Wadim Striełkowski National University of Ireland, Galway1
Adam Wasilewski IERiGZ
Should I work or should I go?
Estimating elasticities of labour supply: a case of Polish rural workers2
Pracować lub nie pracować?
Elastyczność podąży pracy: badania wśród wiejskich przędsiębiorców w Polsce
Abstract
Models explaining the life-cycle of labor supply predict a positive relationship between hours
of work supplied and transitory changes in wages. We tested this prediction using a sample of
wages and hours of Polish rural entrepreneurs from Mazoweckie and Warmia-Mazury provinces,
whose wages are correlated within days but uncorrelated between days.
Wage elasticities computed tend to be positive (although not greater from zero). Our
interpretation of these findings is that Polish rural entrepreneurs: (i) tend to “chase the profits”
whenever possible across days, and (ii) follow the intertemporal substitution rather than set daily
targets.
Abstrakt
Funkcjonujące w ekonomii klasycznej modele podaży pracy przewidują pozytywne
(dodatnie) zależności pomiędzy czasem pracy i przeciętnym wynagrodzeniem. Potwierdzają to
badania przedstawione w niniejszym opracowaniu, które zostały przeprowadzone na podstawie
danych i informacji o przedsiębiorcach prowadzących działalność gospodarczą na obszarach
wiejskich woj. mazowieckiego i warmińsko-mazurskiego.
Z przeprowadzonych badań wynika również, że elastyczność wynagrodzeń jest dodatnia i
kształtuje się na poziomie nieco większym od zera. W konsekwencji nasuwają się następujące
wnioski: (i) wiejscy przędsiębiorcy „gonią sie za zyskiem” kiedy tylko jest to możliwe, oraz (ii)
zamieniają czas pracy z czasem odpoczynku – intertemporalnie.
Keywords: labour supply, SMEs, rural development
Słowa kluczowe: podaż pracy, MSP, rozwój obszarów wiejskich
JEL classification: J22, J23, M13
1
Corresponding author: National University of Ireland, Galway, IDARI project. Tel: + 48505703821, email: Wadim.Strielkowski@centrum.cz, w.strielkowski1@nuigalway.ie
2
This paper has been financed under the IDARI project of the European Commission Fifth Framework
Program, Quality of life and the Management of Living Resources, Key Action 5.
1
1. Introduction
In this paper we would like to focus on testing the daily-targeting hypothesis of
labour supply versus the intertemporal substitution hypothesis in case of rural
entrepreneurs in the selected provinces of Poland.
In spite of some general economic heuristics seeing labour supply as the function
with the intertemporal substitution properties, some evidence suggests that it might not be
so. Especially in the case of entrepreneurs, self-employed businessmen and agricultural
workers labour supply might follow different pattern: it might have negatively significant
wage elasticity. In other words it means that some groups of workers tend to have short
time horizon in their decision about how much labour they will supply and the
unexpected daily increase in daily income might lead them to the decision to quit work
early.
These conclusions lead us to setting up a framework in order to test this causality in
case of small rural entrepreneurs in Poland. We will concentrate on measuring the sign of
elasticity of labour supply and finding evidence for the one of the labour supply
hypothesis mentioned above.
The analysis we are trying to undertake is of a special importance when defining the
success of rural SMEs in Poland. The perception of success, the factors leading to the
success are all dependent on the psychological motives of the entrepreneurs.
2. Intertemporal substitution and the daily targeting
General models of labour supply tend to explain that the number of hours worked
should react positively on the positive wage changes. Workers substitute labour and
leisure intertemporally, i.e. working more when wages are high and consuming more
leisure when its price (the foregone wage) is low (e.g. Lucas, Rapping, 1969).
For the consumer both consumption and leisure are goods. She chooses the point
where the highest indifference curve touches her budget constraint. Usually in the
economic theory it is assumed that leisure is the normal good and its amount should
increase with the increase of income. The increase of wage is usually predicted to cause
the consumer to supply more labour to the market. And finally, after a certain point,
consumer decides to provide less labour and takes advantage of the higher wage.
2
The point that the consumers (or workers) tend to work more when the wages are
high is the commonly accepted logic of Economics, however seems to be quite difficult
to verify.
Various studies report estimated elasticities of the intertemporal substitution tending
to be low and even negative depending the data collected (e.g. Mankiw, Rotemberg and
Summers, 1985; Browning, Deaton, and Irish, 1985; Altonii, 1986). One work by
Camerer et al (1997) studied the daily labour supply decisions of New York City cab
drivers. In that case cab drivers, like many others privately-employed workers tended to
have very short time horizons and were more likely to quit work when if receiving a
sudden, unanticipated increase in daily income.
It has been noted in the research literature that the ideal test of labour supply response
to the wage increase should be in the context in which wages are “transitory”- relatively
constant (correlated) within a day but uncorrelated across days (e.g. MaCurdy, 1981, p.
1074). Such data are available e.g. for rural entrepreneurs in Poland represented by the
sample of small business proprietors. In analogy with Camerer et al (1997) it seems
reasonable to state that rural entrepreneurs deal with wages that fluctuate on a daily basis
(due to demand shocks caused by weather, conventions, holidays and traditions, etc.). On
a busy day the entrepreneurs have a high turnover of customers and earn a higher hourly
wage. This notion seems to be proved by some earlier studies concerning the labour
supply of farmers (see for example Berg, 1961; Orde-Brown, 1946) or self-employed
entrepreneurs (Wales, 1973).
The advantage of studying rural entrepreneurs is that apart from the rules and
conventions imposed by the cooperatives, trade unions and entrepreneurial societies they
are free to choose the number of hours they work each day.
Using the data on number oh hours worked and the average wages per hour, it proves
possible to investigate the relationship between wages and hours worked and thus find
evidence for either the intertemporal substitution or daily-targeting hypothesis. According
to the logic sketched previously an entrepreneur who follows the daily-targeting will keep
the shop (factory, manufactory) open long hours on the day when the customers are
seldom and close it early when the daily target is reached.
3
3. Theoretical considerations: formal model
To see how the econometric model can de derived, let us re-write the equation of a
well-know microeconomic model of labour supply with respect to wage in terms of
wL  w L
Lw L w
elasticities:

ConstU
L wLy
y yL
ei  ec  ei (wL / y)
i.e.
(1)
(2)
The gross wage elasticity of the supply of hours = compensated wage elasticity +
income elasticity of supply of hours (weighted by the ratio between labour and nonlabour income). Thus the estimated regression function takes the form:
ln(L)     ln w  c ln y ...
(3)
Putting aside the considerations of initial income we can write:
ln(L)     ln w  u
(4)
In this case β can be interpreted as elasticity (see e.g. Maddala, 1992). This form
(highly popular in econometric works) is called double-log specification (Verbeek, 2002).
We will calculate simple correlation between ln(L) and ln(w), where ln(L) is log
(hours) and ln(w) is log (wages). In addition, scatter plots of log hours and log wages will
be created to show the sign of the correlation. The negative coefficient β would signalize
hypothesis of negative elasticity of labour supply. Once again, the model can be formally
presented in the following way:
Yln(hours)    1 X ln(wages)  u
(5)
Where Y is log hours, X1 is log wages. β is the parameter to be estimated.  is an
intercept of the model, stating that in case there are no wages paid, there still will be
hours of labour supplied (especially when we analyze the small business proprietor or
rural entrepreneur, it might be so: she or he will still be waiting for customers even if
everything is against him, i.e. weather, temperature, etc.). It takes some time to realize
that the day is bad and it would be reasonable to quit without making any profit.
4. Data collection
The data to verify our hypothesis has been obtained using the surveys in the two
selected provinces of Poland: Mazoweckie and Warmia-Mazury provinces. The data
4
collection proceeded by the means of am administrated questionnaire and has been done
in collaboration with the Institute of Agricultural and Food Economics in Warsaw.
We have questioned 30 randomly-sampled rural entrepreneurs (owners or head
managers of the small and medium enterprises) engaged in retailing, services and food
production. The questions in the survey mainly focused on obtaining the data on the
entrepreneur’s position, number of employees, income structure, position on the market
and financial information regarding hours of work every day and average wages.
The following charts summarize the structure of the surveyed SMEs (type of business
and employment structure):
Chart 1:Surveyed SMEs by type of
business activity
Chart 2:Number of employess in the
surveyed SMEs
>6
Other
10%
Crafts
20%
3-6 empl.
Food
processi
ng
43%
1-3 empl.
family
Retail
trade
27%
0
5
10
15
Emloyees
There were 2 datasets derived from the survey: dataset 1 with average hours of labour
per every week day with average wages per day (210 observations), and dataset 2 with
average earnings per month and average number of hours worked per month (60
observations). The data has been processed using the SPSS software package.
5. Empirical results.
We run regressions for both datasets using the log-linear form described above. Here
is the summary of the main findings:
Sample
Log daily wage
Log monthly wage
Constant
R2
Sample size
Number of surveyed
Table 1: Summary of the model findings
Dataset 1: week days
Dataset 2: monthly average
0.449 (0.032)
0.742 (0.057)
0.201 (Adjusted R2: 0.181)
210
30
0.383 (0.055)
0.773 (0.106)
0.147 (Adjusted R2: 0.118)
60
30
Dependent variable is the log of hours worked (average values). Standard errors are shown in parentheses.
5
It appears that in none of the two cases the beta estimates are negative. The
determination coefficients are 18 and 11 per cent respectively. This gives us grounds to
reject the daily targeting hypothesis; moreover it seems that the determination of labour
supply in the case of Polish rural farmers lies elsewhere but in the average wages.
Below are the scatter plots and histograms for both datasets. We can see that hours
worked and wages have a positive correlation: the increase of wages leads to increase of
hours. Besides the histograms reveal that in both cases the average number of hours is
around eight in the first dataset and around ten in the second.
Chart 3: Scatter plot: Dependent variable LOG_HRS Chart 4: Histogram: Hours of labour
Dataset 1
Dataset 1
20
1.1
1.0
.9
.8
10
LOG_HRS
.7
.6
Std. Dev = 2.07
Mean = 8.5
.5
-.5
0.0
.5
1.0
1.5
2.0
N = 42.00
0
2.5
4.0
6.0
8.0
10.0
12.0
LOG_WG
HOURS
Chart 5: Scatter plot : Dependent variable LOG_HRS
Dataset 2
Chart 6: Histogram: Hours of labour
Dataset 2
14
1.3
12
1.2
10
1.1
8
6
1.0
LOG_HRS
4
.9
Std. Dev = 2.59
2
Mean = 10.5
N = 32.00
0
.8
1.2
1.4
LOG_WG
1.6
1.8
2.0
2.2
2.4
2.6
2.8
6.0
8.0
10.0
12.0
14.0
16.0
18.0
HOURS_1
6. Conclusions
It seems that the hypothesis of negative wage elasticities has no empirical evidence in
the case of Polish rural entrepreneurs. Moreover, the empirical model suggests that there
is a tendency for substituting labour and leisure intertemporally.
6
Entrepreneurs are likely to follow some other consideration than the daily targeting.
There are several explanations for that: firstly, it might be that Polish economy is still
undergoing the transformational processes and the accumulation of capital is still being
the main motive of the businessmen, thus making as much profits as possible might be
the only goal; and secondly, there might be some behavioral and perhaps psychological
concern when the real incomes are concealed and the entrepreneurs are reluctant to
communicate their real wages and labour supply preferences (which might have biased
out model) in fear of e.g. fiscal or governmental control.
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