5.3   Goodness of Fit

The final analysis in this study compares actual observed levels of labour supply with those predicted by the model (see Tables 5 to 7). The probabilities of being in each of the categories of labour supply and the expected hours of labour supply are reported. Using a simulation procedure, drawing 1000 times from the estimated parameter distribution, empirical confidence intervals are constructed around the expected number of hours and the probabilities of being in each of the categories of labour supply (following Van Soest, 1995). This procedure incorporates the uncertainty associated with the parameter estimates as they are reflected in the estimated standard deviations.

From the tables, it is clear that the lowest part-time hours categories are somewhat underpredicted and the category with the highest hours is somewhat overpredicted. It is also clear that the model cannot capture the peak in observed hours at around 40 hours per week. As a result this category is underpredicted, whereas the neighbouring categories are overpredicted. The peak at 40 hours is likely to have been caused by institutional factors, which are not captured by the model.

Fewer labour supply points are allowed for married men given the low number of married men working part-time hours (which could have been caused by factors on both the supply and the demand side). However, given the probability approach used in the simulation of changes, small changes in labour supply can still be captured even in a ten-hour interval labour supply specification. A small change in labour supply means they may, for example, have a small probability of moving from 30 to 40 hours.

From the range in the confidence intervals, it can be seen that most estimates are relatively precise, but the results for sole parents are clearly less accurate than for the other groups. This is not unexpected, when we compare the precision of the estimated parameters between the different groups. Besides the wider range of the expected hours or the probability of being at the different hours points, the mean and median are further from the actually observed values. When the expected hours are calculated at the point estimates the predicted levels are close to the observed values (see Table 4), but when drawing repeatedly from the distribution of parameters, the expected hours are overestimated.

In addition to predicted values for the whole sample, the tables also present expected labour supply for three age categories in the last rows of table 4 to 6 and correspond well to the actual average hours of labour supply in the different age groups. Expected labour supply by subgroup appears to follow the movements in actual hours quite closely. For the smaller subcategories (such as individuals over 50 years old) the confidence intervals become wider, because individual deviations from the predicted values play a larger role, whereas in larger groups these are averaged out.

Comparing the labour supply in the three age groups for the different demographic groups, it is clear that labour supply is highest in the age category of 31 to 50 years for single and married men. Labour supply is only slightly lower for the youngest age group, but individuals over 50 years seem to reduce their labour supply considerably. Not unexpectedly, married women and sole parents behave differently. Married women have a similar level of labour supply when they are younger than 30 and when they are between 31 and 50 years of age. There is also much less decrease in the labour supply of sole parents and married women going from the middle to the older aged group. An altogether different pattern is observed for sole parents, who have the lowest labour supply when they are under 30 and the highest when they are between 31 and 50 years of age, which only reduces slightly for those over 50. This is most likely linked to the age of their children.

The expected effects of certain policy changes could be calculated by computing the expected hours in each of the categories, accounting for the changed tax and benefit rules in the computer programs, and comparing these results to the expected hours using the current tax and benefit rules. Calibration is often used to fix the results in the base case to the observed discretised values, so that the simulation starts from these values. Examples of policy simulations using similar models to the ones described in this paper can be found in Creedy, Kalb and Kew (2003) or Kalb, Kew and Scutella (2003).