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. Background 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 (wi?? 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 (1i?? 2) and the income effect (2i?? 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 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. Model
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. Data 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). 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 i?? 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 i?? 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. Conclusion 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.