Inequality Trends in Sweden 1978

Transcription

1 Inequality Trends in Sweden David Domeij and Martin Flodén September 18, 28 Abstract We document a clear and permanent increase in Swedish earnings inequality in the early 199s. Inequality in disposable income and earnings net of taxes and transfers also increased, but much less than the increased inequality in pre-government earnings. These di erent developments are most likely explained by the generous Swedish welfare system. Consistent with these observations, we see no clear trend in consumption inequality. We also estimate stochastic processes for household earnings. A simple random-walk process captures much of the life-cycle dynamics. But we nd clear evidence that the true earnings process is not a random walk. We demonstrate that some estimation methods result in severe upward bias in the estimated volatility of permanent shocks if serial correlation in temporary shocks is ignored. Our estimation results show that the increase in earnings inequality is almost entirely driven by an increase in residual earnings inequality. Moreover, this increase was mostly generated by an increased volatility of persistent shocks. JEL classi cation: Keywords: 1 Introduction This paper documents trends in Swedish earnings, income and consumption inequality between 1978 and 24. We document a clear and permanent increase in Swedish earnings inequality in the early 199s. Inequality in disposable income and earnings net of taxes and transfers also increased, but much less than the increased inequality in pre-government earnings. We see no clear trend in consumption inequality. From a welfare perspective, it is important to understand why earnings inequality rose. For example, the policy consequences may be very di erent if the inequality was generated by changes in the returns to observable characteristics, such as education, rather than by changes in unobservables, such as luck. It is also important to understand the We thank Paul Klein, Roine Vestman, and participants at the PIER IGIER conference 27 for helpful comments. We also thank the Swedish Retailing Institute for providing data. Financial support from the Jan Wallander and Tom Hedelius Foundation at Svenska Handelsbanken and the Swedish Research Council is gratefully acknowledged. Department of Economics, Stockholm School of Economics, Box 651, SE Stockholm, Sweden, david.domeij@hhs.se, martin. oden@hhs.se.

2 dynamics of inequality over the life-cycle. In particular, increased volatility of temporary earnings shocks can more easily be insured than increased volatility of persistent shocks, and therefore have less important welfare implications. To investigate the causes behind the increased inequality, we estimate stochastic earnings processes. We nd that the increased inequality was almost entirely driven by an increase in unobservables, i.e. in residual earnings inequality. Moreover, we document that the rise in residual inequality was mostly generated by an increased volatility of persistent shocks. 1 Our nding that inequality in earnings net of taxes and transfers has increased much less than inequality in pre-government earnings suggests that the Swedish welfare state has been e ective in providing insurance. Further support for this is that although the persistent shocks are relatively di cult to insure against at the household level, consumption inequality has not increased. The paper also makes a methodological contribution. Household earnings is often conveniently assumed to follow a random-walk process. That process provides a parsimonious speci cation of the income process, and is therefore useful in applied work. We show that the random-walk speci cation captures much of the Swedish earnings process when we also allow for serial correlation in the temporary shocks. The stochastic income processes are typically estimated using some minimum distance method. Parameters in the earnings process are then chosen so that some moments implied by the process are close to the corresponding empirical moments. If the true earnings process is a random walk, the choice of moments to focus on is of little importance. But we demonstrate that the choice of moments is of crucial importance for the resulting parameter estimates if the true earnings process deviates slightly from a random walk. More speci cally, our results indicate that it is important to use moment conditions that explicitly describe how earnings inequality evolves over the life cycle and over time. A number of previous papers have studied trends in Swedish inequality. There is ample evidence that Swedish income inequality fell substantially between 197 and 199. Most of the Swedish wage compression occurred in the 197s and was mainly a result of narrowing age, education and gender wage di erentials. 2 Our nding that Swedish earnings inequality increased in the 199s con rms previous ndings in Johansson (26) and Björklund and Freeman (28). The rise in inequality during the 199s did, however, not fully o set the falling inequality during the 197s. Johansson (26) shows that the Gini coe cient for family income in 22 was clearly below its 197 value and much below its 195 value. Nordström Skans et al. (26) nds that much of the rising wage inequality during the 199s can be attributed to rising wage dispersion between rms, and Gustavsson (26) nds evidence that the returns to observable individual-speci c qualities contributed to higher inequality. Domeij (28) nds that much of the rise in residual earnings inequality was generated by changes in the 1 Gustavsson (27) estimate a similar earnings process but focuses on male earnings and uses only data for In line with our results, he nds that most of the rising inequality is explained by an increased volatility of persistent shocks. But Gustavsson s results are not identical to ours. Whereas we nd that the variance of persistent shocks increased from the 198s to the 199s, we do not nd an increase between 1991 and This di erence may be explained by Gustavsson s short time period, and his assumption that shock prior 1991 had the same variance as those in See for example Edin and Holmlund (1995). 2

3 industry composition and educational patterns. A number of developments in the Swedish economy may explain why the falling inequality during the 197s was reversed during the 199s. First, the Swedish wage-setting process was reformed in several steps. The system with centralized wage bargaining broke down in the mid 198s and was replace by a higher degree of industry-wide bargaining. In the early 199s, the public sector went from grade-based wage setting to individual wage setting. Starting in the mid 198s and accelerating in the early 199s, a number of markets were deregulated and became more competitive, which made wage compression more di cult to achieve. Possibly, these trends were reversed in 1997 after the Agreement of Industry Development and Wage Formation was signed. This agreement stipulated common guidelines for wage setting across industries. Second, several macroeconomic imbalances were accumulated during the 198s, a process that cumulated with a major crisis in the early 199s. Between 199 and 1993, the unemployment rate increased from 2 percent to 11 percent, GDP fell by 4:5 percent, and the public debt increased from 43 to 72 percent of GDP. The second half of the 199s was characterized by high GDP growth and scal consolidation. The unemployment rate fell, but not all the way back to the pre-crisis level. Finally, following the crisis Sweden let the currency oat and implemented in ation targeting in , joined the European Union in 1995, and reformed the scal framework starting in the mid 199s. These reforms had major impact on the Swedish economy, although it is unclear to what extent they contributed to changes in income inequality. Our study uses several di erent data sources. A common feature of these sources is that all income data is based on tax registers. We consequently avoid problems associated with top coding, incomplete recall, and biased and low response rates. We instead face another potential problem. A major tax reform ("the tax reform of the century", see Agell et al., 1996), was implemented in The tax reform aimed at broadening tax bases and reducing marginal tax rates. Following this reform, some items in the tax registers were reclassi ed. This led some researchers to, in particular Edin and Fredriksson (2), to challenge the comparability of pre- and post-reform income data. Böhlmark and Lindqvist (26) on the other hand demonstrate that although comparability in principle could be questioned, the problems are minor in practice. We carefully try to compose income de nitions that are comparable over time, and we do not see important breaks in our time series around the tax reform. The paper is structured as follows. The next section describes the data, our sample selection procedures, and compares the implied aggregate time series to the national accounts. Section 3 documents facts for inequality in earnings, income, and consumption over time. Section 4 documents similar facts for inequality over the life cycle. In Section 5, we estimates stochastic earnings processes. Section 6 concludes. 3

4 2 Data and sample selection We mainly use data from three di erent data sets. Our main source of income and earnings data is LINDA (Longitudinal Individual Data for Sweden), while we use HINK (Household Survey on Income) for hours, wages, wealth, and HUT (Household Expenditure Survey) for consumption. For some calculations, we also use LOUISE (Longitudinal Education, Income, and Employment Data for Sweden). 2.1 The LINDA database LINDA is a register-based longitudinal data set compiled by Statistics Sweden from the Income Register based on led tax reports, the Census (in 5 year intervals from 196 to 199), and other registers. It consists of a large panel of individuals and their family members (as de ned for tax purposes), resulting in approximately 3; individuals per year. 3 We use data from 1978 to 24. As household head, we use the oldest adult male in the household. 4 In households without adult males, the oldest female is de ned as the head. We only keep households where the head is between 25 and 59 years old and where the head was sampled by LINDA. For each household we record the sex and age of the head together with the number of adults, children, and consumption equivalents in the household. 5 From 199 and on, we also have some information about education. We construct three education classes: less than high-school, high-school graduates, and some college education. We calculate pre-government earnings (y) and disposable income (y D ) for as the measure of labor income suggested by Statistics Sweden (26) to be comparable between years in LINDA. Pre-government earnings consist of wages and salaries, the part of business income reported as labor income, and taxable compensation for sick leave and parental leave, while disposable income consists of the sum of factor income and positive transfers minus taxes and negative transfers. We construct comparable measures for We calculate nancial capital income (y A ) as the sum of three components, each restricted to be non-negative. The rst component is the sum of net interest income, net dividends, and net realized capital gains. The second component is income from roomers and boarders, and the third component is 35 percent of net business income. Finally, we calculate post-government earnings (y T ) as the di erence between disposable income and capital income. Nominal values were converted to 24 SEK using the CPI. The rst columns in Table 1 show how earnings and income has developed over time in our sample. We are often interested in measures of residual inequality. When using the LINDA data, we calculate residual income (" y ) by running year-speci c regressions of log income against a complete set of age dummies (D a ) together with the number of consumption equivalents 3 See Edin and Fredriksson (2) for a further description of the LINDA data set. 4 Men between 17 and 24 are classi ed as adults if the oldest woman in the household is less than 18 years older than the man. 5 We use the OECD consumption equivalence scale. The number of consumption equivalents is then 1 for the rst adult, plus :7 times the number of additional adults, plus :5 times the number of children (aged -16). 6 STATA code is [will be] available on our web pages. 4

5 (E) and family dummies (D f ). There are 15 family dummies, indicating single men, single women, and couples with, 1, 2, 3, and 4+ children. The regression we run is then ln y i;t = D y t + 1;tD a i;t + 2;t D f i;t + 3;tE i;t + " y i;t (1) where D y are year dummies. In some speci cations we also control for the education levels reported between 199 and 24. We then run the regression ln y i;t = D y t + 1;tD a i;t + 2;t D f i;t + 3;tE i;t + 4;t D e i;t + " y i;t (2) where D e are dummies indicating less than high-school, high-school graduates, or some college education. 2.2 The HINK database The HINK data set is a revolving panel with 1; 2; households per year, based both on registers and telephone surveys conducted by Statistics Sweden. Sampling occurs at the individual level, all household members of the sampled individual are included, and the sampled individual stays in the sample for two consecutive years. 7 We have data for 1975, 1978, and 198 to We de ne the household head as in LINDA, and we include households where the household head is between 25 and 59 years old. To obtain a representative sample of households we weight households by household size. 8 Pre-government earnings, post-government earnings, and disposable household income are de ned in accordance with the de nitions in LINDA, except that the earnings measures now include two thirds of business income instead of the reported labor part of business income. Annual hours (l) are the reported number of hours worked per week times the reported number of weeks worked. The hourly wage (w) are then calculated as the respective individual s pre-government earnings divided by the number of hours worked. For calculations based on wage data, we only include individuals where the hourly wage is above half the minimum wage. According to Skedinger (27) the minimum wage in the service sector was around SEK 6 (in 24 SEKs) throughout the 198s. We use two measures of wealth. Total net wealth (a + ) is calculated by Statistics Sweden using estimated real estate values together with information on other assets. Financial net wealth (a) is calculated as total net wealth minus the estimated real estate values net of mortgages. The nal columns in Table 1 show how average wages, hours, and wealth have developed over time in our sample. When using the HINK data, we calculate residual wages by running year-speci c regressions of wages against a quartic polynomial in age, the number of consumption equivalents, and family dummies. There are 5 family dummies, indicating single men without children, 7 Non-married cohabitants without children form a household in HINK but two separate households in LINDA. Furthermore, a maximum of two adults are included in a HINK household, but LINDA does not have that restriction. 8 The weights are N=n where N is the number of households in the sample and n is the number of household members that could have been sampled. 5

6 single women without children, couples without children, singles with children, and couples with children. 2.3 The HUT database The HUT data set is a cross-sectional survey carried out by Statistics Sweden. A representative cross-sectional sample of Swedish individuals between ages and 74 years is chosen, and all household members of the sampled individual are included in the survey. We use data from the surveys in 1985, 1988, 1992, 1996, and We weight households as in the HINK data, and we use the same de nition of the household head. This results in around 2; remaining households in the rst years, and about half as many in the later years when the sample size was reduced. The data collection in HUT consists of several steps. An initial interview is rst conducted about the household composition. Second, the household is asked to keep book of all expenditure during a two-week period. During this period the household records all expenditure of all household members. 9 In connection with the bookkeeping a questionnaire is lled out concerning the expenditure during the previous year for: housing, holiday cottages, petrol, insurance, traveling abroad, and the purchase of certain durable goods. Expenditure on clothing, shoes and traveling within Sweden is collected in the same way for the previous two-month period. We calculate non-durable consumption (c) as the measure of total consumption expenditure minus rent paid for tenants, mortgage payments, repairs, and vehicle purchases. The measure of consumption including services from housing (c + ) is calculated as non-durable consumption plus rents for tenants, mortgage payments, and repairs. Disposable income was calculated in HUT by linking the person to the Income Register based on led tax reports. Disposable income concerns the year of the survey and consists of the sum of factor income and all transfer income (e.g. pension payments, unemployment bene ts, paid sick-leave, housing assistance, etc.) net of taxes. Table 1 reports average consumption according to these di erent measures for each of the sample years. When using the HUT data, we calculate residual consumption by running year-speci c regressions of consumption against the number of consumption equivalents and age and family dummies. We use dummies for the age groups 25 33, 34 42, 43 51, and The family dummies are the same as in the HINK data. 2.4 The LOUISE database Since we only have HINK data on wages between 1978 and 1992, we also report some statistics computed from the LOUISE database where we have information from 199 to 22. LOUISE is a register-based longitudinal data set compiled by Statistics Sweden 9 An equal number of households start the bookkeeping every week during the survey year. 1 We use di erent methods to control for age in the three datasets because of the di erence in sample sizes. 6

7 from the Income Register based on led tax reports, the 199 Census 199, and other registers. It basically covers the full population aged 16 and above. 2.5 Comparison with other sources Figures 1-3 show the aggregate implications from our data together with the aggregates reported in the national accounts. 11 Figure 1 shows that per capita labor income in the LINDA database closely tracks the wage sum reported in the national account. The income measures are however consistently higher in LINDA than in the national accounts. The largest di erence (8 percent) is recorded in 1991, which is the year after the "tax reform of the century" where we would anticipate some measurement problems and inconsistencies. 12 For recent years the di erence is between 1 and 3 percent. Figure 2 shows that the consumption data in HUT di er more substantially from the values reported in the national accounts. Per capita consumption in HUT is consistently lower than in the national accounts, and the di erence varies between 7 and 1 percent. The total hours worked relative to the population aged 25 to 59 according to the HINK database and the labor force surveys are reported in Figure 3. The HINK data display some instability but the average levels are similar to those in the labor force surveys. Table A1 in the Appendix compares the time series for equivalized earnings and disposable income from the di erent data sets. The values are mostly consistent. We have not excluded households with low income. Trends and uctuations in the variance of earnings are therefore mostly driven by uctuations in the unemployment rate, which increased temporarily in the mid 198s and then more permanently in the early 199s. Table A2 further shows that our three data sets, LINDA, HUT, and HINK, are similar in terms of average age of the household head, household size, and number of consumption equivalents. 3 Time series facts Figure 4 shows how the inequality in hourly wages has developed between 1975 and 1992 according to various measures. Panels (a) and (d) show a clear fall in overall wage inequality. The fall in inequality occurred both at the top of the distribution (panel b) and at the bottom of the distribution (panel c). Panels (a) to (c) in Figure 5 report the evolution of wage premia along the education, gender, and experience dimensions, whereas panel (d) reports evolution of residual wage inequality. The fall in wage inequality between 1975 and 1992 depicted in Figure 4 can be explained by the substantial fall in the education premium and residual inequality in panels (a) and (d). The education premium appears to have increased somewhat in the 199s. 13;14 There are however no clear trends for the gender or experience premia. Figure 11 For these comparisons, we include all households or individuals in the datasets. That is, we do not focus on household heads or households with heads in working age. 12 Agell et al. (1996) summarize the important aspects of the tax reform. 13 See Domeij and Ljungqvist (28) for more details on the evolution of the Swedish skill premium. 14 A shortcoming of the Louise data is that while it contains data on hours worked for 199, we have 7

8 6 shows that wage inequality has fallen both for men and women. There is also a clear fall in the dispersion of hours among women. But there are no trends in the dispersion of male hours or the correlations between wages and hours. Table 2 shows that this correlation on average was :24 for men and :23 for women between 1978 and This table also shows a strong positive correlation between head and spouse hours. Figure 7 documents a clear increase in earnings inequality in the rst half of the 199s. Panel (a) shows similar patterns and magnitudes for the development of the variance of raw, equivalized, and residual earnings. This indicates that most of the increased inequality is driven by an increase in residual inequality. Panel (b) consequently shows that the inequality explained by the age and family components has been relatively stable. Controlling for education in addition to age and family composition has little impact. Only a small part of inequality is explained by education, and there are no clear trends in the educational component. Panel (a) also shows that the changes in inequality largely coincides with changes in unemployment. But unemployment does not explain all of the increased inequality. Figure 8 shows that inequality increased across the whole distribution. Inequality at the top shows a clear increase in the last 15 years as displayed in panel (b). Moreover, the unemployment rate and most measures of inequality fell in the late 199s, but inequality at the very top has continued increasing as indicated by the p99=p9 ratio. Figure 9 and Table 3 show that the Swedish welfare system has moderated the e ects on inequality throughout the period, and in particular during the turbulent 199s. The variances of post-government earnings, i.e. earnings after taxes and transfers, and disposable income are much lower than the variance of pre-government earnings. Furthermore, inequality in post-government earnings remained remarkably stable when unemployment and pre-government earnings inequality increased dramatically in the 199s. Inequality in disposable income has however increased. The Gini coe cient, for example, increased from :24 in the early period to :247 in the more recent period. The di erent developments for post-government earnings and disposable income indicate an increased dispersion of capital income. Table 3 indeed shows that inequality in capital income was higher in the more recent time period according to all measures. Figures 1-12 show various measures of consumption inequality. There are no clear trends in these gures but a small increase in consumption inequality cannot be ruled out. Panels (a) and (b) in Figure 13 indicate that both the level of nancial wealth and total wealth fell during the 198s. At the same time, inequality as measured by the Gini coe cient increased. Table 4 reports correlations between di erent income and earnings measures, consumption, and wealth. The correlations between wealth and other variables are remarkably low. This is possibly a consequence of the Swedish welfare system. The comprehensive pension system and generous social insurance systems reduce the need to accumulate private wealth for life-cycle and precautionary reasons (Domeij and Klein, 22). Table 3 also shows that a large fraction of the population has no private wealth. to extrapolate that information for the years Speci cally, we assume that the average hours of work for detailed demographic groups (agegendereducationindustry) is given by its 199 value multiplied by a yearagegender speci c factor, such that average hours worked in agegender groups are consistent with Statistics Sweden s estimates for the period 1991 to 22. See Domeij and Ljungqvist (28) for further discussion. 8

9 4 Life-cycle pro les To examine how inequality in some variable x develops over the life cycle, we calculate 2 h;s = var (ln x h;s) where h denotes an age group and s a year or cohort. We then regress this variance against age and year or cohort dummies, 2 h;s = + 1 D h h;s + 2D s h;s + " h;s: (3) Figure 14 and 15 report the life-cycle pro les 1 Dh;s h for wages, earnings, and consumption when we control for year and cohort e ects, respectively. 15 The life-cycle pro les for wage inequality are completely di erent in these two gures. Inequality increases over the lifecycle when we control for time e ects but falls when we control for cohort e ects. We see no obvious approach to sort out which of the methods that results in the most representative life-cycle pro le. But the explanatory power of the cohort dummies is clearly better, possibly indicating that the downward-sloping pro le is most representative. Also the life-cycle pro les for earnings inequality in panels (b) and (c) di er when we control for time and cohort e ects. Several observations indicate that time e ects are important for capturing the earnings inequality. First, in these regressions the explanatory power of the time dummies is much better. Second, the Swedish economy went through a major crisis in the early 199s, and this crisis simultaneously a ected all cohorts. This suggests that time e ects are important. Moreover, when controlling for cohort e ects but only using data from 1993 and on, we obtain a life-cycle pattern similar to the one we obtained with time e ects. Third, the time e ects estimated from (3) closely follows the Swedish unemployment rate, as is shown in Figure 16. The correlation between the time e ects and the unemployment rate is :92. We have also added the unemployment rate u when controlling for cohort e ects. We then estimate the life-cycle pro le from 2 h;k = + 1 D h h;k + 2D k h;k + 3u k+h + " h;k where k denotes the birth year of a cohort. The results are reported in panels (b) and (c) in Figure 15, and show that the life-cycle pro les then become atter and somewhat more similar to those obtained when controlling for time e ects. 5 Earnings dynamics 5.1 Basic process and estimates The LINDA data set follows households over time and allows us to examine the dynamics of household earnings and income over time and over life-cycles. We are in particular 15 For the wage regressions in HINK, we use dummies for age groups 25 29, 3 34,..., 55 59, and cohorts , , ,..., , For the earnings regressions in LINDA, we use a complete set of age and cohort dummies but we exclude cohorts with ve or fewer observations (i.e , and ). For the consumption regressions in HUT, we use dummies for age groups 25 33, 34 42, 43 51, 52 59, and cohorts , , , , ,

10 interested in the dynamics of residual earnings. We rst consider the earnings process ln y i;h;t = x i;h;t t + i;h;t + i + " i;t ; (4) i;h;t = i;h 1;t 1 + i;t if h > 1 (5) i;1;t = i;t (6) where x are household observables, and subscripts i, t, and h denote individuals, time, and age (starting at h = 1 at age 25), respectively. Moreover, is a permanent earnings component, i N(; 2 ) an individual-speci c xed e ect, " i;t N(; 2 ";t) a temporary earnings shock, and i;t N(; 2 ;t) a permanent earnings shock. We rst estimate this process with GMM using moments based on log di erences of the earnings residual. Let g i;t = ln y i;h;t x i;h;t t and note that the process (4)-(6) then implies that var(g t ) = 2 ;t + 2 ";t + 2 ";t 1 (7) and cov(g t ; g t+s ) = 2 ";t if s = 1 otherwise (8) We use a variety of criteria for including households in our sample. The estimation approach requires that we can follow households over time, and we have a maximum of 26 earnings di erences on a single household. We include households where we have information on n earnings di erences g i;t, and where n is 2 or 2. There is no information about hours worked in LINDA. Consequently, we cannot condition the sample on labor supply. All households with zero (or negative) earnings are excluded from the sample since we work with logarithms. We also consider a stricter exclusion criterion in order to remove households that are not strongly attached to the labor market. The e ective hourly minimum wage in Sweden in 24 was around SEK 75 (Skedinger, 27), and we exclude households with earnings less than half this minimum wage multiplied by 16 hours and 12 months. For other years, we adjust the minimum wage by calculating the mean real earnings for each year, estimating a linear time trend for these means and removing that time trend from the SEK 75 minimum wage. 16 Table 5 reports the estimation results. 17 As expected, the selection criteria are important. All estimated variances are substantially higher in column I where we include all households with at least 2 observations than in column II where we exclude households with low earnings. Requiring 2 observations rather than 2, as in columns III and IV, further reduces the estimates. The processes for post-government earnings, reported in columns V-VIII are less volatile than those for pre-government earnings in the rst columns. Figure 18 and 19 show the life-cycle pro les of residual earnings in the data for the sample selection criteria used in Table 5. In the baseline samples in panels (a), there are virtually 16 This method implies a minimum wage around SEK 6 in the 198 s, consistently with values reported by Skedinger and used in our analysis of wages in HINK. 17 To obtain the estimates in Table 5, the variances 2 ";t and 2 ;t were restricted to be constant over time. Estimated time-speci c variances are plotted in Figure 17. The resulting average variances are similar when time variation is allowed. 1

11 no increase in residual inequality over the life cycle. This indicates that permanent shocks are small and stands in sharp contrast to the estimates reported in columns I and V in Table 5. An estimated variance of permanent shocks of 2 = :197 implies an accumulated increase in the variance by 6:9 after 35 years on the labor market. Flat or U-shaped lifecycle pro les are most likely a consequence of a loose attachment to the labor market for young households. When we use stricter selection criteria, we nd a clear increase in inequality over the life cycle. As a general result, however, we note that the estimated variances of the permanent shocks ( 2 ) are unrealistically high. For example, in panel (d) in Figure 19, the variance increases from :5 to :12 over the life cycle, but the estimated process in column VIII in Table 5 implies that the variance increases from :5 to :6. In the next subsection we consider alternative methods to estimate the income process, and alternative speci cations of the process. 5.2 Alternative estimation methods Estimation of the permanent shocks in the process (4)-(6) hinges crucially on the assumption of no serial correlation in the temporary shocks " when the identifying moments are (7)-(8). To see this, consider the process estimated by Blundell et al. (28) on U.S. data. They estimate the process ln y i;t = x i;t t + i;t + " i;t + " i;t (9) i;t = i;t 1 + i;t (1) and nd 2 " = :415, 2 = :12, and = : Suppose that this is the true data generating process. An econometrician assuming 1 = and using equations (7)-(8) to estimate the process will then nd ^ 2 = :196 rather than the true value 2 = : Ignoring the moving average term thus results in a substantial upward bias of the variance of permanent shocks even when the moving error parameter is small. We now consider a more general earnings process where we allow for moving average terms and persistent shocks that are not necessarily permanent, ln y i;h;t = x i;h;t t + i;h;t + i + " i;t + 1 " i;t " i;t 2 ; (11) i;h;t = i;h;t 1 + i;t if h > 1 (12) i;1;t = i;t : (13) To estimate this process we follow Guvenen (28) and Heathcote et al. (24, 28). Let e i;h;t = ln y i;h;t x i;h;t t. The information used to identify the process is then described by var(e h;t ) = var ( h;t ) ";t ";t ";t 2; (14) 18 These estimates are for Blundell et al. report year-speci c estimates for To simplify the following discussion we assume that variances are constant over time. 19 This process implies that var(g t) = " and cov(g t; g t+1) = (1 ) 2 2 ". The econometrician would therefore set ^ 2 " = cov (g t; g t+1) = (1 ) 2 2 ", and ^ 2 = var (g t) 2^ 2 " = ". 11

12 and 8 < var ( h;t ) ";t ";t 1 if s = 1 cov(e h;t ; e h+s;t+s ) = 2 var ( h;t ) + 2 : ";t if s = 2 s var ( h;t ) + 2 otherwise (15) where the variance for the persistent component is var ( 1;t ) = 2 ;t; and Xh 1 var ( h;1 ) = 2(h 1) var ( 1;1 ) + 2 ;1 2j if h > 1; j= var ( h;t ) = 2 var ( h 1;t 1 ) + 2 ;t if h > 1, and t > 1: We describe in the appendix how we aggregate these moment conditions across individuals and how we use data to calculate the corresponding empirical moments. We use three alternative aggregation methods. The rst method, suggested by Krueger et al. (28) and used widely in the literature is summarized in Appendix A.1. 2 This method aggregates moments across individuals of di erent ages resulting in time series of average variances and covariances between the di erent years. The second method is summarized in Appendix A.2. This method instead aggregates moments across years, resulting in life-cycle pro les of average variances and covariances between di erent ages, as those reported in Figures The third method, used by Heathcote et al. (28), maintains all time-series and life-cycle information and does not aggregate in any dimension. Under all three methods, the moment conditions (14)-(15) use more explicit information about how inequality evolves over the life cycle than the moment conditions (7)-(8). One may therefore suspect that, even if the moving-average terms are ignored, estimation based on (14)-(15) is more robust to serial correlation in the temporary shocks than (7)-(8). 21 Indeed, estimation based on the richer information in the moment conditions (14)-(15) results in much lower estimates of the variance of permanent shocks. Table 6 reports estimates of the process (4)-(6) with 1 = 2 = and = 1 using the di erent moment conditions and aggregation methods. The rst column replicates column II in Table 5. The following three columns report estimation results based on the moment conditions (14)-(15) and show that the estimated variance of the permanent component then falls by a factor between ve and ten. Figures 2 and 21 compare the di erent estimation methods. In Figure 2, we report time series of empirical variances and covariances of households residual earnings. Those are the moments that the rst aggregation method uses to identify the parameters of the stochastic process. In Figure 21, we report life-cycle pro les of empirical variances and covariances 2 Guvenen (27) and Blundell et al. (28) are recent examples. 21 When we generate arti cial data from Blundell et al. s process and estimate a process based on (14)- (15) under the restriction that 1 = 2 =, and = 1, we nd 2 " = :4 and 2 = :1 under all aggregation methods. This is close to the true process, 2 " = :415 and 2 = :12. 12

13 of households residual earnings. 22 Those are the moments that the second aggregation method uses to identify the parameters of the stochastic process. Together with these empirical moments, we also plot the moments implied by our estimated processes. We restricted the variances 2, 2 ", 2 to be constant over time. As expected, the estimated processes are therefore unable to capture the time-series uctuations in Figure 2. We however note that estimates based on moments (14)-(15) capture the average empirical moments. The development of earnings and inequality over the life-cycle is typically of high importance in economic analysis. The estimated earnings process must therefore be consistent with the key empirical life-cycle moments. Panel (a) in Figure 21 shows that estimates based on the moment conditions (7)-(8) imply life-cycle developments that are totally di erent from what we see in the data. As we demonstrated above, these moment conditions imply that the estimated variance of permanent shocks, 2, is biased upwards in the presence of serial correlation in the temporal shocks. This upward bias in 2 implies an unrealistic increase in inequality over the life-cycle. Panels (b) and (c) show implications of estimates based on (14)-(15). These estimates are in line with the life-cycle developments. Estimates based on the second aggregation method, in panel (c), exploits more of the life-cycle information and consequently better capture the empirical moments than those under the rst aggregation method, in panel (b). As also seen in Table 6, the second aggregation method results in higher estimates of the initial xed e ect, 2, but lower estimates of the permanent shock 2. In Figure 21, this results in a higher intercept (from high 2 ) and lower slope (equal to 2 ). As expected, however, estimates based on the rst aggregation method better captures time-variation in the parameters. Year-speci c variances of the temporary and permanent variances 2 ";t and 2 ;t were allowed when estimating the processes reported in Figure 22. The process reported in panels (a) and (c) was estimated with the rst aggregation method whereas the process in panels (b) and (d) was estimated with the second aggregation method. As before, we see that the latter method ts well with the empirical life-cycle pro les in panel (d). The time-series variations in panel (b) are however not similar to the underlying empirical paths. This pattern is con rmed by the nal four columns in Table 6, where we report estimation results when allowing for year-speci c variances. The average estimates are not a ected when we aggregate the moments over ages (columns V and VI) or when we do not aggregate the moments (column VIII). But when aggregating over years (column VII), much of the speci c information is lost and it is di cult to identify the year-speci c variances. The standard errors of the parameter estimates in column VII are thus relatively large, and the averages deviate substantially from those in column III where variances were restricted to be constant over time. These ndings indicate that to estimate a process that is consistent with empirical lifecycle pro les and also identi es year-speci c variances, it may be necessary to use the 22 For example, the rst point on the solid line in Figure 2 is the variance of residual earnings in 1978 averaged over all households, and similarly the rst point on the dashed line is the covariance of residual earnings between 1978 and 1979, again averaged over all households. The rst point on the solid line in Figure 21 is the variance of residual earnings for 25-year olds averaged over all years, and the rst point on the dashed line is the covariance of a household s residual earnings at ages 25 and 26, again averaged over all years. Figures 2-21 report variances, and covariances at horizons 1, 2, and 1 years. In the estimations we use covariances at all available horizons. 13

14 richer information set available when not aggregating the moments. We report implications of the random-walk process estimated with these moments in the left-hand panels in Figure 23. The estimated process then has implications similar to the empirical counterparts, both in the time-series and life-cycle dimensions. In particular, the estimated variances of permanent shocks imply that the cross-sectional variance of residual earnings approximately doubles over the life cycle, just as in the data. Table 7 reports estimates of the random walk process for the same samples as in Table 5, but using this method. This table again documents the dramatic di erence in estimated variances when using the moments (14)-(15) rather than (7)-(8). 23 Another interesting observation in Table 7 is that the variance of the initial xed e ect, 2, is low. For example, that variance is consistently lower than the variance of one annual temporary shock. At age 25, the temporary shocks explain approximately half of the cross-sectional earnings inequality. Because of permanent (or persistent) shocks, inequality increases over the life-cycle. At age 59, the inequality explained by temporary shocks has fallen to approximately a quarter. In Table 7, we also report average variances of the temporary and persistent shocks before and after 199. For both pre- and post-government earnings, the volatility of permanent shocks was substantially larger in the more recent time period. Closer inspection of the full time-series of estimated variances (see e.g. Figure 24 below) reveals that much of the larger volatility in the recent time period is explained by the turbulent crisis period in the early 199s. For pre-government earnings, the variance of temporary shocks also increased substantially during the crisis, but there is not such increase in the volatility of temporary shocks in post-government earnings. 5.3 Alternative stochastic process So far we have only focused on estimation of the process (11)-(13) under the restriction that it is a random walk ( = 1) with serially uncorrelated temporary shocks ( = ). But in the left-hand panels in Figure 23, we see indications that the random-walk process is too restrictive to capture all important life-cycle aspects. In particular, the random walk process forces the variances and covariances to be linear in age, but we see concavity in the empirical life-cycle pro les. We also see that the covariances cov (h; h + j) fall as the horizon j increases, whereas the random walk process implies that the covariance does not vary with the horizon. To investigate the importance of allowing for a richer speci cation of the process, we now allow for persistent but not necessarily permanent shocks ( < 1) and moving-average terms ( 6= ). Tables 8 and 9 report estimates of the process (11)-(13) for pre- and postgovernment earnings under two di erent sample selection criteria. In Table 8, we include households where we observe at least 2 income di erences g i;t but we exclude households with low earnings. In Table 9, we only include households where we observe at least 23 Estimation based on the level moments for e h;t in (14)-(15) does not use information from the moments for the di erences g t in (7)-(8). Column II in Table A3 and panels (a) and (c) in Figure 24 consequently show that the moments for g t implied by the process estimated with level moments deviate from the empirical moments. If matching the moments for g t is important, one may give weight also to the di erence moments in the estimation process. But we will see in the next subsection that a richer stochastic process ts better to the di erence moments even when those momets are not used to estimate the process. 14

15 2 income di erences but we do not exclude households with low earnings. Overall, the results are similar to those reported in Table 7. The variances of the permanent shocks are similar to those in the corresponding columns in Table 7, and the autoregressive parameter is estimated to be close to unity. The moving-average components are typically estimated to be large, but the total variance of the temporary shocks ( " ) is similar to that in Table 7. We see in the right-hand panels in Figure 23 that the most general process, estimated in column IV in Table 8, has implications that t well with the empirical moments both in the time-series and life-cycle dimension. But the improvement relative to the parsimonious random-walk process reported in the left-hand panels of the gure is not dramatic. Column IV in Table A3 and panels (b) and (d) in Figure 24 however show that the empirical moments based on income di erences, (7)-(8), are captured much better by the ARMA(1,2) process than by the random-walk process. Panel (d) in Figure 24 shows that the empirical variance of di erenced income residuals, var (g t ), falls over the life-cycle, a feature not captured by the ARMA(1,2) process. We have considered two further modi cations of the estimated process to allow for richer lifecycle dynamics. First, we followed Guvenen (28) and allowed for heterogeneous income pro les. Equation (11) was then replaced by ln y i;h;t = x i;h;t t + i;h;t + i + i h + " i;t + 1 " i;t " i;t 2 ; (16) where i is the individual component in the life-cycle pro le of income. This component has zero mean, variance 2 and correlation with the individual xed e ect i. Estimation of (16) together with (12)-(13) thus involves estimation of the two additional parameters 2 and. The Swedish data give no support to this speci cation. Using the sample and ARMA(1,2) speci cation corresponding to column IV in Table 8, we found 2 = and that the other parameter estimates were una ected. Second, we allowed for age-speci c components in the volatility of temporary shocks and replaced (11) by ln y i;h;t = x i;h;t t + i;h;t + i + " i;h;t + 1 " i;h;t " i;h;t 2 ; (17) where " i;h;t ~N ; 2 ";h;t. Our estimates for 2 ";h;t indeed show a clear life-cycle pro le. Again using the sample from column IV in Table 8, we found that the variance of the temporary shocks falls by 45 percent between ages 25 and 35, and that they then remain roughly constant. 24 Averaged over the life-cycle, however, the temporary variance is the same as in Table 8, and allowing for age-speci c variances did not a ect the other parameter estimates. Figure 25 presents the full time-series of estimated variances of temporary and persistent shocks, estimated with the ARMA(1,2) process for pre- and post-government earnings as in columns IV and VIII in Table 8. As indicated already in Table 7, the volatility of persistent shocks increased in the early 199s. This increased volatility coincides with 24 The empirical variances reported in panel (d) in Figure 24 are matched more accurately when allowing for these age-speci c variances, but life-cycle pro le of the covariances of residual income di erences then ts somewhat worse to those in the data. The nal columns in Table A1 however show that the average levels of both the variances and covariances are captured somewhat more accurately when allowing for age-speci c variances. 15

16 the large macroeconomic crisis that hit the Swedish economy in that period (see e.g. the unemployment series in Figure 7). In particular, the gure suggests that volatility was high in the crisis period, and that much of that volatility had permanent e ects on household earnings. 6 Concluding remarks The broad picture of the development of income, wealth, and consumption inequality that we document in this paper is consistent with previous studies. We clearly see that income inequality has increased during the last decades. Previous studies also document a dramatic reduction in income inequality during the 197s. We do not date the turning point, but we nd some evidence that in particular earnings inequality increased permanently during the macroeconomic crisis in the early 199s. Inequality in disposable income and earnings net of taxes and transfers has also increased, but much less than the increased inequality in pre-government earnings. These di erent developments is most likely explained by the generous Swedish welfare system. Consistent with these observations, we see no clear trend in consumption inequality. The increase in earnings inequality is almost entirely driven by an increase in residual earnings inequality. But we only control for age, family composition and the level of education. Changes in the households type of education and their sectorial belonging therefore show up in the residual. Domeij (28) shows that such compositional changes contributed to the increased inequality in Sweden during the 199s. We also estimate stochastic processes for household earnings. A simple random-walk process can capture much of the life-cycle dynamics. But we also nd clear evidence that the true earnings process is not a random walk. First, movements in and out of the labor market are important, in particular for young households. Explicitly allowing for the extensive margin may be important. Second, we nd evidence of serial correlation in the temporary shocks. We point out that some estimation methods result in severe upward bias in the estimated volatility of permanent shocks if the presence of such serial correlation is ignored. Moreover, when allowing for persistent rather than permanent shocks, we nd that the autoregressive parameter is close to unity. Still, the random-walk speci cation somewhat overestimates the increase in inequality over the life-cycle. We nd a clear increased volatility of earnings shocks during the severe macroeconomic crisis in the early 199s. For pre-government earnings, the volatility of both temporary and persistent shocks remained high after the crisis. Abstracting for the crisis period, the volatility of persistent shocks in post-government earnings was only slightly higher in the recent time-period relative to the 198s, and there is a small downward trend in the volatility of temporary shocks. Table 1 shows how the changed volatility of temporary and persistent shocks contributed to the rise in Swedish income inequality. If the volatility of shocks had remained at the pre-199 level, then the variance of residual pre-government earnings in 24 had been :164 instead of :21. For post-government earnings, the variance would have been :14 instead of :121. The table also shows that most of the rise in inequality was generated 16