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Consumption, income, and wealth inequality in Canada

Consumption, income, and wealth inequality in Canada
Consumption, income, and wealth inequality in Canada

Review of Economic Dynamics13(2010)

52–75

Contents lists available at ScienceDirect

Review of Economic Dynamics

https://www.doczj.com/doc/5717874675.html,/locate/red

Consumption,income,and wealth inequality in Canada?Matthew Brzozowski a,Martin Gervais b,?,Paul Klein c,Michio Suzuki d

a York University,Canada

b University of Southampton and IFS,United Kingdom

c University of Western Ontario,Canada

d Bank of Japan,Japan

a r t i c l e i n f o a

b s t r a

c t

Article history:

Received7October2009 Available online24October2009

JEL classi?cation:

D12

D31

Keywords:

Income inequality

Consumption inequality

Wealth inequality In this paper,we document some features of the distribution of income,consumption and wealth in Canada using survey data from many different sources.We?nd that wage and income inequality have increased substantially over the last30years,but that much of this rise was offset by the tax and transfer system.As a result,the rise in consumption inequality has been relatively mild.We also document that wealth inequality has remained fairly stable https://www.doczj.com/doc/5717874675.html,ing both con?dential data and publicly available data,we are able to gauge the extent to which the publicly available data conceals aspects of inequality that con?dential data reveals.

?2009Elsevier Inc.All rights reserved.

1.Introduction

In this paper we use a variety of data sources to document some salient facts concerning the distribution of wages,hours worked,income,consumption and wealth in Canada.In general,our datasets have two access levels,one publicly available (Public-Use Files,or PUF)and one only available through Research Data Centres(RDC)administered by Statistics Canada. While our main conclusions are drawn from RDC data,we also discuss the extent to which noise introduced by Statistics Canada to protect individuals’identity distorts various measures of inequality.

Income inequality over the last30years or so has risen quite substantially in Canada.Wage inequality,as measured by the variance of log wages,doubled from1977to2005.Indeed,the level and trend of wage inequality,however measured, are remarkably similar to the U.S.over the same period of time(see Heathcote et al.,2010,in this issue).In Canada,most of this rise occurred within skill groups,as the skill premium remained fairly stable until the mid-1990’s,in contrast to the U.S.where the skill premium has been rising consistently since1980.1As we move towards more inclusive measures of income,such as family earnings or total income before taxes and transfers,U.S.and Canadian inequality remain noticeably similar.

Perhaps the most striking?nding of this study is the remarkable role played by the tax and transfer system both to compress inequality and to absorb changes in before-tax income inequality.Disposable income inequality,as measured by

?We would like to thank Jim Davies and David Green for their many comments and suggestions on this project,as well as two anonymous referees,

the Editors,and seminar participants at the Bank of Japan and the Philadelphia conference on Heterogeneity in Macroeconomics and for useful comments. Gervais and Klein gratefully acknowledge?nancial support from the Social Sciences and Humanities Research Council of Canada.The views expressed in this paper are those of the authors and do not necessarily re?ect the o?cial views of the Bank of Japan.

*Corresponding author.

E-mail addresses:brzozows@yorku.ca(M.Brzozowski),gervais@https://www.doczj.com/doc/5717874675.html,(M.Gervais),pklein2@uwo.ca(P.Klein),michio.suzuki@boj.or.jp(M.Suzuki). 1Boudarbat et al.(2006)point out,however,that the rise in the education premium in Canada starts much earlier once experience is controlled for.

1094-2025/$–see front matter?2009Elsevier Inc.All rights reserved.

doi:10.1016/j.red.2009.10.006

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7553

the variance of the log,was essentially?at from1977until1990,a period over which the variance of log pre-government income increased by more than10points.Although disposable income inequality has increased since1990,its rise pales in comparison to that of pre-tax income inequality.2While transfer payments—the main ones being,in order of importance in mitigating income inequality:social assistance,unemployment bene?ts,and various child bene?t programs—are mainly responsible for absorbing changes in pre-government income inequality,both taxes and transfers play a signi?cant role in compressing income inequality.Given the evolution of disposable income inequality,it should come as no surprise that consumption inequality also rose only moderately over our sample period.

An interesting feature of income inequality in Canada is that its evolution revolves around recessions.From1976to 2005,the Canadian economy experienced two recessions:one at the beginning of the1980’s and one at the beginning of the1990’s.Unlike the U.S.,Canada did not experience a recession at the turn of the century.During each recession,wage and income inequality rose substantially,and the declines that followed were not su?cient to offset the rise,resulting in more inequality over time.3While a similar pattern can be detected for disposable income inequality,the movements are much milder and,at least in the1980’s,the rise during the recession was fully offset thereafter.

The previous?ndings also bear on patterns of inequality over the life-cycle,in the sense that the age-pro?le of inequal-ity is much?atter for disposable income(and consumption)than for pre-government measures of income.Interestingly, wage inequality increases almost linearly over the life-cycle,suggesting the presence of highly persistent wage shocks (see Storesletten et al.,2004).However,the rise for earnings inequality tends to start later in life,and fails to show a clear monotonic(let alone linear)pattern.This lack of linearity leads us to question the validity of a unit root process as the main driving force for earnings,although this speci?cation seems reasonable for wages.

Notwithstanding the caveats stated in the previous paragraph,we estimated wage and earnings(permanent–transitory) processes from our Canadian data.Our main?nding is that a very high fraction of the overall cross-sectional variance and also a high fraction of the risk faced by households is accounted for by the“permanent”component as opposed to the transitory component of the process.However,this result is sensitive to the speci?cation of the statistical model.Irrespective of the many caveats,it is interesting to note that in line with our main results discussed above,the tax and transfer system substantially reduces both permanent and transitory earnings risk.

A highly desirable property of distributions is log normality.With that property,a distribution can be fully characterized by its?rst two moments,and two distributions are unambiguously comparable with respect to the degree of inequality. In our data,the cross-sectional distribution of consumption is much closer to log-normal than that of income,much like Battistin et al.(2007)?nd in U.S.and U.K.data.Interestingly,but perhaps not surprisingly given our discussion above, disposable income is also found to be more log-normal than pre-government income.

The main results of this study are closely related to those found in Frenette et al.(2007).Using income data from the Census,they?nd that the1980’s were characterized by a strong rise in before-tax income inequality,but that most of that rise was absorbed by the Canadian tax and transfer system,with the result that after-tax(and transfer)income inequality remained constant.They further report that while before-tax income inequality also increased in the1990’s,this time the tax and transfer system failed to fully offset the rise.As a result,after-tax income inequality also rose in that decade,albeit not to the same extent as pre-tax income inequality.While our?ndings are similar,we choose to stress how small the increase in disposable is relative to the increase in before-tax income inequality,as opposed to their emphasis on the fact that disposable income inequality did rise in the1990’s.

Now the reason why Frenette et al.(2007)use Census data rather than survey data is mainly because they doubt the validity of results obtained though survey data.4Indeed,Frenette et al.(2006)show that income inequality trends in survey data are inconsistent with both Census and tax data.However,perhaps because of these inconsistencies,Statistics Canada implemented a revision to the weights in survey data,mainly in order for the surveys to be consistent with information (from the Canadian Revenue Agency)on wages and salaries.5Although such a revision almost necessarily entails distorting other aspects of the data(such as employment to population ratios)and brings about a break in the series because the revision was only applied retroactively to1990,it seems to have brought income inequality results closer to those that emerge from Census data.Indeed,a look at income inequality from Public-Use Files,which for the most part still feature the pre-revision weights,con?rms that the choice of Frenette et al.(2007)to use Census data was warranted.Our results from Public-Use Files look much like theirs from survey data,and when we compare those results to the results emerging from the revised weights,we are inclined to support their view that the old survey weights led to a distorted depiction of the evolution of income inequality in Canada.6

The rest of the paper is organized as follows.The next section describes our various sources of data and our sample selection.Section3compares measures of average income,consumption,and employment that emerge from survey data to their respective aggregate counterpart.Our main?ndings appear in Section4,where we discuss the evolution of cross-

2It should be noted that the tax and transfer system appears to compress inequality especially at the bottom of the distribution,as evidenced by much smaller movements in the variance of log disposable income than in the Gini coe?cient.

3Heathcote et al.(2010)document that this phenomenon,whereby recessions have a long-term effect on inequality,is also observed in U.S.data.

4While using Census data may have advantages over survey data,it also presents at least two serious drawbacks:(i)the lack of information on taxes paid,which need to be estimated,and(ii)the frequency of data collection(5-year intervals),which can mask changes that occur at higher frequencies.

5The details of this revision and its impact on survey income data can be found in Lathe(2005).

6Our results are not directly comparable,however,as they use a very different sample and a different way to equivalize earnings.

54M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Table1

Data sources.

Data source Variables Sample period

FAMEX Income,expenditure1969,1978,1982,1986,1992,1996

SHS Income,expenditure1997–2005

SCF Income,hours worked1977,1979–1997

SLID Income,hours worked1996–2005

SFS Income,wealth1999,2005

sectional inequality,inequality over the life-cycle,as well as income process estimates and log-normality tests.Section5 examines the advantages of working with RDC data relative to Public-Use Files.A brief conclusion is offered in Section6.

2.Sources of data

2.1.Datasets

As is typically the case,Canada does not have a single survey from which information on consumption,income and wealth is available.Table1lists the data sources with the main variables used and the sample period covered by each data set,which we brie?y describe below(see Appendix A for details).

We take consumption data from the Survey of Family Expenditures(FAMEX)for1969,1978,1982,1986,1992,and1996 and the Survey of Households Spending(SHS)for1997–2005.7In addition to consumption,both surveys contain data on income and standard characteristics(other than education from1997to2003)at the household level,or something close to a household(similar to consumer units in the Consumer Expenditure Survey for the U.S.).See Appendix A.1for details.

For earnings and hours worked,we use data from the Survey of Consumer Finances(SCF)for1977and1979–1997and the Survey of Labour and Income Dynamics(SLID)for1996–2005.8While the SCF only provides cross-sectional data,the SLID has a panel dimension.Speci?cally,the SLID consists of overlapping samples interviewed in six consecutive years,with new waves introduced in1993,1996,1999,2002,and2005.In any given year since1996,then,there are two waves of data available.Because the sample size of the SLID is relatively small from1993to1995,the SCF is deemed to contain better information for these years.Accordingly,we do not use SLID data prior to1996.See Appendix A.2for details.

Wealth data is hard to come by in Canada.The SCF had a wealth supplement in1977and1984,called the ADSCF,and the Survey of Financial Securities(SFS)was introduced in1999and ran again in2005.Because of inconsistencies between the two Surveys,we only use the SFS in this paper.9The unit of analysis in the SFS is the economic family.This survey offers standard balance sheet data from which net worth can be constructed,as well as income and some characteristics of the economic family and the head of the family.See Appendix A.3for details.

2.2.RDC data versus Public-Use Files

Some of the data sets described in Section2.1have two access levels:one publicly available and one only available within the con?nes of Research Data Centres(RDC)located at various institutions throughout the country and administered by Statistics Canada.While the data that we made available emanate from Public-Use Files(PUF),most results contained in the paper emanate from proprietary or RDC data.The main advantage of using RDC data is that these data are not modi?ed in any way or,if they are,a?ag identifying observations that have been modi?ed is supplied in RDC data.

The severity of distortions introduced in PUF data varies across surveys.At one extreme,PUF data for consumption (FAMEX/SHS)are for our purposes identical to RDC data.At the other extreme the panel dimension of SLID data is only available through RDC.10But for income and wealth data,PUF data have some characteristics removed(SCF/SLID)and observations have been shu?ed(SLID)to preserve the anonymity of some of the respondents,mainly households at the top of the distribution.Finally,wealth data(SFS)from our Public-Use Files suffers from the typical top-coding problem that work with many survey data must confront.In Section5we investigate the extent to which using PUF data can replicate results obtained from the original,RDC data.

2.3.Survey weights

The sampling frames of all the surveys used in this study are based on the Labour Force Survey(LFS),a monthly survey equivalent of the Current Population Survey(CPS)in the U.S.Initially,each individual in the LFS sample is given a weight

7FAMEX data are also available for1974,1984,and1990.However,since the survey covers only urban areas and have a smaller sample for those years, we do not include the data in our analysis.

8We do not use SCF data for1978because data on usual hours worked are missing for that year.SCF data was also collected in the early1970’s. However,we chose not to use years prior to1976for consistency reasons.Appendix A.2documents the inconsistencies in detail.

9Morissette et al.(2002)outline ways to make the ADSCF compatible with the SFS.

10The Cross-National Equivalent Files(CNEF)prepared by the Department of Policy Analysis and Management at Cornell University contain a version of the panel aspect of SLID.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7555

Table2

Summary statistics.

198619962005

FAMEX SCF FAMEX SCF SLID SHS SLID SFS

Age40.7640.2541.9241.5740.8143.2742.7943.01 Family size3.11 2.822.87 2.69 2.64 2.85 2.42 2.64 %University0.140.180.190.220.200.300.260.26 With spouse0.710.650.670.600.590.670.540.62 %Immigrant0.190.190.210.180.17n/a0.160.20 Observations71421409471961613413,779902810,814<3868 Notes:The row labeled“Age”reports the age of the head of the household.The2005SHS only provides categorized data on the age of the head.We assign each household head the middle value of the age range to which the person belongs,and report the average over the assigned ages.

equal to the inverse of the probability of selection.These weights are then adjusted to account for non-response and to match census estimates(or projections)for various age-sex groups by province and major sub-provincial areas.

Our income surveys are typically conducted as a supplement to the April(SCF)or January(SLID)LFS,much like the March Supplement to the CPS.Since both SCF and SLID consist of sub-samples of the LFS,the weights for these surveys are initially based on LFS weights.These weights are?rst adjusted for non-response in SCF/SLID(but not for LFS non-response,as this has already been taken care of in the LFS weights),that is,the weight of non-respondents are distributed to respondents. The non-response adjusted weights are then calibrated to ensure that estimates on relevant characteristics of the population (age,sex,province,family size,and household size)match up with census data(or projections from a recent census).

Because of contradicting evidence on the degree and evolution of income inequality coming from different sources of data(tax data,census data,and survey data),as evidenced for instance by the work of Frenette et al.(2006),Statistics Canada recently revised their strategy to calibrate the survey weights.This new strategy adds wages and salary to the set of targets to calibrate survey weights.The targets themselves come from T4slips(equivalent to W4slips in the U.S.),which are employer remittances to Canada Revenue Agency(formerly Revenue Canada)for payroll tax purposes.This new strategy to impute weights is currently used for all surveys that we use in this study,and has been implemented retroactively to 1990for SCF/SLID,and to1996for FAMEX/SHS.All SFS data uses this new methodology as well(see Lathe(2005)for more details).

The result of this new calibration strategy,documented in Rea and Greenlee(2005),is that more weight is given to observations with low/zero wages and salary as well as to observations with high wages and salary.The reason is that a disproportionate fraction of respondents are from the middle of the wages and salary distribution.Practically,as far as SCF data is concerned,this revision implies a higher level of inequality in wages and salary,which carries over to pre-tax income inequality and to a lesser extent to after-tax or disposable income inequality at the individual level.Ultimately,this revision had a similar impact on family/household level income inequality.This revision and its impact should therefore be kept in mind when interpreting the evolution of income and consumption inequality over time in the rest of the paper.

2.4.Sample selection and statistics

The details of our samples are contained in Appendix B.Each sample used in this study is labeled in this appendix.We refer to these labels throughout the paper.Brie?y,we restrict our samples to households whose head is at least25years or age and no older than60.11We also exclude observations with missing characteristics(gender,education,family type, marital status,and province of residence).For income data,we exclude any observation whose income was missing or imputed,as well as observations with a wage rate less than half the minimum wage.We also exclude observations with positive earnings and zero hours worked.For consumption data,we exclude part-year households and households with annual food expenditure less than400Canadian dollars.12In addition,since the territories(Northwest Territories,Nunavut, and Yukon)were not covered by FAMEX surveys,we exclude households from the territories in SHS as well.Finally,for wealth data we exclude outliers and families with missing wealth information.After these restrictions have been imposed, we only exclude observations as necessary to compute the statistics of a particular?gure or table—typically excluding non-positive values of a particular variable.

Table2compares our samples along broad dimensions for three different years.13Except for particularly low fractions of people with a university degree in FAMEX data,and a particularly high fractions of married couples in FAMEX/SHS data, our data sets are fairly consistent with one another.

11The head of household is de?ned as follows:1.If the household has just one member,that is the head.2.If the household has several members,take the set of eldest males between25and60.If this set is a singleton,the only member is the head.3.If the set is empty,take the set of eldest females between25and60.If that set is a singleton then the only member is the head.4.If at this stage we have a set with more than one member(either a set of eldest males or a set of eldest females),choose the member with the highest sum of labour earnings plus the absolute value of business income.If that still does not break the tie,appoint as head the member with the lowest personal id number.

12A full-year household is de?ned as having at least one full-year member,i.e.,a member who was in the household for the entire year;a part-year household is composed entirely of part-year members.

13The samples used for Table2consist of Sample A from Tables11(FAMEX and SHS),13(SCF),15(SLID),and16(SFS).

56M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Table3

Aggregate statistics:1976–2005.

1976–20051976–19791980–19841985–19891990–19941995–19992000–2005

Population 1.10 1.05 1.09 1.35 1.150.92 1.02

Real GDP 2.83 3.81 2.08 3.51 1.52 3.81 2.48

Real GDP per head 1.73 2.760.99 2.150.37 2.89 1.46

Real GDP per hour 1.200.46 1.770.10 1.80 1.64 1.20 Employment rate0.670.630.640.670.660.670.71

Notes.The?rst four rows display average annual growth rates of the variable.Employment rates are annual average employment rates for the20–69age group over the relevant period.

Sources.Population:Statistics Canada,Table051-0001;GDP:Statistics Canada,Table380-0002;Hours worked and employment rates:Labour Force Survey.

Fig.1.Disposable income per capita.

3.Means

The purpose of this section is to compare the evolution of average income and consumption from micro data to their counterparts from national statistics.A similar exercise is performed on employment rates.Before presenting these compar-isons,we provide a brief overview of the Canadian economy.

Table3displays aggregate statistics for the Canadian economy over the1976to2005period,the years covered by most of our micro data.Over those30years,the population of Canada grew at an average annual rate of1.1percent,from23to over32million people.Meanwhile GDP grew at an average annual rate of2.8percent,so GDP per head grew at average rate of1.7percent per year.Both?gures are slightly lower than in the U.S.,where GDP and GDP per head grew at average rates of3.0and2.0percent per year,respectively.Similarly,GDP per hour only grew at an average annual rate of1.2percent over that period in Canada,compared to1.5percent in the U.S.

Fig.1displays real disposable income per capita as reported in the System of National Accounts(SNA)as well as its implied counterparts constructed from survey data.14While the gap between SNA and survey data increased over the years covered by the SCF,it is reassuring that it has been shrinking under SLID.In the last survey year available,as shown in the ?rst panel of Table4,average disposable income was over90percent of the SNA?gure,either from SHS or SLID data.

Fig.2shows that a similar situation prevails for consumption,at least over the SHS years(since1997),with a gap sitting between80and82percent(see second panel of Table4).Furthermore,the ratio of non-durable consumption to income from SHS is consistently only around5percentage points lower than the same ratio from SNA data,as shown in the third panel of Table4for2005.Thus,the situation in Canada for consumption data is not as dire as in the U.S.,where the gap has been rising consistently over the last25years.15For example,Slesnick(2001)reports that the ratio of per capita consumption in the Consumer Expenditures Survey(CEX)to the NIPA estimate of Personal Consumption Expenditures was 0.68in1980,0.61in1990,and0.56in1995.Similarly,Battistin(2003)?nds that the ratio of non-durable expenditures in CEX to the NIPA estimate fell from around80percent in1985to around65percent in the late1990’s.

14All real series in this section were de?ated by the CPI using base year2003.For all survey data,the full sample was used,that is,no sample restrictions were imposed.

15See Crossley and Pendakur(2006)for a discussion of the quality of expenditure survey data in Canada.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7557

Fig.2.Non-durable consumption per-capita.

Table4

Survey to aggregate ratios(%).

1978198619962005

Mean disposable income

FAMEX/SHS93.190.395.791.8

SCF88.384.983.4n/a

SLID n/a n/a84.191.0

Mean non-durable expenditures

FAMEX/SHS86.590.085.882.8

Ratio of non-durable expenditures to disposable income

FAMEX/SHS49.951.646.548.8

SNA53.751.851.954.0

Fig.3.Employment to population ratio.

Fig.3displays employment to population ratios at the aggregate level and from survey data over the sample period. It should be noted that the aggregate employment series also comes from a survey—the monthly Labour Force Survey (LFS).Also note that while most questions in our income surveys pertain to the year prior to the survey year,employment questions in SCF data pertain to the current month(typically April).By contrast,employment information in SLID is available

58M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Fig.4.Basic inequality in hourly wages.Notes.1977–1997:SCF.1996–2005:SLID.

for every month of the previous year.Furthermore,as mentioned in Section2.3,both SCF and SLID surveys are conducted as a supplement to the LFS,that is,they consist of sub-samples of the LFS.16It is therefore surprising to see signi?cant discrepancies between the two series.The discrepancies emanate from two distinct sources.First,the SCF had unusually small samples in1977,1979,1981and1984,which explains the anomalies prior to1990.17The post1990discrepancies can be explained by the2003historical revision of the weights discussed in Section2.3.As a result of this revision,which was applied retroactively to1990,higher weights were assigned to low/no earnings individuals as well as high earnings individuals and had the effect of increasing substantially the fraction of the population not in the labour force.This is re?ected in Fig.3as a low employment to population ratio post-1990in SCF data.18

4.Dimensions of inequality

4.1.Individual level inequality

Fig.4displays four measures of wage inequality.19The wage is de?ned as average hourly earnings,and earnings include wages and salaries as well as the labour share(62percent)of income from self-employment.20The top-left panel shows that wage inequality,as measured by the variance of log wages,increased substantially in the late1970’s and early1980’s, and somewhat more modestly in the early1990’s and around2000.The top-right panel of that?gure shows that a similar pattern emerges when wage inequality is measured by the Gini coe?cient.Over the entire sample,the variance of log wages doubled and the Gini coe?cient increased by9points,from0.28to0.37.It is interesting to note that while high wage earners have been consistently gaining on the median over the sample period(lower right panel),low wage earners falling behind the median is the main reason behind the increase in wage inequality in the late1970’s and early1980’s (lower left panel).Notice that while inequality tends to increase during recessions,its tendency to go back down in between recessions is very mild.

16Since the SCF is typically conducted as a supplement to the April LFS,both series in Fig.3refer to the month of April.For1976and1983,SCF data pertained to the month of May,and so we chose that month for the aggregate series as well for these two years.SLID offers monthly labour force data,so we also used the month of April for the years covered by SLID.

17Survey years1977and1979,which contain data pertaining to1976and1978,have other problems—in particular hours worked is missing—so we dropped these years for the rest of the analysis.

18This is con?rmed by a similar?gure(not shown)constructed using weights available prior to the revision,which shows essentially no discrepancy between the SCF and LFS numbers over the1990’s.

19The samples used in this section consist of Sample A from Tables12and14.

20The labour share of income is taken from the SNA;an average is computed over the period1961:1to2002:1.Speci?cally,the labour share is de?ned as the ratio of wages,salaries and supplementary labour income plus taxes less subsidies on factors of production and gross domestic product at market prices less accrued net income of farm operators from production less net income of non-farm unincorporated business including rent.The precise data source is Matrix6520from CANSIM1.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7559

Fig.5.Wage premia and residual wage inequality.Notes.1977–1997:SCF.1996–2005:SLID.

The bottom-right panel of Fig.5shows that the above pattern of wage inequality is very similar to the pattern of residual wage inequality—inequality unexplained by observables—suggesting that most of the increase in wage inequality cannot be explained by observables.The top-left panel of Fig.5shows the education premium,de?ned as the average wage of males with at least a university certi?cate,a diploma,or a bachelor’s degree,relative to the average wage of males without any such degrees.Interestingly,the education premium remained fairly constant from the beginning of the sample until the mid 1990’s.21Since then,the education premium rose from an average of around40percent from the beginning of the sample until1995to just below60percent in2005.Meanwhile,the fraction of the population with a university degree increased monotonically from14percent in1977to28percent in2005.These patterns are quite different from those observed in the U.S.,where the college premium and the supply of college graduates have been rising simultaneously since the late1970’s (Heathcote et al.,2008).These observations suggest that as opposed to the U.S.,the rise in wage inequality in Canada has mainly occurred within education groups.

The bottom-left panel of Fig.5displays the gender premium,that is,the average wage of males relative to that of females.The gender premium narrowed considerably until the mid1990’s,from37percent in1977to just over20percent in1995,but it has failed to decline in more recent years,averaging around27percent over the SLID years.As a result, the gender gap in Canada is now close to that in the U.S.,but the drop in the gender premium since the late1970’s was more spectacular in the U.S.,where the wage premium was at a much higher level(65percent)than in Canada(37percent) in the late1970’s(Heathcote et al.,2008).The top-right panel suggests that the reverse has happened to the experience premium,measured as the average wage of males aged45–55relative to those between25and35years of age.This premium increased until the mid1990’s and declined sharply during the dot-com years of the late1990’s.However,the experience premium came back up over the last5years of the sample.

The top-left panel of Fig.6shows that,qualitatively,the evolution of wage inequality for both men and women mimics that of the entire population(top-left panel of Fig.4).The widening of the gap between male and female wage inequality which occurs in the1990’s may be an artifact of the retroactive revision of survey weights—recall that as a result of the weight revision,more weight was given to observations with low or no income,which may have affected male and female wages differently.The last10years of SLID data suggest that the variance of log wages for men is around5log points higher than that of women.

Inequality of hours worked,as shown in the top-right panel of Fig.6,paints a drastically different picture for men and women.First,as one would expect,the level of hours inequality is much higher for women than for men throughout the sample.Second,inequality of hours worked for men is much more responsive to business cycle?uctuations than that of women:from1981to1983the variance of log hours for men increased by10points(from0.11to0.21)while it only increased by3points for women(from0.48to0.51);similarly,the variance of log hours from1990to1993increased by

21As pointed out in the introduction,Boudarbat et al.(2006)point out that the rise in the education premium starts much earlier once experience is controlled for.

60M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Fig.6.Inequality of labour supply.Notes.1977–1997:SCF.1996–2005:SLID.

7points for men(from0.19to0.26)and by1point for women(from0.45to0.46).22It is also interesting to note that over the entire sample period,the variance of hours worked for women trended down,while that of men has been essentially stable since the recession of the early1980’s.Finally,the bottom panels of Fig.6show that the correlation between hours worked and wages for men and women alike has been rising throughout the sample period,approaching zero from below. It is interesting to note that the same pattern is observed in the U.S.(see Heathcote et al.,2010).

4.2.Family level inequality

This section pertains to inequality at the economic family level,where a family is de?ned as a group of individuals living at the same address and related by blood,marriage or adoption.23

The next two?gures display various measures of family earnings inequality,where family earnings is the sum of the family members’wages and salaries plus the labour part(0.62)of self-employment income.24Fig.7shows that observables (family type,education,age and region of residence)do not explain much of the trend in earnings inequality,despite the fact that the variance explained by education has generally trended up over the sample period.On average,observables explain around23percent of the variance of equivalized earnings.All measures of inequality in Fig.8show a large rise over the two recessions:the variance of log equivalized earnings increased by14points(from0.59to0.65)from1981to 1983and by20points(from0.59to0.79)from1990to1993.Both episodes were marked by the median gaining on the poor and the rich gaining on the median,although the magnitude of the former is much more pronounced than the latter. Notice that the pattern around recessions is slightly different from wage inequality(see Fig.4),as family earnings inequality measured by the variance of the log tends to decrease after recessions.Note,however,that the level of the Gini coe?cient kept increasing over the last10years of the sample.Over the entire sample,the variance of log earnings increased by 18points(from0.52to0.70)and the Gini coe?cient by7points(from0.31to0.38).

Fig.9shows the variance of log income for many measures of income as well as earnings of household heads.25The top-left panel shows that the distance between pre-government earnings of the head(y H)and of the family(y L)is typically around10to12points.This relatively large distance between these two measures of income inequality suggests that there is substantial family insurance.The bottom-left panel shows that?nancial income(the difference between y and y L+)has virtually no impact on inequality.While private transfers(the difference between y L and y L+,shown in the top-left panel) do not play a big role in mitigating inequality,its role has been increasing over time.But certainly the most startling feature

22We similarly found the following variables to?uctuate more for males than for females over business cycles:the employment to population ratio, unemployment rate,and participation rate for the population aged15and above in Canada.

23Economic families may differ from households,de?ned as a person or a group of persons living at the same address.

24The sample used for these two?gures consists of Sample D from Tables13and15.

25The sample used for this?gure consists of Sample C from Tables13and15.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7561

Fig.7.Earnings inequality and its decomposition.Notes.1977–1997:SCF.1996–2005:SLID.

Fig.8.Basic inequality of equivalized earnings.Notes.1977–1997:SCF.1996–2005:SLID.

of this?gure is the role played by the tax and transfer system,which is shown in the bottom-right panel as the distance between pre-government income(y)and disposable income(y D).Not only does disposable income exhibit much less inequality than pre-government income,but the degree of inequality is also much less variable than that of pre-government income.This suggests both that Canadian policy has been and remains redistributive,and that it smooths cyclical shocks to pre-tax income inequality.

62M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Fig.9.From wages to disposable income.De?nitions.y H:pre-government earnings of head;y L:pre-government family earnings;y L+:pre-government non-?nancial income of family;y:pre-government family income;y D:total family disposable income.Notes.1977–1997:SCF.1996–2005:SLID.

To get some perspective on the redistributive effects of public policy,it is useful to look at the effects of different aspects of policy separately,as illustrated in Fig.10.26The most obvious distinction is that between tax policy on the one hand and transfers on the other hand,noting that this distinction is to some extent a matter of arbitrary?at.The most important government transfer programs in Canada come under three headings:unemployment bene?ts,social assistance and various child bene?t programs.Together these programs are more signi?cant in bringing down inequality than the tax system is,as illustrated in the top panel of Fig.10.The bottom panel suggest that of the three transfer programs,social assistance has the largest impact,followed by unemployment bene?t.Note,however,that the role of child bene?ts has increased since that program was reformed in1993(see Frenette et al.,2007).

This?gure also shows some noticeable changes over time.The?rst is that the correlation between pre-government inequality and post-government inequality seems to have disappeared(see bottom-right panel of Fig.9as well).Post-government inequality exhibits very small cyclical?uctuations after1996and those movements that do occur are uncor-related with the corresponding movements in pre-government earnings and income.27Finally,while after-tax inequality remained fairly stable over the?rst half of our sample period,it increased quite substantially(8points)in the second half, from0.24in1989to0.32in2005.28

Table5presents more evidence of our last result.29In particular,Fig.10showed that transfer programs were most important in curbing the rise in before-tax income inequality.The evolution of the50/10and90/50ratios shown in Table5 suggests that,as one might expect,these transfers were most successful in curbing income inequality at the bottom rather than at the top of the distribution.This table is also meant to compare our results to those of Frenette et al.(2007),who use income data from the Census to characterize the evolution of income inequality over the1980–2000period.They conclude that most of the strong rise in before-tax income inequality over the?rst decade was absorbed by the tax and transfer system,leaving after-tax(and transfer)inequality unchanged.However,the equally strong increase in before-tax inequality in the1990’s was accompanied by an increase in after-tax(and transfer)inequality,albeit not of the same size.Our results

26The sample used for this?gure consists of Sample B from Tables13and15with the bottom0.5percent of pre-government income trimmed.We chose to use a broader sample for this?gure as it is important to include observations with zero earnings in examining the role of government policies such as the unemployment insurance and social assistance.However,because the sample selection is very inclusive,the statistics became sensitive to very few observations,which explains our trimming strategy.

27It is interesting to note that over the SLID years(from1996),there was no recession in Canada.Over that sample period,pre-government income inequality is falling while disposable income inequality is rising.An interesting interpretation of these movements,which was suggested by a referee,is that over these“good times”government programs have become less progressive while at the same time the poor were catching up to the rich.Indeed, over that period of time the P50–P10ratio for pre-government income decreased,while that of disposable income didn’t move very much.

28This suggests that public policy has become gradually less redistributive in its effects,though not necessarily in its intent,since the beginning of the 1990’s.

29The same sample as Fig.10is used for this table.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7563

Fig.10.From pre-government income to disposable income.De?nitions.y:pre-government family income;y D:total family disposable income;y+tran: pre-government family income plus total transfers;y?tax:pre-government family income minus total taxes paid;y+ui:pre-government family income plus unemployment bene?ts;y+sas:pre-government family income plus total social assistance transfers;y+cbn:pre-government family income plus child bene?ts transfers.Notes.1977–1997:SCF.1996–2005:SLID.

Table5

Pre-and after-tax income inequality.

Year Pre-government family income(y)Total family disposible income(y D)

Varlog50/1090/50Gini Varlog50/1090/50Gini

19800.4930 2.4427 1.99460.32170.2669 1.9509 1.83990.2741 19850.5858 2.6175 1.99710.33960.2785 1.9675 1.80250.2810 19900.5990 2.7109 2.00160.34110.2622 1.9169 1.80550.2708 19950.7217 3.0276 2.07190.36610.2884 1.9554 1.84330.2847 20000.6846 2.8973 2.05080.37030.2853 1.9647 1.84660.2926 20050.6639 3.0021 2.15090.38050.3188 2.0464 1.91320.3058

Growth(%)

1980–200044.4018.58 5.6615.888.00?2.91 2.04 6.56 1980–199021.5110.980.35 6.03?1.75?1.74?1.87?1.21 1990–200018.14 5.99 5.299.339.92?1.13 3.967.84 1980–198518.837.160.13 5.57 4.370.86?2.03 2.51 1985–1990 2.25 3.570.230.44?5.86?2.580.17?3.64 1990–199520.4911.68 3.517.339.98 2.01 2.09 5.14 1995–2000?2.61?6.00 1.72 1.92?0.03?3.14 1.85 2.68 2000–2005?3.02 3.62 4.89 2.7611.75 4.16 3.61 4.53

Notes.All changes that involve years over which SCF and SLID overlap are computed as the sum of the change in SCF until1996and the change in SLID from1996.

in Table5reinforce that conclusion by reporting increases of much larger magnitude than their estimates from Census data. As we will see in Section5,the weight revision was instrumental in obtaining these results.

4.3.Consumption inequality

We now turn our attention to consumption inequality,where consumption refers to non-durable expenditures.

64M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Fig.11.Consumption inequality and its decomposition.Notes.1969–1996:FAMEX.1997–2005:SHS.

Fig.12.From disposable income to consumption.Notes.1969–1996:FAMEX.1997–2005:SHS.

Fig.11shows that consumption inequality exhibits a rising trend.30In the“raw”data,where no adjustment has been made for family size,the variance of the log has almost doubled in30years.However,this is largely because of the rise in single-member households;the fraction of households that had a single member went up from8percent in1969to21per-cent in2005.Once the data have been divided by the number of adult-equivalents(equivalized),the rise in inequality is less pronounced and only amounts to about3points,from0.2086in1969to0.2446in2005.

Fig.12juxtaposes the changes in consumption inequality as measured in four different ways with the corresponding changes in the inequality of disposable income.31The main thing to take away from that?gure is that consumption in-

30The sample used for this?gure consists of Sample A from Table11.

31The sample used for this?gure consists of Sample B from Table11.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7565

Fig.13.Inequality over the life-cycle(time effects).

equality is consistently lower than disposable income inequality.For the variance of the log,consumption inequality is typically10to15points lower than disposable income inequality.Also,at least for the variance of the logs,the two tend to move up and down together,although consumption inequality is less volatile.Note,however,that these conclusions are based on relatively few years of observation.

4.4.Inequality over the life-cycle

The evidence on life-cycle pro?les of the variance of hours,wages,earnings and consumption is reported in Fig.13,where we control for time effects and Fig.14,where we control for cohort effects.32Interestingly,both?gures are qualitatively similar,although controlling for cohort effects systematically leads to steeper inequality pro?les—albeit not to the same extend as with U.S.data(see Heathcote et al.,2010).For wages,the picture is clear:variance increases monotonically over the life-cycle.For raw earnings,the increase is more or less monotonic,but the pro?le is convex.For equivalized earnings, there is no monotonic increase whether we control for time or cohort effects,the pattern is instead J-shaped.A reasonable conjecture is that earnings inherit this convex pro?le as a combination of permanent wage shocks,inducing a linear log-wage variance pro?le,together with an endogenous labour supply,in particular if the correlation between wages and hours is U-shaped over the life-cycle—a feature emphasized by Blundell and Etheridge(2010)in this issue.33Finally,the bottom panels of Figs.13and14show that the variance of both disposable income and consumption exhibit very little changes in inequality over the life-cycle.This is perhaps a re?ection of the role played by government policy in compressing inequality which we emphasized previously.

The behavior of earnings inequality over the life-cycle is particularly interesting.The lack of a clear monotonic(let alone linear)pattern is in sharp contrast to the results constructed and presented in Storesletten et al.(2004)for the U.S.This matters because it is precisely the linearity of the cross-sectional variance reported there that has motivated the profession to write down a unit root process as the main driving force for earnings;indeed we follow that approach in this paper as well.The facts reported in Figs.13and14cast some doubt on the appropriateness of that approach,at least when applied to Canadian earnings,though it does seem to hold for wages.

32The samples used in these?gures consists of Sample A of Tables12and14for individual level income data,and Sample D of Tables13and15for family level income data.For consumption data,Sample B from Table11is used.

33A convex earnings pro?le may also lend some support for the“heterogeneous income pro?le”emphasized by Guvenen(2009).

66M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Fig.14.Inequality over the life-cycle(cohort effects).

Table6

Disposable income and net wealth.

19992005

Net?nancial wealth/disposable income 2.8841 3.2328

Net total wealth/disposable income 5.6318 6.8045

Net worth/disposable income 6.30667.4307

Gini index of disposable income0.33550.3359

Gini index of net?nancial wealth0.70540.6992

Gini index of net total wealth0.66640.6636

Gini index of net worth0.66030.6590

https://www.doczj.com/doc/5717874675.html, total wealth is net?nancial wealth plus net residential real estate and business https://www.doczj.com/doc/5717874675.html, worth is net

total wealth plus other net wealth including vehicles.(Source:SFS-RDC.)

4.5.Wealth inequality

Morissette et al.(2002)document that wealth inequality went up in Canada from1984to1999.In particular,the Gini coe?cient for equivalized net wealth went up from0.678to0.723over that period of time.We extend this analysis by considering the year2005as well.Note that our numbers are not directly comparable to theirs,chie?y because we con?ne our attention to working-age-headed households.We look at three measures of wealth which we call net?nancial wealth, net total wealth and net worth,https://www.doczj.com/doc/5717874675.html, total wealth is de?ned as net?nancial wealth plus net residential real estate and business https://www.doczj.com/doc/5717874675.html, worth is simply total assets minus total liabilities.

Table6reports wealth to after-tax(disposable)income ratios and Gini coe?cients for our income and wealth measures.34 For all three wealth measures,the wealth to income ratio increased between1999and2005.The Gini coe?cients of the three wealth measures are about twice as large as those of disposable income.For all income and wealth measures,the Gini coe?cient remained stable between1999and2005.Table7reports correlation between income and wealth and the share of the top1and5percentile in the income and wealth distributions.For all wealth measures,the correlation with disposable income has increased between1999and2005.The share of the top1percentile in the wealth distribution is about three times as high as that for disposable income.

34The sample used for this table consists of Sample A from Table16.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7567

Table7

Disposable income and net wealth.

19992005

Correlation coe?cient

(Net?nancial wealth,disposable income)0.36550.4377

(Net total wealth,disposable income)0.35510.4146

(Net worth,disposable income)0.34700.4255

Share of the top1percent

Disposable income0.05410.0583

Net?nancial wealth0.16350.1449

Net total wealth0.16650.1749

Net worth0.15680.1668

Share of the top5percent

Disposable income0.16340.1719

Net?nancial wealth0.41430.3926

Net total wealth0.37020.3817

Net worth0.35140.3639

https://www.doczj.com/doc/5717874675.html, total wealth is net?nancial wealth plus net residential real estate and business https://www.doczj.com/doc/5717874675.html, worth is net

total wealth plus other net wealth including vehicles.(Source:SFS-RDC.)

Relative to the U.S.,wealth is much less concentrated in Canada.For example,the level of the Gini coe?cient,around 0.66,is low relative to an average of0.77as reported by Heathcote et al.(2010)for the U.S.over the last20years or so.More spectacular is the comparison of the fraction of the wealth held by the top of the wealth distribution.While the top5percent in Canada hold about35percent of the wealth,Budría Rodríguez et al.(2002)report that in1998 the top1percent in the U.S.held about that same fraction of the wealth.The top1percent in Canada only hold about 16percent of the wealth.In addition,it appears that income and wealth are more correlated in the U.S.than in Canada:in 1998,the correlation between income and wealth in the U.S.was0.6,whereas that between disposable income and wealth in Canada was only0.35in1999.35

4.6.Wage/income processes

In this section,we examine(exogenous)idiosyncratic income risk that individuals and families face by estimating a stochastic process representing the dynamics of individual wages,equivalized family earnings and equivalized family dis-posable income.36For this estimation,we use data from SLID exclusively as only this survey provides panel data on income variables as well as individual and family characteristics.In order to extract the idiosyncratic component of a given variable, we?rst regress the variable of interest on observables and take residuals from the regression.37We control for age,gen-der,marital status,education,province of residence,immigration status and mother tongue in individual wages,while we control for head’s and spouse’s(if present)characteristics listed above as well as family type and the number of earners for family earnings and disposable income.Let u it denote the residual earnings/income of person/family i at time t.We model the dynamics of the residuals by the following stochastic process:

u it=αit+εit,

αit=αit?1+ηit,

whereαit represents the permanent component of the residual earnings/income,εit represents the transitory component, andηit represents innovation to the permanent component.We assume thatεit andηit are i.i.d.in the cross section with E[εit]=0,E[ηit]=0,V ar(εit)=σ2ε,t,and V ar(ηit)=σ2η,t for all t,that E(εisηit)=0for all s,t and that E(εisεit)= E(ηisηit)=0for all s=t.

In Table8we present results from estimating processes for individual wages,equivalized family earnings and equivalized family disposable income.The estimation process is constructed so as to match the autocovariance function of log differ-ences.38The result is that a very high fraction of the overall cross-sectional variance and also a high fraction of the risk faced by households is accounted for by the permanent component as opposed to the transitory component.39Note that the

35Note that for the U.S.the correlation is with respect to pre-government income,as the Survey of Consumer Finances in the U.S.does not have any tax information.

36The samples used in this section consist of Sample A from Tables12and14for individual level data,and Sample C from Tables13and15for family level data.

37We run the cross-sectional regressions year by year,allowing coe?cients to vary over time.

38See Domeij and Flodén(2010)in this issue for details of our estimation procedures.

39Mechanically,using?rst difference moment conditions,the magnitude of the estimate forσ2εdepends on the covariance between subsequent log differences.If subsequent log differences are not highly correlated,which they are not,we are led to conclude that transitory shocks account for a small fraction of the overall variance and risk.

68M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Table8

Parameter estimates for the earnings process.

Individual wage Equivalized family

earnings Equiv.family disposable income

σ2εσ2ησ2εσ2ησ2εσ2η

19940.05980.05880.02960.10390.00960.0300

19950.05350.05880.03060.09800.00840.0326

19960.05780.05920.02270.09660.00790.0335

19970.06320.05230.02690.09030.00890.0316

19980.05720.05380.02650.08580.00800.0306

19990.07330.04800.01820.09540.00910.0341

20000.07210.04850.01920.08090.01050.0292

20010.06390.05360.01850.08570.00880.0297

20020.05960.05660.02450.07310.01550.0302

20030.05790.05360.02400.06850.01220.0224

20040.05130.05830.02940.06730.00920.0269

20050.05130.06910.02940.08520.00920.0298

Mean0.06090.05470.02500.08590.00980.0301

Notes.σ2εandσ2ηare the variance of the transitory shock and that of the permanent shock,respectively.

Fig.15.Variances of permanent and transitory shocks(wage process).Notes.Estimates based on SLID1993–2005.

estimated variance of the permanent shock for wages,at around0.055,implies much higher inequality over the life-cycle than is reported in Figs.13and14.Indeed,Fig.15shows that estimating our model using moments in levels rather than in ?rst differences produces drastically different estimates.While the variance of transitory shocks based on the moments in levels is much higher than that based on moments in differences,the opposite holds for the variance of permanent shocks. This pattern is evidently not unique to Canadian data,as similar results in this issue can be found for Sweden(Domeij and Flodén,2010),Germany(Fuchs-Schündeln et al.,2010),and the U.S.(Heathcote et al.,2010).

The previous caveat notwithstanding,Table8also reports estimates forσ2η(permanent risk)andσ2ε(transitory risk)for equivalized family earnings and disposable family https://www.doczj.com/doc/5717874675.html,ernment policies such as progressive taxation,social welfare programs,and employment insurance are designed to mitigate earnings risk that families face.In order to examine the extent to which government policies reduce earnings risk,we compare estimates for equivalized family earnings and dis-posable income.Much like our previous?ndings,our results suggest that the tax and transfer system substantially reduces both permanent and transitory earnings risk,with the permanent and transitory risk reduced on average by5.58point (from0.0859to0.0301)and1.52point(from0.0250to0.0098),respectively.

4.7.Log-normality tests

A highly desirable property of distributions is log normality.With that property,a distribution can be fully characterized by its?rst two moments,and two distributions are unambiguously comparable with respect to the degree of inequality.In particular,if earnings are log-normally distributed,it can never happen that the Gini coe?cient goes up but the variance of log earnings goes down.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7569

Fig.16.How log normal are consumption and earnings(1940’s birth cohort).

We investigate log-normality using two approaches.The?rst is formal tests,including the Kolmogorov–Smirnov and the Skewness–Kurtosis test.40These tests tell us whether the deviations from normality that we observe are statistically signi?cant.A further question,though,is whether these deviations are su?ciently large to be important.To address that issue,we use Epanechnikov(1969)’s kernel density estimation in order to compare non-parametrically estimated densities with the corresponding normal densities.

The results from formal tests are on the whole negative.For earnings,we can always reject log-normality,no matter what the test,no matter what the year,no matter what the cohort and no matter what the(reasonable)signi?cance level. The situation with consumption is rather different.As pointed out in Battistin et al.(2007),consumption is more log-normal than earnings.In fact,for observations in1982,1986and1992and using the Kolmogorov–Smirnov test,we cannot reject,at the5percent level,log-normality of the cross-sectional distribution of consumption among two cohort groups:those born in the1940’s and those born in the1950’s.For other tests and other samples,however,we can reject normality.

Turning our attention to the second approach,consider Fig.16.This?gure plots non-parametrically estimated probability density functions along with their normal distribution counterparts for the1940’s birth cohort.41It is very clear from these ?gures that log consumption is closer to normal than log earnings.Indeed,an inspection of the skewness and kurtosis of log consumption reveals that the distribution is very nearly symmetric and exhibits only a little more kurtosis than the normal distribution.The difference is barely visible to the naked eye.Thus log-normality is an excellent approximation of the distribution of consumption.

For earnings,things are quite different.The distributions are visibly skewed to the left(the mean is to the left of the mode)and strongly leptokurtic(the density has a sharper peak and fatter tails than the normal distribution).Log-normality is not a particularly good approximation of the distribution of earnings.42

40All the results in this section are based on data from FAMEX/SHS using sample B from Table11.

41Similar pictures emerge from other survey years and cohorts.

42We also estimated densities for wages from SCF/SLID data,obtaining similar results.Interestingly,log-normality is not as bad an approximation for disposable income.Indeed,there is an instance where we could not reject log-normality of the cross-sectional distribution of disposable income.This was for the1950’s cohort for observations in1982.

70M.Brzozowski et al./Review of Economic Dynamics13(2010)52–75

Table9

Pre-and after-tax income inequality from Public-Use Files.

Year Pre-government family income(y)Total family disposable income(y D)

Varlog50/1090/50Gini Varlog50/1090/50Gini

1980n/a n/a n/a n/a n/a n/a n/a n/a 19860.5639 2.6657 1.99360.32840.2670 1.9610 1.82540.2709 19900.5610 2.6621 1.95520.32730.2498 1.9210 1.76820.2611 19950.6359 2.8613 2.00360.34020.2622 1.9373 1.79190.2665 20000.6080 2.8182 2.02670.34380.2724 1.9639 1.81790.2740 20050.6751 3.0673 2.13700.36760.3103 2.0677 1.88010.2920

Growth(%)

1986–20000.45?3.16 1.810.46?1.95?2.990.26?1.62 1986–1990?0.51?0.13?1.93?0.33?6.45?2.04?3.13?3.60 1990–2000 1.03?3.02 3.810.81 4.92?0.94 3.45 2.09

1980–1985n/a n/a n/a n/a n/a n/a n/a n/a 1986–1990?0.51?0.13?1.93?0.33?6.45?2.04?3.13?3.60 1990–199513.347.48 2.48 3.95 4.980.84 1.34 2.04 1995–2000?12.29?10.55 1.30?3.18?0.13?1.78 2.100.03 2000–200511.038.84 5.44 6.9113.89 5.29 3.42 6.57

Notes.All changes that involve years over which SCF and SLID overlap are computed as the sum of the change in SCF until1996and the change in SLID from1996.

5.A view of inequality from Public-Use Files

It may be of some interest to compare the conclusions about trends in inequality we draw in Section4from the ones that would be drawn from Public-Use Files(PUF).PUF data differ from RDC data in two important respects.First,Statistics Canada introduces noise in PUF data in order to preserve the identity of the respondents.Second,the revised weights are not currently available in PUF for the SCF sample.Below we brie?y review how the main message from RDC data is altered when using public data for income and wealth—recall that for our purpose,there is no distinction between RDC and PUF for consumption data.

5.1.Income inequality

To see what Public-Use Files tell us about trends in income inequality,consider Table9and contrast it with the corre-sponding results from RDC data,displayed in Table5.One striking result is that the level of inequality,however measured,is understated in Public-Use Files.In terms of changes,the difference is even more striking.For example,the Public-Use Files suggest that the level of inequality has barely changed from1986to2000.In particular,it completely misses the increase in inequality in the1990’s,which led Frenette et al.(2007)to abandon survey data in favor of Census data.43These results also cast doubt on previous studies that have used PUF data to document the evolution of various measures of income inequality and their implications(for example,see Burbidge et al.,1997and Beaudry and Green,2000).

5.2.Wealth inequality

One aspect that PUF data typically have problems with is the very top of the distribution(because of top coding),and that is of course particularly important for the wealth distribution.Table10sheds some light on that.The Public-Use Files for the SFS suffer from top-coding problems where each observation above a certain threshold is given the value of that threshold.Since we have access to RDC data,in which no observation is top-coded,we can compare the accuracy of different statistical methods to impute top-coded observations in terms of various measures of inequality.

What we do is the following,taking net?nancial wealth as an example.First we consider the components of net?nancial wealth,like mutual fund holdings,mortgage debt,etc.For each such component,we consider the top decile with the idea that top decile has been drawn from a Pareto distribution.Excluding the top-coded observations,we then use the remaining observations in the top decile to estimate the single(remaining)unknown parameter of the Pareto distribution.This can be done either by least squares or maximum likelihood and we report the results from both approaches in Table10,labeled Public3and Public4respectively.Having estimated the parameter,one can then mechanically compute the mean of the distribution and replace the top-coded values with that mean.As Table10reveals,both methods work pretty well.For the Gini coe?cient of any of the wealth categories,the estimate is at most1percent away from the RDC value.However,the estimates are not as precise for the top1percent.

43Some of the changes between2000and2005are due to the revision of survey weights as SLID data for2000feature old weights based on Census 1996,while the SLID data for2005feature the revised weights based on Census2001.

M.Brzozowski et al./Review of Economic Dynamics13(2010)52–7571

Table10

Comparison of Public-Use and con?dential SFS1999.

Public1Public2Public3Public4RDC data

Share of top1%

Disposable income0.04810.04810.04820.04830.0541

Net?nancial wealth0.12460.14310.18410.19660.1635

Net total wealth0.11610.14240.16230.18310.1665

Net worth0.10660.13230.15090.16830.1568

Gini index

Disposable income0.32520.33030.33190.33200.3355

Net?nancial wealth0.67980.69260.70140.70320.7054

Net total wealth0.63480.65360.66160.66850.6664

Net worth0.62740.64560.65320.65910.6603

Notes.The column designated Public1reports estimates for the sample excluding observations with top-coded values.Public2reports the estimates for the sample including observations with top-coded values.Public3corrects for top-coding by OLS estimation suggested by David Domeij.Public4corrects for top-coding by maximum likelihood estimation.The estimation is conducted for each income and wealth component,since top-coding is done at the component level.For the estimation,the sample of families with the given variable above the90th percentile and below the top-coding threshold is used.

6.Concluding remarks

This paper characterizes various aspects of inequality in Canada over the last30years or so.All measures of income inequality have increased over these years.Most notable is the rise in wage and earnings inequality,which were to a large extent offset by the tax and transfer system to produce a moderate rise in disposable income.As a result,the rise in consumption inequality has also been fairly mild,though still noticeable.While we emphasize the role of government policy in compressing inequality,much work remains to be done to identify the precise role of speci?c components of the tax and transfer system in mitigating the trend as well as movements in income inequality.44Another interesting?nding is the permanent role played by recessions in increasing inequality.Decomposing this rise and analyzing what makes it permanent also seems like a worthwhile endeavor,especially since this phenomenon is not unique to Canada.

In light of the recent work of Frenette et al.(2006)and Frenette et al.(2007),our results suggest that the revision of the weights that Statistics Canada has recently implemented was valuable,in the sense that these revisions brought measures of inequality in Survey data much closer to the evidence emanating from Census data.In particular,our results tend to support the broad conclusion on the evolution of income inequality reached by Frenette et al.(2007).

Appendix A.Detailed sources of data

A.1.Consumption data

The Survey of Family Expenditures(FAMEX)and the Survey of Household Spending(SHS)provide cross-sectional data on individual and household characteristics,income,and expenditure.For both surveys,income and expenditure data refer to a calendar year(called reference year).Data are collected through personal interviews conducted in the?rst quarter following a given reference year.FAMEX data are available for1969,1974,1978,1982,1984,1986,1990,1992,and1996.But the surveys for1974,1984,and1990cover only urban areas and have a smaller sample(around7000households instead of 14,000or so for the years with national coverage).The SHS replaced the FAMEX in1997and has been conducted annually thereafter.Currently,the latest data are for2005.

For1969–1986,expenditure data are collected for spending units.Spending unit is de?ned as a group of persons depen-dent on a common or pooled income for the major items of expense and living in the same dwelling or one?nancially independent individual living alone.In1990,the unit of analysis was replaced by households,which is de?ned as a person or a group of persons occupying one dwelling unit.

Total family disposable income after taxes and transfers(y D)can be constructed for the whole sample period.However, pre-government family earnings(y L),which is de?ned as the sum of wages and salaries and the labour part of self-employment income,cannot be constructed in a consistent manner over time,since wages/salaries and self-employment income are not separately available over the1997–2005period.We use nondurable goods expenditure as our measure of consumption.Nondurable goods expenditure consists of the expenditure on food,alcohol and tobacco,personal care supplies and services,water,fuel,and electricity,household operation,public transportation,operation of automobiles and trucks,apparel,recreation,reading,education,traveler accommodation,health care,and miscellaneous nondurable expendi-tures.We de?ate income by region-speci?c CPI for all items.We de?ate each expenditure component by the corresponding region-speci?c CPI.

Unfortunately,no information on education is available from1997to2003.Thus,we cannot conduct analysis involving education level for those years.

44The most important reforms are probably the replacement in1991of the Manufacturers Sales Tax(MST)with the Goods and Services Tax(GST),which is a federal value added tax,as well as the income tax reform of1987.

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