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

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Trends in Earnings Inequality among Canadian Men, 1985-2005

Yuri Ostrovsky CLSRN-CEA, Toronto 2009

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‘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 = ypermanent + ytransitory 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.

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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.

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recession 1992, last year in Baker and Solon 2003

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Annual variance of men’s log-earnings, 1985-2006

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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

• bservations suggested in Moffitt and Gottschalk (2008)

and compare the results. Major advantage over previous studies: excellent data.

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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.

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Male workers aged 25 to 59 with positive earnings in each year they satisfy age conditions. The first and last observations are discarded

Birth

Year Year

cohort 19841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006 1933/34 1933/34 51 52 53 54 55 56 57 58 59 1935/36 1935/36 49 50 51 52 53 54 55 56 57 58 59

Cohor Cohor Cohort's age t's age t's age

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 1969/70 1969/70

Cohort's age

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

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Sample

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

Sample summary

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Basic idea

Individual earnings: yit=μi+υit, E(υitυis)=0. If E(μi,υit)=0 then Var(yit)=Var(μi)+Var(υit). This simple “between-within” variance decomposition is useful and has been used in numerous studies. Factor loadings: yit=pt·μi+λt·υit. Var(yit)=pt2Var(μ)+λt2Var(υ) depends on pt and λt. Cov(yit,y´is)=ptpsVar(μ) depends only on pt if E(υitυis)=0.

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Auto-correlations

Var(yit) may increase because either pt or λt increase. A rise in pt means less earnings mobility; hence, larger auto-covariances... ... auto-covariances grow faster than variances, so the auto-correlations get larger. If only λt increases then the variances increase but the covariances do not, so the auto-correlations get smaller.

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ybit = pt·(αi+βiXbt+ubit)+εbit

heterogeneous growth

ubit=ubi,t-1+rbit

random walk

εbit=ρ·εbi,t-1+λt·υbit

serial correlation

Var(υbit)=γ0+γ1Xbt+γ2Xbt+γ3Xbt+γ4Xbt

heteroskedastic “residual” transitory variance

2nd moments (e.g. 1945/1946 cohort in 1989): Var(y1945,’89) =

=p289(σ2+σ2β182+2σαβ18+σ2r18)+ρ2Var(ε1945,’88)+λ289(γ0+γ118+γ2182+γ3183+γ4184)

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Model (Baker and Solon)

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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=(pt, σ2α, σ2β, σαβ, σ2r, ρ, λt, σ233/34...σ273/34, γ0...γ4). 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.

Moffitt and Gottschalk (2008): a possible ‘built-in’ time trend in the transitory variance for the left- censored observations. ARMA(1,1): εbi,85 =ρ·εbi,84 + λ85·υbi,85 + ζ·λ84·υbi,84.

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cohort 1985 1986 1987 1988 1933/34 1933/34 52 53 54 55 1935/36 1935/36 50 51 52 53 1937/38 1937/38 48 49 50 51 1939/40 1939/40 46 47 48 49 1941/42 1941/42 44 45 46 47 1943/44 1943/44 42 43 44 45 1945/46 1945/46 40 41 42 43 1947/48 1947/48 38 39 40 41 1949/50 1949/50 36 37 38 39 1951/52 1951/52 34 35 36 37 1953/54 1953/54 32 33 34 35 1955/56 1955/56 30 31 32 33 1957/58 1957/58 28 29 30 31 1959/60 1959/60 26 27 28 29 1961/62 1961/62 26 27 1963/64 1963/64

unobserved censored If λ84, λ83...=1, the censored portion of the variance is Λbi,0. Approximation: Var(ρ·εbi,-1 + ζ·λ-1·υbi,-1) =(1+η·Xb,0)·Λbi,0.

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In the censored portion of the variance only λ84, λ83... are unobserved (age is known).

An alternative approach to the left-censoring problem

age

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The variance decomposition of individual log-earnings, Var(ybit); male workers 40-41 years old, 1985-2005.

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The estimated permanent-to-transitory variance ratio; male workers 40-41 years old

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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.

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Conclusions (II)

Both the original Baker-Solon model and the model with Moffitt- Gottschalk treatment of the left-censored observations provide good fit and very similar estimates of the permanent and transitory variances. The robustness of the results confers a degree of reassurance on the reliability of previous studies. As the overall share of the permanent variance remains much larger than the share of transitory variance, so... ... the focus in future analyses of earnings inequality is expected to remain on long-term inequality and the reasons behind the widening dispersion of permanent earnings.

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Future research...

LAD: different levels of aggregation family earnings inequality? the contribution of husbands’ and wives’ earnings? covariance structure of husbands’ and wives’ earnings?