1. An Analysis of the Impact of SSP on Wages Jeffrey Zabel Economics Department Tufts University Saul Schwartz School of Public Policy and Administration Carleton University Stephen Donald Economics Department University of Texas

2. The Self-Sufficiency Project (SSP)  SSP was a 1992-2007 Canadian research and demonstration project that attempted to “make work pay” for long-term income assistance (IA) recipients by supplementing their earnings.  The long-term goal of SSP was to get lone parents permanently off income assistance and into the paid labour force  We empirically examine one theoretical explanation for the existence of a long-term impact of SSP on employment – wage progression.

3. The Self-Sufficiency Project Participants were randomly divided into a program group and a control group. Program group members qualified for the earnings supplement if they left IA and took up full-time work within twelve months of entering the project. Those who qualified are called the (take-up group). Once qualified, take-up group members received a supplement that roughly doubled their pre-tax earnings during periods of full-time work in the next three years. They could move between IA and supplemented work if they wished.

4. The Self-Sufficiency Project Over the 52 month follow-up period, take-up group members acquired considerably more full- time work experience than comparable control group members. The greater full-time work experience should imply, on average, higher wages for the take-up group relative to comparable control group members (i.e., “relative wage progression”). Take-up group members should also be more likely to work even after the supplement period has ended.

5. Defining Relative Wage Progression 1.We want to know if the treatment (here, the SSP earnings supplement) affected the wage growth of the treatment group. To introduce some ideas, we will use notation developed by Card, Michalopolous and Robins (CMR) who wrote on the same topic. 2.The treatment is offered for T time periods, t=1,…,T. Let s indicate an initial reference date and f indicate a final reference date 3.Let P i =1 if i th person is in treatment group; Pi=0 if i th person is in control group

6. Defining Relative Wage Progression 1.Consider all program group members who are working at time s. 2.Conceptually, they can be divided into two subgroups; (a) those working only because of the treatment and (b) those who work even without the treatment. 3.Let the first group, called the incentivized program group, be denoted by IP i =1 4.Let the second group, called the non- incentivized program group, be denoted by NP i =1

7. Defining Relative Wage Progression 1.Finally, let E is =1 for all participants who are working in period s. 2.One definition of relative wage growth is then as follows:  s,f = E(w if -w is l E is =1,IP i =1) - E(w if -w is l E is =1,P i =0) 3.In words, relative wage growth is the difference between the mean wage growth of the incentivized program group and the working control group.

8. Defining Relative Wage Progression 1.Estimates of relative wage growth must deal with two partial observability problems. 2.First, w if is observed only for a subset of those with E is =1 since not all those working at s are also working at f. 3.Second, the incentivized program group (IP i =1) cannot be directly observed 4.We can, however, observe the number and proportion of the program group that are incentivized by comparing the employment rates of the program and control group at time s. Call that proportion .

9. Defining Relative Wage Progression 1.The wage growth of the program group can be expressed as the weighted average: E(w if -w is l E is =1,P i =1) =  E(w if -w is l E is =1,IP i =1) + (1-  )E(w if -w is l E is =1,NP i =1) 2.Of course, the problem is that we cannot observe whether IP i =1 or NP i =1. CMR address this problem by making the theoretical assumption described in the next slide. We address it by using propensity score matching to estimate membership in the incentivized and non- incentivized program groups.

10. Defining Relative Wage Progression 1.CMR assume that E(w if -w is l E is =1,NP i =1) = E(w if -w is l E is =1,P i =0) 2.That is, CMR assume that the treatment has no effect on the wage growth of the non-incentivized program group. Substituting this expression into equation (1) yields {E(w if -w is l E is =1,P i =1) - E(w if -w is l E is =1,P i =0)} /  3.This is the observable wage growth in the program group minus the observable wage growth in the control group, all divided by the observable proportion . While there is no strong reason to think this assumption is true, one way to test it is to look at the wage growth of those working at baseline. CMR do this and accept that the assumption is reasonable.

11. Using PSM to Estimate the Incentivized Program Group Propensity score matching is appropriate only if there is no unobserved heterogeneity that differentiates the treatment group from the potential comparison group. In Zabel, Schwartz and Donald (2005, 2006) we estimated a structural model of full-time employment durations in SSP that accounted for two kinds of selection: by all experimental participants into full-time work and by the program group into supplement eligibility. We found little or no evidence of unobserved heterogeneity, probably because of the number of available pre-random assignment covariates. CMR also found little evidence of unobserved heterogeneity. Thus, PSM seems like a feasible alternative here.

12. Using PSM to Estimate the Incentivized Program Group Using the entire control group, we estimate a probit model of whether or not the individual had found a full-time job within the first 13 months after random assignment. The predicted probabilities are the relevant propensity scores. We then use the coefficient estimates from the probit model to estimate predicted probabilities (propensity scores) for the program group members who had found work within the first 13 months. (This is the SSP take-up group.)

13. Using PSM to Estimate the Incentivized Program Group We then use one-to-one nearest-neighbour matching (the simplest PSM method) to choose the subset of the take-up group who best match the working control group. That subset is the non-incentivized take-up group (NP i =1). The remaining take-up group members form the incentivized take-up group (IP i =1). We do this for each province separately. We address the problem of the partial observability of starting and ending wages in two ways: (1) by calculating the median wages of the working control group and the non-incentivized take-up group in each month after random assignment. Figure 2 shows those median wages for both British Columbia and New Brunswick; (2) by estimating a wage model described later.

15. Using a wage model to estimate wage progression The second way that we can handle the problem that w if is not observed for all those who are working in time s (and thus have a value for w is ) is to estimate a model of individual wages as a function of months of job experience. Using the coefficient estimates from that model, we can estimate the wage for every member of the sample in every time period. Importantly, we assume that SSP can affect wages only by affecting labour market experience. This rules out a number of other possible avenues for achieving wage progression.

16. Using a wage model to estimate wage progression There are at least two complications in implementing this strategy. The first is the standard problem that individuals select themselves into work non-randomly so we must control for observable and unobservable differences among workers. The second is that the labour market experience variable on the right hand side of the wage equation is likely to be endogenous and we must account for that endogeneity.

17. Using a wage model to estimate wage progression In the standard sample selection mode, the reservation wage equation is: lnWAGE it *=  0 + V it  1 + f(EXP it ; 2 ) +  3t P i +  1i * +  1it * The equation for market wages is: lnWAGE it =  0 + Z it  1 + f(EXP it ; 2 ) +  2i +  2it where V it and Z it are vectors of observable covariates, f(.) is a general function of labour market experience,  1i * and  2i represent unobserved heterogeneity and  1it * and  2it are unobserved error terms. Note that the coefficient on the 0-1 program participation variable is time varying since the incentives of SSP change over the follow-up period.

18. Using a wage model to estimate wage progression In the paper, we employed both a linear and a quadratic specification of labour market experience (months of experience from random assignment to time t). For relatively young, long-term welfare recipients, the linear specification seems to work better (Gladden and Tabor, 2000) and only those results will be discussed. There can be up to 52 observations on log wages and on employment status for each individual so we must account for the correlation of the error terms pertaining to the same individual.

19. Using a wage model to estimate wage progression An individual will work full-time if The equation for the latent propensity to work full-time is Let WFT it = 1 if = 0 otherwise

20. Using a wage model to estimate wage progression Wages are observed if an individual works (WFT it =1)

21. Using a wage model to estimate wage progression The second problem in the model is that experience (EXPER) is endogenous. We instrument for EXPER using the program indicator (PROGRAM)

22. Using a wage model to estimate wage progression Before estimating the market wage equation that includes the inverse Mills ratio and the instrument for labour force experience, we applied the Hausman test to see whether random effects or fixed effects was the appropriate estimation method. Using the test, we rejected the hypothesis of uncorrelated effects and used a fixed effects model. The model is estimated separately for each of the two provinces, New Brunswick and British Columbia but I will discuss only the BC results. In both provinces, the estimated monthly return to experience is roughly half a percentage point per month.

23. Using a wage model to estimate wage progression As noted above, the effect of SSP on wage progression manifests itself through differences in the months of labour market experience accumulated by program and control group members over the 52 month follow-up period. In BC, program group members accumulated an average of 11.6 months of experience; the control group average was 8.2 months. To calculate wage progression for a group or subgroup, we multiply the average months of experience accumulated by that group since baseline by the return to experience estimated from the wage regression. Relative wage progression is then the difference between the subgroups’ estimated wage progressions.

24. Results of the wage progression model The estimated absolute wage progression was 6.5 percentage points for the BC program group and 4.5 percentage points for the BC control group, implying a relative wage progression of 2 percentage points. We can then look at the relative wage progression for the incentivized and non-incentivized groups as we identified them above. To see if there is any effect of SSP after the end of the 36-month supplement eligibility period, we calculated wage progression during the eligibility period and for as many months as possible after it ended. Only the 36- month results will be mentioned here.

25. Results of the wage progression model For the non-incentivized program group in BC, there is virtually no wage progression in either period because the average experience accumulated by the non- incentivized program group was almost identical to the average accumulated by the control group. This is further empirical confirmation of the Card, Michalopolous and Robins assumption. (No such confirmation in New Brunswick though.) For the incentivized program group, however, there was substantial relative wage progression largely because the members of the control group who most closely matched them had accumulated virtually no labour force experience. We estimate a relative wage progression of 9.3 percentage points.

26. Policy Implications SSP clearly was able to induce a group of long- term IA recipients (i.e., the incentivized group) to take up full-time work. Initially, the thought was that the incentivized group would be less job-ready, as indicated here by their demographic characteristics. But, as shown by their wage progression (and also shown in other contexts) SSP seems to have induced the incentivized group to exhibit labour force behaviour like the more job-ready non- incentivized group. That said, there was not enough wage progression to lead to self-sufficiency.