Jerzy Witold Wisniewski

English

Research Papers in Economics

© Copyright by The Nicolaus Copernicus University Scientific Publishing House
DYNAMIC ECONOMETRIC MODELS 
Vol. 8 – Nicolaus Copernicus University – Toruń – 2008 
Jerzy Witold Wiśniewski 
Nicolaus Copernicus University in Toruń 
Econometric Modeling of Monthly Liquidity  
of Small Enterprise 
1. Introduction 
  The central problem of small enterprise is to gain the money supply required 
to meet obligations on time. The lack of sufficient information in a firm causes 
that the financial liquidity plays a particular role in small enterprise. The eco-
nomic activity in small enterprise is usually self-founded; a bank credit is rarely 
taken out. During the whole transformation period a small enterpise was facing 
with the prospect of refusing the credit by a bank. These credits were meant as a 
liquidity bufor (or counterbalancing). Therefore, the financial liquidity of small 
enterprise
1 depends on its ability to sale and collect payment  for sold commodi-
ties and services. The cash deficit is rarly filled with credit. Usually it is filled 
with own resources of firm’s owner amongst others the  money surpluses cumu-
lated as an effect of periodic overliquidity. In this paper the attention is concen-
trated on monthly short-run liquidity of small enterprise. 
2. Simple Method of Measurement the Financial Liquidity of Small 
Enterprise  
  The variety of financial liquidity measures of enterprise does not mean that 
there are always possibilities to apply them, especially in micro-enterprise. The 
main difficulty is the lack of appropriate statistical information. To keep the ac-
counts (so called simplified accounting) is not complicated. However, it is paid 
                                                 
1 The registers of obligations taking into account the maturity dates are very rarely 
kept in small enterprise. The more important role play the registers of liabilities, espe-
cially in gathering financial resources required to lead economic activity. See 
Wiśniewska, Wiśniewski (2007). © Copyright by The Nicolaus Copernicus University Scientific Publishing House
Jerzy Witold Wiśniewski  96
with the lack of important information which could enable the precise diagnosis 
of financial standing and rationally evaluate the future. 
  The collected information about an income and final production gives the 
many benefits to the owner. This enables to compose the very general evalua-
tion of financial liquidity. The comparison of cash (collected payment) with the 
value of final production
2 gives the approximation of financial liquidity. 
 Let  pien denote the value of cash inflow and prod – the value of final pro-
duction. The comparison of these variables enables the evaluation of the finan-
cial liquidity of enterprise. The way of comparison between pien variable and 
prod variable should be considered. 
         First possibility is to compare the current values of cash inflow to the val-
ues of final production
3. If pient ≥ prodt (t = 1,...,n), then the enterprise will own 
sufficient cash resources to meet its obligations in period t. If pient<prodt , then 
it may indicate the lack of sufficient cash resources. It is worth mentioning, that 
the owner is usually able to gather sufficient resources coming from the periods 
when cash surpluses occurred. These surpluses are usually used to meet current 
obligations. Therefore it is seemed that the comparison of cash resources cumu-
lated in given subperiods of each year to cumulated final production is better 
solution.  
         As a result two measures of the financial liquidity of micro-firm will be 
applied. First one is the difference between the cumulated monthly cash inflow 
and cumulated final production
4:  
t t t prod cum pien cum plyn . . − =  (1) 
where:  
, 1 . . t t t pien pien cum pien cum + = − in year t
*, 
, 1 . . t t t prod prod cum prod cum + = − in year t
*, 
(t
* = 1, ..., 11; t = 2,...,12) and  1 1 , 1 1 . , . prod prod cum pien pien cum = =  
         The alternative measure of financial liquidity is the relative measure of li-
quidity calculated as follows: 
). / ( * 100 t t t prod plyn plproc =  (2) 
                                                 
2 Values of final production captures all liabilities of the enterprise and elements not 
creating liabilities, such as depreciation costs and profit.  
3 See Wiśniewska , Wiśniewski (2007). 
4 The use of cumulated values results from the assumption that the owner of small 
enterprise is cautious. He gathers resources in periods of financial surpluses to cover the 
deficit in periods of decreased cash inflow. The owner who does not accumulate finan-
cial resources is usually not able to keep a company in conditions of strong competition. 
Symbol t* denotes the number of a year, symbol t –  the number of month in year t*. © Copyright by The Nicolaus Copernicus University Scientific Publishing House
Econometric Modeling of Monthly Liquidity of Small Enterprise  97
The plproct variable is expressed in percentages. It informs how many percen-
tages of final production in month t determine the cumulated quarterly financial 
liquidity of enterprise. 
3. Empirical Description of the Financial Liquidity of Small Enter-
prise 
  The monthly financial liquidity of production enterprise was carried out 
from January 1996 to December 2006. The figures 1 and 2 depict the time series 
of plynt and plproct. The substantial seasonal fluctuations of cumulated liquidity 
and relative liquidity can be observed. However, the amplitude of seasonal fluc-
tuations is decreasing. This indicates the growing stabilization of the liquidity. 
Moreover, both measures of liquidity are positive in most of periods and con-
siderably greater than zero in many periods. This suggests the good or very 
good financial standing of enterprise. 
 
Figure 1. Cumulated monthly financial liquidity of the GR enterprise in 1996–2006 (in 
thousands of PLN) 
 
Figure 2. Cumulated relative monthly financial liquidity of the GR enterprise in 1996–
2006 (in  %)  
  Figures 3 and 4 present the structure of absolute and relative financial li-
quidity of enterprise in 1996-2006 period. The distribution of absolute liquidity 
is seemed to be normal. The distribution of relative liquidity is distinctly right-
skewed. The average absolute liquidity equals to 106 thousands PLN, but aver-
-80
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0
40
80
120
160
200
240
280
96 97 98 99 00 01 02 03 04 05 06
PLYN
-100
0
100
200
300
400
500
600
700
800
96 97 98 99 00 01 02 03 04 05 06
PLPROC© Copyright by The Nicolaus Copernicus University Scientific Publishing House
Jerzy Witold Wiśniewski  98
age relative liquidity - more than 31%. The financial standing, on average very 
high, can not lead to the passive attitude of owners. It may happen that in sev-
eral, each after another periods the lack of liquidity will be observed (negative 
values), which will result in considerable difficulties in management. As a result 
the threat of bankruptcy of enterprise may occur, if the liquidity values are 
lower than zero. 
 
Figure 3. The structure of cumulated monthly financial liquidity of the GR enterprise in 
1996–2006 (in thousands of PLN)  
 
Figure 4. The structure of cumulated relative monthly financial liquidity of the GR en-
terprise in 1996-2006 (in %) 
  Detailed analysis of liquidity indicates that the measures of liquidity were 
negative in 7 out of 132 months. The worst situation took place in the period 
from September to December 1998, when the financial liquidity measures were 
negative. In the month with the worst financial standing the cumulated cash in-
flow was only about 6.37% lower than the executed final production
5. In 1999-
2006 period the measure of financial liquidity of enterprise was negative only in 
January 2004. 
      At the same time we can observe overliquidity in many periods. In 29 out of 
132 months the surplus  of cumulated cash inflow over cumulated final produc-
tion was visible. This surplus exceeded 50%, but its maximal value was equal to 
                                                 
5 Such small deficiency of cash did not cause the threat to meet obligations, especial-
ly those the most urgent.  
0
4
8
12
16
20
-40 0 40 80 120 160 200 240
Series: PLYN
Sample 1996:01 2006:12
Observations 132
Mean        105.8220
Median    106.9000
Maximum   261.6000
Minimum -65.70000
Std. Dev.    62.05925
Skewness   -0.163547
Kurtosis    3.564897
0
4
8
12
16
20
0 100 200 300 400 500 600 700
Series: PLPROC
Sample 1996:01 2006:12
Observations 132
Mean        140.9761
Median    121.7621
Maximum   696.7456
Minimum -50.43554
Std. Dev.    118.2956
Skewness    1.723375
Kurtosis    7.631321© Copyright by The Nicolaus Copernicus University Scientific Publishing House
Econometric Modeling of Monthly Liquidity of Small Enterprise  99
210%. This means that there were the possibilities of gathering the financial re-
sources in months characterized by overliquidity, which could be used in 
months characterized by negative liquidity. It is worth to mention that the over-
liquidity usually occurred in the first 3 – 5 months of the year with the excep-
tion of two years: 2003 and 2004, when liquidity in the first months of the year 
was striking higher, especially in comparison with the second half of the year. 
It is worth to mention that the dispersion of the financial liquidity measures was 
high, i.e. the standard deviations of both variables representing the liquidity 
were high. However, it was mainly the effect of differentiation between the 
normal liquidity and overliquidity. 
4. Empirical Equations of Financial Liquidity 
  The mechanism of monthly financial liquidity of the enterprise, described 
by  plynt  variable, is presented by the following dynamic econometric model:  
plynt = 48.22 + 0.797 plynt-1 – 0.162 plynt-5 – 0.146 plynt-12 + 0.209 pbrutt-2 + 
                (3.413)   (16.774)              (3.385)             (2.775)                (2.857)                
 
– 0.212 pbrutt-10 + 0.322 pbrutt-12 – 4.744 st – 110.4 wrz – 150.2 pa –98.59 ls + 
   (2.861)                 (3.920)                 (2.784)    (4.502)         (6.095) )    (3.744) 
 
– 1.211 t
*st – 0.344 t
*lu – 0.350 t
*lp + 0.565 t
*wrz + 1.117 t
*pa +  
        (4.621)         (2.556)         (2.581)          (2.174)              (4.199)  
                    + 0.776 t
*ls + u1t ,         ·                             (3) 
                         (2.841) 
 
R1
2 = 0.829, Su1 = 27.278, DW1 = 2.079. 
  In the model we can observe autoregressive dependences and following 
variables: t – time variable, indicating month’s number (t = 1,...,132); pbrutt-2, 
pbrutt-10 and pbrutt-12 – value of income from gross sale with lags respectively: 
2, 10 and 12 months. The seasonal dummies are the separate group of exoge-
nous variables. They take unit value in a given month and zero otherwise. The  
symbols denote respectively: st – January, lu – February, mar – March, kw – 
April, mj – May, cze – June, lp – July, sie – August, wrz – September, pa – Oc-
tober, ls – November
6. 
  From equation (3) results that the autoregression of first order for plynt vari-
able plays the most important role, and the autoregression of 5th and 12th order 
capture the periodicity of this variable. The dominant role for the financial li-
                                                 
6 Residuals in each of empirical equations (3) and (4) are denoted respectively: u1, 
u2; other symbols denote respctively: coefficients of determination – R1
2, R2
2, standard dev-
iation of residuals – Su1, Su2, the Durbin-Watson statistics – DW1, DW2. Below the es-
timates of structural parameters in brackets are t-Student statistics. Calculations and fig-
ures have been done using  EViews 4 package. Both models describe the variability of 
financial liquidity with sufficient accuracy for the purpose of management. In both equ-
ations the autocorrelation of residuals is not observed.   © Copyright by The Nicolaus Copernicus University Scientific Publishing House
Jerzy Witold Wiśniewski  100 
quidity has the income from gross sale being the sum of gross invoices gross in 
a given month, which further is transformed into cash inflow. In the model the 
constant seasonality and changing seasonality (as a result of decreasing ampli-
tude) occur. Actual and fitted values of monthly cumulated financial liquidity 
calculated from equation (3) and residuals are presented in Fig. 5. 
 
Figure 5. Actual and fitted values (calculated from equation (3)) of monthly cumulated 
financial liquidity of the GR enterprise and residuals in 1996–2006 (in thou-
sands of PLN)
7  
 
Figure 6. Actual and fitted values (calculated from equation (4)) values of monthly cu-
mulated relative financial liquidity of the GR enterprise and residuals in 
1996–2006 (in %) 
  The alternative dynamic empirical model describing plproct variable has the 
following form
8: 
  plproct = 3.749 + 0.661 plproct-1 + 120.0 st + 13.71 mar – 0.881 t
*st + u2t     (4) 
                   (1.967)   (15.982)                (11.448)     (2.819)          (6.418) 
 
  R2
2 = 0.771, Su2 = 14.96, DW2 = 2.307.   
  Model (4) describes the mechanism of variability of the relative financial 
liquidity in the enterprise. In this model. the autoregression of first order for 
                                                 
7 The right axis refers to actual and fitted values of monthly cumulated financial li-
quidity of the enterprise, the left axis – to residuals (in Fig. 5 and 6).   
8 Symbols here are identical as in model (3). Compare footnote 6. 
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Residual Actual Fitted
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96 97 98 99 00 01 02 03 04 05 06
Residual Actual Fitted© Copyright by The Nicolaus Copernicus University Scientific Publishing House
Econometric Modeling of Monthly Liquidity of Small Enterprise  101
plproct variable occurs. which reflects the inertia in variable plproct. Moreover. 
very strong. positive seasonality in January and March can be observed. Con-
stant seasonal effect of January is systematically decreased by introducing into 
the model the additional dummies to take into account the changing seasonality. 
Actual and fitted values of monthly cumulated relative financial liquidity of the 
GR enterprise (calculated from equation (4)) and residuals are presented in   
Fig. 6.  
5. Summary 
  The simple method of calculation and modeling the financial liquidity of 
small enterprise shown the sufficient accuracy for the purpose of current man-
agement in the enterprise. The analysis of figures (liquidity measures) already 
enables to evaluate the size of liquidity and the scale of seasonal fluctuations. 
The application of appropriate. not complicated econometric models enables to 
predict the scale of future financial liquidity. This gives the owner the informa-
tion about the expected levels of liquidity. which require proper accumulation 
of financial resources needed to maintain the safety of production process. This  
also indicates the periods. in which the relative easiness in financing the in-
vestment expenditure appears. 
  The presented in paper solutions should be recommended to the owners of 
small enterprises and it should be a task for well educated graduates of eco-
nomic studies. The common application of these solutions may help to increase 
the safety of economic turnover in Poland. 
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Econometric Modeling of Monthly Liquidity of Small Enterprise

http://www.dem.umk.pl/dem/archiwa/v8/12_Wisniewski.pdf

Econometric Modeling of Monthly Liquidity of Small Enterprise

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