Profit Persistence
An Application of a Dynamic Panel Method
Term paper for the course “Econometric Methods for Panel Data”
Vienna, June 30, 2005
Gürkan Birer
Matr.nr.: 0254010
Michael Weichselbaumer
Matr.nr.: 9640369
2UK 300632 Ökonometrische Methoden für Paneldaten
Lehrveranstaltungsleiter: O. Univ.-Prof. Dr. Robert Kunst
Contents
1 Introduction
1
2 Method
2.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
3
3 Models
3.1 Time Dummies . . . . . . . . . . . . . . . . . . . . .
3.2 Dynamic Panel . . . . . . . . . . . . . . . . . . . . .
3
4
4
4 Results
4.1 Time Dummies . . . . . . . . . . . . . . . . . . . . .
4.2 Dynamic Panel . . . . . . . . . . . . . . . . . . . . .
7
7
8
5 Conclusion
10
1
Introduction
In a competitive economy firm profits above the average should diminish over time. Hence, the empirical question of interest is if
this can be observed and thus confirmed for a given set of data or
if profits tend to persist. The problem is normally analysed as a
time-series problem, since in the structural model profit persistence
is dominated by the influence of past profits (Goddard & Wilson
1999). This means that for every individual firm a particular ARparameter is estimated from the corresponding individual time series
of profits.
In our work we want to investigate this question using panel data
methods. Our approach differs from the time-series approach in two
important ways: first, we hypothesise that persistent profits do not
exist and hence exclude the intercept; second, we model a single
coefficient of disappearance of profit deviations from the average,
meaning that the speed of convergence is the same for all firms –
and thus over all industries. In terms of model specification this
implies the formulation with a single parameter for the influence of
lagged profits.
The next section gives a bit more of the underlying method to
provide the reader with some understanding of the time-series approach and the arising differences from our approach. Additionally,
it defines the variables included and describes the data. Section 3 describes the estimated models: a time-dummy model and a dynamic
panel. This splitting is retained in section 4, where the results are
presented. We conclude with section 5.
2
Method
First we describe the dependent variable in a bit more detail. Then,
a summary for the explanatory variables is given for those that are
usually associated with the possibility of profits above the average
and we were able to construct from our database. Afterwards, two
different models are presented for estimation of persistence of profits
above average over time: a model with time dummies hoping that
one can observe the effect of competition in decreasing time dummies; a dynamic model with the alternative and dominantly used
modelling strategy of persistence shown in a positive autoregressive
coefficient. Both models are used in a random effects version, since
we assume that the firms that are in our database and remain in
the sample after the construction process of our explanatory vari1
ables is like a sample obtained from random draws of all firms in the
economy. In both estimations we apply the same set of explanatory
variables.
2.1
Variables
First, the dependent variable: The profit of a firm that we use is
defined as the ratio of profit after taxes and before interest to total
assets. Taxes are excluded since effective tax-rates may differ and
firms should then base their decision on entry or exit on the after-tax
profit. Interest paid is included since total assets in the denominator
do also encompass those assets financed by debt (argumentation
follows Maruyama & Odagiri 2002).
Profit of firm i at time t is denoted πit . The variable of interest,
denoted ρit , is the deviation of firm i’s profit at time t from the
average profit of all firms in year t. It is calculated as follows:
ρit =
where
π̄t =
πit − π̄t
π̄t
N
1 X
πit
N n=1
Next, a description of the calculation of the explanatory variables
that we used and the basic intuition.
Industry Dummy Our data is classified into four-digit codes following the Standard Industrial Classification (SIC) of the United
States Government. It classifies every firm for every year according to their main field of production and is thus called
”Primary SIC-Code”1 . We use the industries classified in the
large groups 2 and 3, the classes of manufacturing and construction, and reduce them to the three-digit-level, since only
this level is specified accurately for all usable observations.
Market Share This is calculated as share in sales of aggregate
sales in the three-digit-level industry where a firm is classified. Though all firms with availability of sales are used to
compute aggregate sales and not only those firms which are
used in the very final data set for computation (i.e. where all
variables are available), it remains an approximation. There
1 Though this classification system was replaced by the North American Industry Classification System (NAICS), we use the old SIC-Codes, since our data is originally classified in
SIC and the last year we use is 1996.
2
are different causes that support the inclusion of market share
as an explanatory variable, for example higher market power,
higher efficiency due to economies of scale. We expect it to be
positively related to profitability.
Risk As a proxy for risk we calculate the standard deviation of
industry profits, again at the three-digit-level. This variable is
also expected to have a positive relationship.
Growth of Industry It is calculated as the percentage growth in
aggregate sales per three-digit-industry-level. We adopt the
usual expectation that the relationship is positive, since more
rapid growth relieves competitive pressure due to supposedly
higher demand.
Growth in the Number of Competitors Calculated as the percentage change in the absolute number of competitors in the
industry. If it is high, competition should also increase and
higher profits are expected to vanish.
Entry/Exit Profits, in turn, depend on both actual and threatened
entry. Since one has at most data about actual entry, entry’s
impact on profits must always be understated. Thus, in timeseries models of profit persistence entry is dropped as an explanatory variable and is treated as a latent variable (Goddard
& Wilson 1999).
2.2
Data
The data stems from the Standard & Poors database Compustat.
After adaptations necessary due to missing data for some variables
and after the construction process that is as usual subject to the
trade-off between number of years and number of observable individuals, we obtain a balanced sample of 900 U.S.-American firms
for the time period of 1985 to 1996. The operations of the firms are
spread over 98 three-digit-classes of SIC.
3
Models
Now we will describe the two different models that we want to use
for measuring the effect of competition over time: a simple random
effects model with time dummies and a dynamic panel with random
effects.
3
3.1
Time Dummies
In a first trial, we model the persistence with time dummies and hope
that the increase in competition will be reflected in diminishing time
effects. As described above, we chose some other explanatory variables to control for important influences on profits. The estimation
equation is:
πit = Constant + MSit β1 + RiskIndustry,t β2 + ∆CompetitorsIndustry,t β3
+∆OutputIndustry,t β4 + Zλ,it λt + uit
with
3.2
uit = µi + νit
µi ∼ i.i.d.(0, σµ2 )
νit ∼ i.i.d.(0, σν2 )
µi , νi independent
Dynamic Panel
As mentioned above, from the economic point of view the inclusion
of a lag of the dependent variable as an explanatory variable is
legitimate. The model then takes the form (Baltagi 1995, pp.125):
0
yit = γyi(t−1) + xit β + uit ,
i = 1, . . . , N
t = 1, . . . , T
where uit = µi + νit – a one way error component model.
For the estimation of the dynamic panel, it is well documented in
the literature that the OLS estimation will lead to biased and inconsistent parameter estimates, even if the νit are not serially correlated,
because yit and yi(t−1) are both a function of µi and hence yi(t−1) is
correlated with the error term. For the fixed effects estimator the
within transformation – the multiplication with the mean-adjusting
matrix – wipes out the µi , but still the estimators will be biased,
since νi(t−1) is contained in ν̄i , which is thus correlated with yi(t−1) .
The same holds for random effects models. Only if T tends to infinity, the fixed effects estimator of γ and β will be consistent for the
dynamic error component model. Since our data has the shape of a
cross section panel with N large and T small, we do not rely on this
property. A possibility to avoid the bias is the first-difference transformation of the data, because it wipes out the individual effects but
does not create the problem of correlation. Among the alternative
methods that use first-differencing, we choose for our dynamic panel
regressions the method developed by Arellano & Bond (1991). First
4
we describe the method and than we discuss some of the advantages
of using this method than the other methods like the well known
method of Anderson & Hsiao (1981).
In their paper, Arellano & Bond start with the simplest autoregressive specification with random effects in the form:
yit = γyi(t−1) + ηi + νit ,
|γ| < 1
They assume lack of serial correlation in the error terms but not
necessarily independence over time, i.e. they assume that E(νit ) =
E(νit νis ) = 0.
The model works as follows. First they take the first differences
to get rid of the individual effects that leads to an equation of the
form
yit − yi(t−1) = γ(yi(t−1) − yi(t−2) ) + vit − vi(t−1)
So for the first period (t=3) we have
yi3 − yi2 = γ(yi2 − yi1 ) + vi3 − vi2
and for the second period (t=4) we have
yi4 − yi3 = γ(yi3 − yi2 ) + vi4 − vi3
and if we continue in this iterative way we get for the last period
(t=T):
yiT − yi(T −1) = γ(yi(T −1) − yi(T −2) ) + viT − vi(T −1)
They use the GMM (Generalized Method of Moments) for obtaining
an optimal estimator of γ. The advantage of using GMM is that
it will still work even if we have no information about the initial
conditions and the distributions of vit and µi – hence it is preferred
to other estimation methods like Maximum likelihood or OLS.
The GMM estimator γ̂ is based on sample moments, defined as
N
−1
N
X
0
0
Zi ν̄i = N −1 Z ν̄
i=1
0
0
0
0
where ν̄ = (ν̄1 , . . . , ν̄N ) – the column vector of all ν̄i , which, in turn
is the column vector of the first differences of the νit for all t. Thus,
0
ν̄i has length T − 2 (since it is reduced by one observation due to
first differencing and another one by formulation of a model with lagorder one) and ν̄ has length T − 2 times the number of individuals,
5
0
0
N . Z is a N (T − 2) × m matrix consisting of (Z1 , . . . , ZN ), which
are used as instruments.
The estimator γ̂ is given by:
0
0
γ̂ = argminγ (ν̄ Z)AN (Z ν̄)
where AN is the so-called weighting matrix. Any such matrix would
lead to unbiased estimates of γ, provided that the instruments are
orthogonal to the errors. The choice of the instruments is an important factor because they should be highly correlated with the
dependent variables and uncorrelated with the errors. Under these
assumptions for the simplest AR(1) specification Arellano & Bond
provide a set of instruments for the GMM estimation. The instrument matrix will be of the form:


[yi1 ]
0


[yi1 , yi2 ]

Zi = 
...


0
[yi1 , . . . , yi,T −2 ]
These instruments are different from the ones that suggested by Anderson & Hsiao (1981). From their Monte-Carlo study, Arellano &
Bond provide evidence that the AH-estimates are either biased due
to reasons of singularity or, in the best case, are more inefficient.
That is why we have chosen to use the Arrelano-Bond method explained so far.
What now remains among the central issues that have to be considered in the chosen estimation method are two tests that we want
to describe shortly: first, a test procedure that can be used for testing if the errors vit are serially uncorrelated or not. This test is very
important because the GMM estimators are only consistent if these
errors are serially uncorrelated; second, since for T > 3 it will be an
over-identified system – in other words, there will be more equations
than unknowns – we need an over-identifying restrictions test. They
suggest the test that has been developed by Sargan.
Now, a few more words about the
extended model with exogenous variables, which has the following
form:
Model with exogenous variables
0
yit = γyi(t−1) + β xit + ηi + νit ,
|γ| < 1
where νit are not serially correlated. The GMM estimator of the
6
coefficient vector will be
0
0
0
0
0
0
(γ̂, β̂) = (X̄ ZAN Z X̄ )−1 X̄ ZAN Z ȳ
where the matrix of instruments Z will include the same instruments
ˆ This
as before for γ̂ plus an additional set of instruments for beta.
additional set can be formed in two ways: if xit are strictly exogenous, in other words, E(xit , νis ) = 0 for all t, s, then all the x are
valid instruments for all the equations; if the xit are predetermined
in the sense that E(xit , νis ) 6= 0 for s < t and zero otherwise, then
only xi1 , . . . , xi(s−1) are valid instruments.
4
Results
Now we want to present the results of the two models introduced
above:
4.1
Time Dummies
For the first panel regression where we had four explanatory variables and time dummies the results are quite fuzzy (see table 1).
Out of the four explanatory variables only two of them – market
share and risk – turn out to be significant at the five percent level
with risk unexpectedly having a negative coefficient. The only significant explanatory variable with the correct sign turns out to be
the market share (2.04 with z=5.48). The two variables that were
not significant at any meaningful level – ∆competitors and ∆sales
– had the correct sign. Only four out of 12 time dummies were significant at the five percent level and they had different signs. The
industry dummies were not significant. Thus the estimations below
did not include them.
Theoretically, the time dummies should all be insignificant, because we subtracted yearly averages from our dependent variable.
Hence, the time-dummies can not explain differences between the
years by construction. But since we calculated the deviations from
the yearly means before dropping observations where not all necessary data was available, though the data to calculate profits was
available, positive or negative average yearly deviations can still remain. What we can conclude now is that the data that remains
after dropping some observations due to data limitations is representative with respect to the sample from which we calculated the
yearly profit averages for most years at least.
Besides that, the overall model can explain only up to five percent
of the change in the dependent variable. The first explanation for
7
Table 1: Results from the time-dummy-estimation on profits above the mean
(1985-1996)
Explanat. variable
Market Share
Risk
∆Competitors
∆Sales
Year86
Year87
Year88
Year89
Year90
Year91
Year92
Year93
Year94
Year95
Year96
constant
συ
σ²
ρ
Observations
Coefficient
2.040
-.211
-.814
-.0528
0.097
0.601
-0.753
-0.371
-0.001
-0.448
-0.094
-0.020
0.071
-0.306
-0.289
-0.549
(Std. Err.)
(0.373)
(0.072)
(1.458)
(0.123)
(0.204)
(0.201)
(0.213)
(0.205)
(0.200)
(0.198)
(0.199)
(0.208)
(0.200)
(0.201)
(0.201)
(0.153)
z
5.48
-2.93
-0.56
-0.43
0.48
2.99
-3.53
-1.81
0.00
-2.26
-0.47
-0.10
0.35
-1.52
-1.44
-3.58
P > |z|
0.000
0.003
0.577
0.668
0.633
0.003
0.000
0.070
0.997
0.024
0.637
0.922
0.723
0.128
0.150
0.000
0.996
4.002
0.058 (fraction of variance due to ui )
900 groups
12 obs./group
the results is that the model was not correctly specified. When we
check the correlation structure of the explanatory variables we can
say that they are not highly correlated. Another reason can be that
the data suffers heavily from outliers. As a result we find that this
simple method could not capture the effect of competition over time
and continue with the results of the dynamic panels.
4.2
Dynamic Panel
The performance of the dynamic panels with or without the set of
explanatory variables from above – we assume that all are strictly
exogenous – is slightly better than the models from above. At least
we see (in tables 2 and 3) a positive (rather small) and highly significant autoregressive parameter γ. In the dynamic setting risk has
the correct sign but now it turns out to be insignificant and unexpectedly the market share now turns out to have a big negative and
highly significant coefficient which is totally contradicting economic
theory. As we mentioned before Stata gives two test results which
8
may be interpreted as follows: the Sargan test which is used to test
the validity of the over-identifying restrictions (or the validity of the
instruments) has been rejected. The results of the serial autocorrelation tests are quite good. In both panels the null hypothesis
that there is no second order serial autocorrelation in the error term
could not be rejected.
Table 2: Results from the dynamic-panel-estimation (1985-1996)
Explanat. variable
ρt−1
Coefficient
0.168
(Std. Err.)
(0.013)
z
13.06
P > |z|
0.000
χ2(54) =321.76
Prob≥ χ2 =0.000
average autocovariance in residuals of order 1 is 0:
z = -50.54 Prob>z = 0.000
average autocovariance in residuals of order 2 is 0:
z = -0.89 Prob>z = 0.375
900 groups
10 obs./group
Sargan test of over-identifying restrictions:
Arellano-Bond test that
H0 : no autocorrelation
Arellano-Bond test that
H0 : no autocorrelation
Observations
Table 3: Results from the dynamic-panel-estimation with exogenous variables
(1985-1996)
Explanat. variable
ρt−1
Market Share
Risk
∆Competitors
∆Sales
Coefficient
0.168
-5.374
0.011
-1.861
0.140
(Std. Err.)
(0.013)
(1.878)
(0.096)
(2.043)
(0.164)
z
13.05
-2.86
0.12
-0.91
0.86
P > |z|
0.000
0.004
0.904
0.363
0.392
χ2(54) =317.94
Prob≥ χ2 =0.000
average autocovariance in residuals of order 1 is 0:
z = -50.57 Prob>z = 0.000
average autocovariance in residuals of order 2 is 0:
z = -0.89 Prob>z = 0.375
900 groups
10 obs./group
Sargan test of over-identifying restrictions:
Arellano-Bond test that
H0 : no autocorrelation
Arellano-Bond test that
H0 : no autocorrelation
Observations
The coefficients of the lagged dependent variables are
the same in both estimations. The cases of the wrong sign of market
share and non-significant parameters for all of the exogenous variables made us suspicious for the reliability of our database. The rela-
Discussion
9
tionships seem to be reasonable and a lot of empirical evidence could
be found for them. Additionally, a persistence of profit-deviations
from the mean by only 16.8 percent from one year to the next seems
too low and is also too low in light of estimates from the dominantly
used method of estimating the autoregressive parameters from every
time-series individually (as done, e.g. in Goddard & Wilson 1999,
Maruyama & Odagiri 2002; see also the references there.).
5
Conclusion
We conclude that our method is not useful to model the persistence
of profits. Probably one could try to model a different data set,
hoping that the expected relationships with the exogenous variables
will hold then and be significant. Additionally, the estimation of
individual coefficients of persistence, γi , could be necessary and thus
yield better results. This is suggested by the argument that the
internal structure and functioning of firms is likely to differ as well
as that different firms face different entry and mobility barriers –
though there is no strong evidence that the convergence process
differs between above- and below-mean profit firms (Mueller 1990,
p.194-196). Still, the doubt that our method should be preferred
over the time-series approach mentioned remains strong.
10
References
Anderson & Hsiao (1981), ‘Estimation of dynamic models with error components’, Journal of the American Statistical Association
76, 598–606.
Arellano, M. & Bond, S. (1991), ‘Some tests of specification for panel
data: Monte carlo evidence and an application to employment
equations’, Review of Economic Studies 58, 277–297.
Baltagi, B. H. (1995), Econometric analysis of panel data, John
Wiley and Sons, New York.
Goddard, J. & Wilson, J. (1999), ‘The persistence of profit: a new
empirical interpretation’, International Journal of Industrial Organization 17, 663–687.
Maruyama, N. & Odagiri, H. (2002), ‘Does the ’persistence of profits’ persist?: a study of company profits in japan, 1964-97’, International Journal of Industrial Organization 20, 1513–1533.
Mueller, D. C. (1990), The dynamics of company profits. An international comparison, Campridge University Press.
11