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Some Models for the Evolution of Financial
Statement Data
by
Paul V. Dunmore
Discussion Paper Series 223
November 2013
ISSN 1175-2874 (Print)
ISSN 2230-3383 (Online)
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© 2013 Paul V. Dunmore
Some Models for the Evolution of Financial
Statement Data
Abstract
Financial statement numbers may be represented as a vector which evolves over time.Conventional models of this process, such as the basic equation that Ronen and Yaariuse to analyze the evolution of sales (deflated by assets) and the Jones models and itsvariants for identifying non-discretionary accruals, are mathematically impossible andtherefore mis-specified for empirical work. This paper presents various improvements onthese models, culminating in a multivariate linear model for the time-series evolution ofthe logarithms of positive accounting variables. This model leads to specific predictionsabout long-term growth rates and long-term ratios which appear to be new. Examinationof various data sets suggests that these predictions are borne out to reasonable accuracy.Non-positive variables such as Net Income cannot be log-transformed and cannot besuccessfully modeled by the inverse hyperbolic sine transformation (a generalization ofthe logarithm), but can be represented as the difference of correlated positive variables.Applications of the model include company valuation using the residual income model,modeling distress risk, and identifying expected (non-discretionary) accruals for earningsmanagement studies.
KEYWORDS: Accounting variables, earnings management, Jones model, firm growth,financial ratios, distress, residual income, valuation.
Some Models for the Evolution of Financial StatementData
1 Introduction
This paper presents some models for the growth of financial statement variables for
individual companies. The maintained requirement throughout is that the models be
mathematically credible and comply with bookkeeping requirements. These apparently
natural constraints are not satisfied by models commonly used in the accounting liter-
ature, and it should therefore be expected that empirical work based on the defective
models must itself be defective. For example, the fundamental hypothesis test in any
statistical work is that the asserted model is inconsistent with the data, that is, that the
null hypothesis is rejected. If the model is mathematically impossible, it is to be expected
that it will frequently be inconsistent with the data: a significant finding rejecting the
null hypothesis may mean nothing more than this, and may tell us nothing about the
question being investigated.
1.1 A time-varying vector
Very generally, the numbers in a set of financial statements may be viewed as a vector
xt of values at time t. If there are n components to the vector, then at any moment the
financial statements may be represented by a point in an n−dimensional space, which
wanders around the space as time passes. An immediate question is: Can we write an
equation which describes how the financial statements of a firm normally move around
in this space?
It must be possible to pose any research question which can be answered using financial
statement information as a question about anomalies in the path traced out in this space.
The cause of these anomalies may lie outside the financial statements themselves, as
when earnings are manipulated in response to bonus-plan incentives (Healy, 1985; Burns
and Kedia, 2006; Mergenthaler et al., 2012), or when firms close to debt default adopt
accounting methods that ease the covenant constraints (El-Gazzar et al., 1989). But a
powerful test of anomalies in that path requires a good model for the expected or normal
path; it is that issue that this paper addresses.
The ability to characterize a normal path has practical applications. For example, under
clean-surplus accounting and appropriate convergence conditions, the value of a firm is its
current book value plus the present value of its future residual income stream (Feltham
1
and Ohlson, 1995; Penman, 2004). Given a firm’s current financial statements, the ability
to forecast its future residual income stream holds the key to valuation. Firm-specific
information is of course of the greatest value, but having information on the probable
future track of the firm given its starting point would allow a valuation which is an
improvement over the naıve model of constant growth. Another example is in the analysis
of corporate distress, for which accounting information is known to be a good predictor
(Altman, 1968; Altman et al., 1977; Ohlson, 1980). If a firm currently has the deformed
financial statements which imply distress, an understanding of how those statements can
be expected to evolve should contain clues about the probability that the statements
will get worse and lead to failure, or will improve and lead to recovery. Of course, since
bankruptcy is a strategic decision made by managers and/or creditors, prediction of the
actual outcome should not be expected; but a statement about how the probability of
failure should evolve over time, conditional only on the starting position of the firm, may
still have value for researchers and practitioners.
The following table shows some symbols that I will use without further comment (Table 1
uses these symbols but also gives the Global Vantage equivalents). Financial statement
items will not be deflated unless this is explicitly stated.
Symbol Meaning Symbol Meaning
A Total Assets CA Current AssetsL Total Liabilities CL Current LiabilitiesNCA Noncurrent Assets NCL Noncurrent LiabilitiesQ Equity RE Retained EarningsPPE Property, Plant and Equipment INV InventoryS Sales revenue COGS Cost of goods soldR Total revenue X ExpensesDEPR Depreciation SGA Selling, General & Admin ExpensesD Dividends NI Net incomeCFO Cash from Operations
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1.2 Constraints on the vector
The financial-statement vector may be subject to both equality and inequality constraints.
Typical examples are
At = Lt +Qt (1)
NIt = Rt −Xt (2)
REt = REt−1 +NIt −Dt (3)
CAt ≥ 0
At ≥ CAt
Equality constraints at a single time can be evaded by considering only a subset of
the variables: for example, if At and Lt are known, then Qt is known; so the vector
x should not include Q if it includes both A and L, and should not include NI if it
includes both R and X. Inequality constraints can all be reduced to non-negativity
constraints: for example, if xt includes CAt and NCAt (but not At), then the condition
At ≥ CAt is automatically met as long as NCAt is non-negative. Dealing with non-
negativity constraints will be considered in section 4.2 below.
The difficult set of constraints to deal with are those such as (3) that connect the vectors
x at different times. If we could discover an “invariant” – some function of xt which
is equal to the same function of xt−1 and so does not vary over time – then we could
use it to define a lower-dimensional manifold of allowed values of x; equations such as
A − L − Q = 0 define such a manifold (the right-hand side, 0, is independent of time),
and eliminating Q from the vector x is a way of ensuring that all points do lie in the
allowed manifold. But equation (3) does not define an invariant.
One might try to work around the problem by recalling that REt is just the cumulative
revenues less expenses and dividends since the firm was founded, so that the vector xt
might include these cumulative revenues, expenses and dividends instead of REt and NIt.
The latter can be determined as
NIt = CumRt − CumRt−1 − CumXt + CumXt−1
REt = CumRt − CumXt − CumDt
The articulation between balance sheets in different years then holds automatically, and
RE could be eliminated from the set of variables to be modelled. Unfortunately, the
cumulative revenues and expenses are not available from the financial statements, have
no economic significance in themselves, and over time will grow far larger than any other
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component of the accounts.
It might be thought that equation (3) is not really a problem, as it merely defines REt
as the cumulative sum of NI minus D, which can be positive or negative. In conjunction
with (1), however, we can see that (3) imposes a connection between balance sheets at
different dates: for example, assets must equal liabilities plus contributed capital plus
other reserves plus retained earnings, and so these values are linked together across time.
Further, there are cases such as the inventory equation, INVt = INVt−1 + Purchasest −COGSt, where all values must be non-negative, so that there is a restriction affecting
cumulative purchases and COGS.
At present, therefore, the problem of enforcing constraints between vectors x at different
times does not have a clear general solution in the time-series formulation. However,
if the evolution of the firm’s accounts is assumed to occur in continuous time, then a
solution appears possible. It is to that representation that I now turn.
1.3 Discrete or continuous time?
Most research studies implicitly consider financial statements as being prepared at dis-
crete times: balance-sheet figures change annually, and income-statement and cash-flow-
statement items represent events during a year. This leads to the formulation that I
suggested above, where time is indexed by years, and values at time t are compared to
those at time t − 1 and perhaps t − 2. Such a view leads naturally to a formulation
in terms of conventional time-series analysis. For analysis of quarterly financial state-
ments, it is necessary to start the analysis again at the beginning, and develop a seasonal
model with quarterly disturbances (which will not in general be one-quarter of the annual
disturbances).
But it may be more realistic to envisage the firm’s accounts as being affected by a contin-
uous hailstorm of transactions. Every time another item is swiped through the checkout
at a supermarket, the financial statements of the supermarket chain alter by a few dol-
lars. Larger transactions, such as dividends or debt transactions, occur less often and
in larger amounts. The financial statements for the year do not describe single annual
transactions, but the cumulative results of this activity over the period.
In principle, although not in practice, it would be possible to present a new set of financial
statements each minute, updated to reflect the most recent transactions, another minute’s
accruals for wages and depreciation, and their associated tax effects. That is, the vector
xt wanders about its n−dimensional space continuously, shaken by a vast number of tiny
transactions like a pollen grain being driven through Brownian motion as it is struck by
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untold numbers of water molecules. The annual (quarterly) statements simply reflect
where the firm ended up after a year’s (quarter’s) worth of these continuous activities.
This leads to a model in which xt evolves in continuous time, and the associated math-
ematics is that of a stochastic process rather than a time-series process (Tippett, 1990;
Ashton et al., 2004). No special difficulties arise in considering quarterly accounts rather
than annual accounts. Further, the continuous description opens questions that cannot
be raised in the time-series description, such as the characteristics of the transaction
storm (for example, the frequency and the size of the transactions may vary with the
season and with the business cycle).
In a continuous-time description, flow variables must be interpreted as rates per unit
time. Sales revenue is not an annual figure, but the rate at which sales occur, which
might be expressed in dollars per minute, or annualized to dollars per year. But even if
it is expressed in dollars per year, that is not the same as being expressed in dollars – it
is a rate at which revenue accrues, not an amount of revenue. This leads to changes in
some of the constraints: for example REt = REt−1 +NIt −Dt must be replaced by
dREtdt
= NIt −Dt (4)
where NIt and Dt are now understood to be the rates per unit of time at which profit
accrues and dividends are paid. This may be easier to work with, because instead of an
equation which compares xt at different times, we have linear equations involving x and
its derivatives. Since a stochastic model requires us to specify the time derivatives of xt,
it may be possible to enter these constraints into this specification.
2 A defective conventional model
As a typical example of a defective model which requires improvement before it should
be used for empirical work, I will consider equation (9.1) of Ronen and Yaari (2008, p.
378). Collecting up terms, this equation is
St = (1 + λ)φSt−1 + (1 + λ)(1− φ)µ+ εt = αSt−1 + β + εt
with the obvious definitions α = (1 + λ)φ and β = (1 + λ)(1− φ)µ.
Several problems with this model are quickly apparent.
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2.1 Identifiability
The three parameters λ, φ and µ cannot be identified from the two parameters α and
β that can be recovered from time-series data. If α = 0 then we know that φ must be
zero, but β gives us only the product (1 + λ)µ. If β = 0 then we know that φ must be 1
(assuming that µ can only be positive), and then λ = α − 1, but µ is undetermined. If
α = β = 0.5, say, then all of the following combinations (and infinitely many more) are
possible
λ 4.00 1.00 0.00 -0.33 -0.44
µ 0.11 0.33 1.00 3.00 9.00
φ 0.10 0.25 0.50 0.75 0.90
This does not matter if (9.1) is used only to define simulations, because we can start
with assumed values of λ, φ and µ, and in effect the values of α and β are computed
from these for the simulation; but it would be a problem if parameters are to be inferred
from data. It is also obvious that Ronen and Yaari’s identification of λ as growth, µ as
mean sales, and φ as persistence cannot be correct, because the behavior of the system is
defined only by the values of α and β, and we get the same values of α and β for different
values of Ronen and Yaari’s parameters.
2.2 The mean is not usually µ, and may not exist
This is an extension of the previous point that µ cannot be identified. Ronen and Yaari
describe µ as the mean value of sales, but this cannot be correct. If the mean E(S) does
exist, then it must satisfy the equation
E(S) = αE(S) + β
so that
E(S) =β
1− α=
(1 + λ)(1− φ)µ
1− (1 + λ)φ(5)
= µ
(1 +
λ
1− (1 + λ)φ
)(6)
Equation (5) shows that the mean does not exist if (1 + λ)φ = 1 and is negative if
(1 + λ)φ > 1; equation (6) shows that the mean is equal to µ only if λ = 0. (Recall that
0 ≤ φ ≤ 1 so that 1− φ is positive.)
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2.3 Relevant variables must be omitted
In equation (9.1), λ and φ are pure numbers between 0 and 1. If Sales is measured in
millions of dollars, then each term on the right-hand side of equation (9.1) must be in
millions of dollars. This is correct for (1 + λ)φSt−1, which is two numbers multiplied by
millions of dollars. It can only be correct for the second term if µ is also measured in
millions of dollars (and for the third term if εt is measured in millions of dollars also,
which gives rise to heteroscedasticity).
So what determines the size of µ? It must be different for different firms, since some are
much bigger than others and µ must be correspondingly greater. There is no alternative
possibility except that µ must be a function of variables that reflect the firm size (whether
this be assets, liabilities, equity, profit, or others, or some combination of them).
But in that case, equation (9.1) necessarily has an omitted-variables problem. We cannot
understand how sales evolve unless we understand what variables actually go into this
process.
2.4 Heteroscedasticity
It is also clear that ε cannot be serially independent white noise as Ronen and Yaari
claim, because the size of the disturbances must be at least roughly proportional to S; if
the process allows St to grow over time, then the variance of ε cannot be a constant σ2
as claimed.
2.5 The model allows Sales to be negative
As shown by equation (5) above, if (1 + λ)φ > 1 then the expected sales is negative;
but even if (1 + λ)φ is less than 1 there is a possibility that some individual values of
sales could be negative, and if (1 + λ)φ is only a little less than 1 then this will happen
frequently. This is clearly unacceptable.
3 Problems with the persistence concept
Footnote 1 of Ronen and Yaari (2008, p. 378) defines the persistence of a variable Z
as the partial derivative ∂Zt+1/∂Zt of Zt+1 with respect to Zt; loosely, if a shock causes
Zt to increase by 1 unit, the persistence is the consequential increase in the next value
Zt+1. One way of describing how financial statements evolve is to report the persistence
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of various items: it is supposed, for example, that highly persistent components of income
should have more value relevance than items that quickly die away (Frankel and Litov,
2009).
If the sales process is written as
St = αSt−1 + β + εt (7)
then the persistence is α. Ronen and Yaari cite Dechow and Schrand (2004, Table 2.1),
who show that sales has greater persistence than operating income (and on down to other
profit variables). However, Ronen and Yaari mention in passing that the variables were
deflated by total assets, apparently without realizing that this completely changes the
analysis.
3.1 The persistence of deflated sales
Suppose that the sales process and the assets process are similar:
St = α1St−1 + β1 + εt
At = α2At−1 + β2 + ηt
The parameters α1, α2, β1, and β2 can be estimated directly for any firm without deflating
the variables. Now consider the ratio ut = St/At, the deflated sales (which is also the
Asset Turnover Ratio). How does this evolve, and what is its persistence?
We can use the relationship St−1 = ut−1At−1 to write
ut =StAt
=α1St−1 + β1 + εtα2At−1 + β2 + ηt
(8)
=α1ut−1At−1 + β1 + εtα2At−1 + β2 + ηt
=α1
α2
ut−1 + β1+εtα1At−1
1 + β2+ηtα2At−1
from which we get the persistence of u:
∂ut∂ut−1
=α1
α2
(1 +
β2 + ηtα2At−1
)−1
(9)
This is a random variable (because it includes the disturbance ηt) and its expected value
does not depend only on the parameters of the sales and asset processes but also on the
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firm size (through At−1).
But this is not the only way of organizing equation (8): we could equally well write it as
ut =α1St−1 + β1 + εt
α2St−1/ut−1 + β2 + ηt
The differentiation is a little more complicated, but the result is
∂ut∂ut−1
=α1
α2
1 + β1+εtα1St−1(
1 + ut−1β2+ηtα2St−1
)2So we have two quite different formulas for the same persistence (and they cannot be
different ways of writing the same thing because they include different sets of variables).
Both formulas show the persistence to be α1/α2 multiplied by some random bias factor
whose median is 1 but whose expected value (mean) is not 1.1 Neither of them gives an
estimate of the persistence of sales, which is α1.
No doubt, Dechow and Schrand (2004) would say that they were actually measuring the
persistence α3 of the asset turnover ratio assuming the process
ut = α3ut−1 + β3 + ξt
but equation (8) shows that this is not consistent with assuming that sales and assets
evolve in accordance with the process (9.1). One of these must be wrong.
4 Improving the model
Ronen and Yaari’s equation (9.1) is invalidated by the strong heteroscedasticity, the
omitted variables, and the possibility that S can become negative in contravention of
bookkeeping rules. Inferences about persistence of financial information are invalidated
by careless deflation. This section considers some simple ways in which the model might
be improved, and the consequences for the persistence concept.
1Even if β2 = 0 in equation (9), so that the expected value of the term in parentheses is 1, the expectedvalue of its reciprocal is actually infinite. For empirical work, this implies that occasional large outlierswill be found in the observed value of the persistence; trimming outliers will bring the observed samplestatistics back towards the median, α1/α2. How far the expected sample statistic differs from α1/α2 willdepend on the extent of trimming, and is thus an artefact of the method rather than a characteristic ofthe sample (much less of the underlying process).
9
4.1 Adding an omitted variable
Instead of treating β as a constant, let us multiply it by a firm size variable (see discussion
in section 2.3). Assets is the obvious possibility, although not the only one. This would
give
St = α1St−1 + β1At−1 + ε1t (10)
At = α2St−1 + β2At−1 + ε2t (11)
These equations do not have intercepts, for the reason explained in section 2.3. The asset
turnover ratio ut = St/At evolves as
ut =StAt
=α1St−1 + β1At−1 + ε1tα2St−1 + β2At−1 + ε2t
(12)
=α1ut−1 + β1 + ε1t/At−1
α2ut−1 + β2 + ε2t/At−1
(13)
This is still a complicated non-linear function, with an even more complicated persistence.
If ut−1 is small enough, the persistence is approximately α1/β2 − α2β1 with some bias;
but if ut−1 is large enough the persistence tends to zero, proportionately to 1/u2t−1.
The idea can be generalized if we suppose that x is a vector of accounting variables which
evolves according to the equation
xt − xt−1 = Γxt−1 + εt (14)
or, in a form tht generalises equations (10) and (11),
xt = (Γ + I) xt−1 + εt (15)
where ε is a vector of disturbances, Γ is a square matrix of coefficients, and I is the
identity matrix. Breaking out the identity matrix, rather than combining it with Γ, will
simplify the notation later. The (i, j)th element of Γ will be written as γij. The evolution
of any ratio uij,t = xi,t/xj,t would follow an equation similar to equation (13).
The continuous-time analogue of equation (14) is obviously the stochastic vector differ-
ential equation:dxtdt
= Γxt + εt (16)
The model in equation (15) corrects the omitted-variables problem in Ronen and Yaari’s
(9.1), although it leaves open the question of which variables need to be included in x.
But it does not fix the other problems, notably heteroscedasticity and the fact that some
10
variables are wrongly allowed to become negative.
4.2 Transforming the variables
Limiting attention for now to non-negative accounting variables, let us suppose that
an equation similar to (15) actually applies to yt = log(xt). Then it does not matter
that equation (15) allows the elements of y to become negative, because x = exp(y) is
guaranteed to be strictly positive. Introducing a constant vector β (justification below),
we replace equation (15) with
yt = β + (Γ + I) yt−1 + εt (17)
or alternatively
x1,t = eβ1xγ11+11,t−1 x
γ122,t−1x
γ133,t−1...e
ε1,t (18)
x2,t = eβ2xγ211,t−1xγ22+12,t−1 x
γ233,t−1...e
ε2,t
... ...
The point of the vector β can now be seen: it allows for multiplicative constants in each
row of equation (18), allowing the different variables to be of different sizes (for example,
CA will tend to be smaller than A, and so we expect βCA to be less than βA in general).
The log transformation also corrects for heteroscedasticity: in equation (17), a value of
0.01 for εi,t means a disturbance of about 1% in the corresponding accounting variable
(precisely, the disturbance is a factor of e0.01=1.01005...). This mans that ε does not scale
with the size of the firm, so that heteroscedasticity should not be a significant issue.2
This transformation imposes an additional restriction on the matrix Γ in equation (17).
β should not scale with firm size, but should be a constant just as the elements of Γ
are constant. All of the firm-size effect should be captured by the powers of x. For the
right-hand side of equation (18) to be measured in millions of dollars, it is necessary that
the exponents in each row of the equation should sum to 1, so that the numbers in each
2This does not assert that there is no remaining heteroscedasticity, only that the greatest cause –variation of the residuals with firm size – has been removed.
11
row of Γ should sum to 0:
γ11 + γ12 + γ13 + ... = 0
γ21 + γ22 + γ23 + ... = 0
...
4.3 Ratios
If y = log(x) then the ratio of any two variables in the set is given by
uij,t =xi,txj,t
= eyi,t−yj,t (19)
The matrix Z of the differences in the transformed values (that is, zij = yi − yj) is the
logarithm of the whole set of ratios of the accounting variables in x.
4.4 Equilibrium growth rates
If the firm is growing at a constant rate λ, then the difference between yt and yt−1 is on
average λ for each element; that is, from equation (17),
E(yt)− yt−1 = β + Γyt−1 = λ
or
Γyt−1 = λ− β (20)
with the apparent solution
yt−1 = Γ−1(λ− β) (wrong!)
provided that the matrix inverse exists. On the face of it, this cannot be correct, because it
implies that yt−1 is independent of t, so that the firm is not growing. However, the earlier
condition that every row of Γ must sum to 0 implies that the rows are linearly dependent;
hence the determinant of Γ is zero and the inverse Γ−1 does not exist. Equation (20) is
correct, but the proposed solution is not.
This single set of linear conditions should be expected to reduce the rank of Γ by 1 rather
than by 2 or more, and it is easily checked numerically that this is the usual result. Thus
there is one free parameter in the system of equations (20).
The analysis of the two-variable and three-variable cases is presented in Appendix A.
These examples suggest that a general solution may be obtained by adding a single row
12
to equation (20) to stipulate that y1 = 0: the augmented set of equations is
Γy = −β
where
Γ =
(Γ −1
1, 0, 0, . . . 0
)y =
(y
λ
)β =
(β
0
)(21)
where 1 is a vector whose elements are all 1.
The solution of this set of equations for the vector y includes the value of λ; it must
have y1 = 0 (which is a check on the numerical accuracy of the solution), and all of the
other y values are expressed as the difference from y1. Of course, this does not affect the
matrix Z which gives the logarithm of all the ratios; it is defined by the differences of the
y values, and is not affected by adding any constant to all of them.
The idea, implicit in equation (21), that long-term growth rates and long-term ratios are
connected appears to be new. It will be relevant when considering firm valuation, later.
4.5 Persistence
The model in equation (17) describes how past values of non-negative variables affect
future values, and it therefore provides a basis for computing the persistence of accounting
variables. Suppose that there is a small change in the disturbance for a particular variable
j at time t−1, so that εj,t−1 is replaced by εj,t−1+dε. Then yj,t−1 changes by dyj,t−1 = dε,
and in the next period equation (17) shows that the transformed variables change by
dyi,t = (δij + γij) dε (22)
where δij is the Kronecker delta, 1 if i = j and 0 otherwise. Hence the persistence of the
variable j isdyj,t
dyj,t−1
= 1 + γjj
Transforming back to the accounting variable xj = exp(yj) gives the persistence
dxj,tdxj,t−1
=exp (yj,t) dyj,t
exp (yj,t−1) dyj,t−1
=xj,txj,t−1
(1 + γjj) (23)
13
The ratio xj,t/xj,t−1 is 1 plus the growth rate of the variable xj. If there is constant
growth, the ratio is eλ and so the persistence is
dxj,tdxj,t−1
= eλ (1 + γjj) (24)
Thus, accounting values tend to have greater persistence in fast-growing firms.
This is not, however, the coefficient that would be found by regressing xj,t on xj,t−1.
From equation (18) it is clear that the relationship is non-linear, and moderated by the
values of other variables. xj,t is an increasing function of xj,t−1, and so a linear regression
will give a positive (and no doubt statistically significant) slope. But the slope is purely
sample-specific: different samples with different ranges of xj and other variables will give
different slopes, none of which is the persistence. Indeed, outlier deletion and Winsorising,
which are both common practices in empirical work, will themselves alter the regression
slope. Since equation (7) cannot correctly describe how St evolves, a regression based on
that equation does not yield the persistence of Sales. Equations (23) and (24) should be
regarded as showing how to measure persistence, rather than as giving testable predictions
of what might be found by a conventional regression for persistence. This in turn has
implications for theorizing and measuring how persistence of accounting values might be
related to their relevance for firm value.
We can also estimate the effect on one variable (i) of a shock to another variable (j). If
i 6= j, equation (22) givesdyi,t
dyj,t−1
= γij
so thatdxi,t
dxj,t−1
=xi,txj,t−1
γij =xj,txj,t−1
uij,tγij (25)
where uij,t is the ratio xi,t/xj,t. Not only does this “cross-persistence” tend to be larger
in faster-growing firms, it tends to be larger when the ratio of the variables is greater.
A different approach is necessary for analysing the persistence of ratios (that is, deflated
variables). In this model, future values of accounting variables are caused by past values
of those and other accounting variables: there is no causal link between past and future
values of ratios. (For an alternative model in which future ratios are caused by past
ratios, see Dunmore (forthcoming).) However, past ratios are caused by past variable
values, which also cause future variable values and hence future ratios; so we expect some
correlation between past and future ratios.
For definiteness, suppose that the accounting vector xt has components St, At, x3,t, . . . ,
and consider the asset turnover ratio (deflated Sales) ut = St/At. By equation (18), the
14
ratio is
ut =StAt
= eβS−βASγSS+1−γASt−1 AγSA−1−γAA
t−1 xγS3−γA33,t−1 . . . eεS,t−εA,t
Define θ = (γSS − γAS − γSA + γAA)/2 and ϕ = (γSS − γAS + γSA − γAA)/2 so that
γSS − γAS = θ + ϕ and γSA − γAA = ϕ− θ; then
ut = eβS−βAS1+θ+ϕt−1 A−1−θ+ϕ
t−1 xγS3−γA33,t−1 . . . eεS,t−εA,t
= eβS−βAu1+θt−1 (St−1At−1)ϕ xγS3−γA3
3,t−1 . . . eεS,t−εA,t (26)
Equation (26) shows that the relationship between ut−1 and ut is not linear but follows
a power law, moderated by some power of firm size√St−1At−1 and by other variables.
There will be a linear relationship between the logarithms of the ratio in successive years;
the logarithm of the ratio will have persistence 1 + θ on average.
Provided that θ > −1, equation (26) shows that ut is an increasing function of ut−1,
so that a linear regression of ut on ut−1 will return a positive slope coefficient which
will no doubt be statistically significant in most cases. Differentiating equation (26) and
suppressing the time index shows that the slope is
eβS−βA(1 + θ)uθ(SA)ϕxγS3−γA33 . . .
The average slope in a sample will be related to the sample average of uθ. If θ and ϕ
and γS3− γA3 are all nearly zero, the regression slope will be approximately the constant
eβS−βA , and under these strong conditions this may be expected to be the persistence of
the ratio.3
5 Accounting variables that may not be positive
5.1 Can the log transform be generalised?
Some variables (equity, profit, accruals) may be negative, and many others (extraordinary
items) are often zero. For these variables, the logarithmic transformation cannot be
3To give a rough idea of the differences, suppose that the only two variables in the vector are Stand At; then the requirement that the rows of Γ sum to zero requires that θ = γSS + γAA and ϕ = 0,so that the slope is proportional to uθ and independent of firm size. Anticipating the numerical valuesfrom Panel A of Table 4, the autoregression slope of deflated sales is 0.845u−0.142. The true persistenceof the asset turnover ratio is 0.006u from equation (25), assuming that the firm grows at the long-runrate λ; the true persistence of undeflated sales is 0.062 from equation (24) with the same growth rate.Comparing these results shows how great a bias arises, first from ignoring the effects of deflation, andsecond from assuming that persistence can be estimated using the wrong equation (7).
15
applied. An obvious generalization of the logarithm is the inverse hyperbolic sine function
yi = sinh−1(xi/θ) = log
(xi +
√x2i + θ2
)− log θ (27)
and its inverse
xi = θ sinh(yi) = (θ/2)(eyi − e−yi
)(28)
Equations (27) and (28) are written using the same scale factor θ for each variable, but
this is not essential: it would be possible for each variable to have its own scale factor.
If xi is much larger than θ, yi is almost exactly log(2xi/θ); if xi is large and negative
(much less than −θ), yi is almost exactly − log(−2xi/θ); and if the magnitude of xi is
much less than θ, yi is approximately xi/θ. Thus the sinh−1 function behaves like the
logarithm when the argument has large magnitude, and connects these two logarithmic
functions together smoothly with a nearly straight line through the origin, as shown in
Figure 1.
This looks like a convenient generalization of the log transform to allow for negative vales.
On closer inspection, however, it fails badly as a basis for the sort of inferences that we
wish to draw. Consider the behaviour of profit as a function of assets (the data is a
random sample of 1,000 firm-years for global manufacturing firms), shown in Figure 2.
There are clearly two separate bands, and no regression model can correctly describe the
relationship between these variables.
The source of the problem is that a firm with $100M in assets will have profits or losses
of a few million dollars (say, most likely between -5M and +5M). There is a reasonably
high probability that profits will be between $1M and $5M, a smaller but still moderate
probability that they will be between $-1M and $-5M, but almost no probability that
they will be between $1,000 and $5,000. On a logarithmic (or sinh−1) scale, then, the
probability density is fairly high around a few million in profits or losses, but very low
around a few thousand in profits or losses. The density is bimodal, with the peaks moving
further apart as the scale increases, and this is just the pattern seen in Figure 2.
Although the sinh−1 looks attractive at first glance, it cannot work with an equation such
as equation (17).
5.2 Negative values are differences of other values
An original purpose of double-entry bookkeeping was to represent negative numbers at
a time when mathematicians had no such concept. If expenses exceed revenues, the
balance in the Income Summary account is not a negative profit, but a positive loss (a
16
debit balance instead of the usual credit balance). In their original representation, all
accounting numbers are non-negative; but for modelling purposes, some numbers must
be allowed to have either sign (that is, we have a single Income variable which may be
positive or negative).
Some cases are easily dealt with: equation (1) tells us to eliminate equity (which may
be negative) in favour of assets and liabilities; equation (2) tells us to eliminate profit
and use revenue and expense instead. But some are more difficult: CFO is the difference
between operating inflows and outflows of cash, but these components are not stored in
commercial databases (and may not even be known if the firm presented its Cash Flow
Statement using the indirect format). Accruals may be positive or negative, but they
are the difference between two numbers (income and CFO) which may themselves be
negative. However, if we can operationalize the underlying non-negative variables, then
we can estimate their evolution over time using equation (17), and subsequently extract
the required differences of the forecast values.
Cash inflow from operations largely comes from revenues, and so an initial approximation
might be to use total revenue to estimate it; possibly revenue plus opening receivables
less closing receivables might produce a slightly better estimate, but in practice the two
estimates give nearly the same result. If cash inflow is R, then cash outflow must be
CFOout = R − CFO, and this must be positive (virtually always – in practice, about
0.4% of manufacturing firms gave a negative value of R−CFO, which is rare enough to
be negligible). Similarly, total expenses may be estimated by X = R −NI, and in turn
accruals may be estimated as NI − CFO = (R −X) − (R − CFOout) = CFOout −X,
where CFOout and X are positive.
In this way, we can construct non-negative accounting values which have meaning and
from which the desired values can be recovered. We can fit parameters β and Γ in
equation (17) using the logarithms of these non-negative variables (for example, in a
single industry), and estimate the covariances of the residuals. Once we have done that,
then for any firm to which these estimates apply,
1. Knowing the values of y up to time t − 1, we can estimate the vector yt and its
covariances, assumed to be multivariate normal.
2. The corresponding non-negative accounting variables can be recovered as ey, which
will be multivariate log-normal with known parameters.
3. Derived variables such as NI can be recovered as eyR − eyX , which is the difference
of two correlated log-normals. Its distribution is not known in closed form, but
confidence intervals can be constructed by simulation.
17
4. If desired, simulation can be applied to equation (17) with the fitted parameters, to
show the evolution of the financial statements of a typical firm in the fitted industry.
In principle, one could use these ideas to develop formulae for the persistence of ratios
such as Return on Assets, where the numerator need not be positive and so must be
expressed as a difference between two positive variables, or even Return on Equity, where
both numerator and denominator must be so expressed. That extension will not be
pursued here.
6 Testing the model
6.1 Predictions
The model offers some quite specific and testable predictions, for sets of non-negative
accounting variables that form a “basis” for the dynamics, with no variables missing
from the set. They are not presented as formal hypotheses for conventional testing,
because they are expected to be only approximately correct since the underlying model
is a simplification; with large samples the null hypothesis will certainly be rejected. But
what matters is that the predictions are “good enough”, rather than that they cannot
be rejected at some conventional significance level. Thus, the success of the predictions
should be evaluated judgmentally.
1. Each row of the matrix Γ sums to 0; equivalently, each row of Γ + I sums to 1. The
latter formulation offers a sense of how large a mismatch in the sum is important.
2. The residuals are roughly normal, not autocorrelated (although they may be corre-
lated cross-sectionally), and their variance is roughly constant.
3. Since the elements of β and Γ are the result of economic forces, they are likely to
vary from industry to industry and (perhaps to a lesser extent) from country to
country. However, where different firms are subject to the same economic forces,
these elements should not vary from firm to firm.
4. The long-run growth rates derived from elements of Γ using equation (20) are
realistic firm growth rates.
5. The long-run ratios derived from equation (19) where y is given by equation (20)
are realistic ratios.
18
These predictions typically concern the magnitude of some number, not merely the sign
of a relationship. They are therefore much stronger claims than are usual in accounting
research. For example, if actual firm growth rates are around 10% and the theory predicts
that they should be about 25%, the theory clearly fails even though the prediction has
the correct (positive) sign. But if the theory predicts that the growth rates should be
about 11%, this may be taken as strong support that it captures a significant feature
of economic reality, even if a hypothesis test using a large sample could show that 10%
and 11% are significantly different. If these predictions do appear substantially consistent
with the empirical evidence, then the resulting model should be considerably more robust
than those that have been used previously, such as Ronen and Yaari’s (9.1).
6.2 Data
I tested the model using Global Vantage data for machinery manufacturing firms (SIC
code 35) for the years 1993-2012. Firms with data available were accepted from any coun-
try. The accounting variables used (with their Global Vantage codes for reference) are
shown in Panel A of Table 1. For consistency, the data was accessed in US dollars con-
verted at a fixed exchange rate, so that numbers from different countries are comparable
but growth rates are not distorted by fluctuating historical exchange rates. From these
variables, I computed the non-negative variables shown in Panel B of Table 1. From
the positive variables one can construct NI = R − X and ACCR = CFOout − X as
previously discussed.
Only firms with at least 10 consecutive years of data were retained; sample sizes are
given in each table. Examination of the data revealed that missing values are sometimes
recorded in Global Vantage as the @NA code, but sometimes are recorded as 0. Genuine
values of exactly zero are possible, but they seem to be very rare for the variables selected
(they are common for extraordinary items); accordingly, all values of 0 were treated as
missing. Firm-years which failed basic sanity checks (such as having current assets exceed
total assets) were discarded.
There are various problems with the data which cannot necessarily be corrected. One
issue, of course, is acquisitions and demergers, which can cause abrupt changes in all
financial variables that cannot be predicted from previous accounting information. An-
other problem is changes in classification, such as occurred in the Indian manufacturer
Forbes Co Ltd:
19
2007 2008 2009 2010 2011
Sales 215.018 221.191 239.187 198.226 335.434
COGS 109.005 114.803 230.043 137.795 170.083
SGA 82.944 91.882 2.593 111.510 129.348
COGS + SGA 191.949 206.685 232.636 249.305 299.431
Evidently, the way that expenses were classified between COGS and Selling, General &
Administrative expenses changed in 2009 and changed back in 2010. The result is that
any model which reasonably predicts SG&A to be about 100 in 2009 will be wrong by a
factor of 40, about 9 standard deviations. I investigated some cases where the residuals
from the model were extreme outliers (at least eight times the standard deviation and
therefore with a probability of less than 1 in 1015). There are two kinds of explanation for
such outliers: one is that the model is wrong so that the distribution of errors is not as
expected; the other is that the specific data points are in error. After examining several
cases similar to Forbes Co Ltd, it appeared that mergers or demergers or defective data
were the usual explanations, so that the correct treatment is to delete these points from
analysis. Accordingly, I present results using all data points and again after deleting firm-
years where one or more residuals had exceeded 4 standard deviations (about 1 chance
in 16,000).
6.3 Results
For discussing results, I focus on Sales and Assets, but I introduce other variables into the
vector as well. The results are presented in Tables 2 – 4 for the simplest case xT = (S,A).
Table 2 shows unconstrained OLS regression results, when all parameters are free to vary,
Table 3 gives the results where each row of Γ is constrained to sum to 0, and Table 4 uses
only cases which are not outliers. The first of these allows an assessment of whether the
rows actually do sum to about 0, and the others give more efficient estimates.
It can be seen in Table 2 that the rows of Γ do in fact sum to nearly 0 (more nearly so for
Sales than for Assets). The residuals are weakly autocorrelated and not very skewed, but
are seriously long-tailed (kurtosis 30-40). Their standard deviation is 0.404 for Sales and
0.309 for Assets, implying that the model can predict Sales and Assets one year ahead
with a typical accuracy of about 35-50%. The correlation between residuals for Sales and
Assets for each firm-year is 0.508, much greater than the lagged (auto-)correlations4. The
4This suggests that Seemingly Unrelated Regression may give better results than OLS. However, allregressions in this section were re-run using SUR, and the results are almost always identical; a fewnumbers differed by 1 in the last place shown in the tables.
20
predicted long-term logarithmic growth rate of 0.169 (that is, annual growth of 18.4%)
is greater than the actual growth rate of 0.064 found in the sample. It is possible that
the firms in the sample have not reached their long-term state, so that these growth
rates need not be exactly equal, but the predicted long-term growth rate is implausibly
large. The corresponding long-term asset turnover ratio (deflated Sales) is 0.586, which
is implausibly low and is much less than the sample average of 0.865; for consistency with
the theory, this sample average is calculated as the exponential of the mean difference
log(S/A) = log(S)− log(A).
However, Table 3 shows that the picture changes if the efficiency of the estimation is
improved by imposing the constraint that each row of Γ must sum to zero. The esti-
mated long-term growth rate becomes 0.076, only slightly above the observed growth
rate in the sample, and the asset turnover ratio becomes 0.844, close to the sample aver-
age. It appears that the efficiency gain from imposing the constraint is important, even
though violations of the constraint are not severe when it is not imposed. Moments and
correlations of the residuals are not much affected by the change in estimate, however.
The high kurtosis is a concern when fitting regression models, as it shows that the resid-
uals are not normally distributed. Kurtosis without much skewness suggests a small
proportion of symmetrically extreme high and low values, which as previously discussed
are likely to be caused by mergers and divestments. Excluding these cases should give
more accurate estimates of the behavior of normal firms. Table 4 repeats the analysis
after deleting firm-years where either the Sales or Assets residual exceeds 4 standard de-
viations in either direction. This reduces the moments of the residuals (as it must), but it
does not bring much improvement in the closeness of the other statistics to the theoretical
expectations. Autocorrelation increases, however: the unexpected mergers and divest-
ments introduce random shocks into the time series of residuals, which breaks up the
autocorrelations, so it is expected that removing them will increase the autocorrelations.
The next step is to enlarge the set of variables to include more than just Sales and
Assets. Introducing more variables may improve the precision with which Sales and
Assets themselves are explained, provides explanations of the other variables, and should
generally improve the fit of the theory to the data. This is done in Table 5, where Current
Assets, Total Liabilities, and Total Expenses have been added to the set of variables, and
in Table 6, where PPE, Current Liabilities, COGS, Selling General & Administrative
expenses and Depreciation have been added as well. For these tables, results are given
only for the constrained model with outliers deleted (comparable to those results in
Table 4).
When coefficients are not constrained to sum to zero, they do in fact remain close to zero
21
as more variables are added. These row sums are not tabulated, but for S, A, CA, L and
X they are -0.006, -0.020, -0.021, -0.006, and -0.015 respectively; and for S, A, CA, PPE,
CL, L, COGS, SGA, DEPR, and X they are -0.008, -0.020, -0.020, -0.013, -0.017, -0.008,
-0.009, -0.016, -0.003 and -0.017 respectively.
Systematic changes in the regression coefficients are evident. When only S and A are
considered, the change in log S is a declining function of St−1 (implying some weak mean
reversion) and an increasing function of At−1: since the rows sum to zero, the second
is a necessary consequence of the first. When more variables are added, however, the
dependence on St−1 remains nearly the same, but the dependence on Assets vanishes,
to be replaced by a similar dependence on Current Assets. (It may be that a particular
component of Current Assets, plausibly Inventory, presages an increase in Sales, but that
has not been checked.) Table 6 shows that the negative relation between past and current
Sales is partly caused by Sales being a proxy for COGS and SGA expenses: perhaps these
are evidence of channel stuffing (in which heavy marketing is used to shift more goods
than are sustainable, leading to a drop in Sales next period).
The determinants of changes in Assets behave rather differently as more variables are
added. The modest dependence on past Assets does not change much, but the depen-
dence on Sales strengthens as more variables are added. In Table 6 the strong positive
dependence on Sales is partly offset by a strong negative dependence on COGS. Since
Sales and COGS are only weakly mean reverting, an increase in either will be fairly per-
sistent (the persistence is 1 + γjj); an increase in Sales will thus tend to drive up Assets
(receivables, cash, inventory, fixed assets) and an increase in COGS will tend to bleed
assets (inventory, cash) for some time. Similar effects can be seen for CA, PPE, SGA
and depreciation, and even (although much more faintly) for liabilities.
As more variables are added to the accounting vector, the standard deviations of the
residuals fall, but only slightly; higher moments and correlations do not change much.
Long-term predicted growth rates and ratios stay close to sample values, except for ratios
involving PPE.
Taken as a whole, the expectations that can be examined using this data set appear
to be fairly well borne out. Of course, further research is needed to see how far these
preliminary findings can be generalized.
7 Potential applications of the model
Having a model for the usual evolution of accounting data is useful in a number of
contexts. I have assumed that the disturbances in equation (17) have no cause, being
22
purely white noise. Many research designs will focus on identifying causes which will
divert the disturbances from this behavior. Two slightly different approaches are possible.
First, the hypothesized causes may be added to the right-hand side of equation (17)
as exogenous variables, effectively modifying the residuals, and the effects on observed
financial statement numbers can then be examined. Second, equation (17) may be taken
as a definition of the disturbances, and the residuals may be regressed on the hypothesized
causal variables. However, since equation (17) is iterated year after year, any causal
variable that affects any residual will have effects on all financial statement variables
indefinitely far into the future. Thus, regression of residuals on causal variables may
need to consider a distributed-lag covariance structure.
I briefly explore three specific examples where the model may be useful: the Jones model
for identifying earnings management; the residual income model for firm valuation; and
Altman-type models for assessing financial distress and asset impairment.
7.1 The Jones model for earnings management
Research on earnings management needs a reference point, to show what unmanaged
earnings should be: the difference between actual reported earnings and this benchmark
is a measure of the degree to which earnings have been managed. The model due to
Jones (1991) is still widely used as such a benchmark, sometimes with minor variations.
Jones’s assumption was that total accruals TAt, the difference between reported earnings
and operating cash flows, are generated by the process
TAt = α + β1(St − St−1) + β2PPEt + At−1εt
which is deflated by lagged assets:
TAt/At−1 = α(1/At−1) + β1(St/At−1 − St−1/At−1) + β2PPEt/At−1 + εt (29)
(the notation is that of Ronen and Yaari’s (10.13), and is a little different from what I
used above).
The parameters of equation (29) are estimated separately for each firm during an esti-
mation period when earnings management is not suspected, then equation (29) is used
in the event period to identify the expected accruals. The difference between the actual
and expected accruals (that is, the residual) is taken to be the amount by which earnings
has been managed. One problem, which has been recognized in the literature, is that
we do not know whether earnings have been managed in the estimation period, so the
23
parameters may already reflect earnings management.
But there is also a severe omitted-variables problem, since α must scale with the size of
the firm. Consequently, it is difficult to justify the interpretation that the residual in the
event period represents earnings management rather than just mis-specification of the
model. It would be better to choose a set of variables x which includes at least CFOout
and X, and possibly others which help to improve the prediction of these variables. It is
not clear whether assets needs to be included in the set; that would have to be found by
trying it. The variables chosen must together follow equation (17) after transformation,
with a suitable Γ whose rows sum to 0. It can be estimated from all firms in the same
industry, since the parameters Γ and β are driven by underlying economic, technical and
managerial factors which are likely to be the same across an industry. The history of
individual firms is thus averaged out; in particular, one need not assume that the firm
under test did not engage in earnings management during the estimation period. The
expected accruals for year t can then be found as
Accrualst = CFOoutt −Xt (30)
with a confidence interval which can be found from the covariances of the residuals εCFOout
and εX . The difference between this number and the actual accruals may be evidence of
eanings management.
The lognormal distribution is well known (e.g. Aitchison and Brown, 1966), but little is
known about the distribution of the sums of lognormals and virtually nothing about the
distribution of the difference. The only paper which appears to examine the distribution
of the difference is Lo (2012); Lo cites several earlier papers, but in fact all of them seem
to consider only approximations for the sum. (The distribution of sums and differences
must be fundamentally different because the sum can take only positive values.) Lo gives
a closed-form approximation (his equation 2.11) which is a shifted lognormal, together
with a series expansion to correct the approximation (2.16). However, it is difficult to
express Lo’s solutions explicitly. In practice, the required confidence intervals can be
estimated by simulation, since the parameters of the underlying model (including the
correlations between the logarithms of the non-negative variables) are known.
7.2 Residual income valuation of firms
Under suitable convergence conditions, the value of a firm can be expressed (Nissim and
Penman, 2001; Penman, 2004) as the book value of its equity plus the present value of
24
its future stream of residual income, discounted at the appropriate market rate ρ:
V0 = Q0 +∑t≥1
NIt − ρQt−1
(1 + ρ)t(31)
This identity applies regardless of the accounting principles followed, so long as they
respect the clean surplus requirement. Since the future values of income and equity are
unknown, they must be estimated, starting from the latest available financial statements.
The usual approach is to make informed forecasts for the next few years, then assume a
pattern of constant growth after the forecast horizon.
The present model offers a better starting point for such forecasts. Given the current
financial vector x0, where x contains at least the variables R, X, A and L, equation (17)
can be iterated to find the expected value of x (and hence NI = R−X and Q = A−L)
for each year in the future, and the sum in equation (31) can be worked out explicitly.
There is no need to use a fixed forecast horizon, since the result of iterating equation (17)
converges automatically to the appropriate growth rate for a firm in this industry. Of
course, if better firm-specific information is available, it can be used to refine this naıve
estimate, but the model already provides strong guidance about what tracks of future
income and equity are plausible.
7.3 Financial distress
The earliest distress prediction models were based primarily on accounting information.
They have since been supplemented by structural models such as KMV, but structural
models require a market in relevant securities, and so banks evaluate the credit risk
of their portfolios (much of which consists of privately held companies with no traded
securities) primarily using accounting-based models for which they collect the required
data from their clients. The classic, and still widely-quoted, model is by Altman (1968):
in a version that does not use any market data (Altman, 1993) it is
Z = 0.717CA− CL
A+ 0.847
RE
A+ 3.107
EBIT
A+ 0.420
A− LL
+ 0.998S
A(32)
Of course, not all firms with a poor Z score actually default. Corrective management
action or fortunate improvements in product markets may rescue a distressed firm, share-
holders may recapitalize it, or it may be taken over. But it is also worthy of note that
a single value of Z may be produced by a wide range of different vectors x, and the
future evolution of x is driven by all of its components. Thus, different firms having the
same value of Z may have very different expected future trajectories in accounting space
25
and hence different future paths of Z itself. One firm may recover rapidly, another may
go rapidly downhill, and yet another may linger in a distressed state for a long time.
Equation (17), applied to a vector that includes A, L, CA, CL, S, Contributed Capital,
Interest Expense, and suitable components of Tax Expense, can give a forecast of Z and
hence a more refined understanding of the likely outcome for a distressed firm.
8 Limitations
The model of equation (15) and (17) makes several fundamental assumptions:
1. Future values of accounting variables are caused only by current values of the same
accounting variables, plus unexplained random disturbances. The disturbances, of
course, bring in the real-world events which actually cause the corporate financial
history. In one sense, equation (15) is a tautology, since it may be treated as a
definition of the disturbances that are consistent with the actually observed xt.
Both accounting research and financial statement analysis then become questions
about the history, future, and causes of these disturbances.
2. The simplest assumption, that εt comprises multivariate-normal disturbances with
zero mean and constant covariance matrix, must be too simple. Even before con-
sidering the external forces that drive the shocks, it is clear that shocks for different
variables in the same firm-year are highly correlated (see the correlations between
residuals for Sales and Assets in Tables 2–6). However, applying Seemingly Un-
related Regression to allow for contemporaneously correlated disturbances in the
different components of the vector appears to make no practical difference in esti-
mation, so this limitation may not be practically important.
3. The model assumes, and requires, that the variables in xt are strictly positive. If
any xi,t is zero, equation (18) shows that all variables for this firm must be zero for
all future years. Since relevant accounting variables are almost never zero (although
missing values may be coded as zero), this assumption is not very damaging; but it
is clearly not correct. Replacing the log function with the sinh−1 transformation of
equation (27) would correct this, though at a cost in additional complexity. Given
the other limitations of the model, it is not clear whether this refinement would be
worthwhile.
However, the model does correct many of the mathematical problems with conventional
models such as Ronen and Yaari’s equation (9.1) and the variants of the Jones model.
26
By moving attention away from the large and highly heteroscedastic accounting variables
to residuals that are of roughly uniform size and have (to a first approximation) simply
defined properties, the model may open the way to more powerful methods of research
using financial statement data.
27
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Dunmore, P. V. (Forthcoming). Temporal properties of financial variables, ratios and their
polar-coordinate bearings. In McLeay, S. and Christodoulou, D., editors, Advanced
Methods and Applications in Financial Analysis. Cambridge University Press.
El-Gazzar, S., Lilien, S., and Pastena, V. (1989). The use of off-balance sheet financing to
circumvent financial covenant restrictions. Journal of Accounting, Auditing & Finance,
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operating and financial activities. Contemporary Accounting Research, 11(2):689 – 731.
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Healy, P. M. (1985). The effect of bonus schemes on accounting decisions. Journal of
Accounting and Economics, 7:85–107.
Jones, J. J. (1991). Earnings management during import relief investigations. Journal of
Accounting Research, 29(2):193–228.
28
Lo, C. F. (2012). The sum and difference of two lognormal random variables. Journal of
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Mergenthaler, R. D., Rajgopal, S., and Srinivasan, S. (2012). CEO and CFO career
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Tippett, M. (1990). An induced theory of financial ratios. Accounting & Business Re-
search, 21(81):77–85.
29
A Simple cases for equation (20)
This appendix presents explicit general solutions to equation (20) when there are either
two or three variables in the set.
Consider the two-variable case, with
Γ =
(−a a
b −b
)(A.1)
(note that the rows must sum to 0). Then, omitting the time subscript t−1 and writing
the vector y as
(y1
y2
), equation (20) gives
(a
−b
)(y2 − y1) =
(λ− β1λ− β2
)(A.2)
which has a consistent solution for (y2 − y1) only if
a
−b=λ− β1λ− β2
so that λ =aβ2 + bβ1a+ b
and y2 = y1 +β2 − β1a+ b
.
Thus the vector y has one degree of freedom, as it must, for the correct value of λ.
Note that the ratio exp(y2− y1) is constant as the firm grows. Also, if aβ2 + bβ1 = 0 then
λ = 0 so that the firm does not grow. The condition β = 0 is therefore sufficient but not
necessary to ensure that there is no growth.
The three-variable case is similarly straightforward. We must have
Γ =
−a− b a b
c −c− d d
e f −e− f
(A.3)
and we find
λ =(ce+ de+ cf)β1 + (ae+ af + bf)β2 + (ad+ bc+ bd)β3
ce+ de+ cf + ae+ af + bf + ad+ bc+ bd
y2 = y1 +−(d+ e+ f)β1 + (b+ e+ f)β2 + (d− b)β3ce+ de+ cf + ae+ af + bf + ad+ bc+ bd
y3 = y1 +−(c+ d+ f)β1 + (f − a)β2 + (a+ c+ d)β3ce+ de+ cf + ae+ af + bf + ad+ bc+ bd
30
Again, there is a long-term growth rate which depends on Γ and β, and a set of ratios
which are consistent with that growth rate.
31
Tables and Figures
Table 1: Variables used in the testing. * Indicates a variable that should not be negative.
Panel A: Values sourced from the databaseSymbol Variable GV code
CA Total Current Assets* ACTPPE Property, Plant and Equipment (net)* PPEA Total Assets* ATCL Current Liabilities* LCT
Long-term Debt* DTLL Total Liabilities* LTS Sales* SALECOGS Cost of Goods Sold* COGSSGA Selling, General and Admin Expenses* SGADEPR Depreciation* DPNI Income before extraordinary items IBCFO Cash Flow from Operations OANCF
Panel B: Derived non-negative variablesSymbol Variable Definition
X Expenses* SALE – IBCFOout Operating Cash Expenditure* SALE – OANCF
32
Table 2: The model for the variable pair (Sales, Assets) for machinery manufacturing firms(SIC = 3500-3599). OLS regression.
Panel A. Regression coefficients and row sums, with standard errors in parentheses.Sample size = 14,008. Two-sided significance flags: * = 0.001, + = 0.01.
β S A Sums
S 0.097* -0.144* 0.135* -0.009(0.010) (0.006) (0.004) .
A 0.204* 0.041* -0.064* -0.023(0.005) (0.008) (0.004) .
Panel B. Contemporaneous correlations between residuals of the different equations.Also, for each equation, the standard deviation, skewness and kurtosis of the residuals.
S A Stdev Skewness Kurtosis
S 1.000 0.508 0.404 -1.191 39.119A 0.508 1.000 0.309 1.568 31.430
Panel C. Correlations between residuals of each equation and the lagged residuals ofeach equation in the set. Autocorrelations along the diagonal.
S A
S 0.049 0.090A 0.218 0.156
Panel D. Long-term ratios consistent with the long-term growth of 0.169. Sample ratiosgiven in parentheses; sample growth rate is 0.064.
S A
S 1.000 0.586(1.000) (0.865)
A 1.707 1.000(1.156) (1.000)
33
Table 3: The model for the variable pair (Sales, Assets) for machinery manufacturing firms(SIC = 3500-3599). OLS regression but with the row sums constrained to be zero.
Panel A. Regression coefficients and row sums, with standard errors in parentheses.Sample size = 14,008. Two-sided significance flags: * = 0.001, + = 0.01.
β S A
S 0.051* -0.146* 0.146*(0.003) (0.005) (0.005)
A 0.082* 0.036* -0.036*(0.005) (0.003) (0.005)
Panel B. Contemporaneous correlations between residuals of the different equations.Also, for each equation, the standard deviation, skewness and kurtosis of the residuals.
S A Stdev Skewness Kurtosis
S 1.000 0.509 0.404 -1.116 38.790A 0.509 1.000 0.312 1.881 32.262
Panel C. Correlations between residuals of each equation and the lagged residuals ofeach equation in the set. Autocorrelations along the diagonal.
S A
S 0.050 0.089A 0.218 0.147
Panel D. Long-term ratios consistent with the long-term growth of 0.076. Sample ratiosgiven in parentheses; sample growth rate is 0.064.
S A
S 1.000 0.844(1.000) (0.865)
A 1.185 1.000(1.156) (1.000)
34
Table 4: The model for the variable pair (Sales, Assets) for machinery manufacturing firms(SIC = 3500-3599), after deleting firm-years with residuals of more than 4 standard deviations.OLS regression but with the row sums constrained to be zero.
Panel A. Regression coefficients and row sums, with standard errors in parentheses.Sample size = 13,773. Two-sided significance flags: * = 0.001, + = 0.01.
β S A
S 0.059* -0.090* 0.090*(0.002) (0.004) (0.004)
A 0.074* 0.052* -0.052*(0.004) (0.002) (0.004)
Panel B. Contemporaneous correlations between residuals of the different equations.Also, for each equation, the standard deviation, skewness and kurtosis of the residuals.
S A Stdev Skewness Kurtosis
S 1.000 0.548 0.298 -0.064 7.427A 0.548 1.000 0.236 0.818 7.925
Panel C. Correlations between residuals of each equation and the lagged residuals ofeach equation in the set. Autocorrelations along the diagonal.
S A
S 0.123 0.170A 0.227 0.233
Panel D. Long-term ratios consistent with the long-term growth of 0.069. Sample ratiosgiven in parentheses; sample growth rate is 0.064.
S A
S 1.000 0.895(1.000) (0.865)
A 1.118 1.000(1.156) (1.000)
35
Table 5: The model for the variables (Sales, Assets, Current Assets, Liabilities, Expenses) formachinery manufacturing firms (SIC = 3500-3599), after deleting firm-years with residuals ofmore than 4 standard deviations. OLS regression but with the row sums constrained to be zero.
Panel A. Regression coefficients and row sums, with standard errors in parentheses. Sam-ple size = 13,525. Two-sided significance flags: * = 0.001, + = 0.01.
β S A CA L X
S 0.115* -0.092* 0.001 0.089* 0.016* -0.014(0.006) (0.008) (0.005) (0.008) (0.009) (0.007)
A 0.065* 0.081* -0.047* 0.034* -0.030* -0.038*(0.007) (0.006) (0.008) (0.005) (0.008) (0.009)
CA -0.009 0.083* 0.057* -0.099* -0.036* -0.004(0.009) (0.007) (0.006) (0.008) (0.005) (0.008)
L -0.024* 0.012 0.073* 0.012 -0.123* 0.026+(0.008) (0.009) (0.007) (0.006) (0.008) (0.005)
X 0.115* 0.070* 0.030* 0.094* 0.015+ -0.209*(0.005) (0.008) (0.009) (0.007) (0.006) (0.008)
Panel B. Contemporaneous correlations between residuals of the different equations. Also,for each equation, the standard deviation, skewness and kurtosis of the residuals.
S A CA L X Stdev Skewness Kurtosis
S 1.000 0.560 0.552 0.435 0.842 0.283 -0.192 6.882A 0.560 1.000 0.845 0.690 0.485 0.222 0.794 7.400CA 0.552 0.845 1.000 0.582 0.452 0.260 0.512 6.385L 0.435 0.690 0.582 1.000 0.476 0.308 0.396 6.286X 0.842 0.485 0.452 0.476 1.000 0.258 0.012 6.218
36
Panel C. Correlations between residuals of each equation and the lagged residuals of eachequation in the set. Autocorrelations along the diagonal.
S A CA L X
S 0.138 0.193 0.141 0.079 0.191A 0.223 0.237 0.159 0.133 0.318CA 0.203 0.205 0.131 0.096 0.276L 0.211 0.144 0.090 0.074 0.232X 0.101 0.154 0.103 0.075 0.114
Panel D. Long-term ratios consistent with the long-term growth of 0.065. Sample ratiosgiven in parentheses; sample growth rate is 0.064.
S A CA L X
S 1.000 0.893 1.538 2.016 0.989(1.000) (0.874) (1.478) (1.957) (0.974)
A 1.119 1.000 1.722 2.257 1.107(1.144) (1.000) (1.691) (2.239) (1.115)
CA 0.650 0.581 1.000 1.311 0.643(0.677) (0.591) (1.000) (1.324) (0.659)
L 0.496 0.443 0.763 1.000 0.491(0.511) (0.447) (0.755) (1.000) (0.498)
X 1.011 0.903 1.555 2.038 1.000(1.026) (0.897) (1.516) (2.008) (1.000)
37
Tab
le6:
Th
em
od
elfo
rth
eva
riab
leve
ctor
(Sal
es,
Tot
alA
sset
s,C
urr
ent
Ass
ets,
Pro
per
tyP
lant
and
Equ
ipm
ent,
Cu
rren
tL
iab
ilit
ies,
Tot
alL
iab
ilit
ies,
Cos
tof
Good
sS
old
,S
elli
ng
Gen
eral
and
Ad
min
istr
atio
nE
xp
ense
s,D
epre
ciat
ion
,an
dT
otal
Exp
ense
s)fo
rm
ach
iner
ym
anu
fact
uri
ng
firm
s(S
IC=
3500
-3599)
,aft
erd
elet
ing
firm
-yea
rsw
ith
resi
du
als
ofm
ore
than
4st
and
ard
dev
iati
ons.
OL
Sre
gres
sion
,w
ith
the
row
sum
sco
nst
rain
edto
be
zero
.
Pan
elA
.R
egre
ssio
nco
effici
ents
and
row
sum
s,w
ith
stan
dar
der
rors
inpar
enth
eses
.Sam
ple
size
=11
,705
.T
wo-
sided
sign
ifica
nce
flag
s:*
=0.
001,
+=
0.01
.
βS
AC
AP
PE
CL
LC
OG
SS
GA
DE
PR
X
S0.
094*
-0.0
58*
-0.0
010.
080*
-0.0
030.
019
0.00
2-0
.044
*-0
.029
*0.
012+
0.02
2(0
.021
)(0
.016
)(0
.005
)(0
.005)
(0.0
12)
(0.0
08)
(0.0
08)
(0.0
04)
(0.0
11)
(0.0
13)
(0.0
15)
A-0
.068
+0.2
52*
-0.0
51*
0.03
7*0.
009
0.00
8-0
.035
*-0
.109
*-0
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*-0
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-0.0
58*
(0.0
15)
(0.0
21)
(0.0
16)
(0.0
05)
(0.0
05)
(0.0
12)
(0.0
08)
(0.0
08)
(0.0
04)
(0.0
11)
(0.0
13)
CA
-0.0
85*
0.21
5*
0.05
8*-0
.098
*0.
001
0.03
0*-0
.059
*-0
.078
*-0
.038
*0.
001
-0.0
33(0
.013
)(0
.015
)(0
.021
)(0
.016)
(0.0
05)
(0.0
05)
(0.0
12)
(0.0
08)
(0.0
08)
(0.0
04)
(0.0
11)
PP
E-0
.240*
0.3
05*
0.0
210.
072*
-0.0
21*
-0.0
05-0
.028
*-0
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.067
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.029
*-0
.147
*(0
.011
)(0
.013
)(0
.015
)(0
.021)
(0.0
16)
(0.0
05)
(0.0
05)
(0.0
12)
(0.0
08)
(0.0
08)
(0.0
04)
CL
-0.1
49*
0.02
60.0
030.
105*
0.01
7*-0
.211
*0.
074*
-0.0
32+
-0.0
38*
-0.0
100.
064*
(0.0
04)
(0.0
11)
(0.0
13)
(0.0
15)
(0.0
21)
(0.0
16)
(0.0
05)
(0.0
05)
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12)
(0.0
08)
(0.0
08)
L-0
.108
*0.
083*
0.06
6*0.
020
0.01
00.
005
-0.1
26*
-0.0
51*
-0.0
34*
-0.0
070.
033
(0.0
08)
(0.0
04)
(0.0
11)
(0.0
13)
(0.0
15)
(0.0
21)
(0.0
16)
(0.0
05)
(0.0
05)
(0.0
12)
(0.0
08)
CO
GS
0.03
10.
088*
-0.0
150.
099*
0.00
20.
036*
-0.0
08-0
.158
*-0
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*0.
012+
0.00
1(0
.008
)(0
.008
)(0
.004
)(0
.011)
(0.0
13)
(0.0
15)
(0.0
21)
(0.0
16)
(0.0
05)
(0.0
05)
(0.0
12)
SG
A-0
.151*
0.26
5*
0.03
8+0.
076*
-0.0
25*
-0.0
01-0
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-0.1
09*
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00*
0.00
4-0
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.012
)(0
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)(0
.004)
(0.0
11)
(0.0
13)
(0.0
15)
(0.0
21)
(0.0
16)
(0.0
05)
(0.0
05)
DE
PR
-0.5
33*
0.32
8*
0.09
5*0.
005
0.05
3*-0
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-0.0
20-0
.151
*-0
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.005
)(0
.012
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.008
)(0
.008)
(0.0
04)
(0.0
11)
(0.0
13)
(0.0
15)
(0.0
21)
(0.0
16)
(0.0
05)
X0.1
11*
0.2
39*
0.0
53*
0.07
4*-0
.019
*0.
019
-0.0
020.
005
-0.0
090.
013+
-0.3
74*
(0.0
05)
(0.0
05)
(0.0
12)
(0.0
08)
(0.0
08)
(0.0
04)
(0.0
11)
(0.0
13)
(0.0
15)
(0.0
21)
(0.0
16)
38
Pan
elB
.C
onte
mp
oran
eous
corr
elat
ions
bet
wee
nre
sidual
sof
the
diff
eren
teq
uat
ions.
Als
o,fo
rea
cheq
uat
ion,th
est
andar
ddev
iati
on,
skew
nes
san
dkurt
osis
ofth
ere
sidual
s.
SA
CA
PP
EC
LL
CO
GS
SG
AD
EP
RX
Std
evS
kew
nes
sK
urt
osis
S1.0
000.
576
0.57
00.3
210.
463
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934
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300
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Pan
elC
.C
orre
lati
ons
bet
wee
nre
sidual
sof
each
equat
ion
and
the
lagg
edre
sidual
sof
each
equat
ion
inth
ese
t.A
uto
corr
elat
ions
alon
gth
edia
gonal
.
SA
CA
PP
EC
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0.10
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7
39
Pan
elD
.L
ong-
term
rati
osco
nsi
sten
tw
ith
the
long-
term
grow
thof
0.05
5.Sam
ple
rati
osgi
ven
inpar
enth
eses
;sa
mple
grow
thra
teis
0.06
4.
SA
CA
PP
EC
LL
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GS
SG
AD
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RX
S1.0
00
0.94
81.
560
11.4
623.
230
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61.
683
3.73
946
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3(1
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)(1
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15)
(2.8
67)
(2.0
03)
(1.5
06)
(5.4
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(33.0
94)
(0.9
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A1.0
55
1.0
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408
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81.
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3.94
548
.864
1.02
7(1
.137
)(1
.000
)(1
.694)
(5.7
04)
(3.2
60)
(2.2
77)
(1.7
12)
(6.1
70)
(37.6
35)
(1.1
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CA
0.6
410.
607
1.00
07.
346
2.07
01.
420
1.07
92.
396
29.6
780.
623
(0.6
71)
(0.5
90)
(1.0
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(3.3
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(1.9
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(1.3
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(1.0
11)
(3.6
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(22.2
23)
(0.6
67)
PP
E0.
087
0.08
30.
136
1.00
00.
282
0.19
30.
147
0.32
64.
040
0.08
5(0
.199
)(0
.175
)(0
.297)
(1.0
00)
(0.5
72)
(0.3
99)
(0.3
00)
(1.0
82)
(6.5
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(0.1
98)
CL
0.3
100.
293
0.48
33.
549
1.00
00.
686
0.52
11.
158
14.3
370.
301
(0.3
49)
(0.3
07)
(0.5
20)
(1.7
50)
(1.0
00)
(0.6
99)
(0.5
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(1.8
93)
(11.5
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(0.3
47)
L0.4
510.
428
0.70
45.
172
1.45
81.
000
0.75
91.
687
20.8
970.
439
(0.4
99)
(0.4
39)
(0.7
44)
(2.5
04)
(1.4
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(1.0
00)
(0.7
52)
(2.7
09)
(16.5
25)
(0.4
96)
CO
GS
0.59
40.
563
0.92
76.
810
1.91
91.
317
1.00
02.
221
27.5
150.
578
(0.6
64)
(0.5
84)
(0.9
89)
(3.3
31)
(1.9
04)
(1.3
30)
(1.0
00)
(3.6
03)
(21.9
79)
(0.6
60)
SG
A0.
267
0.25
30.
417
3.06
60.
864
0.59
30.
450
1.00
012
.386
0.26
0(0
.184
)(0
.162
)(0
.274)
(0.9
24)
(0.5
28)
(0.3
69)
(0.2
78)
(1.0
00)
(6.1
00)
(0.1
83)
DE
PR
0.0
22
0.0
200.
034
0.24
80.
070
0.04
80.
036
0.08
11.
000
0.02
1(0
.030
)(0
.027
)(0
.045)
(0.1
52)
(0.0
87)
(0.0
61)
(0.0
45)
(0.1
64)
(1.0
00)
(0.0
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X1.0
28
0.9
741.
604
11.7
823.
320
2.27
81.
730
3.84
347
.602
1.00
0(1
.006
)(0
.885
)(1
.499)
(5.0
47)
(2.8
85)
(2.0
15)
(1.5
15)
(5.4
59)
(33.3
01)
(1.0
00)
40
Figure 1: Function sinh−1(x) (solid line) and logarithmic approximations log(2x) forx > 0 and − log(−2x) for x < 0.
−4 −2 0 2 4
−2
−1
01
2
41
Figure 2: Relation between profit and total assets, using sinh−1 transformations for both.1,000 firm-years of manufacturers (SIC 35 and 36), various countries.
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0 2 4 6 8 10 12
−5
05
10
asinh(Assets)
asin
h(P
rofit
bef
ore
extr
aord
inar
y ite
ms)
42
School of Accountancy
Massey University
Discussion Paper Series
2013 No 223 Some Models for the Evolution of Financial Statement Data by Paul V. Dunmore.
2011 No 222 Half a Defence of Positive Accounting Research by Paul V. Dunmore.
2010 No. 221 Has IFRS Resulted in Information Overload? by M. Morunga and M. Bradbury. No. 220 Kiwi Talent Flow: A Study of Chartered Accountants and Business Professionals
Overseas by J.J. Hooks, S.C. Carr, M. Edwards, K. Inkson, D. Jackson, K. Thorn and N. Alfree.
No. 219 The Determinants of the Accounting Classification of Convertible Debt When
Managers Have Freedom of Choice by H.E. Bishop. No. 218 The Definition of “Insider” in Section 3 of the Securities Markets Act 1988: A Review
and Comparison With Other Jurisdictions by S. Zu and M.A. Berkahn. No. 217 The Corporatisation of Local Body Entities: A Study of Financial Performance by J.J.
Hooks and C.J. van Staden. No. 216 Devolved School-Based Financial Management in New Zealand: Observations on
the Conformity Patterns of School Organisations to Change by S. Tooley and J. Guthrie.
No. 215 Management Accounting Education: Is There a Gap Between Academia and
Practitioner Perceptions? by L.C. Hawkes, M. Fowler and L.M. Tan. No. 214 The Impact of Events on Annual Reporting Disclosures by J.J. Hooks. No. 213 Claims of Wrongful Pregnancy and Child Rearing expenses by C. M. Thomas. No. 212 Web Assisted Teaching: An Undergraduate Experience by C.J. van Staden, N.E.
Kirk and L.C. Hawkes. No. 211 An Exploratory Investigation into the Corporate Social Disclosure of Selected New
Zealand Companies by J.A. Hall. No. 210 Should the Law Allow Sentiment to Triumph Over Science? The Retention of Body
Parts by C.M. Thomas.
No. 209 The Development of a Strategic Control Framework and its Relationship with
Management Accounting by C.H. Durden. No. 208 ‘True and Fair View’ versus ‘Present Fairly in Conformity With Generally Accepted
Accounting Principles’ by N.E. Kirk. No. 207 Commercialisation of the Supply of Organs for Transplantation by C.M. Thomas. No. 206 Aspects of the Motivation for Voluntary Disclosures: Evidence from the Publication
of Value Added Statements in an Emerging Economy by C.J. van Staden.
No. 205 The Development of Social and Environmental Accounting Research 1995-2000 by M.R. Mathews.
No. 204 Strategic Accounting: Revisiting the Agenda by R.O. Nyamori. No. 203 One Way Forward: Non-Traditional Accounting Disclosures in the 21
st Century by
M.R. Mathews and M.A. Reynolds. No. 202 Externalities Revisited: The Use of an Environmental Equity Account by M.R.
Mathews and J.A. Lockhart. No. 201 Resource Consents – Intangible Fixed Assets? Yes … But Too Difficult By Far!! by
L.C. Hawkes and L.E. Tozer. No. 200 The Value Added Statement: Bastion of Social Reporting or Dinosaur of Financial
Reporting? by C.J. van Staden 2000 No. 199 Potentially Dysfunctional Impacts of Harmonising Accounting Standards: The Case
of Intangible Assets by M.R. Mathews and A.W. Higson. No. 198 Delegated Financial Management Within New Zealand Schools: Disclosures of
Performance and Condition by S. Tooley. No. 197 The Annual Report: An Exercise in Ignorance? by L.L. Simpson. No. 196 Conceptualising the Nature of Accounting Practice: A Pre-requisite for
Understanding the Gaps between Accounting Research, Education and Practice by S. Velayutham and F.C. Chua.
No. 195 Internal Environmental Auditing in Australia: A Survey by C.M.H. Mathews and M.R.
Mathews. No. 194 The Environment and the Accountant as Ethical Actor by M.A. Reynolds and M.R.
Mathews. No. 193 Bias in the Financial Statements – Implications for the External Auditor: Some U.K.
Empirical Evidence by A.W. Higson. No. 192 Corporate Communication: An Alternative Basis for the Construction of a
Conceptual Framework Incorporating Financial Reporting by A.W. Higson No. 191 The Role of History: Challenges for Accounting Educators by F.C. Chua. No. 190 New Public Management and Change Within New Zealand’s Education System: An
Informed Critical Theory Perspective by S. Tooley. No. 189 Good Faith and Fair Dealing by C.J. Walshaw. No. 188 The Impact of Tax Knowledge on the Perceptions of Tax Fairness and Tax
Compliance Attitudes Towards Taxation: An Exploratory Study by L.M. Tan and C.P. Chin-Fatt.
No. 187 Cultural Relativity of Accounting for Sustainability: A research note by M.A.
Reynolds and R. Mathews.
No. 186 Liquidity and Interest Rate Risk in New Zealand Banks by D.W. Tripe and L. Tozer No. 185 Structural and Administrative Reform of New Zealand’s Education System: Its
Underlying Theory and Implications for Accounting by S. Tooley.
No. 184 An Investigation into the Ethical Decision Making of Accountants in Different Areas of Employment by D. Keene.
No. 183 Ethics and Accounting Education by K.F. Alam. No. 182 Are Oligopolies Anticompetitive? Competition Law and Concentrated Markets by
M.A. Berkahn. No. 181 The Investment Opportunity Set and Voluntary Use of Outside Directors: Some
New Zealand Evidence by M. Hossain and S.F. Cahan. No. 180 Accounting to the Wider Society: Towards a Mega-Accounting Model by M.R.
Mathews. No. 179 Environmental Accounting Education: Some Thoughts by J.A. Lockhart and M.R.
Mathews. No. 178 Types of Advice from Tax Practitioners: A Preliminary Examination of Taxpayer’s
Preferences by L.M. Tan. No. 177 Material Accounting Harmonisation, Accounting Regulation and Firm
Characteristics. A Comparative Study of Australia and New Zealand, by A.R. Rahman, M.H.B. Perera and S. Ganesh.
No. 176 Tax Paying Behaviour and Dividend Imputation: The Effect of Foreign and Domestic
Ownership on Average Effective Tax Rates, by B R Wilkinson and S.F. Cahan. No. 175 The Environmental Consciousness of Accountants: Environmental Worldviews,
Beliefs and Pro-environmental Behaviours, by D. Keene. No. 174 Social Accounting Revisited: An Extension of Previous Proposals, by M.R.
Mathews. No. 173 Mapping the Intellectual Structure of International Accounting, by J. Locke and
M.H.B. Perera. No. 172 “Fair Value” of Shares: A Review of Recent Case Law, by M.A. Berkahn. No. 171 Curriculum Evaluation and Design: An Application of an Education Theory to an
Accounting Programme in Tonga, by S.K. Naulivou, M.R. Mathews and J. Locke. No. 170 Copyright Law and Distance Education in New Zealand: An Uneasy Partnership, by
S. French. No. 169 Public Sector Auditing in New Zealand: A Decade of Change, by L.E. Tozer and
F.S.B. Hamilton. No. 168 Dividend Imputation in the Context of Globalisation: Extension of the New Zealand
Foreign Investor Tax Credit Regime to Non-resident Direct Investors, by B. Wilkinson.
No. 167 Instructional Approaches and Obsolescence in Continuing Professional Education
(CPE) in Accounting - Some New Zealand Evidence, by A.R. Rahman and S. Velayutham.
No. 166 An Exploratory Investigation into the Delivery of Services by a Provincial Office of
the New Zealand Inland Revenue Department, by S. Tooley and C. Chin-Fatt. No. 165 The Practical Roles of Accounting in the New Zealand Hospital System Reforms
1984-1994: An Interpretive Theory, by K. Dixon.
No. 164 Economic Determinants of Board Characteristics: An Empirical Study of Initial Public
Offering Firms, by Y.T. Mak and M.L. Roush. No. 163 Qualitative Research in Accounting: Lessons from the Field, by K. Dixon. No. 162 An Interpretation of Accounting in Hospitals, by K. Dixon. No. 161 Perceptions of Ethical Conduct Among Australasian Accounting Academics, by G.E.
Holley and M.R. Mathews. No. 160 The Annual Reports of New Zealand's Tertiary Education Institutions 1985-1994: A
Review, by G. Tower, D. Coy and K. Dixon. No. 159 Securing Quality Audit(or)s: Attempts at Finding a Solution in the United States,
United Kingdom, Canada and New Zealand, by B.A. Porter. No. 158 Determinants of Voluntary Disclosure by New Zealand Life Insurance Companies:
Field Evidence, by M. Adams. No. 157 Regional Accounting Harmonisation: A Comparative Study of the Disclosure and
Measurement Regulations of Australia and New Zealand, by A. Rahman, H. Perera and S. Ganeshanandam.
1995 No. 156 The Context in Which Accounting Functions Within the New Zealand Hospital
System, by K. Dixon. No. 155 An Analysis of Accounting-Related Choice Decisions in the Life Insurance Firm, by
M.A. Adams and S. Cahan. No. 154 The Institute of Chartered Accountants of New Zealand: Emergence of an
Occupational Franchisor, by S. Velayutham. No. 153 Corporatisation of Professional Practice: The End of Professional Self-Regulation in
Accounting? by S. Velayutham. No. 152 Psychic Distance and Budget Control of Foreign Subsidiaries, by L.G. Hassel. No. 151 Societal Accounting: A Forest View, by L. Bauer. No. 150 The Accounting Education Change Commission Grants Programme and Curriculum
Theory, by M.R. Mathews. No. 149 An Empirical Study of Voluntary Financial Disclosure by Australian Listed
Companies, by M. Hossain and M. Adams. No. 148 Environmental Auditing in New Zealand: Profile of an Industry, by L.E. Tozer and
M.R. Mathews. No. 147 Introducing Accounting Education Change: A Case of First-Year Accounting, by L.
Bauer, J. Locke and W. O'Grady. No. 146 The Effectiveness of New Zealand Tax Simplification Initiatives: Preliminary
Evidence from a Survey of Tax Practitioners, by L.M. Tan and S. Tooley. No. 145 Annual Reporting by Tertiary Education Institutions in New Zealand: Events and
Experiences According to Report Preparers, by D. Coy, K. Dixon and G. Tower. No. 144 Organizational Form and Discretionary Disclosure by New Zealand Life Insurance
Companies: A Classification Study, by M. Adams and M. Hossain.
No. 143 Voluntary Disclosure in an Emerging Capital Market: Some Empirical Evidence from
Companies Listed on the Kuala Lumpur Stock Exchange, by M. Hossain, L.M. Tan and M. Adams.
No. 142 Auditors' Responsibility to Detect and Report Corporate Fraud: A Comparative
Historical and International Study, by B.A. Porter. No. 141 Accounting Information Systems Course Curriculum: An Empirical Study of the
Views of New Zealand Academics and Practitioners, by G. Van Meer. No. 140 Balance Sheet Structure and the Managerial Discretion Hypothesis: An Exploratory
Empirical Study of New Zealand Life Insurance Companies, by M. Adams. No. 139 An Analysis of the Contemporaneous Movement Between Cash Flow and Accruals-
based Performance Numbers: The New Zealand Evidence - 1971-1991, by J. Dowds.
No. 138 Voluntary Disclosure in the Annual Reports of New Zealand Companies by M.
Hossain, M.H.B Perera and A.R. Rahman. No. 137 Financial Reporting Standards and the New Zealand Life Insurance Industry: Issues
and Prospects, by M. Adams. No. 136 Measuring the Understandability of Corporate Communication: A New Zealand
Perspective, by B. Jackson. No. 135 The Reactions of Academic Administrators to the United States Accounting
Education Change Commission 1989-1992, by M.R. Mathews, B.P. Budge and R.D. Evans.
No. 134 An International Comparison of the Development and Role of Audit Committees in
the Private Corporate Sector, by B.A. Porter and P.J. Gendall. No. 133 Taxation as an Instrument to Control/Prevent Environmental Abuse, by G. Van
Meer. No. 132 Brand Valuation: The Main Issues Reviewed, by A.R. Unruh and M.R. Mathews. No. 131 Employee Reporting: A Survey of New Zealand Companies, by F.C. Chua. No. 130 Socio-Economic Accounting: In Search of Effectiveness, by S.T. Tooley. No. 129 Identifying the Subject Matter of International Accounting: A Co-Citational Analysis,
by J. Locke. No. 128 The Propensity of Managers to Create Budgetary Slack: Some New Zealand
Evidence, by M. Lal and G.D. Smith. No. 127 Participative Budgeting and Motivation: A Comparative Analysis of Two Alternative
Structural Frameworks, by M. Lal and G.D. Smith. No. 126 The Finance Function in Healthcare Organisations: A Preliminary Survey of New
Zealand Area Health Boards, by K. Dixon. No. 125 An Appraisal of the United States Accounting Education Change Commission
Programme 1989-1991, by M.R. Mathews. No. 124 Spreadsheet Use by Accountants in the Manawatu in 1991: Preliminary
Comparisons with a 1986 Study, by W. O'Grady and D. Coy.
No. 123 An Investigation of External Auditors' Role as Society's Corporate Watchdogs?, by
B.A. Porter. No. 122 Trends in Annual Reporting by Tertiary Education Institutions: An Analysis of Annual
Reports for 1985 to 1990, by K. Dixon, D.V. Coy and G.D. Tower. No. 121 The Accounting Implications of the New Zealand Resource Management Act 1991,
by L.E. Tozer. No. 120 Behind the Scenes of Setting Accounting Standards in New Zealand, by B.A. Porter. No. 119 The Audit Expectation-Performance Gap in New Zealand - An Empirical
Investigation, by B.A. Porter. No. 118 Towards an Accounting Regulatory Union Between New Zealand and Australia, by
A.R. Rahman, M.H.B. Perera and G.D. Tower. No. 117 The Politics of Standard Setting: The Case of the Investment Property Standard in
New Zealand, by A.R. Rahman, L.W. Ng and G.D. Tower. No. 116 Ethics Education in Accounting: An Australasian Perspective, by F.C. Chua, M.H.B.
Perera and M.R. Mathews. No. 115 Accounting Regulatory Design: A New Zealand Perspective, by G.D. Tower, M.H.B.
Perera and A.R. Rahman. No. 114 The Finance Function in English District Health Authorities: An Exploratory Study,
by K. Dixon. No. 113 Trends in External Reporting by New Zealand Universities (1985-1989): Some
Preliminary Evidence, by G. Tower, D. Coy and K. Dixon. No. 112 The Distribution of Academic Staff Salary Expenditure Within a New Zealand
University: A Variance Analysis, by D.V. Coy. No. 111 Public Sector Professional Accounting Standards: A Comparative Study, by K.A.
Van Peursem. No. 110 The Influence of Constituency Input on the Standard Setting Process in Australia, by
S. Velayutham. No. 109 Internal Audit of Foreign Exchange Operations, by C.M.H. Mathews. No. 108 The Disclosure of Liabilities: The Case of Frequent Flyer Programmes, by S.T.
Tooley and M.R. Mathews. No. 107 Professional Ethics, Public Confidence and Accounting Education, by F.C. Chua
and M.R. Mathews. No. 106 The Finance Function in Local Councils in New Zealand: An Exploratory Study, by
K. Dixon. No. 105 A Definition for Public Sector Accountability, by K.A. Van Peursem. No. 104 Externalities: One of the Most Difficult Aspects of Social Accounting, by F.C. Chua. No. 103 Some Thoughts on Accounting and Accountability: A Management Accounting
Perspective, by M. Kelly.
No. 102 A Unique Experience in Combining Academic and Professional Accounting Education: The New Zealand Case, by M.R. Mathews and M.H.B. Perera.
1990 No. 101 Going Concern - A Comparative Study of the Guidelines in Australia, Canada,
United States, United Kingdom and New Zealand with an Emphasis on AG 13, by L.W. Ng.
No. 100 Theory Closure in Accounting Revisited, by A. Rahman. No. 99 Exploring the Reasons for Drop-out from First Level Accounting Distance Education
at Massey University, by K. Hooper. No. 98 A Case for Taxing Wealth in New Zealand, by K. Hooper. No. 97 Recent Trends in Public Sector Accounting Education in New Zealand, by K. Dixon. No. 96 Closer Economic Relation (CER) Agreement Between New Zealand and Australia:
A Catalyst for a new International Accounting Force, by G. Tower and M.H.B. Perera.
No. 95 Creative Accounting, by L.W. Ng. No. 94 The Financial Accounting Standard Setting Process: An Agency Theory
Perspective, by G. Tower and M. Kelly. No. 93 Taxation as a Social Phenomenon: An Historical Analysis, by K. Hooper. No. 92 The Development of Corporate Accountability, and The Role of the External Auditor,
by B.A. Porter. No. 91 An Analysis of the Work and Educational Requirements of Accountants in Public
Practice in New Zealand, by M. Kelly. No. 90 Chartered Accountants in the New Zealand Public Sector: Population, Education
and Training, and Related Matters, by K. Dixon. No. 89 Cost Determination and Cost Recovery Pricing in Nonbusiness Situations: The
Case of University Research Projects, by K. Dixon. No. 88 An Argument for Case Research, by R. Ratliff. No. 87 Issues in Accountancy Education for the Adult Learner, by K. Van Peursem. No. 86 Management Accounting: Purposes and Approaches, by M. Kelly. No. 85 The Collapse of the Manawatu Consumers' Co-op - A Case Study, by D.V. Coy and
L.W. Ng. No. 84 Governmental Accounting and Auditing in East European Nations, by A.A. Jaruga,
University of Lodz, Poland. No. 83 The Functions of Accounting in the East European Nations, by A.A. Jaruga,
University of Lodz, Poland. No. 82 Investment and Financing Decisions within Business: The Search for Descriptive
Reality, by D. Harvey. No. 81 Applying Expert Systems to Accountancy - An Introduction, by C. Young. No. 80 The Legal Liability of Auditors in New Zealand, by M.J. Pratt.
No. 79 "Marketing Accountant" the Emerging Resource Person within the Accounting
Profession, by C. Durden. No. 78 The Evolution and Future Development of Management Accounting, by M. Kelly. No. 77 Minding the Basics - Or - We Were Hired to Teach Weren't We?, by R.A. Emery and
R.M. Garner. No. 76 Lakatos' Methodology of Research Programmes and its Applicability to Accounting,
by F. Chua. No. 75 Tomkins and Groves Revisited, by M. Kelly. No. 74 An Analysis of Extramural Student Failure in First Year Accounting at Massey
University, by K. Hooper. No. 73 Insider Trading, by L.W. Ng. No. 72 The Audit Expectation Gap, by B.A. Porter. No. 71 A Model Programme for the Transition to New Financial Reporting Standards for
New Zealand Public Sector Organisations, by K.A. Van Peursem. No. 70 Is the Discipline of Accounting Socially Constructive? by M. Kelly.
No. 69 A Computerised Model for Academic Staff Workload Planning and Allocation in University Teaching Departments, by M.J. Pratt.
No. 68 Social Accounting and the Development of Accounting Education, by M.R.
Mathews. No. 67 A Financial Planning Model for School Districts in the United States - A Literature
Survey, by L.M. Graff. No. 66 A Reconsideration of the Accounting Treatments of Executory Contracts and
Contingent Liabilities, by C. Durden. No. 65 Accounting in Developing Countries: A Case for Localised Uniformity, by M.H.B.
Perera. No. 64 Social Accounting Models - Potential Applications of Reformist Proposals, by M.R.
Mathews. No. 63 Computers in Accounting Education: A Literature Review, by D.V. Coy. No. 62 Social Disclosures and Information Content in Accounting Reports, by M.R.
Mathews. No. 61 School Qualifications and Student Performance in First Year University Accounting,
by K.C. Hooper. No. 60 Doctoring Value Added Reports: A Shot in the Arm - Or Head?, by P.R. Cummins. No. 59 The Interrelationship of Culture and Accounting with Particular Reference to Social
Accounting, by M.B.H. Perera and M.R. Mathews. No. 58 An Investigation into Students' Motivations for Selecting Accounting as a Career, by
Y.P. Van der Linden.
No. 57 Objectives of External Reporting: A Review of the Past; A Suggested Focus for the Future, by Y.P. Van der Linden.
No. 56 Shareholders of New Zealand Public Companies: Who Are They?, by C.B. Young. No. 55 The Impacts of Budgetary Systems on Managerial Behaviour and Attitudes: A
review of the literature, by K.G. Smith. No. 54 Can Feedback Improve Judgement Accuracy in Financial Decision- Making?, by
K.G. Smith. No. 53 Heuristics and Accounting: An Initial Investigation, by M.E. Sutton. No. 52 British Small Business Aid Schemes - any Lessons for New Zealand?, by A.F.
Cameron. No. 51 What are Decision Support Systems?, by M.J. Pratt. No. 50 The Implementation of Decision Support Systems - A Literature Survey and
Analysis, by M.J. Pratt. No. 49 Spreadsheet Use by Accountants in the Manawatu, by D.V. Coy. No. 48 The Search for Socially Relevant Accounting: Evaluating Educational Programmes,
by M.R. Mathews No. 47 The Distributable Profit Concept - Let's Reconsider!, by F.S.B. Hamilton. No. 46 A Consideration of the Applicability of the Kuhnian Philosophy of Science to the
Development of Accounting Thought, by Y.P. Van der Linden. No. 45 Matrix Ledger Systems - MLS A New Way of Book-keeping, by P.R. Cummins. No. 44 A Tentative Teaching Programme for Social Accounting, by M.R. Mathews. No. 43 Exploring the Philosophical Bases Underlying Social Accounting, by M.R. Mathews. No. 42 Objectives of External Reporting - Fact or Fiction?, by C.B. Young. No. 41 Financial Accounting Standards. Development of the Standard Setting Process in
the U.S.A. with Some Comments Concerning New Zealand, by G.L. Cleveland. No. 40 Attitudes of British Columbia Accountants Towards The Disclosure of Executory
Contracts in Published Accounts, by M.R. Mathews and I.M. Gordon. No. 39 A Critical Evaluation of Feyerabend's Anarchistic Theory of Knowledge and its
Applicability to Accounting Theory and Research, by A.M. Selvaratnam. No. 38 Rationalism and Relativism in Accounting Research, by C.B. Young. No. 37 Taxation and Company Financial Policy, by K.F. Alam and C.T. Heazlewood. No. 36 Accountancy Qualifications for 2000 AD" A Black Belt in Origami?, by P.R.
Cummins and B.R. Wilson. No. 35 Towards Multiple Justifications for Social Accounting and Strategies for Acceptance,
by M.R. Mathews. No. 34 Company Taxation and the Raising of Corporate Finance, by K.F. Alam.
No. 33 Current Cost Accounting in New Zealand, (An Analysis of the Response to CCA-1), by A.F. Cameron and C.T. Heazlewood.
No. 32 Watts and Zimmerman's "Market for Accounting Theories": A Critique Based on
Ronen's Concept of the Dual Role of Accounting, by L.W. Ng. 1985 No. 31 Investment Decisions in British Manufacturing, by K.F. Alam. No. 30 Educating the Professional Accountant - Getting the Right Balance, by M.R.
Mathews. No. 29 Corporate Taxation and Company Dividend Policy, by K.F. Alam. No. 28 The "Interpretive Humanistic" Approach to Social Science and Accounting
Research, by L.W. Ng. No. 27 Changes in Cost Accounting Since 1883, by L.W. Ng. No. 26 A Comparison of B.C. and Washington State Accountants on Attitudes Towards
Continuing Education, by M.R. Mathews and I.M. Gordon. No. 25 A Suggested Organisation for Social Accounting Research - Some Further
Thoughts, by M.R. Mathews (Out of Print). No. 24 Canadian Accountants and Social Responsibility Disclosures - A Comparative
Study, by M.R. Mathews and I.M. Gordon (Out of Print). No. 23 Foreign Exchange Risk Management: A Survey of Attitudes and Policies of New
Zealand Companies, by W.S. Alison and B. Kaur (Out of Print). No. 22 Factors Affecting Investment Decisions in U.K. Manufacturing Industry: An Empirical
Investigation, by K.F. Alam (Out of Print). No. 21 Corporate Decision Making, Tax Incentives and Investment Behaviour: A
Theoretical Framework, by K.F. Alam. No. 20 A Comparison of Accountants Responses to New Ideas: Washington State CPA's
and New Zealand CPA's, by M.R. Mathews and E.L. Schafer. No. 19 Corporate Taxation and the Dividend Behaviour of Companies in the UK No. 18 Tax Incentives and Investment Decisions in UK Manufacturing, Industry by K.F.
Alam (Out of Print). No. 17 The Accountants' Journal: An Adequate Forum for the Profession?, by D. Kerkin. No. 16 Structured Techniques for the Specification of Accounting Decisions and Processes
and Their Application to Accounting Standards, by J. Parkin. No. 15 Objectives of Accounting: Current Trends and Influences, by D.J. Kerkin. No. 14 Professional Ethics and Continuing Education, by M.R. Mathews. No. 13 Valuation in Farm Accounts, by H.B. Davey and E. Delahunty (Out of Print). No. 12 Views of Social Responsibility Disclosures: An International Comparison, by M.R.
Mathews. No. 11 The Role of Management Accounting in Small Businesses, by M.Chye and M.R.
Mathews (Out of Print).
No. 10 What Accountants Think of (Certain) New Ideas (The Results of a Limited Survey),
by M.R. Mathews. No. 9 The Matching Convention in Farm Accounting, by E. Delahunty and H.B. Davey. No. 8 Some comments on the Conceptual Basis of ED-25, by B.R. Wilson (Out of Print). No. 7 The FASB's Conceptual Framework for Financial Accounting and Reporting: An
Evaluation, by M. Chye. No. 6 Marketing - A Challenge for Accountants, by F.C.T. Owen. No. 5 Value Added Statements: A Reappraisal, by M. Chye. No. 4 A Survey to Obtain Responses of Accountants to Selected new Ideas in Accounting,
by M.R. Mathews (Out of Print). No. 3 Continuing Education: The New Defence of Professionalism, by M.R. Mathews. No. 2 Socio-Economic Accounting - A Consideration of Evaluation Models, by M.R.
Mathews. 1981 No. 1 The Role of Accounting Standards Vis-a-Vis the "Small" Company, by C.T.
Heazlewood.