An Empirical Study into the Determinants of an Individuals Supply of Labour
An Empirical Study into the Determinants of an Individual’s Supply of Labour
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 hours worked for a part-time worker i.e. 4 hours a day, 5 days a week. The distribution of hours are positively skewed but can be said to follow a normal distribution with the majority of the observations within one standard deviation (11.32) of the mean of 30.61 hours.
Table 2: Continuous/Ordinal Variables
From the descriptive statistics of the continuous/ordinal variables it can be read that on average a person in employment is of good health with O-levels as their highest education level. The legal minimum wage set by the government of ₤3.40 for all is not being followed by all firms due to the minimum value of wage being ₤1.60. The modal value of hours is as expected 40 hours or a normal full-time contract. The majority of participants also had zero non income earning such that all income for these individuals was derived from wages and not dividend or rent payments.
Another important consideration is that the maximum number of hours worked is 84 which may be a potential outlier or misreported entry. I will see if this observation causes major disruption to the model and if so omit the observation. However it is still technically feasible that an individual does indeed work 84 hours a week (half the hours of the week) if they are working more than one job so the observation might not be so readily disregarded.
Table 3: Binary Variables
From the descriptive stats of the binary variables I can calculate the percentages of observations for each variable. 67% of individuals are married, 55% of the observations are female etc. Of particular note is the very low percentage of people who are members of a trade union (19%). This suggests that the effect of trade unions upon hours worked may not be as strong as Earle and Pencavel (1990) suggests.
Figure 4: Scatter plot of Hours against Wage
An initial glance of Figure 4 suggests there may be some justification for the backward bending labour supply curve although it is not as distinct as in the literature. There appears to be more evidence of the substitution effect being greater at low levels of wage (w<w*) than the income effect than the evidence of the income effect being greater than the substitution effect at high levels of wage (w>w*) as reported by Fehr and Goette (2005).
Model 1: Original Model estimated using Ordinary Least Squares as outlined in the Model section
Model 2: Model 1 with Married, Trade Union and Health removed as explanatory variables and with White Heteroskedasticity-Consistent Standard Errors & Covariance
Model 3: Model 2 with all male observations removed and Married added as explanatory variable
Model 4: Model 2 with all female observations removed and Married added as explanatory variable
**/* = significant at the 1% / 5% level respectively
T statistics are in parentheses
The initial model regression generated 9 variables and the intercept significant at the 1% level and 2 variables significant at the 5% level. The R2 of 0.3988 suggests a high goodness of fit for panel survey data and a high f-stat of 112.23 indicated joint significance of the variables.
Of the variables significant at the 5% level the variable with the highest magnitude was the dummy variable Male. The model indicates that if a person is male he will on average work 11 hours more than a woman all other factors held constant, a similar result to Linda et al. (1990). The next highest magnitude of statistical importance was the dummy variable Permanent. The model calculated all other factors held constant that a person would work on average 3.88 hours more in a permanent job than a temporary job. Also of note is that even though non income earnings are significant at the 1% level the magnitude of the effect is very marginal (-0.0005) suggesting it is not a major consideration on average as to the number of hours worked.
Surprisingly the sign of satisfy is negative when the expected sign was positive. This may suggest a degree of Endogeneity within the satisfy explanatory variable. Instead of an individual choosing to work more hours due to being satisfied in their occupation satisfaction is derived from not having to work too many hours. This may lead to problems in the specification of the model.
Redundant Variable Test (Model 1)
The explanatory variables of Married, Trade Union and Health status were not individually significant at the 10 % level for Model 1. Membership of a trade union could be insignificant due to reduced membership and power of trade unions as mentioned previously. The insignificance of Health could be due to it being a normative question whereas Married is only significant for females as studied later. A redundant variable test was therefore carried out to test for collective insignificance. The low f statistic confirms they are jointly insignificant and as such were omitted from Model 2.
Heteroskedacity Test (Model 1)
Due to the concentration of observations around certain categories in the dependent variable hours worked I felt that heteroskedacity of the error term may be an issue within the model. I used the White Heteroskedacity Test of which the null hypothesis is that the error term is homoskedastic. Due to the p-value of the f statistic being less than 0.01 I had to reject the null hypothesis and accept the error term was heteroskedastic in nature. This is a problem which had to be adjusted for otherwise OLS would no longer be BLUE as it would lose efficiency and give incorrect standard errors. To adjust for this each subsequent model was run with White Heteroskedasticity-Consistent Standard Errors & Covariance.
Model 2 was based on the following equation.
The regression on this model generated 9 variables and the intercept significant at the 1% level and 2 variables significant at the 5% level therefore all variables were statistically significant. The R2 of 0.3977 suggests a high goodness of fit for panel survey data and a high f-stat of 112.23 indicated joint significance of the variables. Due to the white adjustment in the OLS regression I was able to undertake statistical inference with more confidence. The co-efficients of model 2 were of similar magnitude to model 1 except the Child12 variable exerted a marginally stronger negative effect on hours worked (-3.5→-3.8).
Multicollinearity Test (Model 2)
Checking for multicollinearity in Model 2 I used the condition that if any explanatory variable showed correlation of greater than 0.8 with another explanatory variable then this was evidence of multicollinearity. As can be seen from the tabulation of correlations this only occurs between age and agesq and between wage and wagesq which is to be expected. Hence I can reject the hypothesis that multicollinearity exists in the model.
Specification Test (Model 2)
To check for misspecification in the model I used the Ramsey Reset test which runs a regression with the dependent variable included in the model at incremental powers. 3 fitted terms were used to test for misspecification. The null hypothesis of the Ramsey Reset test is that the model is correctly specified. Due to the p-value of the f statistic being less than 0.01 the null hypothesis of correct specification had to be rejected and I had to accept that alternate hypothesis that Model 2 was incorrectly specified.
Unfortunately a flaw of the Ramsey Reset test is that it cannot specify how the model is misspecified. As mentioned previously it may be due to the Endogeneity of the satisfy variable, the variables in the current model being in incorrect form or because important variables have been omitted. Logging the wage variables and including other explanatory variables did not improve the Ramsey RESET results hence I was unable to correctly specify the model according to the test.
Turning Points (Model 2)
Using the co-efficients of wage and wagesq I was able to calculate the turning point of the backward bending labour supply curve or in other words calculate the value of w*. My model suggests that for the average individual the value of w* is £12.66 and this is the point where the income effect of a wage rise is larger than the substitution effect.
For an individual working 40 hours a week this suggests a weekly income of £506.40. I also chose to calculate where the turning point for age would be with the model indicating that a person works the highest amount of hours age 30 and then begins to decline. This can be accounted for due to this being the age when individuals maybe thinking of having children.
Models 3 and 4 were based on the following equation
I decided to re-add Married into Models 3 and 4 to see if it had an effect on either male or female observations as literature suggested that it would have a negative effect on females.
Both Model 3 and Model 4 saw a dramatically reduced goodness of fit when compared with the sample as a whole as measured by the R2 (0.1802 and 0.1680 respectively) but for the female model the R2 is similar to previous studies of female labour supply. The f statistic for both models however still suggested joint significance of the variables.
The major indicators in Model 3 with only female observations is that the Child12 variable now had the highest magnitude with on average and other factors held constant a female having children under 12 caused them to work 5.83 hours less a similar conclusion to Grant et. al (1990). Also the married variable became significant at the 5% level for females suggesting when a woman became married she on average, all other factors held constant worked fewer hours. Education became insignificant in the female only sample suggesting that this does not affect a woman’s choice in hours worked.
The major observation in Model 4 with only male observations is just how few of the explanatory variables are now significant. A man’s age and lack of education still has a positive effect upon how much he works as reported by (Keane and Wolpin, 1997) but Married, Child12 and Promotion opportunities are all insignificant for men. Hence a man’s labour supply is influenced by fewer factors than a woman’s.
Turning Points (Model 3) Turning Point (Model 4)
The turning points for Model 3 suggested that compared to the sample as a whole w* was marginally higher and the age at which hours worked began to decreased was 26. This in comparison to the male only sample where the backward bending supply curve does not hold for men as wagesq became statistically insignificant. The agesq variable was still significant and generated a turning point of 42. This suggests that women on average begin to start working fewer hours earlier in life than men, leading to the conclusion in the family unit a man is still seen as the major income earner.
Wage Elasticity (Model 3) Wage Elasticity (Model 4)
Using the mean values for wage rate and hours worked calculated in the descriptive statistics I then calculated an estimate of women’s and men’s respective wage elasticities at this value. The conclusion reached is that both women’s and men’s wage elasticities are quite wage inelastic with a woman’s wage elasticity being slightly more elastic than a man’s.
My analysis has brought me to the conclusion that the backward bending supply curve holds for female workers but not for male workers. This is not surprising as females tend to have more choice as to working more/less hours as males are still typically seen as the major breadwinner in households so their choice to work more or less hours is severely restricted. Thus a woman’s wage elasticity will tend to be more elastic than a man’s.
Unfortunately due to the limited nature of the dataset I was unable to give a full analysis of the labour market. An individual’s supply curve reflects an individual’s desired hours of work, whereas the labour demand curve of firms represents the offered hours. Hence there may be divergence between the number of hours an individual is willing to work and the number of hours they are offered to work. This is demonstrated in Figure 4.
Figure 4: Offered/Wanted Hours Divergence
This is due to the inherent inflexibilities of the labour market. Many firms only offer full time contracts and part time contracts with little flexibility to work more or less hours. Overtime hours are an example whereby an individual wishes to work more hours than they are initially contracted. A useful question to be added to the BHPS dataset therefore could be “No of hours willing to work” to give a truer reflection of an individual’s labour supply.
An alternative investigation of number of hours worked can be achieved by recoding those in full time and part-time employment in terms of a binary dependent variable and running a regression using the Probit or Logit methods. This may eliminate the mis-specification suffered by the OLS model used in this study. A more correct wage variable might have also calculated using the marginal tax rate a person faces as this would be a more accurate reflection of the wage incentive to work.
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Model 1 E-views Output
Model 2 E-views Output
Model 3 E-views Output
Model 4 E-views Output
SPSS Cumulative Frequency of No of Hours
No. of hours normally worked per week
Assumptions of OLS
- Model is Linear:
- Expected value of Error term is 0:
- Explanatory variables are independent of the error term:
- Variance is constant at :
- Error terms are independent:
- Error term is normally distributed: