School of Accountancy Private Bag 11 222 COLLEGE OF BUSINESS Palmerston North New Zealand P + 64 6 356 9099 www-accountancy.massey.ac.nz

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)

MASSEY UNIVERSITY

SCHOOL OF ACCOUNTANCY

DISCUSSION PAPER SERIES

Editor: Professor Jill Hooks

The discussion paper series of the School of Accountancy is intended to provide staff and postgraduate students of the School with a means of communicating new and developing ideas in order to facilitate academic debate. Discussion papers should not necessarily be taken as completed works or final expressions of opinion. All discussion papers are quality-assured, being formally peer-reviewed prior to publication. Views expressed are those of the authors, and are not necessarily shared by the School of Accountancy. Normally discussion papers may be freely quoted or reproduced provided proper reference to the author and source is given. When a discussion paper is issued on a restricted basis, notice of an embargo on quotation/reproduction will appear on this page. Abstracts of discussion papers, and most full papers, are available as pdf documents at

http://www-accountancy.massey.ac.nz (click on “Research” then "Discussion Papers")

A list of all discussion papers published by the School is available at the back of this publication. A hard copy of any full paper, provided it is in stock, may be obtained from

Sim Loo School of Accountancy Private Bag 11-222 Massey University Palmerston North New Zealand Email: y.loo@massey.ac.nz

© 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

2

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

3

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

4

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.

5

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.)

6

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

7

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

8

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

References

Aitchison, J. and Brown, J. A. C. (1966). The Lognormal Distribution. Cambridge

University Press.

Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corpo-

rate bankruptcy. Journal of Finance, 23(4):589–609.

Altman, E. I. (1993). Corporate financial distress and bankruptcy: A complete guide to

predicting and avoiding distress and profiting from bankruptcy. Wiley, 2nd ed edition.

Altman, E. I., Haldeman, R. G., and Narayanan, P. (1977). ZetaTM analysis: A new

model to identify bankruptcy risk of corporations. Journal of Banking & Finance,

1(1):29–54.

Ashton, D., Dunmore, P., and Tippett, M. (2004). Double entry bookkeeping and the

distributional properties of a firm’s financial ratios. Journal of Business Finance and

Accounting, 31(5-6):583–606.

Burns, N. and Kedia, S. (2006). The impact of performance-based compensation on

misreporting. Journal of Financial Economics, 79:35–67.

Dechow, P. M. and Schrand, C. M. (2004). Earnings Quality. Research Foundation of

CFA Institute.

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,

4(2):217–231.

Feltham, G. A. and Ohlson, J. A. (1995). Valuation and clean surplus accounting for

operating and financial activities. Contemporary Accounting Research, 11(2):689 – 731.

Frankel, R. and Litov, L. (2009). Earnings persistence. Journal of Accounting & Eco-

nomics, 47(1/2):182–190.

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

Applied Mathematics, Article ID 838397.

Mergenthaler, R. D., Rajgopal, S., and Srinivasan, S. (2012). CEO and CFO career

penalties to missing quarterly analysts forecasts. Working paper.

Nissim, D. and Penman, S. H. (2001). Ratio analysis and equity valuation: From research

to practice. Review of Accounting Studies, 6(1):109–154.

Ohlson, J. A. (1980). Financial ratios and the probabilistic prediction of bankruptcy.

Journal of Accounting Research, 18(1):109–131.

Penman, S. H. (2004). Financial statement analysis and security valuation. McGraw-Hill,

Boston, 2nd edition.

Ronen, J. and Yaari, V. (2008). Earnings Management: Emerging Insights in Theory,

Practice, and Research. Springer Series in Accounting Scholarship. Springer, New York.

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

.047

*-0

.008

-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

.100

*-0

.067

*-0

.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)

(0.0

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

.055

*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

.008

-0.1

09*

-0.1

00*

0.00

4-0

.139

*(0

.012

)(0

.008

)(0

.008

)(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

.019

-0.0

20-0

.151

*-0

.038

*-0

.144

*-0

.110

*(0

.005

)(0

.012

)(0

.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

0.44

20.

934

0.53

90.

295

0.87

70.

267

-0.2

216.

214

A0.

576

1.00

00.8

49

0.4

960.

612

0.69

20.

516

0.41

60.

300

0.48

50.

204

0.92

47.

406

CA

0.57

00.8

49

1.0

000.

276

0.57

50.

585

0.50

60.

360

0.18

60.

461

0.24

50.

539

6.27

3P

PE

0.3

21

0.4

960.

276

1.00

00.

313

0.39

20.

301

0.32

90.

371

0.31

50.

257

0.74

79.

850

CL

0.46

30.6

12

0.5

750.

313

1.00

00.

817

0.43

90.

347

0.20

10.

476

0.32

60.

072

5.20

3L

0.44

20.

692

0.5

85

0.3

920.

817

1.00

00.

420

0.36

80.

262

0.46

90.

292

0.37

36.

175

CO

GS

0.93

40.5

16

0.50

60.

301

0.43

90.

420

1.00

00.

481

0.26

40.

866

0.27

4-0

.068

6.77

0S

GA

0.53

90.4

16

0.36

00.

329

0.34

70.

368

0.48

11.

000

0.36

70.

606

0.21

80.

417

7.41

5D

EP

R0.

295

0.30

00.1

86

0.37

10.

201

0.26

20.

264

0.36

71.

000

0.36

40.

281

0.43

38.

114

X0.

877

0.48

50.4

61

0.3

150.

476

0.46

90.

866

0.60

60.

364

1.00

00.

244

0.09

06.

016

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

LL

CO

GS

SG

AD

EP

RX

S0.

122

0.1

560.

111

0.16

70.

047

0.06

50.

125

0.21

20.

184

0.15

4A

0.2

46

0.2

160.

139

0.24

00.

087

0.12

20.

244

0.30

00.

306

0.29

4C

A0.2

270.

188

0.11

60.

203

0.05

90.

090

0.22

90.

256

0.18

30.

256

PP

E0.

119

0.13

50.

072

0.20

10.

080

0.10

80.

123

0.20

70.

357

0.17

3C

L0.2

250.

113

0.06

20.

151

-0.0

180.

039

0.21

90.

220

0.20

40.

235

L0.2

14

0.1

250.

072

0.16

60.

032

0.07

00.

207

0.22

50.

242

0.22

8C

OG

S0.1

130.

141

0.09

20.

166

0.04

20.

065

0.10

70.

208

0.18

20.

140

SG

A0.1

020.

141

0.09

70.

171

0.07

70.

095

0.10

80.

121

0.22

80.

132

DE

PR

0.0

83

0.1

200.

094

0.12

50.

073

0.09

50.

073

0.12

00.

217

0.10

7X

0.1

04

0.1

340.

087

0.16

50.

046

0.06

70.

101

0.20

10.

201

0.11

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

CO

GS

SG

AD

EP

RX

S1.0

00

0.94

81.

560

11.4

623.

230

2.21

61.

683

3.73

946

.307

0.97

3(1

.000

)(0

.879

)(1

.489)

(5.0

15)

(2.8

67)

(2.0

03)

(1.5

06)

(5.4

25)

(33.0

94)

(0.9

94)

A1.0

55

1.0

001.

646

12.0

953.

408

2.33

81.

776

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

30)

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

00)

(3.3

68)

(1.9

25)

(1.3

45)

(1.0

11)

(3.6

43)

(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

99)

(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

25)

(1.8

93)

(11.5

45)

(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

31)

(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

30)

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.

+

+

+

+

++

+

+

+ +

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

++

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

++

+

++

+

+

+

++

++

+ +

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++ +

+

+

+

++

+

+

++

++

+

+

+

+

+

+

+

+

+

+

++

+

+

+

++

+

+

+

++

++

+

+

+

+++ +

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

++

+

+

+

+

++

++

+

+

+

++

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+ + +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

++

+

++

++

+

++

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+++

+

++

+

+

+

+

++

+

+

+ +

+

+

+

+

++

+

++

+

+

+

++

+

+

+ +

++

+

+++

+

+

+

+

+

+

+

++

+

+

+

+ ++

+++

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ ++

++

++

+

+

+

+

+

+

+

+

+++

+

+

+ +

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

++

+

+ ++

+

+

++

+

+

+

+

+

+

+

+

+

++

+

+++

+

+

+

+

++

++

+

++

+++

+

++

+

+

+

+

+

+

++

+

+

+

+

+

+

+

++

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

++

+ +++

+

+

+

++

+

+

+

+

+

+

+

+

+

+++

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

++

++

+

+

+ +

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

++

+

++

+

+

+

+

+ +

+

+

++

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

++

+

+

+

++

+

+

+

+

++

+

+

+

+

+

+ +

+

+

+

+

+

+

++

+

+

+

+

+

+

+

++

+

+

++

++

+

+

+

+ +

+

++

++

+

++

++

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+++

+

+

+

++

+

++

+

+

+

+

++

+

+

++

++

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

++

+

+

+

+ +

+

+

+++

+

++

+

+

+

+

+

+ +

+

+

+

+

++

+

+

+

+++

+

+

+

++

++

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

++

++

+++

+

+

+

+

+

++ ++

++

+

+ +

+

++

+

+

+

++

+

++

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+

++

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

++ +

+

+

+

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+ +

+

+ +

+

+

+

+

+

++ +

+

+

+

++

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

++

+

++

+

++

+

+

+

+

+

+

++

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.