RDP 2007-05: Labour Force Participation and Household Debt 5. Estimation Results
June 2007
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Detailed results from the cross-section and panel models for the debt and asset variables are presented in Sections 5.1 and 5.3 respectively. The results from our tests for the endogeneity of debt are discussed in Section 5.2. In general, we find that in both the cross-section and panel models, coefficients on the standard variables that typically enter into labour supply equations have the expected sign and are consistent with other studies.^{[15]} For example, partnered females are less likely to work while the opposite is true for partnered males. Those with a university education are significantly more likely to work, while those with poor health are less likely. Women with young children are significantly less likely to participate in the labour force, reflecting the well-known M-shaped pattern in LFP with peaks at ages 20–24 and 45–54, before and after the key child-rearing ages. For men, these effects are not so apparent.
In line with the literature, the coefficients and marginal effects on participation are smaller and less significant for men than women. This finding is consistent with men's greater attachment to the labour force and higher average participation rate (Killingsworth and Heckman 1986; Pencavel 1986; Birch 2005).^{[16]}
5.1 Cross-section Results
Results from the cross-section probit models are shown in Tables B1 and B2 in Appendix B. Table 3 provides more detailed results for debt and assets; in particular, the marginal effects of debt and assets conditional on strictly positive debt holdings are given. Overall, debt has the expected positive and significant effect on participation. After controlling for the effects of debt, income and demographic characteristics, assets are not found to have a significant effect on participation.
Coefficients |
Median (non-zero mortgage debt) | Selected unit | Marginal effects^{(a)} (percentage points) | |||||
---|---|---|---|---|---|---|---|---|
Women | ||||||||
Owner-occupied mortgage debt outstanding | −3.62×10^{−7} | $98,000 | $10,000 | −3.96×10^{−2} | ||||
Owner-occupied mortgage debt-to-income ratio | 1.66×10^{−5}*** | 1.91 | 0.1 | 1.81×10^{−5}*** | ||||
Debt-servicing ratio | −2.35×10^{−3}*** | 0.22 | 0.1 | 4.73×10^{−1}*** | ||||
Sq root of debt-servicing ratio | 4.05×10^{−1}*** | |||||||
Other debt outstanding | 1.54×10^{−6}*** | $3,000 | $1,000 | 1.69×10^{−2}*** | ||||
Other debt-to-income ratio | 3.63×10^{−5} | 0.08 | 0.1 | 3.97×10^{−5} | ||||
Financial assets | 8.60×10^{−9} | $6,700 | $1,000 | 9.41 x10^{−5} | ||||
Non-financial assets | −1.09×10^{−7} | $212,000 | $10,000 | −1.19×10^{−2} | ||||
Observations | 2,999 | Pseudo R^{2} | 0.35 | |||||
Men | ||||||||
Owner-occupied mortgage debt outstanding | 1.64×10^{−6} | $100,000 | $10,000 | 4.30×10^{−2} | ||||
Owner-occupied mortgage debt-to-income ratio | 9.73×10^{−6} | 3.90 | 0.1 | 2.56×10^{−6} | ||||
Debt-servicing ratio | −5.29×10^{−4}*** | 0.42 | 0.1 | 1.36×10^{−2}*** | ||||
Sq root of debt-servicing ratio | 6.72×10^{−2}*** | |||||||
Other debt outstanding | 1.73×10^{−6} | $4,000 | $1,000 | 4.55×10^{−3} | ||||
Other debt-to-income ratio | 3.02×10^{−6} | 0.15 | 0.1 | 7.95 x10^{−7} | ||||
Financial assets | −2.44×10^{−7} | $6,800 | $1,000 | −6.42×10^{−4} | ||||
Non-financial assets | 1.26×10^{−7} | $198,000 | $10,000 | 3.32×10^{−3} | ||||
Observations | 2,568 | Pseudo R^{2} | 0.48 | |||||
Notes: ***, ** and * represent significance at the 1, 5 and 10 per cent
levels respectively. (a) Marginal effects estimated at the median of strictly positive (or non-zero) owner-occupied mortgage debt, with other characteristics set at samnle medians. See Appendix B. Tables B1 and B2 for full results. |
Most of the effect of owner-occupied mortgage debt is captured by the debt-servicing ratio, with a positive and significant effect on the probability of LFP for both men and women. For men, of all debt variables in the model, only the debt-servicing ratio has a positive and significant effect.
For men and women, the marginal effect of the debt-servicing ratio is positive and significant over the relevant range of the ratio. The marginal effect shown in Table 3 is for an increase in the ratio of 0.1 (from its non-zero median, that is, the median ratio of all strictly positive ratios).^{[17]} For women, this is estimated to increase the probability of participation in the labour force by 0.47 percentage points, all other things being equal and at their median values. For men, it increases the propensity to participate by a much smaller 0.01 percentage points, when considering a man with median characteristics.
The level of owner-occupied mortgage debt does not appear to have a significant effect on the probability of LFP. However, for women, the ratio of owner-occupied mortgage debt to income does have a positive and significant, albeit small, effect on LFP propensities.
For women, the level of other debt is statistically significant. Every $1,000 of additional other debt is associated with a 0.02 percentage point increase in the probability of participation. The ratio of other debt to income is not found to have a significant effect on the probability of LFP. Further analyses of the predicted probabilities are presented in Section 6.
The models have reasonable explanatory power. For women, the pseudo R^{2} is 0.35, and for men it is 0.48. The average predicted probabilities also appear reasonable; for women, the average predicted probability of participation is 72.3 per cent. This is equal to the actual proportion of the sample in the labour force. For men, the average predicted probability is 92.3 per cent and is also equal to the actual proportion of the sample in the labour force.
For discrete choice models, Greene (2003) also suggests a summary measure of predictive ability based on the proportion of the sample for which labour force status is correctly predicted. For women, labour force status is correctly predicted for 82 per cent of the sample, with correct predictions for 92 per cent of those in the labour force and for 59 per cent of those not in the labour force. These results can be compared with that which would be found using a naïve model in which every woman is predicted to be in the labour force. Under a naive model, correct predictions of participation would be made 72 per cent of the time. Thus, the model gives an improvement of 10 percentage points in predictive ability over the uninformed guess.
For men, labour force status is correctly predicted for 95 per cent of the sample overall, with correct predictions for 98 per cent of those in the labour force but only for 50 per cent of those not in the labour force. In comparison to the naive prediction, the model provides an improvement of only 3 percentage points, reflecting the fact that men are more likely to participate. As a result, there is less to gain from modelling their participation decision.
We carried out a number of robustness checks. To account for possible non-linearity in the debt-servicing ratio, we replaced the debt-servicing ratio and its square root with a dummy variable as an indicator of large debt-servicing ratios, and the interaction of this dummy variable with the level of the debt-servicing ratio; qualitatively similar results were found. Results were also similar when each debt variable was winsorised at the 97.5^{th} percentile.^{[18]} Furthermore, when owner-occupied mortgage debt and its ratio to income were omitted, the debt-servicing variables remained significant and the coefficient estimates were broadly similar. Removing the debt-servicing variables yielded a positive but insignificant coefficient on the level of owner-occupied mortgage debt for women, while for men the level became significant at the 10 per cent level.
Domeij and Flodén (2006) argue that ignoring the effects of assets and debts can bias coefficient estimates towards zero. We found that this may be the case. In a model excluding the asset and debt variables, the marginal effects of many of the demographic and income variables appear smaller; the debt and assets are jointly significant when included.
5.2 Testing for the Endogeneity of Debt
As described in Section 3.2, the exogeneity of debt to labour supply can be tested using the two-step instrumental variables approach of Rivers and Vuong (1988). This requires valid instruments for the six debt variables. Valid instruments must be correlated with debt but not with the error in the labour supply equation.
Measures of house prices are used elsewhere in the literature as an instrumental variable (Bottazzi 2004). They are correlated with owner-occupied mortgage debt and repayments but are less likely to be correlated with current LFP. Two sources of house price data are available: self-reported data from HILDA for the price of one's home when purchased, and postcode-matched house price data sourced from Australian Property Monitors (APM) for 1993.^{[19]} For the self-reported data, the assumption of no correlation between the house price and the error in the labour supply equation is less likely to hold for more forward-looking households. However, shocks to LFP and house prices in the years since the house purchase should ensure that house prices are exogenous to current LFP.
Testing for endogeneity is conducted using each of these sources of house price data in turn. In each case, the house price and its square are used as instruments, giving two instruments. The house price as a ratio to household income (excluding individual labour income) provides a third instrument.^{[20]}
Whether or not the house is the first home ever purchased should also influence the level of owner-occupied mortgage debt and repayments – with the mortgage and repayments likely to be higher if it is the first home because first-home buyers are less likely to have accumulated a substantial deposit. Indeed, the data show that those living in their first home ever purchased have larger debts (in levels) than non-first-home buyers. Moreover, whether it is their first home ever purchased or not should not be directly related to LFP. Thus, a categorical variable is used which equals 0 if the home is rented, 1 if the person is a first-home buyer and 2 otherwise.
In a similar manner, the year in which the house was purchased should be directly related to debt and repayments, as a house purchased more recently is likely to have a greater amount of debt outstanding on it. Again, the year of purchase should not be related to current LFP, particularly the further into the past the house was purchased.
Other instruments considered were the initial level of owner-occupied mortgage debt at the start of the loan, the number of credit cards and measures of how much financial risk the individual is willing to take. The first of these was found to offer little additional independent variation beyond that of the house price when purchased. The number of credit cards and the measures of willingness to take financial risk were judged to be invalid as the number of credit cards is likely to be related to LFP just as debt is, while the appetite for risk may be influenced by whether they have a job as well as their job security.
To test for endogeneity, the order condition must be satisfied; the number of instruments must be at least equal to the number of endogenous variables. Since only five instruments are available and there are six potentially endogenous debt variables, subsets of the debt variables were tested for endogeneity while the remaining debt variables were assumed exogenous or omitted. First, one debt variable was assumed endogenous, while the remaining five were assumed exogenous or omitted. Instruments were chosen if they were significant in the reduced-form debt equation (Equation (3)) at the 5 per cent level. When more than one instrument was relevant, overidentifying restrictions were tested using generalised residuals (Gourieroux et al 1987). Next, the exogeneity of relevant pairs of debt variables were tested; owner-occupied mortgage debt and its ratio to income, other debt and its ratio, and debt-servicing ratio with its square root. In this case, two or more instruments needed to be relevant. Similarly, the procedure was repeated for groups of three endogenous debt variables and then four.
The overidentification tests pointed to valid instruments in a large number of cases, although the instruments were generally weaker for owner-occupied mortgage debt to income, other debt to income and the debt-servicing ratio, particularly for men. Potentially, the instruments were weaker for the debt-servicing ratio because those making excess repayments were more likely to be in the labour force. When two or more variables were assumed endogenous, the overidentification test was less likely to suggest valid instruments.
For both men and women, the evidence suggests that debt is exogenous to labour supply when using either the self-reported data or postcode-matched house price data.^{[21]} That is, it appears that increased indebtedness induces greater participation, while the reverse effect, that greater current participation leads to higher indebtedness, is not found to be statistically significant.^{[22]} A caveat is that this result is conditional on the instrumental variables methodology.^{[23]} In addition, the result may reflect the fact that borrowing decisions associated with large purchases are often re-examined only infrequently and, therefore, that they are largely pre-determined when making current LFP decisions. Also, while our model accounts for the spouse's labour force status, we are essentially modelling the individual. In order to obtain a loan (or increase debt), a bank would examine the circumstances of the household overall, and our model may not adequately capture this.
Overall, since the explanators are generally exogenous, the probit estimates of Section 5.1 are preferred over the less efficient instrumental variables estimates of this section (for brevity, these results are not presented).
5.3 Panel Results
This section details the panel data results, which control for individual heterogeneity but assume that debt can be treated as exogenous. Full results from the panel models are shown in Tables B3 and B4 in Appendix B. Table 4 presents the estimates of the coefficients on owner-occupied mortgage debt and assets using both the random- and fixed-effects estimation methodologies. The random-effects estimates are preferred: they are estimated on the full sample rather than on the subset of those who have changed labour force status at least once during the sample period and, unlike fixed-effects, random-effects allows an examination of the marginal effects and associated predicted probabilities of participation.
Probit random-effects | Logit coefficients | ||||||||
---|---|---|---|---|---|---|---|---|---|
Coefficients | Median^{(a)} | Selected unit | Marginal effects^{(a)} (percentage points) | Random effects | Conditional fixed effects | ||||
Women | |||||||||
Owner-occupied mortgage debt outstanding | 4.87×10^{−7}* | $110,000 | $10,000 | 1.77×10^{−2} | 9.45×10^{−7}** | −2.84×10^{−7} | |||
Owner-occupied mortgage debt-to-income ratio | −2.04×10^{−6} | 2.08 | 0.1 | −7.42×10^{−7} | −4.57×10^{−6} | 1.58×10^{−5} | |||
Debt-servicing ratio | −1.32×10^{−4} | 0.22 | 0.1 | 1.11×10^{−2}*** | −2.49×10^{−4}* | −3.99×10^{−4} | |||
Square root of debt-servicing ratio | 2.92×10^{−2}*** | 5.58×10^{−2}*** | 4.03×10^{−2} | ||||||
Value of owner-occupied home | −9.80×10^{−8} | $210,000 | $10,000 | −3.56×10^{−3} | −1.55×10^{−7} | 3.37×10^{−8} | |||
Observations Number of women | 13,672 3,350 |
13,672 3,350 |
3,375,890 | ||||||
Men | |||||||||
Owner-occupied mortgage debt outstanding | 2.10×10^{−6}*** | $113,000 | $10,000 | 3.76×10^{−3} | 3.99×10^{−6}*** | 3.73×10^{−6}** | |||
Owner-occupied mortgage debt-to-income ratio | 7.62×10^{−6} | 4.30 | 0.1 | 1.37×10^{−7} | 1.25×10^{−5} | 3.53×10^{−5} | |||
Debt-servicing ratio | −2.33×10^{−4}*** | 0.46 | 0.1 | 4.12×10^{−4}*** | −4.22×10^{−4}*** | −9.00×10^{−4} | |||
Square root of debt-servicing ratio | 3.13×10^{−2}*** | 5.94×10^{−2}*** | 7.94×10^{−2} | ||||||
Value of owner-occupied home | 4.07×10^{−7} | $200,000 | $10,000 | 7.31×10^{−4} | 6.67×10^{−7} | 4.73×10^{−7} | |||
Observations Number of men | 11,374 2,822 |
11,374 2,822 |
1,018 253 |
||||||
Notes: ***, ** and * represent significance at the 1, 5 and 10 per cent
levels respectively. (a) Marginal effects estimated at the median of strictly positive (or non-zero) owner-occupied mortgage debt, with other characteristics set at sample medians. See Appendix B, Tables B3 and B4 for full results. |
The random-effects estimates show that owner-occupied mortgage debt has a significant positive effect on the LFP decision (Table 4). The level of owner-occupied mortgage debt is an important influence and its coefficient is highly significant and positive. The debt-servicing ratio also has a significant impact on participation, as in the cross-section results. The value of the owner-occupied home, a measure of housing assets, is not significant. Estimates of the marginal effects are also shown in Table 4. For each of the four owner-occupied mortgage debt variables, the marginal effects are reported according to a reasonable increase in the respective debt variables from their nonzero medians (the exact units are indicated in the table; all other variables, including the value of the owner-occupied home, are set at the sample median).
The marginal effects for the debt-servicing ratio are statistically significant, although small. The effects are smaller than those found in the cross-section model, although a direct comparison is difficult to make as the methodology differs and the non-housing debt and asset variables are not available in the panel. Nonetheless, as was the case for the cross-section results, the marginal effect of the ratio is smaller for men than for women.
For a woman with median characteristics, the marginal effect of an increase in the debt-servicing ratio of 0.1 from the non-zero median of 0.22 is estimated to increase the probability of participation in the labour force by 0.01 percentage points, other things being equal. For a man with median characteristics, an increase of 0.1 in the ratio is estimated to increase the probability of participation by 0.0004 percentage points. Further interpretation of the results is offered in Section 6.
The conditional fixed-effects logit estimates are imprecisely estimated, potentially due to the much smaller sample size. The exception is the level of owner-occupied mortgage debt for men, where a positive and significant effect is found. Although the coefficient on this variable is similar to the random-effects estimate, the Hausman test for the consistency of the random-effects logit favours the fixed-effects logit estimates for both men and women.^{[24]} Nevertheless, for the reasons discussed in Section 3.3, the random-effects estimates are preferred.
The random-effects models fit the data reasonably well. For women, labour force status is correctly predicted for 82 per cent of the sample overall; an improvement of 9 percentage points in comparison with the naive predictor. For men, labour force status is correctly predicted for 95 per cent of the sample overall, representing an improvement of 3 percentage points in comparison with the naive prediction. Also, the average predicted probabilities from the model are close to the actual proportions of those participating. For women, the average predicted probability is around 77 per cent for the random-effects models compared to 73 per cent of the sample that reports being in the labour force. For men, these figures are 94 per cent and 92 per cent respectively.
Some sensitivity tests were undertaken to ascertain whether attrition over the sample period influenced the results. For women, some simple tests suggested by Verbeek and Nijman (1992) imply that attrition over the waves is not having a significant effect on our estimates. For men, the same tests suggest that attrition may have some influence on the results, but results from estimation over a balanced sub-panel were qualitatively similar.
Much of the empirical literature focuses exclusively on home owners' labour supply response to debt. Renters face a down-payment constraint and so are likely to need to work before obtaining a mortgage. Thus, using the sub-sample of home owners, 70 per cent of the total sample in this case, may yield stronger results for the debt coefficients. However, the results (not reported) show that this was not the case; for both the random- and fixed-effects models, the coefficients remained largely unchanged, although for women, the level of owner-occupied mortgage debt became insignificant.
The literature also assumes that partnered women have greater flexibility in their participation decisions, and so their response to changes in debt would be larger than the response of single women. The models were re-estimated using the sample of partnered women. While the debt-servicing ratio coefficients were smaller and became insignificant, the coefficient on owner-occupied mortgage debt increased and retained its significance. Thus, changing the sub-sample to be consistent with other studies made little qualitative difference to the results.
Footnotes
Full results for the cross-section and panel models are available in Tables B1, B2, B3 and B4 in Appendix B. [15]
In addition, due to the large proportion of men with LFP = 1, and the flattening of the probit curve at this upper range, it is not surprising to find smaller effects for men. [16]
For women, an increase of that size corresponds to a movement along the distribution of strictly positive debt-servicing ratios from the median to around the 70^{th} percentile. For men, to induce a similar movement along the distribution, a larger increase in the ratio of 0.4 is needed. [17]
Winsorising involved replacing data above the 97.5^{th} percentile of the distribution with the value at the 97.5^{th} percentile. [18]
The APM data provide median quarterly house and unit prices for suburbs grouped by price deciles for the main capital cities (Sydney, Melbourne, Brisbane, Adelaide, Perth and Canberra). The suburbs are matched to postcode data; the postcode and price data are then matched to the HILDA sample. If postcodes appear in more than one of the price deciles (because the same postcode is often used for neighbouring suburbs), the matched prices were averaged to give one price per postcode. The calendar-year average of the median quarterly house price is used. Because data are only available for the cities listed above, around 40 per cent of the sample is lost when these house price data are used. However, testing suggested that there was no systematic difference between the full sample and the sub-sample of those living in one of these capital cities. [19]
The denominator, household income (excluding individual labour income), should also be exogenous to the individual's current LFP as it is household income excluding the individual's earned income. [20]
Endogeneity tests were also carried out on a sub-sample of younger women (aged 25–35 years) using the self-reported house price data. Young people are more likely to be making joint decisions on debt, LFP and family formation – Del Boca and Lusardi (2003) also separately examine younger women. However, the evidence suggests that debt is also exogenous for the sub-sample of younger women. [21]
Fortin (1993) also found mortgage debt to be exogenous to labour supply for partnered women in Canada. [22]
An alternative approach is to model LFP and indebtedness in a simultaneous equation framework. Del Boca and Lusardi (2003) estimate such a model and find a marginally significant effect of participation on the likelihood of having a mortgage. However, they were able to exploit an exogenous change in the institutional structure of the Italian mortgage market in order to identify the direction of causality, while we have been unable to identify any exogenous variation to use for identification in the Australian case. [23]
A Chamberlain random-effects probit was also estimated (Wooldridge 2002). It assumes that the correlation between the unobserved individual effect and the explanatory variables follows a conditional normal distribution with a linear expectation and constant variance, rather than assuming that they are independent. The Chamberlain model also rejects the traditional random-effects estimates, although for women the debt-servicing ratio retains its significant positive effect on participation, and for men the level of home loan debt outstanding also remains significant and positive. The results are available from the authors on request. [24]