Trends in Earnings Inequality among Canadian Men, 1985-2005 Yuri - PowerPoint PPT Presentation

Trends in Earnings Inequality among Canadian Men, 1985-2005 Yuri Ostrovsky CLSRN-CEA, Toronto 2009 Statistics Canada • Statistique Canada

‘Permanent vs. transitory’ approach Traditional approach: changes in the annual distribution of earnings = changes in inequality Usually measured by the Gini, percentile ratios, variance (of log earnings), etc. Limitations: if Y = y permanent + y transitory then changes in the earnings distribution may reflect changes in either or both components. This distinction is essential in assessing the role of human capital References: Gottschalk & Moffitt ‘94, Baker ‘97, Moffitt & Gottschalk ‘02, ‘08, Haider ‘01, Hyslop ‘01, Baker & Solon ‘03, Beach, Finnie & Gray ‘03, Morissette & Ostrovsky ‘06, Pencavel ‘06, Shin & Solon ‘08, etc. Statistics Canada • Statistique Canada 2

Baker and Solon 2003 Analysed changes in the variance of men’s earnings in Canada from 1976 to 1992. Important methodological contribution. Both permanent and transitory variances contributed to the growth in the annual earnings variance. The increase in the permanent variance was proportionally larger than the increase in the transitory variance. Sharp increases in both variances the early 1990s. Statistics Canada • Statistique Canada 3

Annual variance of men’s log-earnings, 1985-2006 1992, last year in Baker and Solon 2003 recession Statistics Canada • Statistique Canada 4

Two main objectives To extend the analysis in Baker and Solon to the period from 1985 to 2005. To test an alternative treatment of left-censored observations suggested in Moffitt and Gottschalk (2008) and compare the results. Major advantage over previous studies: excellent data. Statistics Canada • Statistique Canada 5

Data Longitudinal Administrative Databank (LAD). 1982-2006. 20% random sample of Canadian tax-filers. Detailed and accurate income information. “Once in LAD, always in LAD.” Very high filing rates in Canada; strong incentives to file. Statistics Canada • Statistique Canada 6

Sample Male workers aged 25 to 59 with positive earnings in each year they satisfy age conditions. The first and last observations are discarded Year Year Birth cohort 19841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006 1933/34 1933/34 51 52 53 54 55 56 57 58 59 Cohor Cohort's age Cohor t's age t's age 1935/36 1935/36 49 50 51 52 53 54 55 56 57 58 59 1937/38 1937/38 47 48 49 50 51 52 53 54 55 56 57 58 59 1939/40 1939/40 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1941/42 1941/42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1943/44 1943/44 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1945/46 1945/46 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1947/48 1947/48 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1949/50 1949/50 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 1951/52 1951/52 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 1953/54 1953/54 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 1955/56 1955/56 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 1957/58 1957/58 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 1959/60 1959/60 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 1961/62 1961/62 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 1963/64 1963/64 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 1965/66 1965/66 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 1967/68 1967/68 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Cohort's age 1969/70 1969/70 25 26 27 28 29 30 31 32 33 34 35 36 37 1971/72 1971/72 25 26 27 28 29 30 31 32 33 34 35 1973/74 1973/74 25 26 27 28 29 30 31 32 33 discarded obser discarded obser discarded obser discarded obser discarded obser discarded observations vations vations Statistics Canada • Statistique Canada 7

Sample summary Birth cohort sample size years observed number of years age in initial year sample moments 1933/34 21,430 1985-1991 7 52 28 1935/36 19,570 1985-1993 9 50 45 1937/38 18,640 1985-1995 11 48 66 1939/40 18,430 1985-1997 13 46 91 1941/42 19,500 1985-1999 15 44 120 1943/44 20,380 1985-2001 17 42 153 1945/46 22,470 1985-2003 19 40 190 1947/48 25,470 1985-2005 21 38 231 1949/50 28,220 1985-2005 21 36 231 1951/52 31,060 1985-2005 21 34 231 1953/54 33,450 1985-2005 21 32 231 1955/56 34,610 1985-2005 21 30 231 1957/58 34,750 1985-2005 21 28 231 1959/60 33,910 1985-2005 21 26 231 1961/62 34,400 1987-2005 19 26 190 1963/64 35,160 1989-2005 17 26 153 1965/66 32,030 1991-2005 15 26 120 1967/68 30,300 1993-2005 13 26 91 1969/70 32,180 1995-2005 11 26 66 1971/72 33,330 1997-2005 9 26 45 1973/74 35,410 1999-2005 7 26 28 total: 3,003 Statistics Canada • Statistique Canada 8

Basic idea Individual earnings: y it = μ i + υ it , E( υ it υ is )=0. If E( μ i , υ it )=0 then Var(y it )=Var( μ i )+Var( υ it ). This simple “between-within” variance decomposition is useful and has been used in numerous studies. Factor loadings: y it =p t · μ i + λ t · υ it . Var(y it )=p t2 Var( μ )+ λ t2 Var( υ ) depends on p t and λ t . Cov(y it ,y´ is )=p t p s Var( μ ) depends only on p t if E( υ it υ is )=0. Statistics Canada • Statistique Canada 9

Auto-correlations Var(y it ) may increase because either p t or λ t increase. A rise in p t means less earnings mobility; hence, larger auto-covariances... ... auto-covariances grow faster than variances, so the auto-correlations get larger. If only λ t increases then the variances increase but the covariances do not, so the auto-correlations get smaller. Statistics Canada • Statistique Canada 10

Model (Baker and Solon) y bit = p t · (α i +β i X bt +u bit )+ε bit u bit =u bi,t-1 +r bit ε bit =ρ · ε bi,t-1 +λ t · υ bit heterogeneous growth serial correlation random walk Var(υ bit )=γ 0 +γ 1 X bt +γ 2 X bt +γ 3 X bt +γ 4 X bt heteroskedastic “residual” transitory variance 2nd moments (e.g. 1945/1946 cohort in 1989): Var(y 1945,’89 ) = =p 289 ( σ 2 + σ 2 β 18 2 +2 σ αβ 18+ σ 2r 18)+ ρ 2 Var( ε 1945,’88 )+ λ 289 ( γ 0 + γ 1 18+ γ 2 18 2 + γ 3 18 3 + γ 4 18 4 ) Statistics Canada • Statistique Canada 11

GMM MD estimator The auto-covariance matrix for each birth cohort generate a number of sample moments equal to the number of unique elements in the matrix. Each element (variances and covariances) has a functional representation ƒ( θ ), where θ=(p t , σ 2α , σ 2β , σ αβ , σ 2r , ρ, λ t , σ 233/34... σ 273/34, γ 0 ...γ 4 ). Using the generalized method of moments (GMM), ‘ θ -hat’ is chosen to minimize Δ = [Ω- ƒ (θ)]´W[Ω- ƒ (θ)] , where W is a positive definite weighting matrix . Statistics Canada • Statistique Canada 12

An alternative approach to the left-censoring problem cohort 1985 1986 1987 1988 Moffitt and Gottschalk (2008): a possible ‘built-in’ 1933/34 1933/34 52 53 54 55 time trend in the transitory variance for the left- 1935/36 1935/36 50 51 52 53 1937/38 1937/38 48 49 50 51 censored observations. 1939/40 1939/40 46 47 48 49 1941/42 1941/42 44 45 46 47 1943/44 1943/44 42 43 44 45 ARMA(1,1): ε bi,85 = ρ · ε bi,84 + λ 85 · υ bi,85 + 1945/46 1945/46 40 41 42 43 ζ · λ 84 · υ bi,84. 1947/48 1947/48 38 39 40 41 1949/50 1949/50 36 37 38 39 1951/52 1951/52 34 35 36 37 unobserved 1953/54 1953/54 32 33 34 35 1955/56 1955/56 30 31 32 33 In the censored portion of the variance only λ 84 , 1957/58 1957/58 28 29 30 31 1959/60 1959/60 26 27 28 29 λ 83 ... are unobserved (age is known). 1961/62 1961/62 26 27 1963/64 1963/64 censored age If λ 84 , λ 83 ...=1, the censored portion of the variance is Λ bi,0. Approximation: Var( ρ · ε bi,-1 + ζ · λ -1 · υ bi,-1 ) =(1+ η · X b,0 ) · Λ bi,0 . Statistics Canada • Statistique Canada 13

The variance decomposition of individual log-earnings, Var(y bit ); male workers 40-41 years old, 1985-2005. Statistics Canada • Statistique Canada 14

The estimated permanent-to-transitory variance ratio; male workers 40-41 years old Statistics Canada • Statistique Canada 15

Conclusions (I) the variance of log earnings remained high in the postrecession years, and continued to increase throughout the 1990s and into the 2000s. Both variance components contributed to the growth in the total variance, but contrary to the results for 1976–1992 (Baker and Solon), I found little evidence that the growth in the permanent component was proportionally larger. Statistics Canada • Statistique Canada 16