勞動供給與福利陷阱

讓我們來談談為什么單身媽媽是政府援助的對象——也就是說還有很大的改進余地。隨著扶貧計劃工作家庭租稅抵減的引進，增加了有孩子的低收入家庭的工作激勵，在一定程度上對貧困兒童家庭起到了緩解作用，也激勵了單親父母，尤其是單身媽媽。它的目的是到2010年，減少一半的貧困兒童，并提高70%的單親父母就業率。工作家庭租稅抵減政策的重點扶持對象是單身母親，因為她們很容易貧困潦倒，也面臨著高額的工作消耗。從1970年到 1990年，已婚母親的就業率急劇增加，而單身母親的就業率卻跌至40%以下,仍然比已婚媽媽的就業率低25%。到1970年，單身媽媽的就業率仍然差不多沒有增加。與其他發達國家相比，英國在2001年經濟合作與發展組織的單身媽媽就業率排名中名列15，是葡萄牙的一半。這表明英國可能有更高比例的單身母親成為勞動力。
 
Labour Supply And The Welfare Trap Economics Essay
 
Talk about WHY single mums are a target – i.e. there is a good deal of room for improvement. WFTC was introduced as anti-poverty scheme which increased incentives to work for low-income families with children, with a particular concentration on alleviating child poverty and incentives for lone parents, especially single mothers. It aimed to halve child poverty and raise employment of lone parents to 70 percent by 2010. WFTC particularly targets single mothers as they have a tendency to be poor and face particularly high working costs13. From 1970-1990 employment in married mothers increased dramatically while the employment rate for single mothers actually fell to just under 40 percent, where it remained stagnant at 25 percent below married mothers; in 1970 the employment rates were roughly the same5. In comparison to other developed countries, the UK ranked 15th out of the OECD countries in 2001 in terms of percentage of single mothers employed4, with a percentage employed half that of Portugal. This suggests there is the potential for a much higher proportion of single mothers in the UK to be in the labour-force. These low employment rates have been responsible for the UK having a high prevalence of child poverty with the greatest proportion of children living in workless households in OECD countries6. According to the Institute for Fiscal Studies there are 2.9 million children1 living in poverty (where household income is less than 60 per cent of the median national income, ￡236 a week). On the introduction of WFTC, the government pledged to reduce this number from 3.4 million in 1999 to 1.7 by 2010/20113. WFTC aims to reduce child poverty through the redistribution of income to low-pay families, and also incentivises those families to increase their income by moving into work or increasing their hours.
 
In Section 1 we concentrated on the effect on unemployment, however this is only one part of the scheme. In order to see the other effects of WFTC we should also consider the change in effort induced, to see how the scheme changes incentives more generally. Effort is a highly important factor as it influences the efficiency of the economy. While welfare schemes may see an improvement in unemployment rates, if the decrease in effort outweighs the increase in effort from lower unemployment then this is equivalent to a decrease in productivity. Meghir and Phillips (2004) suggest that for low-skilled individuals, hours worked is a good proxy for effort13. This will also help to show changes in income.#p#分頁標題#e#
 
Labour Supply and the Welfare Trap
 
Leisure is considered a normal good: when income increases, more will be consumed. As leisure increases, income must decrease so people will make the trade-off between leisure and income in a way that maximises their utility, dependent on their preferences. If the wage rate increases, two effects occur: the substitution effect and the income effect. The substitution effect causes people to consume less leisure as it is now relatively more expensive, while the income effect causes people to consume more leisure as they can now afford more. Which of these two effects dominates depends on individual preferences and the wage rate.
 
Welfare distribution schemes are often susceptible to the welfare trap: participants in the scheme do not move into employment or increase their hours as, due to the incentive structure set by the scheme, their marginal gain is not enough to persuade them to do so. For example, as people increase their work hours, the welfare and other perks they receive decreases, effectively causing a very high marginal tax rate and thus a significant disincentive to work9.
 
AFDC
 
The welfare trap can be shown using the Aid to Families with Dependent Children (AFDC) program which existed in America from 1982 to 1996. AFDC created an income structure for a single parents which is shown in figure X10, [1] . It allowed a welfare grant (G) which remained constant until a certain number of hours (h0) was reached. The grant would then be gradually reduced as hours increased until it reached zero (at h1). During the reduction period, welfare decreased as income increased on a one-to-one basis so income remained constant (Y1), effectively creating a 100 percent marginal tax rate. As a participant in the scheme there is no financial incentive to increase hours beyond this point. Eligibility of AFDC did not depend on hours worked and actually decreased the incentive to be employed directly through an income effect. The figure below also shows the corresponding budget constraint and changes in incentives for two individuals10,1. The original budget constraint is the line abc and the introduction of AFDC causes the budget constraint to shift out to abdec, as the scheme participant will have a higher disposable income for every hour worked.
 
The budget constraint diagram shows two individuals’ preferences suffering from the welfare trap. Individual A can increase their utility by increasing his leisure from LA1 to LA2 with no reduction of their income YA, shown by the shift in the indifference curve from A1 to A2. B can increase their utility by actually moving into unemployment shown by the shift in the indifference curve from B1 to B2, as they now have much higher income (YB2) and can afford to consume more leisure.
 
This framework created two distinctive outcomes: those eligible for welfare were unlikely to work beyond h0 due to the 100 percent marginal tax rate and there was a distinct lack of benefits awarded to a single parent who earns over the modest income of Y1, which was particularly low2,7 (from above). This meant that there were negligible effects on both hours worked and poverty rates, which were reflected in the poverty figures in the US. Between 1988-93 only 20 percent of lone mothers who were on AFDC (continuously for a year) were employed at any point and 50 percent female-headed families were classed as living in poverty8.#p#分頁標題#e#
 
EITC
 
The current US Earning Income Tax Credit (EITC) employs a different system and is a good example of how welfare schemes can create incentives to work. EITC uses a “phase-in” period, increasing welfare as movement out of unemployment occurs and employs a more gradual “phase-out” period11. The “phase-in” period is designed to maximise the substitution effect while minimising the income effect to provide greater incentives to start work. The gradual “phase-out” period is implemented to improve on the 100 percent tax rate seen in AFDC. In figure X the introduction of EITC causes the original budget constraint to shift out to the line abdec. The line bd represents the phase-out period and ec, the phase-in period. The welfare for someone who does not work does not change as their income remains at zero. The substitution effect of a wage increase is strictly negative, but the income effect is strictly positive so these two effects work against each other to produce an ambiguous outcome. Figure X shows two different sets of preferences for two individuals which produce two different outcomes in response to the introduction of the EITC.
 
Individual A consumes leisure LA1 and receives income YA1 before the introduction of EITC. When EITC is launched, A can increase their welfare by working fewer hours and reducing their income slightly as shown by the shift in indifference curves from A1 to A2. In this case the income effect outweighs the substitution effect, showing that EITC has caused a decrease in the number of hours worked. However, for individual B, the substitution effect outweighs the income effect causing both an increase in welfare and hours worked. We can see from figure X that both the shape of the new budget constraint and the preferences of the individual determine the effect of the welfare scheme. Overall the effect of such a scheme is ambiguous depending on the number of individuals with certain preferences. The literature shows that EITC and subsequent expansions had a positive effect on participation in the labour force12. EXPAND. Eissa and Hoynes (1998) found that EITC had the effect of a decrease in hours for married men (by 2 percent) and for married women (by between 0.8 and 6 percent), who are more likely to be at the higher end of hours worked, consistent with the theory. Elissa and Liebman (1996) studied the 1987 expansion of EITC, which would have had much the same effect dependent on hours as shown above, and found an insignificant effect on those already working.
 
FC and WFTC
 
Where the EITC’s key aim was to decrease welfare payments, FC and WFTC’s aim is to decrease poverty through increased welfare and incentives to work12. FC used a slightly different structure using a required number of 16 hours for eligibility, greatly increasing incentives to reach this level of work. There was also an additional childcare credit for those working above 30 hours, creating an extra incentive to reach this target. Diagrammatically, it creates a “corner” on the budget constraint which is more likely to capture more indifference curves. As in EITC, FC still used the “phase-out” period to stop the 100 percent marginal rate of tax. WFTC attempts to improve further on FC, as explained in section 1, by being more generous: it increased credit for children under 10, had a higher income threshold, increased welfare for childcare costs and had lower taper rate in the phase-out period (decreasing from 70 to 55 percent). A comparison of the two schemes’ structures is shown below in figure X9.#p#分頁標題#e#
 
The increased generosity of WTFC scheme changed incentives for people with children depending on their hours worked. The first group are those who are unemployed: WFTC increases an already unambiguously positive incentive to work. From this group we would expect increases in employment. The second group are those who were working below the FC eligible income threshold. For this group, if the individual was already working at the corner solution of 30 hours, it is likely that they will be at the same 30 hour corner solution post-reform. This is because they will lose additional childcare credit if they decrease their hours and are unlikely to increase hours as the marginal tax rate is only decreased slightly. Outside of this corner solution WFTC will have a mixed effect depending on the magnitude of the income and substitution effects.
 
The third group are low-income workers who used to be ineligible but due to the increased income threshold are now eligible. WFTC has an unambiguously negative effect on this group as it increases income and significantly increases their marginal tax rate. Specifically for the WFTC, it increases their previous marginal tax rate from 33 percent to just under 70 percent9. The fourth group are those who work just above the new income threshold who may be incentivised to lower their hours and opt in to the welfare system; WFTC here creates incentives to decrease hours worked. One important note to make is that the lower the taper rate, the lower the marginal tax when on welfare, but the greater the number of people it might affect negatively, who have a relatively high income already. The overall effect on hours worked of such a change in the welfare scheme therefore depend on the relative sizes of the groups and the magnitude of the behavioural responses of the groups10. The effect on these groups are shown below in figure X. The gradient change of the budget constraint reflects the decreased taper rate.
 
Effect on single parents and couples
 
We can use the effects above to determine the likely effect on married couples and lone parents who have children. For unemployed single parents, as discussed above, WFTC will have an unambiguously positive effect. For working single parents, the effect will be very dependent on their current hours worked and preferences as explained above and the end effect on labour will be ambiguous. Therefore there should be an increase in labour-force participation and an ambiguous effect on hours worked for.
 
If we consider a married couple with a single earner, there will be very much the same incentives as a working single parent where incentives depend on current hours worked and preferences; the effect on hours worked will be ambiguous although Blundel et al (1987) suggested that the increase in the participation rate is unlikely to be dominated by decreases in hours worked10. Concentrating now on married couples who are both unemployed, as in the single parents case, there is an unambiguously positive incentive for one of the pair to move into employment and we should expect higher participation in the labour force. If we consider a married couple where there is one main earner, the family income has now increased causing a large income effect for the secondary earner, which creates an incentive to decrease hours or to move out of work altogether. Blundel (2000) showed that WFTC created both a positive income effect and a negative substitution effect, creating a double incentive to reduce hours, for those working under a certain number of hours, dependent on the main earner’s income [2] . The requirement for childcare costs of both couples working over 16 hours could also result in an increase in hours worked10. From married couples with one main working partner, we would expect a decrease in employment rates for the secondary earner and ambiguous effects on hours worked for the main earner. NEED TO CHECK THE ELASTICITIES ARE WHAT YOU THINK.#p#分頁標題#e#
 
Most of the literature suggests that males tend to be highly unresponsive to changes in benefit incentives with regards to working hours with some wage elasticities estimated as low as 0.0614 and -0.0415. On the other hand, male participation rates seem to be influenced heavily by welfare schemes such as WFTC13. Females’ participation rates and working hours tend to be sensitive to welfare incentives, especially for lone mothers, where participation elasticity for lone mothers with respect to in-work benefits has been measured at up to 1.816 and Brewer et al (2005) found it is one of the highest of the demographic groups. These elasticities give a good idea of the effects of the welfare and which demographic is most sensitive to welfare schemes, however, they do not give the full picture. Due the non-convex shape of the income structure created by a welfare scheme such at WFTC, negative incentives to work are also created13 (as seen in groups 3 and 4 in figure X).
 
In Section 1 we used the Family Resources Survey which took a random sample of women at monthly time periods. We then compared the proportion of lone mothers who were employed before the implementation of WFTC, with the proportion of lone mothers who were employed after WFTC, using a control group to account for trends and unexpected shocks. This data essentially allowed us to compare the difference in the proportion employed between one random sample collected pre-reform and another random sample post-reform, rather than tracking the changes that occurred in the pre-reform random sample. This could result in biased results if there was a change in composition and the samples of before and after WFTC differed in characteristics which were not included in the model. To get more accurate estimates we can use panel data which would give repeated observations on the same individuals over certain time periods.
 
Panel data allows us insight into the dynamics of the data, which cross-sectional data cannot provide. For example, it helps us determine whether increases in participation are due to an increase in those joining the work force or fewer leaving it. Panel data also gives us the opportunity to control for underlying unobserved differences in the individuals (unobserved heterogeneity) which would otherwise cause omitted variable bias. For example, in our WFTC sample, there may be an underlying propensity to work or unobserved ability which differs for each individual and is not easily included in the model. This omitted variable bias could in theory be corrected using instrumental variables when using cross-sectional data, but it is often difficult to find suitable instruments. The use of panel data will also give us more efficient estimates for the additional reason that there tends to be a higher number of degrees of freedom than with cross sectional data.
 
I will focus on the WFTC’s effect on lone mothers because WFTC is particularly aimed at this demographic and men tend to work full time and have a low response to increases in income13. I will therefore use the same control and treatment groups as used with the FRS data: the treatment group will consist of lone mothers while the control group will consist of single women without children as they are ineligible for WFTC.#p#分頁標題#e#
 
Panel Data
 
The data I will use comes from the British Household Survey (BHPS) which follows the sample individuals year after year. In line with Francesconi and Van der Klauuw (2006), the data includes single females who are over 16 and are at a maximum age of 60 in any year over the period 1991-2003. The data is limited to before 2003, as there was further reform in 2003 when WFTC was separated into Working Tax Credit and Child Tax Credit. I also included yearly GDP data to account for the effects of the business cycle on unemployment. As in section 1, I will remove inconsistent data such as those claiming to be a childless females with children or in paid work while working zero hours, and remove entries with missing data necessary for our model. This results in a pooled sample of 7,948 observations including 1,995 unique single women, 1,499 of which are single females without children and 756 are lone parents. Table X shows summary statistics of the data used. From the table we can see that lone mothers are much more likely to work over 16 hours and over 30 hours as they have to take time to care for their children. The probability of staying in a job (employment persistence) and the probability of entering a job in a given year is broadly similar for the two groups over the period, as is the average age and age leaving full time education. Single women on the other hand, earn on average 110% more a month than lone mothers.
 
The following figures plot the proportion of those in employment over time and the number of hours worked over time.
 
We can see there was a sudden upward trend in the proportion of lone parents employed in 1997 which continued to the end of the data; this is also the case for hours worked as the two are interlinked. How much of this post 1999 increase in both employment and hours can be attributed to WFTC is debatable.
 
The following figures plot the proportions of those who enter work in a given year from being unemployed, or stay in a job for consecutive years. The figures show a volatile but decreasing trend for the proportion entering the workforce for single women without children combined with a slightly increasing trend of those staying in the workforce. This suggests that the slight decrease in employment from 1991 for single women without children is due to a decrease in people entering work. Lone parents have a volatile and very slightly increasing trend of people entering work combined with a steeper upward trend for those staying in work. This would imply that the increase in persistence has been responsible for most of the increase in employment for lone mothers.
 
The Model
 
There are a number of models which can be used to estimate effects when using panel data. The pooled OLS model combines the data over i and t into a regression with NT observations to give constant coefficients of the model:
 #p#分頁標題#e#
yit = ? + ?xit + uit     i = 1, 2… N        t = 1,2… T
 
Where yit is the dependent variable, xit is the explanatory variable and uit is the disturbance term. For consistency, the model requires the error term to be uncorrelated with the explanatory variables both over i and t for consistency. Due to unobserved heterogeneity, the error terms are likely to be correlated for an individual over the time period and the estimator will be inconsistent. We must therefore use an individual-specific effects model as shown below:
 
yit = ?i + ?xit + uit    i = 1, 2… N        t = 1,2… T
 
Where ?i are random variables which differ between individuals but are constant over an individual’s time period: it allows individuals different intercept terms, which are constant in every time period and thus capture the unobserved heterogeneity. The explanatory variable is xit and uit is the error term which is assumed to be independently and identically distributed. Taking the average over the time period we get:       i = 1, 2… N
 
Subtracting the two we find:
 
i = 1, 2… N t = 1,2… T
 
If we estimate this equation by OLS it will give us the same estimate of ? as the original model, which is the marginal effect of xit on yit. This is the fixed effects (FE) model. The individual characteristic is equal to its average over the time period, as we have assumed it is constant over time. This means that when we take the difference it does not feature in the final equation. However, this technique does not allow for estimation of the effects of time-invariant explanatory variables as they would be perfectly collinear with the individual effects. In this example it would mean that would equal 0 and thus ? could not be estimated.
 
In order to estimate this equation by OLS, the Linear Probability Model (LPM) will have to be used as our employment dependent variable is binary, that is someone is either employed or they are not. If written in terms of deviations from 0 or 1 and the probabilities of the deviation occurring, the expectation of the error terms in the model
 
i = 1, 2… N
 
can be written as
 
Calculating the variance of the error term (E[ui2]) we get
 
and thus the random error term suffers from heteroskedasticity. In order to compensate for this we must use the divide our model by the weights which will make the error term homoskedastic. This model can be used in conjunction with the FE model. For simplicity I will not use the Logit model which is only strictly needed if the LPM predicts probabilities above 1 or below 0, which does not occur in the results.
 
The random effects (RE) model is an alternative individual-specific effects model which requires the individual characteristics to be distributed randomly among individuals but still constant over time. If this is the case then the RE model is consistent and asymptotically efficient, using the variance within and between individuals and GLS or FGLS to create efficient weights, whereas the FE model is only consistent, as it only allows for variation within the individual. However, if the fixed effects are not randomly distributed but are correlated with the explanatory variables then the RE model is inconsistent and the FE model should be used. The RE model also allows us to include and estimate the effects of time-invariant explanatory variables. We can test the necessity for the FE model using the Hausman test for endogeneity. The Hausman test can be used to establish whether the difference between the fixed effects and random effects estimators is statistically significant. The null hypothesis of the test is that there is no correlation between the individual effects and the regressors and the RE model can be used. In order to confirm our need for the FE model, we would need a large Hausman test statistic and a significant p value. It is likely that the composition of the single women group will have changed, as WFTC has the effect of making being single more financially attractive, and thus the FE model should be used15.#p#分頁標題#e#
 
As panel data includes cross-sectional and time series data, there is the potential for both serial correlation and heteroskedasticity. The FE model reduces serial correlation significantly as it captures time-invariant unobservable characteristics but there may be heteroskedasticity present in the data. Although this will not effect the estimates, it will affect the standard errors, so I will use robust standard errors in the regression to account for this.
 
The difference-in-differences method (DD) requires the treatment group and the control group to share the same trends and shocks to give accurate results as discussed previously. However, if we look at figure X, visually it appears that the two groups do not share a common trend as employment for lone parents is increasing significantly more than single women without children before the announcement and implementation of WFTC. If we use the difference in difference method, we could wrongly attribute this already increasing employment trend to WFTC, invalidating our analysis. As in Francesconi and van der Klaauw (2006) I will run another regression using the difference-in-difference-in-difference (DDD) method as a comparison which includes a time variable and a time variable interacting with the treatment group, allowing for different trends between the groups.
 
Therefore I will use the following model which includes the DDD method:
 
i = 1, 2… N t = 1,2… T
 
Where the model outcome variable yit is employment, dit is a dummy variable for being a lone parent or not, allows for trends and also different trends between the two groups (the DDD method), pt is the dummy variable for being post reform,is a K?1 vector of variables which could affect employment, ?i are the fixed effects and uit is the independently and identically distributed error term.
 
As the BHPS data is survey data, there are categories which are states of being and are not quantifiable. For example we cannot determine the numerical difference between living in London and living in Scotland. The individual will either live in London or will not. In this way we need to create a number of dummy variables for each of the options in the unquantifiable categories in order to show the effect, for example, of living in London compared with not living in London. We also have to exclude one of the options in each category in our model when we apply the dummy variables as the model will find the effects of the other options in comparison to the excluded option. From the regression we get the results:
 
These results show the impact of WFTC on different types of employment using a number of models. The coefficients in table X show the marginal effect of the variable on the proportion of people employed. The fixed effects difference-in-difference (DD) model shows WFTC is responsible for an 8.2 percent increase in employment, which is significant at the 5 percent level: the coefficient is significantly different from zero with over a 95 percent confidence level. This positive coefficient is consistent with the theory, where WFTC unambiguously increases incentives to work for the unemployed. The other statistically significant coefficients behave as expected, for example having a first degree increases the likelihood that the individual will be employed while having young children reduces the likelihood. The results show that the younger the child, the more time will be needed to care for them and so the fewer the hours worked. House ownership has a high standard error and is not significant in all the models, most likely because people will either work full time and have enough money to buy a house, or will have enough money to own a house and also be retired. As the OLS pooled model does not control for fixed effects it is likely that there will be serial correlation which generally leads to underestimating coefficients and overestimating t-statistics16. This over-estimating of t-test statistics can be seen in the results as the OLS pooled model estimates that 43 coefficients are significant at the 10 percent level or better compared to the FE model which finds 28 coefficients statistically significant.#p#分頁標題#e#
 
We can test the validity of the fixed effects model here using the Hausman test. The test produces a large test statistic (162.14) and a p-value of 0.000. This leads us to believe we should reject the null hypothesis that there is no correlation between the individual effects and the regressors and confirm our need for the FE model.
 
The FE model which uses difference-in-difference-in-difference includes a time trend and a time trend interacting with the lone mothers. The time coefficient suggests that the sample as a whole has a decreasing employment trend. However, the positive coefficient for the time trend interacting with lone mothers suggests that lone mothers are experiencing a different trend, with employment rising by 1.2 percent a year. This would suggest that the trends between the two groups are indeed different and DDD is necessary to find the true WFTC effect. Compared to the DD model, the estimated effect is much smaller at 2.8 percent as the already increasing trend in employment for lone mothers relative to the trend for childless single women is no longer incorporated. However, statistical significance is also lost as time variables will be correlated to some extent and it is harder to identify which time variable is the cause for increasing employment. Francesconi and van der Klauuw (2006) find a statistically significant effect of 5.8 percent on employment when using a FE (DDD) model. It is likely that this result is greater due to the difference in explanatory variables, despite using the same general model, and the sample size will have affected the significance: my number of observations is much fewer.
 
The theory suggests that for those who are unemployed or work under 16 hours, there is an unambiguous incentive to increase hours to 16, where eligibility for WFTC occurs. The results confirm this, showing that WFTC has the effect of increasing the number of people who work 16 hours or over by 9.6 percent. This figure is greater than the effect on labour-force participation, because it increases incentives for both the unemployed and those working under 16 hours, to work 16 hours and over. Francesconi and van der Klauuw (2006) find that the effect on labour force participation is greater than that of the effect on eligible employment which seems strange as it implies that WFTC encouraged some previously unemployed lone mothers to work without actually receiving any of the in-work credits. If they did receive in-work credits then they should be counted in the effect on eligible employment.
 
From the results, we can see that WFTC’s effect on full-time employment is not significantly different to 0, suggesting that the reform did not create an incentive structure which encouraged people to move to full time employment from unemployment or to increase their working time to over 30 hours. The theory in this case shows that it is unlikely that someone would work only just below (only 1.2 percent of the sample work 27-29 hours). The non-negative result also suggests that people were not incentivised to decrease their working time below 30 hours as they face the large disincentive of losing their additional childcare credit [a] .#p#分頁標題#e#
 
The theory predicts that WFTC will have an effect on the number of hours that single mothers work, dependent on the number of hours they worked before the reform. The above results cannot confirm this prediction as they only show movements between unemployment, eligible employment and full-time employment rather than movements within these types of employment.
 
Hours
 
The evidence from the data supports the theory that WFTC unambiguously increases incentives to enter work. However, the theory concludes that the overall effect of WFTC on hours is ambiguous. In order to find the end effect of WFTC on overall hours we can use the panel data and the same model as before [b] but using the log of job hours as the dependent variable in order to achieve percentage changes in hours rather than absolute values.
 
While the fixed effect model allows for individual characteristics, the coefficients will be inconsistent as we will be using censored data. This censoring occurs because our dependent variable cannot be observed at all states: if according to the model the individual’s preferences deem that they should work negative hours, they are subject to a lower limit and can only choose to work a minimum of zero hours and be unemployed. The true (negative) value in this case is therefore not observed.
 
The results show the effect of WFTC on individuals working different hours using a number of models. The FE (DD) regression for total job hours shows that the total number of hours worked for lone parents increased by 3.01 percent as a result of WFTC. Again, as in the employment regression, the smaller WFTC effect coefficient when using the FE (DDD) regression implies that some of the upward trend in hours (seen in figure X (mean hours graph)) is wrongly attributed to WFTC and significance is lost as identification is harder among more time variables.
 
As our data is censored, the implication is that the FE models’ coefficients are inconsistent and so the Tobit model is used as a comparison. I will use the same model as in section 1 [b] with the dependent variable as the natural log of the hours worked and using a Tobit regression which requires:
 
The Tobit model coefficients can then be used to calculate the marginal effects [c] . From the results, these marginal effects appear to be in line with the FE (DD) model and are statistically significant at the 5 percent level. The “in work” regression shows how total hours changed for the working population, removing the impact of increased employment on hours. The positive statistically significant results from all three models suggest that WFTC had the effect of increasing total hours for working lone mothers, and the negative impact on hours on some individuals predicted by the theory was outweighed by the positive impact of WFTC on other individuals.
 
The “working 16-29 hours” regression attempts to show how the incentives changed for those who were working 16-29 hours before the reform. As the panel data follows the same individuals, we should be able to find the effect of WFTC on the individuals who were working 16-29 hours before the reform. I therefore removed from the sample those who were working outside of those hours in the pre-reform period. This resulted in a negative but not statistically significant results in both FE models. This would suggest that for lone mothers working between 16 and 29 hours, the income effect was roughly the same as the substitution effect as a result of WFTC or that there were broadly the same number of people whose substitution effect outweighed the income effect as there were individuals whose income effect outweighed the substitution effect. However, we are using an unbalanced panel which means that the data is not necessarily made up of the same people pre and post reform. If there are different people who are introduced into the panel after the WFTC reform then this will cause a biased estimator. For example, if an unemployed lone mother enters in the post-reform period and replaces a lone mother who worked 16-29 hours from the pre-reform period, it will appear as if WFTC has had the effect of reducing hours from 16-29 to zero and will bias the estimator downwards. As the working hours distribution for lone parents is skewed towards fewer to no hours it is likely that the estimator will be biased downwards. The large standard error for the FE (DD) model could show that the magnitude of the relative substitution and income effects varies greatly for each individual. The smaller coefficient for FE (DDD) implies a greater upward trend for hours in comparison to the control group. We can use the FRS data to see how the average number of hours for those working 16-29 both pre and post reform changes, by using a sample which only includes those working between 16-29 hours. The Tobit model results suggest that the effect of WFTC on the average number of hours for those working between 16-29 hours is not statistically different from zero. These results are consistent with the findings of both Gregg and Harkness (2003), using propensity score matching and Eissa and Liebman (1997) who both conclude that the effects are statistically insignificant.#p#分頁標題#e#
 
We encounter the same problem of unbalanced panel data when trying to calculate the effect on lone mothers working more than 30 hours. If lone mothers enter and replace other lone mothers, unless they work the same number of hours as the individuals they replace, they will bias the results. Again the skewed distribution of hours worked towards fewer hours will bias the effect downwards. The FE (DD) results imply that in response to the WFTC reform, lone mothers who were working 30 hours and over have reduced their hours by 20 percent on average. These result is quite high, possibly due to the fact that a large proportion of lone mothers who work over 30 hours will not work very much more than 30 hours (due to home commitments), in the hours region in which the theory shows has unambiguous negative incentives to decrease work. This is also combined with the downwards bias produced by the unbalanced panel. The Tobit model uses the same model as before where those working below 30 hours are removed from the sample, to give the change in average hours worked for those working 30 hours and over. The results show a statistically significant negative response where the average number of hours is decreased by 1.5 percent. This figure is likely to be more accurate as it does not suffer from the same bias as panel data, however it cannot show if people decrease their hours below 30 hours as a result of WFTC. The likelihood that lone mothers decrease hours below 30 is unlikely as they face the large disincentive of losing their extra childcare credit. The results from the employment regressions suggest that WFTC causes little movement up to working 30 hours or movement from over to below 30 hours. In comparison to the Tobit model results, the FE (DD) results appear fairly implausible and biased.
 
Conclusion
 
In October 1999 WFTC replaced Family Credit to create greater incentives to work for workless or low-income households with the aim of reducing child poverty. I focus on the effects of the reform on single mothers, as they were a particular target, using data from the Family Resources Survey and the British Household Survey. I attempt to identify the effect of WFTC on employment and on hours worked comparing a treatment group consisting of lone mothers with an control group consisting of single women without children who are ineligible for WFTC. On the basis of my fixed effects regression using the difference in difference method results show that WFTC increased labour-force participation by 8.2 percent, eligible employment by 9.6 percent but had no statistically significant effect on full time employment. These results are consistent with the theory that WFTC increases incentives to work 16 hours unambiguously, but does not significantly increase the incentives credit to work 30 hours or over strictly in comparison to FC.
 
My results also show that WFTC increases total hours worked by lone mothers between 15.7 percent and 30.7 percent depending on the model used and also increases the average number of hours worked by those already in a job. The reform does not have a statistically significant effect on hours for those working between 16 and 29 hours according to the results, however it is likely that it does induce negative incentives to work for those working 30 hours and above, decreasing the number of hours worked by 1.5% according to the Tobit model results. These results are also consistent with the theory. A more thorough investigation into the effects on hours worked would require a balanced panel.#p#分頁標題#e#
 
The evidence suggests that WFTC has had a positive impact on employment for lone mothers while keeping incentives to work hours fairly constant. This would have redistributed income in favour of low-income lone mothers and would have likely had a positive impact on reducing child poverty.