RDP 1999-02: Reservation Wages and the Duration of Unemployment 6. Estimation Results

The results of estimating the relationship between the log of unemployment duration, the log of reservation wages, and other explanatory variables are presented in Tables 3a and 3b. Table 3a presents the results required to discuss the role of the reservation wage and the use of instrumental variable (IV) techniques. Table 3b presents the estimated effects of other control variables. The OLS estimates, which are valid under the assumption that there are no omitted variables and that the reservation wage is not duration dependent, are presented in column 1. The reduced form regression of the log of the reservation wage on the explanatory variables and the instruments, which constitute the first stage of the instrumental variables procedure, are presented in column 2, and the second stage estimation results are presented in column 3.

Section 6.1 tests whether OLS or IV estimates are the most appropriate, and discusses whether the reservation wage contains useful information for explaining unemployment duration. Given evidence that OLS estimates are biased, Section 6.2 discusses the validity of the instruments which are used in the first stage of the IV estimation procedure. The results of the IV estimation are discussed more generally in Section 6.3. Results estimated for males and females separately are presented in Appendix B and are discussed in Section 6.4.

6.1 OLS versus Instrumental Variable Estimation

Hourly reservation wages have the expected sign in the OLS regression and a perverse sign in the IV estimates, although both are insignificant (Table 3a). If there are omitted variables or the reservation wage is duration dependent, the IV estimates will be unbiased, but the OLS estimate of the coefficient on the reservation wage will be biased. Whether this bias is present can be tested formally using a Hausman test.

The null hypothesis of the Hausman test is that the IV and OLS estimates are not statistically different, i.e. that the OLS estimates do not have a statistically significant bias. Under the null hypothesis, neither estimate will be biased although the IV estimates will be inefficient. We test this null hypothesis by estimating the log duration equation (Equation 6), replacing the log reservation wage with the predicted reservation wage and the prediction error from the reduced form reservation wage equation (Equation 8).

Testing the equality of the coefficients μ₁, and μ₂ is equivalent to testing the null hypothesis that the OLS estimates are not biased. The F-statistic for this test is 3.72 which has a p-value of 0.054.

Thus, there is some evidence to suggest that the OLS estimates are upwardly biased, and that IV is the appropriate estimation method. The insignificance of the coefficient on the reservation wage from the IV estimates suggests that although the reservation wage is of critical importance in the theoretical economic model, other factors are more important in explaining unemployment duration empirically. Gorter and Gorter (1993), using data for the Netherlands, also find no effect and attribute this to the fact that the job-offer arrival rate is the binding constraint.

It has been noted by several authors that the longer-term unemployed do not receive many job offers and that they usually accept those offers that they do receive.^[14] The data in the SEUP suggest that very few job offers are rejected by Australian job seekers. In sum, 72 per cent of job offers made between September 1994 and September 1996 were accepted with another 1.6 per cent rejected for another job offer and 3.9 per cent rejected because the potential employee already had a job. Only 7.5 per cent of job offers were rejected because the job was unsuitable.

One possible reason for the low level of job offers, and consequently the insignificance of the reservation wage variable, is that reported reservation wages are sometimes below Australia's award system and minimum safety net pay levels. For these respondents, changes in reservation wages are not likely to have an effect on unemployment duration, and this may bias our results away from finding a significant role for reservation wages. This explanation can be discounted, however, as the reservation wage variable remains insignificant when the unemployment duration regression is estimated for a sample restricted to respondents with reservation wages above $10.00, which is clearly above the minimum.

6.2 Instrument Validity

Another important factor to be considered when assessing the results is the validity of the instruments which have been used. A good instrument needs to be correlated with the variable to be instrumented, the log of the reservation wage, and not significantly correlated with the variable of interest, the log of incomplete unemployment duration. From the reduced form first-stage estimates in Table 3a, it is clear that the log of family income has a more significant correlation with the log of reservation wages than does family size, although family size would be expected to have a lower correlation with the log of unemployment duration a priori.

Given that we have two instruments, the log of family income and family size, and only one variable to be instrumented for, we can test the validity of one instrument assuming the validity of the other. In particular, we test whether the log of family income helps explain the log of unemployment duration in a regression where family size has been used as the instrument for the reservation wage.

When this test is done, the t-statistic on the log of family income is 0.061, which is statistically insignificant.^[15] Thus, the over-identifying restriction that the log of family income is a valid instrument is clearly accepted. The fact that it is also highly correlated with the log of the reservation wage equation makes it a good instrument for our purposes.

6.3 General Estimation Results

6.3.1 Factors affecting the incomplete duration of unemployment

The focus of attention of this analysis is to understand the factors which affect the incomplete duration of unemployment. The estimated effects of variables included to control for the factors which affect whether an acceptable job offer arrives, given the reservation wage, accord with our economic priors. They are also consistent with previous estimates presented by Jones (1988) for the UK, and Miller and Volker (1987) for the youth labour market in Australia. Note that where there are mutually exclusive and exhaustive sets of dummy variables, one category has been omitted, and the coefficients should be interpreted as the effect of having the given characteristic relative to having the omitted characteristic. These omitted categories have been included in parentheses in Table 3b.

Unemployment durations for more educated individuals are relatively low, and this is reflected in the results. The duration of unemployment for job seekers who have a degree or diploma is significantly lower than it is for those who did not complete high school. Vocational qualifications also tend to reduce unemployment duration, although this effect is not significant. The results suggest that the unemployment duration experienced by those who completed high school and did not obtain further qualifications is not noticeably different from those who did not complete high school.

Personal characteristics may also affect the probability of receiving a job offer if they are used as a screening device by potential employers or if these characteristics capture search intensity. Older workers clearly experience longer durations of unemployment, whereas other characteristics such as gender, English language proficiency and marital status appear to have little independent effect on unemployment duration.

Previous work experience is also an indicator of the desirability of job seekers to potential employers. Those with no previous work experience do tend to have longer unemployment duration, although this is not a statistically robust result with the marginal significance and the point estimate depending on the estimation method employed. Similarly, higher previous hourly pay, which is likely to capture unmeasured features of previous work experience or individual ability, decreases unemployment duration, although the relationship is again not robust. Those who previously worked in more highly paid jobs are likely to have skills and experience that are relatively attractive to potential employers.

Job seekers who previously worked in the manufacturing industry experience significantly longer durations of unemployment. This appears to suggest that a lack of labour mobility is hampering the employment prospects of those who worked in industries subject to significant structural change. A somewhat more surprising result is that more skilled occupations, in particular managers and professionals, experience longer durations of unemployment than job seekers in low-skilled occupations. At first, this would appear to be difficult to reconcile with the fact that structural change has favoured skilled labour.

One possibility is that education and previous hourly wages capture the skill differentials between job seekers, and that the occupation variables are capturing adverse selection; unemployed individuals in an occupation with low unemployment rates tend to be of poor quality relative to their peers. As such, their unemployment is an important signal of their quality. This is in contrast to occupations with high unemployment rates where the quality of unemployed workers may not be very different to the quality of employed workers.

This result may also indicate a lack of willingness by those who were previously managers or professionals to accept work in a different area. This would be the case if managers and professionals have more occupation-specific human capital and are willing to search longer for jobs which match these skills than other unemployed people whose skills are more generic. This suggests the importance of non-wage characteristics of job offers.

Another possibility is that managers and professionals from declining industries such as manufacturing have skills specific to that industry and have difficulty finding another job. We have attempted to control for this by including a interaction variable which indicates if the job seeker was previously employed as a manager or a professional in the manufacturing industry. This variable is significantly negative, suggesting that this explanation does not have support in the data.

People who left their last job because it was temporary or seasonal have significantly lower durations of unemployment than those who were retrenched or were working for a firm which went bankrupt. Job seekers who left their jobs voluntarily because their conditions of work were unsatisfactory also experience lower durations of unemployment, although this is not statistically significant. This result supports the idea that potential employers use a job-seeker's reason for leaving last job as a screening device (and that leaving because work conditions were unsatisfactory is not deemed to be a bad signal).

However, it could also be taken to indicate that the reason for leaving the last job also measures the search effectiveness and/or preferences of the individual. This is supported by the result that people who left their jobs due to ill health or for child care reasons experience much longer durations of unemployment. While the results are not shown, it is also interesting to note that ill health and child care reasons for leaving employment are more important explanators of unemployment duration for the group of people who did not report a reservation wage. This may be another indication that for some groups, considerations other than the hourly wage are a more important measure of the acceptability of job offers.

The results presented in Table 3b also indicate that the local environment does not have a strong effect on the unemployment duration of job seekers, although this must be qualified to some extent by the lack of information about the state of residence.

Indicators of the impact of financial factors on search effectiveness are highly significant. Eligibility for unemployment benefits increases the duration of unemployment significantly. However, the construction of benefit eligibility implies that ineligibility arises either from the means test or because individuals are only short-term unemployed, and therefore are likely to possess relatively more skills than the long-term unemployed.^[16] This raises some question as to whether the actual effect being captured is one of search intensity or of worker quality.

Higher housing costs are associated with significantly lower durations of unemployment. As argued earlier, this is likely to capture the effect of financial responsibilities on the degree of search effort and consequently on the probability of receiving and accepting a job offer. The result may also indicate that housing costs are correlated with skills and ability, although we believe that we have adequately controlled for this more directly through education variables and previous hourly pay.

6.3.2 Factors affecting the reservation wage

In general, the most important explanators for the reservation wage are work experience variables. Unsurprisingly, the reservation wage of individuals who have previously worked is positively correlated with the previous hourly wage. Also, individuals from more skilled professions have higher reservation wages than low-skilled workers. The highest premium appears to exist for advanced clerical workers. Perhaps more puzzling is that individuals with no previous work experience have higher reservation wages. This may indicate that these individuals have had less experience with the labour market and therefore do not assess their value to employers correctly.

Individuals from ‘other urban areas’, that is, outside capital cities, do appear to have significantly lower reservation wages, as do individuals who have English as their first language. Older individuals have higher reservation wages, which may reflect the greater degree of experience these individuals are likely to have on average. It is also interesting to note that there are several variables which are important for explaining unemployment duration which do not appear in the reduced form reservation wage equation. In particular the variables included to capture financial search incentives, eligibility for unemployment benefits and housing costs, are not significant, although the signs of the point estimates are opposite to what would be expected.

6.4 Estimation Results by Gender

Although the dummy variable for gender which is included in Table 3b is not significant, it is possible that different characteristics influence the outcomes of males and females differently. To this end we have estimated the factors which affect the duration of unemployment and the reservation wages of males and females separately. The results are presented in Appendix B.

The log of family income significantly affects the reservation wages of both genders, although it is interesting that the point estimate of this effect is larger for females. Having obtained a degree or diploma significantly increases the reservation wages reported by males, but does not directly affect their duration of unemployment. For females, however, degree or diploma qualifications do not affect the reservation wage, but do decrease the duration of unemployment.

Older individuals, male or female, have both higher reservation wages and longer durations of unemployment. The reservation wage effect possibly reflects unobserved experience, although it is difficult to use this interpretation to explain the positive correlation with the duration of unemployment. If unobserved experience also captures a higher level of specialised skills, older individuals may require more compensation for these skills to accept a job offer, but they may also be more specific about which jobs they will apply for, which is consistent with a longer duration of unemployment. English speaking ability does not appear to affect the reservation wages of females, but decreases the reservation wages reported by males.

Previous work experience and marital status are more important factors for determining the unemployment duration of males. This probably reflects the fact that women, especially married women with families, are generally more likely to leave the labour force than are males. The unemployment duration of females, is more dependent on observable measures of quality such as educational attainment than on recent labour-market experience. This may also reflect the fact that females have less continuous labour-market participation. The aggregate result that work experience affects reservation wages is driven by the male respondents in the sample.

Footnotes

Jones (1989) found that 85 per cent of a sample of unemployed in the UK in September 1982 accepted job offers they had received; Holzer (1988) found that 66 per cent of a sample of unemployed male youth in the USA in 1981 had not received any job offers in the previous month; and van den Berg (1990) found that job offers arrived very infrequently for a panel of Dutch men, and that 97 per cent of these offers were accepted. [14]

Other transformations of these instruments were considered. However, the basic result that family income is correlated with the reservation wage and uncorrelated with the log of unemployment duration, making it a good instrument, is not affected. [15]

Short-term unemployed may not be captured by our eligibility measure if they were unemployed in September 1996, but had left unemployment by the third interview, and had not been unemployed long enough in the year to September 1996 to say that their main source of income over the year had been social security. [16]