An Empirical Study into the Determinants of an Individuals Supply of Labour

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EC20018                16/12/07        

An Empirical Study into the Determinants of an Individual’s Supply of Labour

James Allen


Why does a person work the number of hours that they do? This has been a question of much research over many years by labour economists. It is a question which has important policy implications for government as to how much they should tax workers income, how high they should set the minimum wage and whether to impose a maximum working week. The information would also be useful to firms in the interests of setting suitable wages and other working conditions.

I aim to answer the question of the determinants of the number of hours worked by individuals. The data I will use for analysis purposes is a condensed dataset of the survey results of wave 15 of the British Household Panel Survey [BHPS] (2005). This survey is conducted annually amongst over 15,000 individuals by ISER at the University of Essex.


Figure 1: Work-Leisure Trade-Off

In Figure 1 an individual faces a choice in the time they allocate for leisure and work day to day. Individuals are assumed in economics to be utility maximising hence the individual faces a constrained optimisation problem. Indifference curves are points which generate the same utility for the individual and the individual is indifferent between them. The aim of the individual is thus to be on the highest indifference curve because revealed preference theory states this is the highest level of utility for the individual.  However this utility is limited by a budget constraint.

Individuals are constrained by the twenty four hours of a day hence the feasible budget constraint does not extend beyond this point.  The budget constraint also does not intercept the hours axis at twenty four. This is because at zero hours work a person will still receive unemployment benefits along with others from the government amounting to an income of YB. Once the person’s reservation wage wR had been met they begin to move along the budget constraint substituting leisure for work. Work is by definition a Giffen good, as the price of work (wage) increases people will consume more but when income rises and people become richer consumption will fall.

The optimum level of work and leisure time initially in this diagram for the individual is point A where the indifference curve I0 lies tangent to the budget constraint. Suppose the wage rate were to rise (w→w1). This would cause the budget constraint to pivot outwards and the individual would be at a higher indifference curve I1. By theoretically taking back the new budget constraint to form a tangency with the original indifference curve I0, the substitution effect (1→2) and the income effect (2→3) can be identified. At each point an indifference curve lies tangent to the budget constraint faced by the individual, the preferred trade-off between leisure and work at that wage level is revealed. By mapping the tangency points over different income levels the individual’s wage-leisure curve is revealed.

Figure 2: Individual’s Backward Bending Labour Supply Curve

Using this wage leisure curve we can derive the individual’s supply curve LS as seen in Figure 2

At point w* the positive income effect is equal to the negative substitution effect. At this point the individual’s supply of labour curve begins to bends backwards. The individual chooses to work less hours the higher the wage rate becomes. Any point below w* the negative substitution effects outweighs the positive income effect. Any point above w* the positive income effect outweighs the negative substitution effect.

This theory will aid me in the construction of the model. I will thus include a wage squared variable to see if this perceived relationship is supported by empirical evidence. Fehr and Goette (2005) reported that at lower wage levels there is a positive relationship between wage and hours supplied.

Although I believe wage to be the most important determinant of labour supply I will investigate other factors previous studies have found to be significant. Earle and Pencavel (1990) suggested a negative relationship between trade union power and the number of hours people worked due to unionised workers having a greater sense of job security. Grant et al. (1990) calculated on average a 9.2 hour difference between men and women in hours worked and that children contributed to women working less hours but not men. Keane and Wolpin (1997) identified that hours supplied were positively related with a man’s age, along with his education level.


My initial regression was estimated using the Ordinary Least Squares [OLS] method due to my dependent variable being continuous and OLS being the Best Linear Unbiased Estimator (BLUE). An alternative model would have been the Tobit model which would have censored the dependent variable at values greater than 0. However because I omitted all of the 0 values I felt this technique was now inappropriate. The initial equation estimated is shown below withrepresenting the random error term generated by the OLS regression.

My model will include the necessary variables to test the backward bending individual labour supply curve, wage and wage squared. Job characteristics of an individual’s employment i.e. whether the job was permanent, promotion opportunities, level of job satisfaction and trade union membership are included.  The environmental factors of an individual relevant to their labour supply i.e. their gender, marital status, age, age squared, level of education and whether an individual has children under 12 are included. The perceived incentive to work more i.e. good health and the perceived disincentive to work more i.e. non income earnings will also be tested for significance.


After deleting all inapplicables a population of 2384 individuals remained from the dataset. I decided from the outset to eliminate any observations which had expected hours worked as zero or inapplicable. This effectively eliminated anyone who wasn’t in paid employment. This was done as otherwise certain variables such as job satisfaction; wage and promotion opportunities would have been unable to be included in the model. However this did lead to sample selection bias and the running of a truncated regression model. Therefore the co-efficient estimates and t statistics generated by OLS can only be interpreted in the context of the currently employed and not for potential entrants into the labour market (the job-seeking unemployed).

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Table 1: Variable Descriptions

Figure 3: Distribution of Hours Worked

Using data of the frequencies of observations for the dependent variable I produced a distribution of the number of hours worked. As can be seen from figure 3 there are many observations in the 37-40 hours category. This can be explained due to the prevalence of full time workers i.e. 8 hours a day, 5 days a week. There is also a large spike of observations around the 20 hour mark. This again can be explained due to it being approximately the number of ...

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