payment delays among polish companies and their impact on economic growth: implications from the...
TRANSCRIPT
Piotr Białowolski, Mariusz Próchniak
Payment Delays Among Polish Companies and their Impact
on Economic Growth: Implications from the Survey Data
Piotr Białowolski (Ph.D.)
Institute of Statistics and Demography, Collegium of Economic Analysis,
Warsaw School of Economics
E-mail: [email protected]
Mariusz Próchniak (Ph.D.)
Department of Economics II, Collegium of World Economy,
Warsaw School of Economics
Al. Niepodległości 162
02-554 Warszawa, Poland
Tel.: +48 22 5649376
E-mail: [email protected]
2
Abstract
In this paper we present a mixture of theoretical and survey-based approaches in measuring
impact of overdue receivables on the growth path of the Polish economy. The theoretical
framework is based on an extension of the Ramsey model. We introduce parameters
associated with costs of delayed payments showing their influence on the convergence path.
We model how these costs impede the growth process. With Survey on Receivables we assess
the scale of the problem with payment delays in Poland showing that it highly interferes with
actual economic growth. The costs of delays at the company’s level are measured explicitly
and are applied to model the relationship between them and both average time of delay and
the share of delayed payments in the portfolio of receivables. With this data we show that the
elasticity of costs with respect to the share of delayed payments is higher than with respect to
average time of delay but also that the elasticity with respect to both these factors is less than
one. The following step combines empirical and theoretical findings by applying estimated
levels of costs associated with overdue receivables to derive a hypothetical convergence path
of the Polish economy in the world free of payment delays. Our results show that the 2011
GDP per capita at PPP index in Poland (EU15 = 100), amounting to 59.1, would increase to
63.4 if the costs associated with overdue receivables were reduced to zero. We also carry out
the robustness analysis based on alternative scenarios which assume that costs of payment
delays are partly reduced.
Keywords: overdue receivables, economic growth, convergence
JEL Classification: G32, L25, O52
3
1. Introduction
Trade credit can be perceived as one of the forces driving the development of companies and
industries thus stimulating the whole economy. This view gains constantly more attention
from different fields of economic studies (e.g. Burkart and Ellingsen, 2004; Mian and Smith,
1992). Apart from the numerous advantages of trade credit, there is always a possibility that a
regular trade credit develops into a delayed payment. As indicated by Bojnec (2002) problems
with receivables are usually a reason for accumulation of overdue payments and insolvency.
These problems might be at least mitigated by some of the common policies: e.g. insurance,
factoring. However, all the preventive policies are associated with costs. When companies
need to undertake preventive measures, their performance (competitiveness) on the market is
likely to be negatively affected. The micro-level costs transmit then onto the whole economy
and influence (impede) the transition processes.
In most economies under transition the legal processes are lengthy and securitization of
receivables is limited. Thus, the state of receivables affects to an even larger degree economic
growth. Demirgüç-Kunt and Maksimovic (2001) show that in countries with large banking
systems (usually more developed and with higher level of social capital) companies tend to
lend and borrow more from each other, but the relative importance of trade credit is higher in
the less developed economies.
These findings direct our attention to the problem of measuring impact of overdue
receivables on the level of costs in the sector of enterprises. This problem cannot be easily
approached by the standard accounting techniques. The costs associated with receivables are
not explicitly included in books and are not homogenous with other costs (Cramer, 1972). A
survey-based approach is an alternative. However, within the standard framework of surveys
on economic activity that are conducted in different sectors on a quarterly or monthly basis
(e.g. manufacturing industry, construction, trade and services) there is only a little space left
4
for the analysis of consequences resulting from overdue receivables. Surveys based on the
standardized questionnaire (European Commission, 2006) focus at most on factors that
impede economic activity of enterprises – barriers – but do not measure the direct impact of
overdue receivables on the level of costs associated with payment delays and the determinants
of these costs.
In this paper a survey based approach was adopted to strengthen the theoretical findings. It
utilizes the results of Survey on Receivables, which was designed to measure the impact of
overdue receivables on the functioning of Polish enterprises. The Survey on Receivables was
launched in January 2009 and in the four year period (2009 – 2012) almost 30000 responses
were obtained (Białowolski, 2009-2012). The survey is conducted on a quarterly basis and is
based on a questionnaire comprising nine questions (detailed wording of questions is
presented in Appendix 1). The number of answers ranged from 1265 in 2012Q3 to 2714 in
2012Q1 with an average of 1859 responses gathered each quarter. The quantitative results on
overdue receivables are provided by answers to the question concerning the share of overdue
receivables in the portfolio of all receivables and the question concerning the term-structure of
overdue receivables, which serves as the base for calculation of average time of delay.
Additionally, there is a question on the level of costs associated with overdue receivables.
These comprise not only those directly associated with payment delays – namely the cost of
interest and the costs connected with vindication. In this category enterprises are also
prompted to include the costs that are present in companies due to their awareness of possible
consequences of payment delays and the costs associated with actions undertaken in order to
counteract them: implementation of a monitoring system, development of legal procedures
but also reduction in the scale of operations which implies reduced profits. Thus the costs
associated with overdue receivables are expected to be much higher than the accounting costs
reported in companies’ books.
5
We apply the results of the Survey on Receivables to calculate not only the average cost of
overdue receivables in all periods but also a relative influence of its determinants. We
incorporate this approach into a framework of an extended Ramsey model of economic
growth. The costs associated with payment delays are applied to calculate impact on the
economic growth, profitability of companies and the speed of convergence of the Polish
economy. Throughout the whole analysis we assume that overdue receivables do not yield
any benefits for the economy. Although a delayed payment constitutes a gain of the debtor,
from the perspective of the economy it negatively affects market efficiency and leads to
deadweight loss.
The paper has the following structure. Section 2 presents the authors’ extension of the
Ramsey model by including costs of payment delays into the standard framework. Section 3
provides the results of statistical and econometric analyses oriented on establishing the level
of costs associated with overdue receivables and their determinants. Section 4 is devoted to
calibration presenting alternative scenarios of the convergence path of the Polish economy
towards Western Europe. Section 5 concludes.
2. The Ramsey growth model with overdue receivables
In this section we present an extension of the Ramsey model (Ramsey, 1928; Cass, 1965;
Koopmans, 1965; Barro and Sala-i-Martin, 2003) to include overdue receivables. We carry
out the analysis for the perfectly competitive economy. After more than 20 years of transition
the theoretical behaviour of the perfectly competitive economy provides a good background
for an empirical analysis for the case of Poland.
We start with the standard framework, namely firms are producing a homogenous product
according to a production function F(K, AL). The factors of production (physical capital K
and labour L) are purchased from households at the prices of (r + ) and w respectively, where
6
r stands for the interest rate (the price of capital), is the depreciation rate, and w represents
the wage rate (the price of labour). An assumption associated with overdue receivables is that
they lead to an increase in the costs of the factors of production. If firms do not obtain money
for the output they sell, they have to borrow funds to pay for capital and labour services. It
can be done either from external or internal sources. Since all the units of output are produced
by both factors: capital and effective labour (the latter one being the product of technology A
and labour L), we assume that overdue receivables increase costs of both inputs.
Firms aim at maximizing profit. Costs related to the overdue receivables should be
included in total costs. Let 1 be the additional cost of capital due to overdue receivables and
2 be the additional cost of effective labour. This yields the following profit maximization
problem:
1 2, maxF K AL r K wL K AL . (1)
Applying the standard profit-maximization conditions, we get:
1'r f k , (2)
2'w A f k kf k . (3)
From equation (2) we can derive that in equilibrium the interest rate is equal to marginal
product of capital (in ‘per unit of effective labour’ terms) minus depreciation rate and minus
additional cost of capital due to overdue receivables. Equation (3) presents the equilibrium
wage rate. Hence, the firms’ optimization yields two equations for input prices. Both of them
are profit maximization conditions implying that each of them represents the equality between
the marginal factor product and the input price.
The analysis of households’ behaviour is the same as in the standard model. The
consumer’s optimization problem is the following:
1
0
1max.
1
n t pccU e dt
subject to: pc pc pc pck w rk c nk , (4)
7
where kpc and cpc stand for per capita capital and consumption, is the rate of time preference,
n is population growth, and is the reciprocal of the elasticity of substitution in the utility
function. The budget constraint indicates that an increase in per capita capital equals income
(from labour and capital) net of consumption and pcnk - a term representing the change in the
level of capital per capita resulting from a change in country’s population. In the budget
constraint all the terms associated with 1 and 2 cancel out. Hence, individual budget
constraint remains unaffected in comparison to the standard solution. Overdue receivables
affect only the behaviour of firms.
The current-value Hamiltonian for the problem (4) is:
1 1
1
pc
pc pc pc
cH w rk c nk
(5)
with the following first-order conditions:
0pc
H
c
,
pc
Hn
k
, pc
Hk
, lim 0
n t
pct
e k
. (6)
The solution to the utility maximization problem is the following (augmented by the
respective transversality condition):
pc
pc
c r
c
, (7)
pc pc pc pck w rk c nk . (8)
Equation (7) is the Euler equation which relates growth rate of consumption to the interest
rate, the rate of time preference, and the elasticity of substitution, 1/.
Combining the behaviour of firms and households yields equations describing the whole
economy. Making use of the following definitions: pcc cA and pck kA (to get ‘per unit of
effective labour’ variables) and substituting (2) and (3) into (7) and (8) respectively yields:
8
1'f k ac
c
, (9)
1 2k f k c n a k . (10)
Equations (9) and (10), augmented by the transversality condition, are the final equations
describing the dynamics of the economy on the optimal growth path.
In the steady-state, the variables per unit of effective labour are constant over time: 0c
and 0k . The steady-state is thus described by the following equations:
1' *f k a , (11)
1 2* * *c f k n a k . (12)
Overdue receivables influence both the transition dynamics and the steady-state values of
capital and consumption, because 1 and/or 2 appear in both equations characterizing the
dynamics of the economy ((9) and (10)) as well as in both equations determining the steady-
state values of capital and consumption per unit of effective labour ((11) and (12)).
<Figure 1>
The effects of overdue receivables are illustrated in Figure 1. The existence of overdue
receivables shifts both the 0c and 0k functions. Hence, overdue receivables affect the
level of consumption in the steady-state as well as the steady-state value of physical capital
and output. With overdue receivables the 0k function shifts leftwards (according to
Equation (11)). Overdue receivables increase marginal productivity of capital in the steady-
state, which means that the stock of physical capital is reduced. The 0c function shifts
downwards due to payment delays, which results in a decrease of the steady-state value of
consumption (however, this shift is not parallel as indicated by Equation (12)).
With overdue receivables the steady-state shifts from point E to F (Figure 1). In the new
steady-state, the equilibrium levels of capital, output and consumption are lower. With
presence of overdue receivables the economy cannot accumulate as much output as without
9
them.
The implications for the economic growth rate should be considered with respect to the
steady-state and transition period. In the steady-state, the growth rate of GDP equals technical
progress plus population growth. Presence of payment delays does not influence any of these
variables and thus the GDP and GDP per capita growth rates in the steady-state are both
unaffected. The impact on economic growth during the transition period is our particular
interest because Poland can still be considered a transition economy. Overdue receivables
decrease the output level in the steady-state, but also they decrease the rate of economic
growth during the transition period.
The theoretical framework, represented by the Ramsey model, demonstrates that in a
transition economy like the Polish one the observed economic growth rates are likely to be
lower due to overdue receivables. As a consequence lower real economic convergence
towards well developed countries is likely to be observed. The catch-up process to the old 15
EU member states (EU15) is much more likely to be prolonged.
3. Average level of costs associated with overdue receivables and their
determinants
Overdue receivables directly but also implicitly affect the cost of companies. Our primary
goal of this section is to provide an estimate of the average share of costs associated with
payment delays in the total costs of Polish companies. It is done for the period 2009 – 2012
and requires transformation of survey responses measured on an interval scale into a single
number representing the average share of costs associated with overdue receivables in the
Polish economy in each quarter (additionally, a procedure for calculation of a plausible
estimate of the average time of delay for each respondent is developed; it is presented in more
details in Appendix 2). Our secondary objective is to evaluate strength of a link between the
10
costs of payment delays and its determinants – the share of overdue receivables in the
portfolio and the average time of delay. We achieve it by estimating a regression model on
data transposed with logarithmic transformation thus obtaining elasticities of costs with
respect to average delay and the share of overdue receivables. Results of the model are
subsequently used in order to calculate the expected costs of delays under different scenarios
assuming reduction in the scale of problems with payment delays.
3.1. Costs of payment delays
We calculate the average share of costs associated with overdue receivables under the
hypothesis that they follow a log-normal distribution. With the λ-statistics from the
Kolmogorov-Smirnov test the hypothesis could not have been rejected in any of the sixteen
quarters between 2009Q1 and 2012Q4 (also in this case different distributions were subject to
consideration, however the Kolmogorov test proves superiority of the log-normal one – the
detailed results on the selection of distribution are presented in Appendix 2). Thus, period
specific estimates can be calculated (Table 1).
<Table 1>
The highest level of costs was observed during the crisis period in 2009. In 2010 and
especially 2011 an improvement in the area of receivables was observed with the best
situation reported at the verge of 2011 and 2012. However, there was a significant increase in
the level of costs associated with payment delays from the beginning of the year 2012, which
coincided with the observed economic slowdown. Correlation between the average level of
costs and quarterly growth of GDP is significantly different from zero and amounts to -0.59.
Initial results based on 16 observations show that the costs are lagging the GDP growth by
two quarters, which means that in deteriorating economic environment there is an additional
impediment for companies that results in higher costs. The companies thus need to not only
11
face lower demand usual in the period of a slow-down, but also higher costs associated with
payment delays. Thus, it might be expected that overdue receivables serve as the factor
prolonging the crisis and strengthening the slow-down.
3.2. Determinants of costs associated with overdue receivables: An econometric model
The selection of variables and specification of relation between the selected explanatory
variables and the level of costs associated with payment delays was a consequence of the
following assumptions. Firstly, costs associated with delays depend on the share of delayed
receivables in the portfolio of receivables and average time of delay. Secondly, the impact (on
the share of costs associated with overdue receivables) of the share of delayed receivables and
average time of delay should be multiplicative. However, the relationship between the share
of bad debt and average time of delay on the costs associated with payment delays, does not
have to be one-to-one (so, if the share of bad debt and average time of delay increase both by
10%, the impact on cost does not have to be equal to 10%). This is due to the possibility of
existence of economies of scale associated with payment delays, which should also be subject
to estimation.
These assumptions led to the following specification of the model for cost associated with
payment delays period:
,
where:
costi – the cost of i-th company associated with overdue receivables,
– period specific parameters, which are later tested for an equality between
periods,
– the share of overdue receivables in the portfolio of i-th company
receivables,
12
– the average time of delay observed for i-th company,
– the error term with assumed normal distribution.
In order to facilitate the estimation procedure, the model was estimated after logarithmic
transformation in the form:
.
Estimation of the model for the whole economy with constrained coefficients yielded:
.024 .007 .011
ln cost .162 .389 ln _ .258 ln _i i i idebt share av debt
where standard errors are given below the estimated coefficients.
Model coefficients were tested with the chi-square test for intertemporal equality. The
results (χ2=61.04; df=45; p-value = 0.056) indicated that there is no reason to reject the null
hypothesis of equal slope of coefficients and intercepts in all periods.
Coefficients of the estimated model provide an important information on the aggregate
impact of overdue receivables on companies’ costs. Parameters α and β can be interpreted in
terms of elasticities - α represents the elasticity of the level of costs with respect to the debt
share and β represents the elasticity of the level of costs with respect to the average delay. The
sum of α and β gives the impression on the elasticity of costs to both the share of overdue
receivables and average time of delay. Positive values of α and β were obtained during the
estimation procedure, which was initially assumed to be the case. Additionally, in the model
the value of α is significantly higher than that of β. It implies that in the Polish economy there
is significantly larger influence of the share of bad debt on the level of costs than it is in
reaction to changes in the average time of delay. Also in the model the values of cumulative
elasticity connected with the sum of α and β proved to be less than one. It implies that
company’s costs react less than proportionally to changes in the bad debt portfolio.
We present the model estimates to develop alternative scenarios of the influence of
overdue receivables on the development of the economy in the past 4 years. The four
13
alternative scenarios assume reduction of both average time of delay and the share of overdue
payments in the portfolio by 25% and 50% in scenario 1 and 2 respectively and reduction in
only one of the areas by 50% with the second held constant. In scenario 3 the share of
payment delays is reduced and in scenario 4 – average time of delay. The predicted values of
the average level of costs in different periods under these scenarios are presented in Table 2.
<Table 2>
We observe the most significant reduction in the level of expected costs of overdue
receivables for the situation where both average time of delay and the share of delayed
payments are reduced by 50% (scenario 2). We note the lowest impact when only the average
time of delay is reduced (scenario 4). However, the most interesting results are drawn from
application of these data to the convergence path of the Polish economy.
4. Calibration of the convergence path of the Polish economy with overdue
receivables
4.1. The basic model
In this section we try to show the impact of the costs of overdue receivables on the pace of
economic growth of the Polish economy and – as a result – on its real convergence towards
the EU15 economies. This assessment is based on a number of assumptions that need to be
introduced into calculations due to two reasons. First of all, the costs of overdue receivables
are derived from survey data that range backwards only till 2009. In order to extrapolate the
average level of costs associated with overdue receivables in earlier years, it is assumed that
the figures from 2009 are also valid for the earlier periods. Second, as it is impossible to
transform unambiguously the changes in the microeconomic situation of the firms into the
behaviour of the whole economy, it must be assumed the way according to which overdue
14
receivables affect the rate of economic growth.
The calibration presented here is based on official data sources and conducted surveys. It
aims at assessing the impact of the costs of overdue receivables on the growth path of the
Polish economy and its pace of income-level convergence towards the EU15.
As we already calculated the percentage shares of the costs of overdue receivables in total
costs of firms (Table 1), we apply the obtained values to derive hypothetical profits present in
an absence of delays. The hypothetical profits are based on information on total costs and
revenues of Polish companies for the years 2009-2011. The calculations are presented in
Table 3.
<Table 3>
In 2011 – the last year for which full data is accessible – total revenues of companies
amounted to 2 294 302 million PLN while total costs equalled 2 169 484 million PLN, which
yielded total gross profits of 124 818 million PLN. Thus, the profitability rate of gross
turnover for 2011 amounted to 5.4%, while the costs of overdue receivables amounted to
7.1% of total costs (see Table 1). In the case of non-existence of overdue receivables, the total
costs would have been reduced by 7.1% to 2 015 451 million PLN. Given this figure, the
hypothetical profit is 278 851 million PLN and the hypothetical profitability rate is 12.2%. It
implies that the percentage increase in both profit and profitability rate would have been
123.4% without overdue receivables (all the figures for 2009 and 2010 are calculated
analogously).
The next step of the calibration process benefits on the fact that, according to the income
method, firms’ profits are included in GDP. Hence, based on the given information on the
share of firms’ profits in GDP, hypothetical value can be also calculated by multiplying the
actual value by estimated change in profits. The calculations are presented in Table 4.
<Table 4>
15
According to the adopted methodology, without overdue receivables, the rate of economic
growth would have been higher by 10.94% in 2009, 10.58% in 2010, and 10.10% in 2011.
For the years before 2009, the average figure of 10.54% is adopted for further analyses.
Although in a single year it is neither bug nor small number, over the whole period under
study, the annual changes can cumulate into a considerable figure.
The initial year of the simulation is 1995 due to two reasons. Firstly, in the first half of the
1990s Poland suffered from the transformation recession. It is difficult to model the
convergence processes towards the EU, while during a transformation recession patterns of
economic behaviour can develop very atypically and applying the mechanisms of well-
developed economies may be misleading. However, different studies show that in the region
(Central and Eastern European (CEE) countries) transformation recession finished by 1995
(see, e.g., Rapacki and Próchniak, 2006; IMF, 2012). Secondly, we wanted to include as much
data as possible because the longer the time period is, the more reliable the results are mainly
because the effects of the overdue receivables cumulate. The earliest reliable data after the
transformation recession come from the year 1995.
Real economic convergence of Poland towards the EU15 is analysed in terms of the
income gap measured by GDP per capita at PPP. The observed changes in the income gap
between Poland and the EU15 countries are compared with the hypothetical changes that
would take place if the Poland’s economy recorded GDP growth rates for the case of non-
existence of overdue receivables. The analysis covers the 1995-2011 period. All the
calculations are presented in Table 5. The official statistics come from the Eurostat database.
<Table 5>
In 1995, GDP per capita at PPP in Poland amounted to merely 37% of the average income
level observed in the EU15. In the following years, the income gap between Poland and the
EU15 was diminishing. As a result, in 2011 Poland’s GDP per capita at PPP amounted to
16
59% of that recorded in the EU15 countries. Although, taking into account a very low starting
point, it is quite a good outcome, income differences between Poland and the old EU member
countries are still very large.
The observed (actual) convergence path is shown in column 2 of Table 5. It is the
consequence of difference in GDP growth rates listed in columns 3 and 4, but also changes in
population and exchange rates. In order to account for changes in population and exchange
rates, GDP indices for the case of constant population and exchange rates were calculated
(column 5) and a multiplicative factor responsible for population and exchange rates was
obtained (column 6). The last two columns of Table 5 show the authors’ estimates of the
hypothetical convergence path for the scenario assuming no costs associated with overdue
receivables. These calculations are based on official real GDP growth rates for the EU15
countries, hypothetical GDP growth rates for Poland, and corrected using the multiplicative
factor. Actual and hypothetical Poland’s convergence paths are compared in Figure 2.
<Figure 2>
In the case of the lack of overdue receivables, the convergence process would occur faster.
According to our simulations in 2011 the GDP per capita at PPP in Poland would constitute
63.4% of the average per capita income level seen in the EU15. It would be an improvement
by 4.5 percentage points as compared with the actual convergence path. This difference can
be treated as the loss caused by the costs related with overdue receivables accruing over the
last 16 years.
These results show that the process of real economic convergence of Poland and the other
CEE countries towards EU15, confirmed in many cross-sectional studies, would be faster and
the number of years needed for the EU countries to reduce by half the distance towards the
steady state (half-life) would be less than the estimated levels of about 13-14 years (see, e.g.,
Próchniak and Witkowski (2013) who use an innovative Bayesian model averaging
17
methodology).
4.2. The robustness analysis
The convergence path showed in the last column of Table 5 presents the hypothetical
convergence path in the case of non-existence of overdue receivables. Such a situation should
be treated as a purely hypothetical one because it is almost impossible to eliminate the
problem of overdue receivables completely. However, it is possible for the economy to reduce
some of the costs related with overdue receivables. In such a case, the Poland’s economy
would converge faster to Western Europe than the official data suggest but not as fast as
evidenced by the hypothetical path in the case of non-existence of overdue receivables. In this
section, we carry out the robustness analysis to show different convergence paths assuming
that some costs related with overdue receivables are abandoned.
The starting point of the analysis refers to the alternative scenarios of estimated levels of
total costs developed in Section 3 (Table 2 shows four scenarios of estimated levels of total
costs under different assumptions as to the reduction of both average time of delay and the
share of overdue payments in the portfolio). Table 6 summarizes cost levels of overdue
receivables in different scenarios considered in this analysis. We use these data to compare
the hypothetical economic growth path in the case of non-existence of overdue receivables
with the alternative hypothetical cases when overdue receivables are abandoned only partly.
The comparison is presented in Table 7.
<Table 6>
When calculating different convergence paths in Table 7, we use the following
assumptions. First, if total costs related with overdue receivables were reduced to zero, we
would obtain the hypothetical convergence path for the case of non-existence of overdue
receivables, presented in the last column of Table 5. Second, if estimated total costs of
18
overdue receivables matched the observed total costs, we would obtain the true convergence
path according to official statistics, presented in the second column of Table 5. Third, the
convergence paths for the alternative scenarios are calculated proportionally and the
proportions are derived from the 2009-2011 averaged levels of total costs, given in the last
column of Table 6.
<Table 7>
The data in Table 7 show that alternative scenarios yield per capita GDP indices ranging
between the observed figures (obtained under the assumption of a 7.6 per cent share of costs
of overdue receivables) and the hypothetical figures obtained for the case of non-existence of
overdue receivables. Among the alternative scenarios, the best outcomes appear under
scenario 2 in which the most significant reduction in the level of expected costs of overdue
receivables is assumed (both average time of delay and the share of delayed payments are
reduced by 50%). In such a case, GDP per capita at PPP in Poland in 2011 would constitute
60.2% of the level seen in the EU15 (the observed figure was 59.1% while the most
‘optimistic’ one would be 63.4%). Under scenarios 1, 3 and 4, the 2011 GDP per capita
indices are slightly lower than in scenario 2, amounting to 59.8 in scenario 3, 59.7 in scenario
1, and 59.5 in scenario 4.
The differences between the alternative scenarios and the official data are not very large at
the first view because estimated levels of total costs related with overdue payments in the
alternative scenarios do not differ much from the observed ones. However, these differences
are by no way negligible. A rise of GDP per capita index even by only 1 percentage point is
very important from the macroeconomic perspective and it is worth for policy makers to
perform actions to increase a given country’s GDP even by this amount. Hence, reduction of
overdue receivables by whatever amount is important for the Polish economy and would
accelerate the catching up process of Poland towards Western Europe.
19
5. Conclusions
In the paper we explore and analyse a number of issues related to the problem of overdue
receivables (payment delays) in the Polish economy. The analysis is based on Survey on
Receivables conducted among Polish companies on a quarterly basis from 2009. The
theoretical framework of the research is based on the authors’ extension of the Ramsey model
to account for overdue receivables. According to it, overdue receivables negatively affect the
rate of economic growth during the transition period and the steady-state level of output.
Hence, from the theoretical point of view, the existence of overdue receivables is likely to
slow down the convergence process of Poland towards EU15 countries.
In the empirical part of the paper, the main conclusions are as follows. First, according to
our estimates, around 7-8% of all the costs of Polish companies can be associated to overdue
receivables. These include extra expenditures connected with monitoring, vindication, and
financial losses due to payment delays. Moreover, there is a large co-movement of costs
associated with payment delays and the GDP growth rate. Second, the econometric model
confirms that the share of overdue receivables in total portfolio of receivables as well as the
average time of delay both positively affect the share of costs associated with overdue
receivables. Estimated coefficients are statistically significantly different than zero confirming
the reliability of the regression model. However, in terms of elasticities the influence of the
share of overdue receivables is much more important for the level of costs than the average
time of delay.
Third, the empirical analysis confirms that overdue receivables are an important factor
impeding the convergence process of the Polish economy towards Western Europe. Results of
calibration show that the 2011 income gap between Poland and EU15 countries amounting to
59.1 (in terms of GDP per capita at PPP index) could have been decreased by about 4.5 pp.
20
(i.e. the index would go up to 63.4) if the level of costs associated with overdue receivables
was reduced to zero. Under the alternative scenarios, where only part of costs related with
delayed payments is abandoned, the 2011 GDP per capita at PPP index would range between
59.5 and 60.2 (EU15 = 100).
Our results mean that currently accumulated gap results in annual GDP per capita lower by
around 1000 euro due to problems with overdue receivables since mid-1990s. It shows also
that overdue receivables that are a pretty neglected factor in the conduct of economic policy
are responsible for around 100 billion PLN lower yearly figure of GDP in Poland (based on
the assumption that the accumulated gap amounts to 4.5 pp. of the average EU15 GDP per
capita). Since 1995, Polish authorities were not able to overcome weak functioning of the
system of legal debt collection but also there was no policy oriented on helping companies
affected by problems with overdue receivables. If this situation is maintained in the future the
gap will widen and annual discrepancies between potentially accessible GDP and its current
values will grow.
References
Barro R.J., Sala-i-Martin X., Economic Growth, The MIT Press, Cambridge – London 2003.
Białowolski P., Survey on Receivables, Quarterly Reports, Gdansk – Wroclaw 2009 – 2012.
Bojnec S., Payments, Insolvency and Finance during Economic Transformation: Slovenia on
the Way to European Union Accession, “Europe-Asia Studies”, 54, pp. 277-297, 2002.
Burkart M., Ellingsen T., In-Kind Finance: A Theory of Trade Credit, “American Economic
Review”, 94, pp. 569-590, 2004.
Cass D., Optimum Growth in an Aggregative Model of Capital Accumulation, “Review of
Economic Studies”, 32, pp. 233-240, 1965.
Cramer J.J., Jr., Incompatibility of Bad Debt “Expense” with Contemporary Accounting
Theory, “The Accounting Review”, 47, pp. 596-598, 1972.
Demirgüç-Kunt A., Maksimovic V., Firms as Financial Intermediaries: Evidence from Trade
Credit Data, “World Bank Policy Research Working Paper”, No. 2696, 2001. Available
at SSRN: http://ssrn.com/abstract=632764.
21
European Commission, EU Economy. The Joint Harmonised EU Programme of Business and
Consumer Surveys, Brussels 2006.
Eurostat, Database. Available at: ec.europa.eu/eurostat.
GUS, Biuletyn Statystyczny, No. 1/2011, No. 4/2012.
IMF, World Economic Outlook Database, October 2012. Available at www.imf.org.
Koopmans T.C., On the Concept of Optimal Economic Growth, in: The Econometric
Approach to Development Planning, North Holland, Amsterdam 1965.
Mian S.L., Smith C.W., Jr., Accounts Receivable Management Policy: Theory and Evidence,
“The Journal of Finance”, 47, pp. 169-200, 1992.
Próchniak M., Witkowski B., Time Stability of the Beta Convergence among EU Countries:
Bayesian Model Averaging Perspective, “Economic Modelling”, 30, pp. 322-333, 2013.
Ramsey F., A Mathematical Theory of Saving, “Economic Journal”, 38, pp. 543-559, 1928.
Rapacki R., Próchniak M., Charakterystyka wzrostu gospodarczego w krajach
postsocjalistycznych w latach 1990-2003 [Economic Growth Characteristics in Post-
Socialist Countries, 1990-2003], “Ekonomista”, 6, pp. 715-744, 2006.
World Bank, Doing Business Report 2012: Doing Business in a More Transparent World;
Doing Business Report 2011: Making a Difference for Entrepreneurs; Doing Business
Report 2010: Reforming through Difficult Times; Doing Business Report 2009;
Washington, D.C. 2009-2012.
22
Figure 1. The impact of overdue receivables on the steady-state in the Ramsey model
c1*
E
k1* k2*
c2* F
23
Figure 2. Actual and hypothetical Poland’s convergence paths measured by GDP per
capita at PPP (EU15 = 100)
Source: Own calculations.
0
10
20
30
40
50
60
70
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
20
10
20
11
Actual data
Hypothetical data
24
Table 1. Average level of costs associated with overdue receivables (2009 – 2012)
Per
iod
20
09
Q1
20
09
Q2
20
09
Q3
20
09
Q4
20
10
Q1
20
10
Q2
20
10
Q3
20
10
Q4
20
11
Q1
20
11
Q2
20
11
Q3
20
11
Q4
20
12
Q1
20
12
Q2
20
12
Q3
20
12
Q4
Base 7.5 8.6 8.4 7.7 7.6 8.2 8.0 7.5 7.4 7.2 7.1 6.9 6.9 7.8 7.9 8.4
Yearly
average 8.0 7.8 7.1 7.7
Source: Survey on Receivables, own calculations.
25
Table 2. Estimated level of total costs associated with payment delays in different scenarios
Period Base Scenario 1 Scenario 2 Scenario 3 Scenario 4
2009Q1 7.5 6.2 5.0 6.0 6.5
2009Q2 8.6 7.2 5.8 6.9 7.5
2009Q3 8.4 7.0 5.7 6.7 7.3
2009Q4 7.7 6.5 5.2 6.2 6.7
2010Q1 7.6 6.4 5.2 6.1 6.6
2010Q2 8.2 6.9 5.6 6.6 7.1
2010Q3 8.0 6.7 5.4 6.5 7.0
2010Q4 7.5 6.3 5.1 6.0 6.5
2011Q1 7.4 6.2 5.0 5.9 6.4
2011Q2 7.2 6.0 4.8 5.8 6.2
2011Q3 7.1 6.0 4.8 5.7 6.2
2011Q4 6.9 5.8 4.7 5.5 6.0
2012Q1 6.9 5.8 4.7 5.6 6.0
2012Q2 7.8 6.6 5.3 6.3 6.8
2012Q3 7.9 6.6 5.3 6.3 6.9
2012Q4 8.4 7.0 5.7 6.7 7.3
Source: Survey on Receivables; own calculations.
26
Table 3. The impact of overdue receivables on the firms’ profits, 2009-2011
No. Specification In PLN million or %
2009 2010 2011
1 Revenues from total activity 1 932 978 2 029 731 2 294 302
2 Costs of obtaining revenues from total activity 1 837 000 1 922 052 2 169 484
3 Profit (gross) 95 978 107 679 124 818
4 Profitability rate of gross turnover (%) 5.0 5.3 5.4
5 Costs of overdue receivables (% of total costs) 8.0 7.8 7.1
6 Costs excluding the costs of overdue receivables 1 690 040 1 772 132 2 015 451
7 Profit in the case of non-existence of overdue receivables 242 938 257 599 278 851
8 Profitability rate in the case of non-existence of overdue
receivables (%) 12.6 12.7 12.2
9 Change in profit (profitability rate) between the cases
without and with overdue receivables (%) 153.1 139.2 123.4
Source: Own calculations based on the survey data and GUS data (Biuletyn Statystyczny GUS, No. 1/2011, tab.
2; No. 4/2012, tab. 2).
27
Table 4. Change in the rate of economic growth resulting from overdue receivables
No. Specification
In PLN million or %
2009 2010 2011
1 Gross domestic product 1 343 657 1 416 392 1 524 659
2 Profit (gross) 95 978 107 679 124 818
3 Share of profit in GDP (%) 7.1 7.6 8.2
4 Change in profit (profitability rate) between the cases
without and with overdue receivables (%) 153.1 139.2 123.4
5 Change in the rate of economic growth in the case of
non-existence of overdue receivables (% per annum)
– individual years 10.94 10.58 10.10
– average 2009-2011 10.54
Source: Own calculations based on the survey data and GUS data (Biuletyn Statystyczny GUS, No. 1/2011, tab.
2, 3; No. 4/2012, tab. 2, 3).
28
Table 5. The impact of overdue receivables on the convergence path of Poland towards
EU15
Year
GDP per
capita at PPP
(EU15 = 100)
Real GDP growth rate (%)
GDP index
calculated
using only
GDP growth
rates
Factor
responsible
for population
and exchange
rates relative
changes
Real GDP
growth rate
(%)
GDP per
capita at PPP
(EU15 = 100)
Poland EU15 Poland Poland Poland Poland Poland
Official data
Hypothetical data: in the
case of non-existence of
overdue receivables
1995 37.1 . . 37.1 . . 37.1
1996 39.1 1.7 6.2 38.7 1.0109 6.9 39.4
1997 40.9 2.7 7.1 40.8 1.0015 7.8 41.4
1998 41.7 3.0 5.0 41.7 1.0018 5.5 42.5
1999 41.7 3.0 4.5 42.3 0.9856 5.0 42.7
2000 41.7 3.9 4.3 41.9 0.9962 4.8 42.9
2001 40.9 2.1 1.2 41.4 0.9879 1.3 42.0
2002 42.1 1.2 1.4 41.0 1.0282 1.5 43.4
2003 43.0 1.2 3.9 43.2 0.9943 4.3 44.5
2004 45.1 2.4 5.3 44.2 1.0211 5.9 46.9
2005 45.1 1.8 3.6 45.9 0.9826 4.0 47.1
2006 46.4 3.1 6.2 46.5 0.9987 6.9 48.7
2007 48.6 3.0 6.8 48.1 1.0105 7.5 51.4
2008 50.5 0.0 5.1 51.1 0.9867 5.6 53.6
2009 55.5 -4.4 1.6 53.6 1.0343 1.8 59.0
2010 57.3 2.0 3.9 56.5 1.0139 4.3 61.2
2011 59.1 1.4 4.3 58.9 1.0031 4.7 63.4
Source: Own calculations based on the survey data, GUS, and Eurostat.
29
Table 6. Estimated levels of total costs in the base and alternative scenarios, annual
average
2009 2010 2011 2009-2011 average
Base scenario 8.0 7.8 7.1 7.6
Alternative scenario 1 6.7 6.6 6.0 6.4
Alternative scenario 2 5.4 5.3 4.8 5.2
Alternative scenario 3 6.5 6.3 5.7 6.2
Alternative scenario 4 7.0 6.8 6.2 6.7
Source: Own calculations based on Table 2.
30
Table 7. Convergence paths of Poland towards EU15 under different scenarios
(GDP per capita at PPP in Poland, EU15 = 100)
Non-
existence of
overdue
receivables
Official data Alternative
scenario 1
Alternative
scenario 2
Alternative
scenario 3
Alternative
scenario 4
Costs of
overdue
receivables (%
of total costs)
0.0 7.6 6.4 5.2 6.2 6.7
Year
1995 37.1 37.1 37.1 37.1 37.1 37.1
1996 39.4 39.1 39.2 39.2 39.2 39.2
1997 41.4 40.9 40.9 41.0 41.0 40.9
1998 42.5 41.7 41.8 41.9 41.9 41.8
1999 42.7 41.7 41.9 42.0 41.9 41.8
2000 42.9 41.7 41.9 42.0 41.9 41.9
2001 42.0 40.9 41.0 41.2 41.1 41.0
2002 43.4 42.1 42.3 42.4 42.3 42.2
2003 44.5 43.0 43.2 43.4 43.2 43.1
2004 46.9 45.1 45.4 45.6 45.4 45.3
2005 47.1 45.1 45.4 45.7 45.5 45.3
2006 48.7 46.4 46.7 47.1 46.8 46.7
2007 51.4 48.6 49.0 49.4 49.1 48.9
2008 53.6 50.5 50.9 51.3 51.0 50.8
2009 59.0 55.5 55.9 56.4 56.0 55.8
2010 61.2 57.3 57.8 58.3 57.9 57.7
2011 63.4 59.1 59.7 60.2 59.8 59.5
Source: Own calculations based on data in Tables 5 and 6.
31
Appendix 1. Survey on receivables - Questionnaire
1. How do you assess change in the financial situation of your company in the past 3 months?
a. Improved; b. The same; c. Deteriorated
2. How will the financial situation of your company change in the forthcoming 3 months?
a. Will improve; b. Will remain the same; c. Will deteriorate
3. Do you have in your company problems with overdue receivables?
a. Yes, and the problem increases; b. Yes, but the problem is at a constant level; c. Yes, but the
problem decreases, d. No, such problem does not exist (proceed to question 9)
4. The share of overdue receivables amounts to ca.. …. % of all receivables.
5. What is the term-structure of overdue receivables in your company (the sum of answers for points a-d
should be equal to 100%)?
a. The delay is up to 3 months ……%; b.The delay is over 3 up to 6 months …….%; c.The delay is
over 6 up to 12 months …….%; d. The delay is over 12 months ……..%.
6. The share of overdue receivables between natural persons and companies in the portfolio of overdue
receivables in your company is (the sum of answers for points a and b should be equal to 100%) :
a. Natural persons …..%; b. Companies ……%
7. Are the overdue receivables a barrier in the operational activity of your company? (more than one
answer can be selected)
a. No; b. Yes, we have to limit our investment; c. Yes, we have to limit the employment or reduce the
wage fund; d. Yes, we have problems with introduction of new products to the market; e. Yes, we have to
increase the prices of goods (or services) provided by our company ; f. Yes, while we cannot make our own
payments; g. yes, other ………………….
8. In your opinion, what is the share of your company costs (approximately) that can be attributed to the not
regular or delayed payments by your customers/cooperators? Please include in the costs, losses connected
with lower turnover, costs of monitoring, vindication and prevention policy.
a. 0%; b. 1%; c. 2%; d. 3%; e. 4%; f. 5% - 9%; g. 10% - 14%; h. 15% - 19%; i. 20% - 29%; j. 30% -
49%; k. 50% and over,
9. How will the problem of overdue receivables evolve in your company in the forthcoming quarter?
a. The scale of the problem will increase; b. The scale of the problem will remain the same; c. The
scale of the problem will decrease; d. There will be no problems with overdue receivables; e. Don’t know.
Respondent’s characteristics
1. In which region is the headquarter of your company (Poland, NUTS 2)
a. Central; b. South; c. East; d. North-West; e. South-West; f. North.
2. The employment level in your company is:
a. up to 49 people; b. 50 – 249 people; c. over 249 people
3. In which sector does your company operates
a. Agriculture, forestry, fishing; b. Manufacturing industry; c. Construction; d. Trade; e. Financial
services; f. Telecommunications; g. Other services
32
Appendix 2. Interval mid-point estimates
Out of the three variables which are essential in the procedure of calculation of the
impact of overdue receivables, one is directly observed at the company’s level – the share of
overdue receivables in the portfolio. The other two are not. The share of total costs associated
with overdue receivables is measured with an interval scale, and the average time of delay is
measured indirectly by the time-structure of delays. With respect to these two variables it was
essential to provide an estimate of the mid-points of the intervals. In order to do so, different
distributions of the variables associated with costs were checked (and fitted) with a simple
procedure oriented on minimizing squares of distances between empirical and hypothetical
distribution. Then it was checked which of the distributions can be assumed the most coherent
according to the λ-statistics from the Kolmogorov-Smirnov test. In the case of both questions
– referring to the cost of payment delays and the average time of delay – the fitted
distributions were only used as a tool in order to select the average value for the intervals
among the competing few. Applying of the average of intervals would be inappropriate as
distributions are likely to be highly skewed.
The term structure, under assumption concerning the distribution, provides additional
information on the average time of delay of overdue receivables for different answer
categories. One of the intervals in the question concerning the term-structure of delays (over
12 months) is open-ended which discards the common procedure to take the mid-point of the
interval. However, with respect to payment delays, it was assumed that after a time required
to run the whole contract enforcing procedure (World Bank, 2009-2012) the delayed payment
should be either considered lost or already regained. In order to check for the plausible
distributions underlying the data, different alternatives were checked and fitted: Continuous
Uniform with data-implied cut-point, Normal, Log-normal, Weibull (incl. exponential) and
Beta. These set comprises the most common continuous uniform assumption and its basic
alternatives which can be used for calculation of the mid-points of intervals.
The distribution of delays in different periods and the values of the λ-Kolmogorov
statistics for the models are presented in Table A.1.
33
Table A.1. Distribution of delays in receivables with respect to industry
Period <3
months
(%)
3 – 6
months
(%)
6 – 12
months
(%)
Over
12
months
(%)
λ –
Continuous
Uniform
λ –
Normal
λ –
Log-
Normal
λ –
Weibull
λ –
Gamma
2009Q1 58.9 16.6 10.9 13.7 13.90 5.57 0.23 0.49 0.65
2009Q2 56.1 18.2 12.7 13.0 10.07 4.03 0.08 0.33 0.44
2009Q3 56.9 17.8 12.2 13.1 11.12 4.45 0.12 0.38 0.50
2009Q4 59.8 16.8 10.4 12.9 15.55 5.82 0.32 0.60 0.78
2010Q1 59.4 17.6 10.9 12.1 14.35 5.12 0.26 0.55 0.70
2010Q2 56.6 17.6 11.2 14.6 12.07 5.34 0.30 0.57 0.71
2010Q3 58.3 17.1 11.6 13.1 12.30 4.79 0.14 0.40 0.54
2010Q4 57.9 16.2 11.3 14.7 14.47 6.26 0.19 0.46 0.63
2011Q1 56.2 15.8 12.0 15.9 13.51 6.38 0.06 0.33 0.49
2011Q2 57.2 16.3 10.5 16.0 10.33 4.89 0.26 0.45 0.57
2011Q3 59.3 15.7 11.7 12.9 12.30 4.73 0.00 0.23 0.36
2011Q4 60.2 16.5 11.0 12.2 13.92 4.94 0.15 0.40 0.55
2012Q1 56.8 16.3 11.6 15.0 15.25 6.91 0.17 0.47 0.66
2012Q2 56.6 15.9 12.4 15.1 11.91 5.37 0.01 0.23 0.37
2012Q3 56.0 16.5 11.7 15.8 10.16 4.82 0.14 0.35 0.48
2012Q4 59.2 17.7 10.7 12.4 11.22 4.11 0.25 0.48 0.60
Source: Survey on Receivables; own calculations.
The results show that with respect to the 5% significance criterion Log-normal, Weibull
and Gamma distributions could not have been rejected. However, the lowest values of λ-
statistics were obtained for log-normal distribution and it was adopted for the purpose of
calculation of the average time of delay at the company level. Additionally, according to the
World Bank’s Doing Business Reports (World Bank, 2009-2012), the time required to
enforce contracts in Poland was in all years was equal to 830 days, which comprises ca. 27.3
months. This value was used as a cut-off point for the estimation of the average delay in the
group of payment delays overdue by more than 12 months. Log-normal distribution is
characterized by rather long-tail which admits rather large share of long-delayed payments.
Additionally, there is another property of log-normal distribution that is counterintuitive at
first sight, namely: the probability density function is increasing up to the value of the mean
of the normal distribution underlying the analysed log-normal distribution. It is however only
seemingly counterintuitive, as the large share of overdue receivables is not perceived as
34
delayed up to certain time of delay, so in order to become aware of the fact that some
receivables in the company are overdue, some time has to elapse.
The value of average time of delay was assessed for each respondent separately
according to the formula:
∑ ,
where represents the average time of delay for the i-th company,
represents for the i-th company the share of overdue receivables delayed by: “0 to 3 months”
for k=1, “3 to 6 months” for k=2, “6 to 12 months” for k=3 and “over 12 months” for k=4;
finally is branch specific value of the average time of delay of overdue receivables
delayed by “0 to 3 months” for k=1, “3 to 6 months” for k=2, “6 to 12 months” for k=3 and
“over 12 months” for k=4.
The variable is calculated with respect to the following scheme. For a respondent
answering that the share of overdue receivables delayed between a and b months, the
expected value of average delay for these receivables is equal to: |
∫
, where is the density function obtained for the given period, and
is the cumulative distribution function for this distribution. As the log-normal
distribution has a finite expected value it is possible to assess average time of delay for
payments overdue by more than 12 months. For these respondents the average delay of
payments overdue by over 12 months was calculated according to the formula
|
∫
.
With respect to the average costs associated with payment delays a similar procedure
was applied and also the plausible distributions underlying the data, different alternatives
were checked and fitted: Continuous Uniform with data-implied cut-point, Normal, Log-
normal, Weibull (incl. exponential) and Gamma. The results are presented in Table A.2.
With respect to the distribution underlying the costs of payment delays only for the log-
normal distribution for all of the periods the null hypothesis was not rejected and that’s why it
was adopted. When calculating the average cost for the interval “above 50% of all costs” the
cut-off value at the level of 100% was used. With respect to this area for each respondent only
one value was imputed and it was corresponding to the average level of costs for the selected
answer category in the question referring to the level of costs associated with payment delays.
35
Table A.2. Distribution of costs
Period Structure of costs (0%; 1%;2%;3%;4%;5-
9%;10-14%;15-19%;20-29%;30-49%;50+%)
λ –
Conti-
nuous
Uniform
λ –
Normal
λ – Log-
Normal
λ –
Weibull
λ –
Gamma
2009Q1 (3.6%;17.0%;10.6%;8.0%;8.7%;22.7%;
12.4%;6.8%;6.2%;2.6%;1.5%) 23.11 4.19 1.24 1.94 2.02
2009Q2 (3.0%;15.4%;8.9%;9.3%;8.6%;22.5%;
13.5%;7.1%;5.2%;3.8%;2.6%) 17.69 2.91 0.97 1.41 1.43
2009Q3 (2.9%;14.1%;12.4%;9.5%;8.2%;21.0%;
14.7%;7.0%;4.8%;3.1%;2.3%) 19.62 3.04 1.16 1.62 1.63
2009Q4 (2.5%;17.5%;10.1%;10.1%;7.9%;21.5%;
13.7%;6.6%;5.7%;2.8%;1.6%) 25.49 4.35 1.26 2.53 2.58
2010Q1 (3.0%;15.4%;12.7%;9.3%;9.2%;20.2%;
14.1%;5.8%;5.6%;3.1%;1.5%) 24.24 4.06 1.29 2.22 2.24
2010Q2 (3.0%;13.9%;11.0%;9.4%;9.0%;20.6%;
14.4%;7.2%;6.8%;2.5%;2.1%) 20.65 3.37 1.25 1.61 1.63
2010Q3 (1.7%;15.8%;11.2%;8.9%;9.0%;21.8%;
13.6%;6.6%;6.9%;2.8%;1.7%) 20.54 3.45 0.94 2.10 2.10
2010Q4 (1.7%;16.4%;11.6%;7.9%;9.8%;21.8%;
13.9%;6.5%;6.4%;2.4%;1.6%) 24.59 3.81 1.15 2.47 2.47
2011Q1 (3.6%;18.6%;10.8%;8.5%;8.4%;21.1%;
11.8%;6.2%;7.0%;2.4%;1.5%) 23.73 4.97 1.16 2.46 2.58
2011Q2 (2.1%;15.7%;11.1%;9.5%;9.9%;20.9%;
14.2%;6.7%;5.9%;2.9%;1.3%) 17.83 2.77 0.96 1.66 1.65
2011Q3 (3.8%;15.1%;12.9%;9.1%;9.0%;20.9%;
12.3%;6.4%;5.3%;3.0%;2.0%) 20.26 3.92 0.71 1.74 1.78
2011Q4 (2.4%;16.7%;13.1%;10.4%;9.1%;22.2%;
12.5%;4.8%;4.8%;2.9%;1.0%) 24.00 3.77 0.72 2.33 2.27
2012Q1 (2.1%;16.4%;12.2%;10.1%;9.9%;22.6%;
13.6%;5.0%;4.8%;2.1%;1.2%) 28.53 3.82 1.02 2.50 2.41
2012Q2 (3.9%;14.8%;11.8%;8.5%;8.4%;22.6%;
12.9%;7.4%;5.6%;2.3%;1.7%) 20.83 3.59 0.83 1.46 1.50
2012Q3 (2.1%;16.2%;9.2%;11.0%;8.6%;21.8%;
13.8%;6.0%;6.9%;2.9%;1.5%) 17.98 3.03 0.85 1.69 1.69
2012Q4 (2.1%;13.5%;9.7%;9.0%;10.0%;22.9%;
15.7%;7.7%;4.6%;2.9%;2.0%) 18.64 2.28 1.05 1.24 1.19
Source: Survey on Receivables; own calculations.