Mobility and Instability in Canadian Earnings

Mobility and Instability in Canadian EarningsAuthor(s): Bruce KennedySource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 22, No. 2(May, 1989), pp. 383-394Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/135675 .

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Mobility and instability in Canadian earnings BRUCE KENNEDY Institute for Research on Public Policy

Abstract. A model of individual earnings dynamics that admits population heterogeneity with respect to both the level and the variability of individual earnings series is applied to an investigation of the distribution of earnings instability among mature male earners. The results tend to support Gibrat's 'law of proportional effect' rather than expectations based on dual labour market theory or on the notion of compensating differentials for unemployment risk. An additional assessment of the amount of transitory variation in Canadian earnings data finds it to be small compared with the permanent component of earnings differences.

Mouvance et instabilite dans les gains au Canada. L'auteur examine la distribution de l'instabilite des gains chez les hommes d'age mur 'a l'aide d'un modele de la dynamique des gains individuels qui tient compte de l'heterogeneite de la population, tant pour ce qui est du niveau que de la variabilite dans les series de gains individuels. Les resultats tendent 'a supporter la loi de l'effet proportionnel de Gibrat plutot que les presomptions fondees sur la theorie duale du march6 du travail ou la notion de differentiels compensatoires pour les risques de chomage. On montre aussi que la variation transitoire dans les donnees canadiennes sur les gains est faible quand on la compare 'a la composante permanente dans les differentiels de gains.

INTRODUCTION AND CONCLUSIONS

Several conflicting hypotheses exist concerning the relationship between the level of earnings of individuals, and the amount of variation or instability they experience in their earnings over time. Gibrat (1931) postulates 'the law of proportionate effect,' which asserts that random changes in personal income are likely to be proportional to the level of income. This implies independence between earnings level and earnings variation, net of scale effects. Individual choice theory (Friedman, 1953) suggests a

This paper is prepared in connection with a pension policy simulation project being conducted by the Social and Economic Studies Division, Statistics Canada, in association with The Institute for Research on Public Policy. I am grateful to Michael Wolfson of Statistics Canada and Rod Dobell of IRp for their guidance and support, to Dave Cogliati of Health and Welfare Canada for the data, and to Robert M. Solow of MIT and Jim McDavid of the University of Victoria for their helpful comments.

Canadian Journal of Economics Revue canadienne d'Economique, XXII, No. 2 May mai 1989. Printed in Canada Imprime au Canada

0008-4085 / 89 / 383-394 $1.50 ? Canadian Economics Association



384 Bruce Kennedy

trade-off between high earnings levels and earnings security, with the implication that earnings level and earnings variation should be positively correlated. Segmented labour market theories assert that high earnings variation is a characteristic that is strongly associated with the low-paying, secondary labour market (Cain, 1976, 1237), implying a negative correlation.

Despite the existence of a rich literature on individual earnings dynamics, the seemingly simple issue raised above remains unresolved owing to a number of factors tending to frustrate research on earnings instability. First, the longitudinal datasets required for this type of research are scarce and those sets available are generally of short duration. Second, there has been a lack of a consistent framework within which to discuss and measure earnings mobility. The terms 'mobility,' 'uncertainty,' 'instability,' and 'variability' are used in the earnings dynamics literature, sometimes interchangeably and sometimes referring to different concepts. Finally, while it has been recognized for some time that earnings instability can be measured only in the context of a model of earnings dynamics, (see David, 1975, 226), the models developed to date are unsuited to investigating the distribution of earnings instability.

Most existing models of individual earnings dynamics use error structures that combine an individual component with either a moving average process (Friedman, 1945; Hause, 1977) or with an autoregressive process (David, 1971; Hause, 1977; Lillard and Willis, 1978; Ashenfelter, 1978). These models have some appeal, for present purposes, because they provided a neat decomposition of individual earnings dynamics into an expected component embodying stability, immobility, and permanent differences, and a random transitory component embodying instability. They cannot address the distribution of earnings instability, however, because the variance of their random components are by assumption constant across individuals.

The other common formulation, 'the random growth rate model' (Hause, 1977; Lillard and Weiss, 1979) has the same limitation and is less useful here because the presence of individual trend components prevents a neat decomposition of longitudinal earnings into variation across individuals and variation over time. The latest development in the field involves adapting ARIMA time-series analysis (curve-fitting) techniques to longitudinal data (MaCurdy, 1982). One starts with a very general error structure and uses adapted Box-Jenkins (1970) diagnostics to identify models that fit the data well. As MaCurdy (1982, 88) points out, the more traditional approaches generally impose a specific error structure on the data without checking its appropriateness or testing alternate specifications. The ARIMA approach, however, can lead to a complex specification that is difficult to interpret structurally in the context of the issues of interest.

The approach taken here has been to specify a model structure on the basis of consistency with existing theory and convention, and appropriateness for performing the intended analysis. Once estimated, the model specification is tested using simulation techniques and ARIMA diagnostics.

Like several models listed in the first group above, the model employed perceives longitudinal earnings data as a set of individual ARI time-series with different intercepts or long-run mean earnings levels. Unlike the earlier models, however, this



Mobility and instability 385

model does not impose any constraints on the distribution of earnings variation across individuals and does not employ a log-eamings domain. The latter point is significant because the conventional transformation to log earnings compresses deviations at high levels of earnings. This can lead to biased assessment of the distribution by level of earnings instability.'

The model is estimated and tested using eighteen-year-long earnings histories of middle aged males with continuous labour force attachment. The data source is a Canada Pension Plan administrative dataset. The specification test suggests that individual earnings dynamics can be well characterized by this heterogeneous ARi

model despite its lack of the individual linear trend components that have become popular.

The primary result is that (for middle-aged Canadian males with continuous labour force attachment) workers at all levels of earnings tend to experience about the same amount of fluctuation in their earnings when fluctuations are measured in terms of percentages of their 'normal' earnings. This is precisely the result predicted by Gibrat's 'law of proportional effect.' 2

The secondary result is that following an unstable period of earnings 'adoles- cence,' few mature individuals make large long-term gains or losses in earnings relative to those of their cohort. Permanent differences between individual levels of earnings, rather than transitory fluctuations, account for the bulk of the earnings differences evident in cross-sectional data. The same 'stylized fact' has also been produced using u.s. data and somewhat different models (see, e.g., Lillard arid Willis, 1978).

The following material describes the data source, the model, the estimation of the model, the findings concerning the distribution and amount of instability, and the specification test performed on the model. The final section comments on the generali- zation of these results from the 'mature male earner' group upon which the analysis is focused to broader populations.

THE DATA

The database used for this analysis is a Canada Pension Plan administrative file called 'Record of earnings file M500 1.' It is very broad in the sense that it contains earnings

1 See for example Wolfson (1975), which uses the coefficient of variation of log earnings as the measure of instability. Also reported in Vaillancourt (1985, 6).

2 This observation may also be consistent with the compensating differentials for unemployment risk hypothesis depending upon assumptions made about risk aversion. The notion of a 'menu of implicit contracts' in conjunction with Arrow's (1971) postulate of decreasing absolute risk aversion suggests a positive association between level and standard deviation of earnings and would find support in this study (see Bellante and Link, 1982, 593). Arrow's second postulate, increasing relative risk aversion, does not find support, since it suggests a negative association between level and cv of earnings. It should also be noted that the observation is not necessarily inconsistent with the coexistence of a low level, high-variation secondary labour market, and a primary labour market within which the level and variation of earnings are positively associated. It is also possible that concentrating on males with continuous labour force attachment (complete unambiguous earnings histories) effectively excludes the secondary labour market from the study.



386 Bruce Kennedy

histories on virtually all Canadian earners outside the province of Quebec. It is authoritative in that the yearly individual earnings data consist of employment earnings plus self-employment earnings, originating from TI income tax forms. It is extraordinarily long, in that it records each individual's yearly earnings going back to 1966. And unlike comparable American data sources, it is not severely censored (earnings in excess of $100,000 per year are recorded in the cPP dataset as $99,999).

A major limitation of this dataset is that it is narrowly focused. Each record contains only the individual's sex, year of birth, and yearly earnings from 1966 through 1983. This lack of explanatory variables, however, is not necessarily a handicap with respect to the measurement of earnings mobility.3 While the cPP administrative database cannot provide explanations of earnings differences in terms of cross-sectional correlates, it still may be considered one of the best datasets that has ever been brought to bear on the question of earnings mobility, and the characterization of individual earnings dynamics.

The second problem with the dataset concerns the interpretation of any years in an earnings history in which no earnings are reported. These observations are ambiguous. They could represent a year in which the individual was chronically unemployed; not in the labour force; deceased; or working in Quebec or outside of Canada. The analysis reported here focuses on middle-aged males with strong labour force attachment, because it is this group that can be most confidently investigated. Most middle-aged males generate unambiguous earnings histories. Furthermore, as is not the case with females, the patterns of labour force behaviour of this group have been quite consistent since 1966.

The first step in performing this data analysis was to draw a random sample of 50,000 eighteen-year-long earnings histories from the cpp record of earnings file. The population for this sample consists of everyone with a social insurance number who had any earned income (for tax purposes) while residing outside the province of Quebec at any time from 1966 through 1983. The analysis presented here pertains to a subset of that sample consisting of all males in the group who were born in 1930 for whom positive earnings were recorded in each year 1966 through 1983. (The size of this group is 262 men, 4,716 observations. The total number of males born in 1930 in the sample of 50,000 records was 446). Some characteristics of the sample are presented in table 1.

THE MODEL

The model is designed to investigate earnings instability in the context of a cohort of individuals moving together through time. The dependent variable is individual

3 Using a model somewhat similar to the one estimated in this study - and a dataset that was shorter in duration but richer in explantory variables - Lillard and Willis (1978) experimented with earnings functions of differing complexity and data requirements. They concluded that their extra explanatory variables helped explain differences in permanent earnings but gave the same breakdown between permanent and transitory earnings as did a naive model using no explanatory variables except time dummies.




TABLE 1 Descriptive statistics on the subsample of 262 males born in 1930 and having complete earnings recordsa

1966 1970 1975 1980 1983

Meannominalearningsofcohort 6,318 8,552 16,025 23,175 28,019 cv of earnings across individuals 41 40 71 57 62

10th 25th Median 75th 90th

Percentiles of the distribution of individual cvs (across years) of nominal eamings 39 46 52 59 70

a An exploration using lexis mapping of earnings differences and trends in the source sample of 50,000 earnings histories is available in Kennedy (1987).

earnings relative to the mean earnings of the cohort, and a life cycle pattern of expected earnings is implied by this choice of dependent variable. Perfect stability is equated with any pattern of individual earnings movements that preserves the relative earnings position of all members of the cohort over time. Instability is generated by movements that change an individual's earnings relative to those of the group.

The model is expressed as follows:

y = mM + p(y it_l - m,) +NtV\' (1 - p2), (1)

where i is the individual subscript t is the time subscript y is cohort relative earnings m is an individual series mean o-is an individual series standard deviation pis a global autocorrelation coefficient N is an independent random variable with a standard normal distribution.

The model in (1) treats each individual relative earnings history as a Markovian (AR1) process. These ARI processes vary between individuals in terms of both their level and their dispersion characteristics (m and o-). (Note that there are no individual linear trends in the model, although a cohort trend is incorporated through the use of the relative earnings domain.) The autocorrelation coefficient in the process is global for three reasons. First, the presence of autocorrelation in earnings data is associated in the literature with global factors such as the length of the accounting period rather than with individual characteristics. Second, simulation experience has shown that the hypothesis that all the individual series have the same value for rho is acceptable in the sense that sets simulated using this assumption display a distribution of rho estimates generated from individual series that is similar to the distribution of individual rho estimates found in the data. Finally, using a global rho value avoids estimating a rho value for each individual. Estimation at the individual level of the other two ARI parameters is onerous enough in itself.



388 Bruce Kennedy

ESTIMATION

The first task here is to demonstrate that equation (1) is a heterogeneous version of the familiar ARI model. In time-series analysis the ARI model is generally expressed as

Yt = yt-I + 8 + et,

where 4 is the parameter of the lagged observation 8 is a constant related to the series mean, and et is an independent normally distributed error term.

The model can be estimated by ordinary least squares regression, and presents no problems other than that of initialization. However, there is an alternate form of the model that can be derived by focusing on three properties of the generated series:

the mean: m = 5/(1 -

the first-order autocorrelation: p =

the series variance: 2 = (-e22/(I-2)

where: O-e2 is the variance of the error term. The ARI model can be expressed in terms of these three descriptive statistics as

follows:

adding m - m to the ARI model above: Yt = m + k(Yt-I - m) - (1- f)m + 5 + et;

substituting for m: Yt = m + (4yt-I - m) - (1- )/(1-) + 5 + et;

simplifying and substituting for 4: Yt = m + P(Yt-I - m) + et.

The variance of the series can now be expressed as

=72 - cr 2t(l - p2).

To produce series with a variance of o-2 requires an error term with variance: cre2 - p2); therefore,

et-Ncr/(l p2)

where N is an independent random variable with the standard normal distribution, and

Yt - m + P(Yt-I - m) + No- \/ (1 - p2).

This is the forn of the ARI model used in equation (1). This arrangement of the ARI model was first applied to simulation by Fiering (1967). Fiering's application (called a Markovian flow model) concerned streamflow simulation for hydrological models. For present purposes the advantage of this form is that the level and dispersion-related parameters are identical to the means and standard deviations of the series. Estimates of these parameters can therefore be generated for thousands of individual relative




earnings series by simply computing mean and standard deviation estimates for each series.

Estimation proceeds as follows: first the means and standard deviations of all of the relative earnings series in the longitudinal dataset are computed. The individual relative earnings series are then standardized (by subtracting their means and dividing by their standard deviations). This creates a set of (by assumption) ARI series that have the same means (0) and standard deviations (1) and (by assumption) the same value of rho. They are, in effect, different realizations of the same ARI process. Estimation of rho proceeds as follows: first the standardized histories are stacked into a single time series and then standard time-series techniques are used. The initialization problem is dealt with through a buffering of the individual history segments with single 'missing value' observations. As per standard time-series analysis practice, these missing values are then replaced by their expected values (0). This will result in.a slight downward bias in the estimate of rho. For the sample of 262 mature males with complete earnings histories rho was estimated to equal 0.49. The rho estimate, however, is used only in the simulation test of the model specification. It is not required for the investigations into the extent and the distribution of earnings instability.

RESULTS

Given a data source, and a framework within which to compute individual earnings levels and measures of individual earnings instability it is a simple matter to explore the relationship between these attributes. For the sample of 262 mature males with complete earnings histories the correlation between individuals' mean relative earnings, and the standard deviation of their relative earnings series is 0.67. This result, however, reflects only the fact that standard deviation is not a scale- independent measure of dispersion. The coefficient of variation (cv) is a scale- independent measure of dispersion, and it shows no significant correlation with mean earnings (r = -0.05, significance probability for Ho: r = 0 is 0.38). This finding amounts to a confimation of Gibrat's law, 'the law of proportionate effect,' which states that random changes in personal income are likely to be proportional to the level of income (Gibrat, 193 1). It is an important result for simulation purposes because it implies that the joint distribution of individual means and standard deviations can be reproduced as described below. To suggest the nature of the joint distribution of individual relative earnings means and standard deviations, figure 1 provides a scatter plot of these values for the sample of males from the 1930 birth cohort who had strictly positive earnings in ever year from 1966 through 1983.

The measure of the amount of earnings instability used here is based on a measure of the amount of stratification in the cohort earnings data. The stratification measure simply asks what portion of the variation in relative earnings observable across individuals at a given point in time can be explained by permanent differences between individuals in their level of earnings (100 x the coefficient of determination of a regression of individual earnings on individual mean earnings). A value of 100 per



390 Bruce Kennedy

Mean Relative Earnings LEGEND: A = 1 OBS, B = 2 OBS, ETC.

I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~A 4.0 +

3*5 I

3.0 + A

A A AA A AA

A.0+ A A A

1 .5+ ABAAA AA A A AA B AA A

AA B AA A A

ABEAA AA A AA AAA AAA BAACAB AA A B AA A A

1.O A BAEAEDAAAAA A BA A A A A BHDCCFAABBA AAB A A

AADACCCAC BDB CA A A A CAB BE AB AB A

AA ABDBDAAB A A

0.5 + B AAABAACB A A ACA A A

A AAA

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Standard Deviation of Relative Earnings

FIGURE 1 The earnings level - earnings variation relationship among 262 randomly selected Canadian males from the 1930 birth cohort who had continuous labour force attachment

cent on this scale would correspond to complete stratification, and no mobility. A value of 0 per cent would be indicative of a situation in which all cross-sectional earnings differences are temporary, with no long-term differences between individuals in mean levels of earnings. An indicator equal to 100 per cent less the percentage of stratification is used as the measure of instability. The earnings of the sample of mature males with complete earnings histories, are found to be 68 per cent stratified (32 per cent instability). Drawing individuals from both sexes of the same cohort (but only from individuals reporting earnings in every year from 1966 through 1983; n =

325) produces a value of 72 per cent stratification (28 per cent instability). This meets with expectations that in the more heterogeneous group encompassing both sexes, permanent differences account for a larger portion of point-in-time earnings differences.

SPECIFICATION TEST

The purpose of this simulation step is to confirm that the model structure imposed and estimated is a reasonable characterization of individual earnings dynamics. The simulation strategy relies on the observation presented above, that the means of the individual relative earnings histories are independent from their coefficients of variation. To conduct the simulation, means and cvs are computed for each individual earnings history. Quantiles from the distribution of the individual means




and from that of the individual cvs are then used to construct an approximation of the cumulative density function for each of these parameters. The standard 'Monte Carlo' technique is then used to assign independently a mean and cv to each member of a set of simulated 'individuals.' Individual standard deviations are then calculated from the assigned means and cvs. This indirect generation of the standard deviation parameters is necessary to reconstruct the proper joint distribution of mean and standard deviation parameters. Simulated individual relative earnings histories are then constructed using equation (1), the assigned individual parameters, and the global rho parameter.

The simulated and actual earnings datasets are compared, using two standard ARIMA diagnostic tools; the autocorrelation function and the partial autocorrelation function. A set of sample autocorrelation functions is provided in figure 2. Presented are the sample autocorrelation function estimated from the data (males with complete earnings histories from the 1930 birth cohort) and another estimated from a simulated earnings set for the same group produced as described above. For comparison purposes the autocorrelation function that would be produced by a Markovian (ARl)

model without individual components (as per Solow, 1951) is also represented along with autocorrelation functions corresponding to the two extreme possibility of complete earnings stratification and complete earnings mobility.

The most striking feature of this figure is the evidently high correlation between observations of an individual's earnings that are separated by as much as seventeen years. After a sharp initial decay, the autocorrelation function for the data seems to trend very slowly toward zero. In time-series analysis failure of the autocorrelation function to approach zero within some 'reasonable' period of time is taken as an indication of non-stationarity. The process of the earnings model assumes that individual earnings series are stationary about their own individual means, but not about the group mean. The corresponding autocorrelation function tends, as suggested in figure 2, not towards zero but towards some constant determined by the distributions of the individual series means and standard deviations. As a result, the simulated and actual autocorrelation functions tend to diverge for very large lag times.

The sample partial autocorrelation function estimated from the data (males with complete earnings histories from the 1930 birth cohort) is shown in table 2. The first-order autocorrelation coefficient is quite large. The higher-order partial autocorrelations, while sometimes significant, are much smaller. This is consistent with similar observations (Solow, 1951) and explains to some extent the popularity of Markov-ARl specifications in earnings models. This pattern compares favourably with that generated by the heterogeneous AR1 model. As should be evident from figure 2 and the structure of the model, the model's partial autocorrelation function consists of a first-order autocorrelation of 0.8 and no significant higher-order partial autocorrelations.

The process of equation (1), while it does slightly overstate long-term earnings stratification, does a reasonable job of imitating individual earnings dynamics as



392 Bruce Kennedy

1 - Complete Stratification

0.9

0.8

0.7

0.6

0. 5

0.4

0.3

0.2

0.1

0. 1 - Complete Mobility

-0.1 X l I I I I -I I I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

LAG IN YEARS + MARKOV ACTUAL L6 SIMULATED

FIGURE 2 Simulated versus actual sample autocorrelation functions (sample of males born in 1930 who reported earnings in every year 1966 through 1983, n = 262)

reflected in sample autocorrelation functions and sample partial autocorrelation functions. It would appear that this model is sufficiently realistic and convenient to serve as a useful framework for analysing earnings instability.

GENERALITY

The model presented above has also been estimated for both sexes and for young, mid-career, and older workers. With the exception of groups of young workers, this structure has been found to be a reasonable characterization of within cohort earnings dynamics. Relative earnings histories across the eighteen to thirty-five age range do not exhibit the continuity of level and variation that is typical of the population as a whole. A sample of males from the 1948 cohort, for example, shows a correlation between 1966 relative earnings and 1983 relative earnings of -0.13 (significance probability for Ho: r = 0 is 0.02). Comparing this value with figure 1 shows that it is much lower than the typical correlation between relative earnings observations separated by seventeen years for mature males. It would appear therefore that at the young end of the working life cycle, there is a considerable amount of sorting out of the 'pecking order' of earnings. Preferences are being established, latent capabilities are being developed and demonstrated, and investments are being made in human




TABLE 2

Lag Partial autocorrelation coefficient (years) (standard error of estimates = 0.01)

1 0.82 2 0.1 3 -0.03 4 0.01 5 -0.05 6 -0.03

capital. By the late twenties, however, a fairly rigid distribution of relative earnings has already been established.

Extension of this study to include intermittent annual earnings histories has been avoided, owing to data limitations described above. Given unambiguous data, several questions would have to be addressed in order to incorporate interrupted earnings histories into this analysis. First, do the model's assumptions of permanent individual mean and variance parameters hold up over long absences from the labour force, or should these characteristics be assigned to labour force spells rather than to individuals? Second, is one's interest in the variability of earned income, including fluctuations caused by labour force withdrawal (in which case nil earnings years would be treated as zeros) or in the earnings instability while in the labour force of a group that includes intermittent workers (in which case 'nil' would be treated as 'missing' when computing individual parameters)? Third, should all earnings histories be weighted equally (whether they contain eighteen or two observations) or should they be weighted in proportion to their contribution to earnings variation observable in cross-sectional data?

Estimates for the entire population of the association between level and instability of earnings will be sensitive to how one chooses to proceed on these issues. Provided that nil years are not treated as zeros, estimates of the amount of instability should decrease if intermittent histories are admitted. This extension would increase the heterogeneity of the group, which should increase the contribution of permanent differences between individuals to total variation.

REFERENCES

Arrow, Kenneth J. (1971) Essays in the Theory ofRisk-Bearing (Chicago: Markham Publish- ing Co.)

Ashenfelter, 0. (1978) 'Estimating the effect of training programs on earnings.' Review of Economics and Statistics 40, 47-57

Belante, D. and A. Link (1982) 'Worker response to a menu of implicit contracts.' Industrial and Labour Relations Review

Box, G.E.P. and G.M. Jenkins (1970) Time Series Analysis (San Francisco: Holden Day) Cain, Glen G. (1976) 'The challenge of segmented labor market theories to orthodox theory:

a survey.' Journal of Economic Literature 1215-57



394 Bruce Kennedy

David, Martin (1971) 'Lifetime income variability and income profiles.' Proceedings of the Annual Meeting of the American Statistical Association. 285-95

-(1975) 'Comments on part 3.' In James Smith, ed., Personal Distribution of Income and Wealth (New York: Columbia University Press)

Fiering, Myron B. (1967) Streamflow Synthesis (Cambridge, MA: Harvard University Press) Friedman, Milton (1953) 'Choice, chance, and the personal distribution of income.' Journal

of Political Economy 61, 277-90 Friedman, M. and S. Kuznets (1945) Income from Independent Professional Practice. (New

York: National Bureau of Economic Research) Gibrat, Robert (1931) Les Ine'galites Economiques (Paris: Recveil Sirey) Hause, J. (1977) 'The covariance structure of earnings and the on-the-job training hypothe-

sis.' Annals of Economic and Social Measurement 6, 335-66 Kennedy, Bruce R. (1987) 'Age, sex, time and earnings.' Joing working paper of The

Institute for Research on Public Policy (Halifax) and the Social and Economic Studies Division of Statistics Canada (Ottawa)

Lillard, Lee and Robert Willis (1978) 'Dynamic aspects of earnings mobility.' Econometrica 46, 985-1012

Lillard, Lee and Yoram Weiss (1979) 'Components of variation in panel earnings data: American scientists 1960-70.' Econometrica 47, 437-54

MaCurdy, Thomas E. (1982) 'The use of time series processes to model the error structure of earnings in a longitudinal data analysis.' Journal of Econometrics 18, 83-114

Solow, Robert M. (1951) 'On the dynamics of the income distribution.' Unpublished PH D thesis, Harvard University

Vaillancourt, Francois (research co-ordinator) (1985) Income Distribution and Economic Security in Canada (Toronto: University of Toronto Press in co-operation with the Royal Commission on the Economic Union and Development Prospects for Canada)

Wolfson, Michael C. (1975) 'The accounting period and the distribution of income in Canada 1965-1970.' Mimeo, Planning Branch, Treasury Board Secretariat, Government of Canada



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Mobility and Instability in Canadian Earnings