Evaluation of the Australian Wage Subsidy Special Youth ...

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116 4.3 Theory underlying propensity score matching methods Matching methods are steeped in experimental and evaluation terminology, and the following exposition which draws on the literature of Rosenbaum and Rubin (1983), Dehijia and Wahba (1998), Heckman, Ichimura and Todd (1997), Heckman, Ichimura and Todd (1998) reflects this. The impact of participating in the programme is defined as (1) ∆ = Y t – Y c where Y t is the potential outcome conditional on participation and Y c is the potential outcome conditional on non-participation. Following Rubin (1974), treatment assignment may be random given a set of characteristics or variables X that are unaffected by the treatment. The potential values of X for the different treatment states coincide, and are thus exogenous. 72 The parameter most commonly estimated is the mean impact of treatment on the treated: (2) θ = E(∆ | D = 1, X=x) = E(Y t – Y c | D = 1, X=x) = E(Y t | D = 1, X=x) - E(Y c | D = 1, X=x) where D=1 denotes treatment, D=0 denotes non-treatment and X is a set of conditioning variables. 73 The evaluation problem arises from the term E(Y c | D = 1, X=x). This is the mean of the counterfactual which, since it is unobservable, must be identified and estimated. This issue in evaluation was earlier discussed in Chapter 1. The construction of a valid comparison group for matching techniques is based on the Conditional Independence Assumption (CIA). Under CIA, potential outcomes Y t ,Y c are independent of the assignment to treatment, when conditional on all pre-treatment 72 Hujer and Caliendo (2000) p9 explain that this is not exogeneity in the econometric sense. Heckman Ichimura and Todd (1997) p610 note that it is not necessary to assume that the expected value of the errors in the model of Y conditional on X are zero, so X can fail to be exogenous in the conventional sense of the term. 73 Population quantities are denoted by capital letters and sample quantities by lower-case letters.
117 covariates that influence the assignment to treatment as well as potential outcomes. The precise form of CIA depends on the parameter being estimated. For the treatment on the treated parameter, the CIA requires that, conditional on observable characteristics, potential non-treatment outcomes are independent of treatment participation. Formally, CIA can be written as (3) Y c ╨ D | X = x, ∀x∈ χ where ╨ denotes independence and χ denotes the part of the attribute space for which the treatment effect is defined. This assumption is sufficient for the treatment on the treated parameter. The fuller CIA assumes that (3a) Y t ,Y c ╨ D | X. However, Heckman et al. (1997) show that for estimating the mean effect of treatment on the treated, CIA for Y c is sufficient. This is because inference of Y c for persons where D=1 is estimated from data on persons where D=0. Hence, after adjusting for observable differences, the mean of the no-treatment (potential) outcome is the same for those receiving treatment as for those not receiving treatment. This allows non-participants’ outcomes to be used to infer participants’ counterfactual outcomes. However, this is only valid if there are non-participants for all participants’ values of X (the support condition): (4) 0 < Pr ( D = 1 | X = x ) < 1 where “Pr” is the probability of participating in the programme of treatment. This ensures that there are no values of the characteristics in X for which the propensity score is zero or one. Heckman, Ichimura, Smith, and Todd (1998) show that failure to ensure common support will give biased estimates. Rosenbaum and Rubin (1983) showed that when this assumption of common support holds together with the CIA, then if treatment assignment is strongly ignorable when X is given, then it is also strongly ignorable for any balancing score, such as the propensity score or probability of participating in the programme.
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i Evaluation of the Australian Wage
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v Declaration I hereby declare that
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in method and assumptions. The orth
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3.3 Data and variables used for est
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List of Tables and Figures Figure 1
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Table A2.0b Univariate Probit of pa
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xv Abstract The job subsidy Special
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1 1: Wage subsidy theory and evalua
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3 programs of providing benefits an
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5 The empirical methods used for th
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7 how the outcomes from these metho
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9 employment effect could be mainly
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11 Real Wage Employment Figure 1.1:
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13 are two types of unemployment, s
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15 Real wages are predetermined whe
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17 Vella (1998), Heckman, Lalonde a
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19 Each individual has two potentia
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21 this case, if there was no data
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23 correlation for the error of the
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25 Table 1.3 collects together some
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27 Table 1.3 Brief overview of rece
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29 necessarily brief. Then, the evi
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31 limited applications, such as fo
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33 who participated. It was conclud
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35 term unemployed for over 12 of t
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37 importance of the subsidy second
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39 differences in characteristics t
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41 Matching methods are theoretical
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43 2.2 SYETP implementation As SYET
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45 In July1978, the subsidy was cal
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47 In January 1979, variations were
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49 benefits were paid at a slightly
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51 2.2.3 SYETP operation Earlier re
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53 ceiling constraints’ applied t
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55 Award Conditions for employment
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57 Harris (2001) claims that during
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59 display boards listed details of
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61 restriction was used. If there w
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63 to the end of the 1980’s. An o
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Page 83 and 84: 67 for Australia using data from th
Page 85 and 86: 69 training, can provide a form of
Page 87 and 88: 71 employer survey estimates were t
Page 89 and 90: 73 provisions for SYETP and extende
Page 91 and 92: 75 withdrawals occurred at similar
Page 93 and 94: 77 Table 2.17 State usage of progra
Page 95 and 96: 79 2.3.1 Stretton (1982, 1984) 53 S
Page 97 and 98: 81 Stretton attributed the success
Page 99 and 100: 83 included in the employment model
Page 101 and 102: 85 completers. Their argument was t
Page 103 and 104: 87 was an issue for the data. Unlik
Page 105 and 106: 89 Table 2.21 Richardson (1998) Est
Page 107 and 108: 91 2.3.5 General discussion Some ge
Page 109 and 110: 93 Controlling for differences in i
Page 111 and 112: 95 taken by a previous researcher a
Page 113 and 114: 97 If employability is assumed to b
Page 115 and 116: 99 suitability of the underlying as
Page 117 and 118: 101 Heckman, Lalonde and Smith (199
Page 119 and 120: 103 effect on employment relative t
Page 121 and 122: 105 Table 3.1, Part A Employment eq
Page 123 and 124: 107 (-1.80) (-1.80) Tradesperson -0
Page 125 and 126: 109 duration of Pre-June 1984 unemp
Page 127 and 128: 111 4: Study 2 Propensity score mat
Page 129 and 130: 113 Propensity score matching provi
Page 131: 115 4.2 Propensity score matching m
Page 135 and 136: 119 (7) E(Y c | D=1) = E P(X) {E[Y
Page 137 and 138: 121 For CIA to be plausible, a ‘r
Page 139 and 140: 123 employment and programme partic
Page 141 and 142: Highest qualification in 1984 (1.56
Page 143 and 144: 127 4.6 Distribution of the propens
Page 145 and 146: 129 Figure 4.3 Histograms of estima
Page 147 and 148: 131 Table 4.5 Summary statistics fo
Page 149 and 150: 133 Table 4.5, that the variance of
Page 151 and 152: 135 Table 4.6 Matching results, Sin
Page 153 and 154: 137 Table 6.3 using Swedish data wi
Page 155 and 156: 139 matching is the ability to weed
Page 157 and 158: 141 Table 4.7 Matching results, All
Page 159 and 160: 143 the unobserved component. If th
Page 161 and 162: 145 5: Study 3 Attrition and non-re
Page 163 and 164: 147 occur by design, because the mi
Page 165 and 166: 149 (1990) extended and improved th
Page 167 and 168: 151 (10) A* = δ 0 + δ 1 x +δ 2 z
Page 169 and 170: 153 again from September to Novembe
Page 171 and 172: 155 5.5.2 Univariate examination of
Page 173 and 174: 157 lower, the job lengths are only
Page 175 and 176: 159 Work limited by health 1984 0.1
Page 177 and 178: 161 The characteristics of the SYET
Page 179 and 180: 163 para-professional Mother not em
Page 181 and 182: 165 comparison group where the shar
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167 5.5.4 Attrition: natural attrit
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169 both sources that impose change
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171 para-professional Father not em
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173 work in later sections, this su
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175 Table 5.6: Effect of selection/
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177 appropriate to discard these fr
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179 Australia/Tasmania. Amongst tho
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181 Table 5.5a Summary statistics b
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183 5.6.1.2 Effects of the non-resp
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185 3 years + -0.35 -0.47 -0.34 -0.
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187 5.7 Multivariate analysis of ef
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189 proportion of time spent unempl
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191 post-school qualification, and
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193 Generally, those variables foun
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195 longj0 Longest job by 1984 < 1
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197 adopted in order to maintain co
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199 6: Study 4 Weighting to counter
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201 Table 6.1, part A Employment eq
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203 Methodist 0.133 0.261 (0.77) (1
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205 CEP referrals 1984 0.143* 0.128
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207 6.2 Results of weighting the PS
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209 The distribution of the propens
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211 Table 6.3 Weighted probit used
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213 (0.76) Tradesperson mtrad 0.20
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215 Table 6.5 Summary statistics fo
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217 Table 6.7 Matching results, sin
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219 6.3 Discussion The comparison o
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221 the selection into SYETP and th
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223 Heteroskedasticity is a violati
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225 Table 7.1, Part A Employment eq
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227 (1.26) (1.28) (1.16) Mothers oc
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229 Other Post-School qualification
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231 7.1.2 Exclusion restriction in
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233 Finally, the third panel of new
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235 Table 7.2 summary of changes to
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237 schooling that was statisticall
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239 (0.25) (0.21) 3 years + -0.50 -
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241 Table 7.4 Summary of distributi
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243 7.2.2 Propensity score matching
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245 original model, but with the pe
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247 maintained, then the Heckman bi
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249 Table 7.6 Weighted Probit used
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251 Table 7.7 Summary of distributi
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253 8: Summary and Conclusions The
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255 over which it ran, the review m
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257 the Heckman and PSM methods wer
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259 posited that that such sensitiv
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261 Description Derivation and deta
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Appendix 2 Tables 263
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2 years 0.28 0.07 (1.70) (1.70) 3 y
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267 Table A2.0b Univariate Probit o
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269 Religion brought up in (1.52) (
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271 hq9_84 Year 9 of school or less
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273 Table A2.1 Continued Means and
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275 mtrad Tradesperson 0.04 0.04 0.
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277 Year 9 of school or less -0.19
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279 Table A2.3 Probit of SYETP part
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281 (0.22) (0.44) (0.67) (0.89) Tra
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283 Table A2.5a Univariate probit f
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285 Manager/professional/para-profe
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3 years + -0.04 (2.13)* CEP referra
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289 Table A2.6 Part A Employment eq
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291 Table A2.6 Part B Selection/par
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301
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BLMR Bureau of Labour Market Resear
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Fay, R.G. (1996) "Enhancing the eff
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Heckman J.J. and Smith, J. A. (1998
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Lewis, H.G. (1963) "Unionism and re
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Quandt, R. (1972) "A new approach t
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Stromback, M. and Dockery, A. (2000
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