a given rolling window) and
DIFSE is ASE – DMSE (DMSE is the mean squared error (x 103)). The sample of firms for each
ten-year window consists of the 500 largest non-financial firms at the start of the window with
available data for the entire 10-year period. Panels B and C of the table reports t-statistics for
between window comparisons (baseline window less deducted window) of mean DIFSE and
mean DIFSE/ASE respectively. Significant t-statistics (0.05 level) are bolded.
41
Table 6
Lead and Lag Revenue Coefficients by Rolling Window
Panel A: Mean Values For Every 10th Rolling Window
Measures
1964-1973
1974-1983
1984-1993
Window
Window
Window
LDREV
0.023
0.017
0.042
(% Positive)
(57.6%)
(54.8%)
(53.8%)
LGREV
(% Positive)
-0.010
(44.0%)
0.010
(52.2%)
-0.022
(51.4%)
1994-2003
Window
0.023
(55.4%)
2004-2013
Window
0.006
(51.2%)
-0.018
(51.2%)
-0.033
(47.2%)
Panel B: t-statistics for Cross-Window Mean Differences for LDREV
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
-0.91
1964-1973
1.60
-0.01
1974-1983
2.07
0.59
1.39
1984-1993
1994-2003
Panel C: t-statistics for Cross-Window Mean Differences for LGREV
Baseline Window
1974-1983
1984-1993
1994-2003
Deducted Window
1964-1973
-1.13
-0.87
2.86
1974-1983
-2.98
-2.91
1984-1993
0.28
1994-2003
2004-2013
-1.53
-1.05
-2.38
1.31
2004-2013
-1.97
-3.66
-0.79
1.09
This table reports mean values of firm specific estimates of the lead (LDREV) and lagged
(LGREV) coefficients from firm-specific regressions of expense on lead, lag, and
contemporaneous revenues. The sample of firms for each ten-year window consists of the 500
largest non-financial firms at the start of the window with available data for the entire 10-year
period. Panels B and C of the table reports t-statistics for between-window comparisons (baseline
window less deducted window) of mean LDREV and mean LGREV respectively. Means
significantly different from 0 and medians significantly different from 50% at the 0.05 level are
bolded in panel A. T-statistic values significant at the 0.05 level are bolded in panels B and C.
42
Table 7
Matching and Earnings Variability
Panel A: Estimates Without Control Variables
Matching Measures
1964-1973
1974-1983
Window
Window
coeff std. err coeff std. err
MEXP%
0.045 -0.580
0.036
-0.448
MISM
0.046
0.047
0.198
0.254
+
LDREV
-0.077
0.051
0.017
0.049
LDREV-0.056
0.046 -0.093
0.049
+
LGREV
0.046
0.020
0.048
-0.186
LGREV0.051 -0.121
0.047
-0.150
1984-1993
Window
coeff std. err
0.041
-0.531
0.045
0.201
0.049
0.048
-0.086
0.047
-0.087
0.049
0.046
-0.225
1994-2003
Window
coeff std. err
0.042
-0.464
0.046
0.182
0.049
0.179
-0.039
0.046
-0.054
0.049
0.046
-0.269
2004-2013
Window
coeff std. err
0.044
-0.392
0.047
0.134
0.047
0.100
-0.087
0.047
0.001
0.048
0.046
-0.220
Overall
coeff std. err
0.019
-0.483
0.021
0.194
0.022
0.054
0.021
-0.072
0.022
-0.062
0.021
-0.197
Panel B: Estimates With Control Variables Included in the Model.
Matching Measures
1964-1973
1974-1983
1984-1993
1994-2003
2004-2013
Overall
Window
Window
Window
Window
Window
coeff std. err coeff std. err coeff std. err coeff std. err coeff std. err coeff std. err
MEXP%
0.044 -0.396
0.034 -0.372
0.044 -0.406
0.042 -0.411
0.042 -0.421
0.019
-0.535
MISM
0.037
0.035
0.038
0.043
0.072
0.042
0.018
0.117
0.109
0.182
0.137
0.125
+
LDREV
0.049
0.035
0.041
0.045
0.043
0.019
0.106
0.079
0.151
0.175
0.133
0.134
LDREV-0.032
0.044 -0.093
0.034 -0.075
0.039 -0.057
0.044 -0.106
0.043 -0.073
0.018
+
LGREV
0.047
0.038
0.034
0.008
0.040
0.022
0.046
0.003
0.044 -0.007
0.019
-0.133
LGREV0.045 -0.128
0.031 -0.214
0.038 -0.216
0.043 -0.268
0.043 -0.224
0.018
-0.320
This table reports coefficient estimates from regressions of earnings variability, measured by firm over ten-year windows, on various
measures reflecting how expenses are matched with revenues for a firm over these same ten-year rolling windows. Variable
definitions for the matching measures and earnings variability are provided in Table 1. Panel B control variables are average log of
book-to price ratio of equity (CEQ/CSHQ*PRCC_F); average log of market value (CSHO*PRCC_F); average log of asset value
(AT); sales variability measured as the standard deviation of a firm’s sales (SALE) over the ten year window; and average log of
operating cycle ((RECT/SALE) + (INVT/COGS)). Separate models are estimated for each matching measure (LREV+ and LDREVare treated as a single measure as are LGREV+ and LGREV-). LDREV+ equals LDREV when LDREV > 0, and is 0 otherwise; and,
LDREV-, which equals LDREV when LDREV< 0, and is 0 otherwise. LGREV+ equals LGREV when LGREV > 0, and is 0
otherwise; and, LGREV-, which equals LGREV when LGREV< 0, and is 0 otherwise. The first five columns report estimates for each
43
of the five non-overlapping ten-year windows in our sample. The overall column pools all of the observations from these five
windows. All data in these regressions are measured using decile ranks formed within windows. Standard errors are reported in
parentheses. In the case of the overall estimation these errors are cluster-adjusted by window.
44
Table 8
Matching and Earnings Persistence
Panel A: Estimates Without Control Variables
Matching Measures
1964-1973
1974-1983
Window
Window
coeff std. err coeff std. err
MEXP%
0.044 -0.105
0.045
-0.175
MISM
-0.019
0.043 -0.007
0.043
+
LDREV
0.047 -0.114
0.049
-0.215
LDREV0.044 -0.153
0.047
-0.248
+
LGREV
0.047 -0.241
0.046
-0.125
LGREV0.047 -0.303
0.046
-0.192
1984-1993
Window
coeff std. err
0.018
0.044
0.042
0.095
0.046
-0.172
0.047
-0.114
0.047
-0.142
-0.078
0.047
1994-2003
Window
coeff std. err
0.044
-0.101
0.070
0.045
-0.088
0.049
-0.050
0.047
-0.045
0.048
-0.011
0.049
2004-2013
Window
coeff std. err
0.045
-0.154
0.043
0.132
0.046
-0.261
0.047
-0.225
0.046
-0.226
0.048
-0.173
Overall
coeff std. err
0.021
-0.103
0.020
0.054
0.021
-0.170
0.021
-0.158
0.021
-0.156
0.022
-0.151
Panel B: Estimates With Control Variables Included in the Model.
Matching Measures
1964-1973
1974-1983
1984-1993
1994-2003
2004-2013
Overall
Window
Window
Window
Window
Window
coeff std. err coeff std. err coeff std. err coeff std. err coeff std. err coeff std. err
MEXP%
0.056 -0.199
0.051
0.005
0.053 -0.078
0.048 -0.142
0.050 -0.097
0.023
-0.155
MISM
0.006
0.045
0.007
0.043
0.046
0.048
0.047
0.044
0.020
0.104
0.142
0.059
+
LDREV
0.059 -0.158
0.050 -0.176
0.052 -0.068
0.052 -0.266
0.048 -0.168
0.023
-0.168
LDREV0.055 -0.173
0.049 -0.107
0.051 -0.028
0.051 -0.256
0.049 -0.144
0.023
-0.169
+
LGREV
0.053 -0.259
0.048 -0.150
0.051 -0.007
0.052 -0.196
0.050 -0.163
0.023
-0.224
LGREV0.055 -0.308
0.047 -0.095
0.051
0.016
0.053 -0.160
0.051 -0.155
0.023
-0.259
This table reports coefficient estimates from regressions of earnings persistence, measured by firm over ten-year windows, on various
measures reflecting how expenses are matched with revenues for a firm over these same ten-year rolling windows. Variable
definitions for the matching measures and earnings variability are provided in Table 1. Panel B control variables are average log of
book-to price ratio of equity (CEQ/CSHQ*PRCC_F); average log of market value (CSHO*PRCC_F); average log of asset value
(AT); sales variability measured as the standard deviation of a firm’s sales (SALE) over the ten year window; and average log of
operating cycle ((RECT/SALE) + (INVT/COGS)). Separate models are estimated for each matching measure (LREV+ and LDREVare treated as a single measure as are LGREV+ and LGREV-). LDREV+ equals LDREV when LDREV > 0, and is 0 otherwise; and,
LDREV-, which equals LDREV when LDREV< 0, and is 0 otherwise. LGREV+ equals LGREV when LGREV > 0, and is 0
otherwise; and, LGREV-, which equals LGREV when LGREV< 0, and is 0 otherwise. The first five columns report estimates for each
45
of the five non-overlapping ten year windows in our sample. The overall column pools all of the observations from these five
windows. All data in these regressions are measured using decile ranks formed within windows. Standard errors are reported in
parentheses. In the case of the overall estimation these errors are cluster adjusted by window.
46
Figure 1. Mean Firm-Specific Mean Squared Error (DMSE):1964-2013
6
DMSE
4
2
2013
2011
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
0
Rolling Year End
This figure reports mean values for DMSE for rolling windows covering data from 1964 - 2013.
DMSE is the mean squared error (x 103) from the regressing expense on contemporaneous
revenue. Regressions are firm-specific time-series estimated over 10-year windows.
Figure 2. Mean Dichev and Tang Coefficient (DTM): 1964-2013
1.15
DTM
1.05
0.95
2013
2011
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
0.85
Rolling Year End
This figure reports mean values for DTM for rolling windows covering data from 1964-2013.
DTM is the coefficient on contemporaneous expense from regressing revenue on lead, lag, and
Contemporaneous expense. Regressions are firm-specific time-series, estimated over 10-year
rolling windows.
47
Figure 3. Mean Direct Regression Revenue Coefficient (D_SALES): 1964-2013
D_SALES
1
0.95
0.9
0.85
2013
2011
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
0.8
Rolling Year End
This figure reports mean values for D_SALES for rolling windows covering data from 19642013. D_SALES is the estimated coefficient on revenue from regressing expense on
contemporaneous revenue. Regressions are firm-specific time-series, estimated over 10-year
windows.
Figure 4: Mean % of Expense Explained by Revenue (MEXP%): 1964-2013
105.00%
MEXP%
100.00%
95.00%
90.00%
85.00%
80.00%
Rolling Year-end
This figure reports mean values for MEXP% for rolling windows covering data from 1964-2013.
MEXP% is the percentage of a firm’s expense over the rolling window that is attributable to
revenue over this same window, based on the estimated revenue coefficient (DSALES) obtained
by regressing expense on revenue. Regressions are firm-specific time-series estimated over 10year windows.
48
Figure 5. Mean Variation Explained by Lead and Lag Sales (MISM): 1964-2013
0.55
MISM
0.35
0.15
-0.05
19731976197919821985198819911994199720002003200620092012
Rolling Year End
This figure reports mean values for MISM for rolling windows covering data from 1964-2013.
MISM is the mean squared error (x103) from regressing expense on contemporaneous revenue
less the mean squared error (x103) from regressing expense on lead, lag, and contemporaneous
revenue. Both regressions are firm-specific time-series, estimated over 10-year rolling windows.
Figure 6. Mean Coefficients on Lead (LDREV) and Lag (LGREV) Sales: 1964-2013
0.08
LDREV
Coefficient Value
0.06
LGREV
0.04
0.02
0
-0.02
-0.04
-0.06
2013
2011
2009
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
-0.08
Rolling Year End
This figure reports mean values for the coefficients on lead (LDREV) and lag (LGREV) revenue
in regressions of expense on lead, lag, and contemporaneous revenue. Regressions are firm
specific time-series, estimated over 10-year rolling windows.
49