SLIDE 1 Wage inequality within and between firms in Cape Town, South Africa
Martin Monziols∗ Andrew Kerr† October 27, 2017
Abstract Research on earnings inequality in South Africa has almost entirely used household survey data. This work has shown the earnings inequality is extremely high and has remained high or even increased in the post-Apartheid period. However it does not shed light on some important processes generating inequality, particularly the extent to which inequality in earnings is driven by inequality in average earnings within and between firms. In this paper we use the RSC levy data for Cape Town, a census of firms, to document wage inequality between firms and also to estimate the contribution of within-firm inequality to overall inequality, using data from the RSC as well as household surveys. One measure for describing earnings inequalities is the variance of the log of earnings. Davis and Haltiwanger (1991) showed that firm survey data on average earnings by firm could be used to estimate the variance within firms, if one could also estimate the overall variance in earnings from household survey
- data. We follow their procedure in this paper to decompose overall earnings inequality into within and
between firm components and thus to measure their relative contributions to overall earnings inequality.
∗ENSAE, ParisTech †DataFirst, University of Cape Town, andrew.kerr@uct.ac.za
1
SLIDE 2
1 Introduction
South Africa is a country with extremely high levels of income inequality. Much of this is due to inequality in earnings for those in the labour market. Leibbrandt et al. (2010) used a variance decomposition to show that 85% of overall income inequality is caused by earnings inequality in the labour market, and that of this, one third is due to the large number of those not working, and two-thirds is due to earnings differences between those in employment. Wittenberg (2017a) has investigated changes in earnings inequality over the post-Apartheid period, finding that, as measured by the Gini coefficient, earnings inequality increased in the 1990s and stabilised at a very high level. Research on earnings inequality in South Africa has focused mainly on household survey data, which has become ubiquitous since the 1993 PSLSD conducted by SALDRU and the public release of household survey microdata from surveys conducted by Statistics South Africa. However no work on earnings inequality has focused on the role of firms in generating inequality in earnings in South Africa. For example an important question is whether inequality in earnings is the result of large average differences in earnings between firms, so that which firm a worker works for is very important, or because within all firms there is a high degree of inequality between well and poorly paid workers, or a situation in between. In this paper we provide a first look at the relative importance of within and between firm inequality in contributing to the extremely high levels of inequality in South Africa, using a census of formal sector firms in Cape Town and household survey data on earnings in employment, following a method suggested by Davis and Haltiwanger (1991). The paper is organized as follows. We first present a review of the literature on inequality in South Africa, as well as research that explores the extent of between and within firm inequality. We then describe the firm and household survey data we use in the paper, and then provide some descriptive statistics from the data. We then explore inequality using Ginis and percentile ratios, before describing and implementing a variance decomposition method for overall inequality, before concluding.
2 Literature Review
2.1 South African Inequality
As noted in the introduction, Leibbrandt et al. (2010) estimated that 85% of overall income inequality is due to earnings inequality in the labour market, and that of this, and two-thirds is due to earnings differences between those in employment. This suggests that inequality in earnings is a very important part of the puzzle in understanding inequality in South Africa. The multiple household-based surveys that have been 2
SLIDE 3 conducted since 1994 (October Households surveys followed by Labor Force Surveys and then Quarterly Labor Force Survey) allowed Wittenberg (2017a) to study changes in inequalities and earnings trends. As Wittenberg (2017a) and Wittenberg (2017b) show, numerous methodological questions arise from these surveys but after taking these into consideration inequality as measured by the Gini coefficient remain high. The Gini in earnings increased from 0.46 at the end of 1994 to 0.55 in 1998q4 and then gravitated around this value - making South Africa one of the most unequal country in the world, while some other developing countries such as Brazil experienced a downward trend in inequality Benguria (2015).
2.2 Inequality within and between firms
The first empirical work estimating inequality within and between firms was Davis and Haltiwanger (1991). The authors used a firm survey to estimate the variance of earnings between firms and an household survey to estimate the total variance of wages, showing that these two pieces of information could then be used in a variance decomposition to estimate the variance of earnings within firms, even though they had no data on individual earnings within firms. This research was motivated by the observation that workers’ characteristics did not explain very much of the variance in earnings. Davis and Haltiwanger (1991) found that around 50% of earnings inequality, as measured by the variance in log earnings, was generated by differences between firms. Chennells and Reenen (1998) found that only about 26% of the overall variation in earnings in the UK was due to differences between firms whilst Cardoso (1999) found that between 66% and 59% of the variance in earnings in Portugal was due to between firm
- differences. Thus there seem to be large differences across countries in the extent to which between firm
differences contribute to overall variance in earnings. One of the issues in using household survey data to estimate the total variance in earnings is that this earnings may be underestimated due to not capturing the extremely high earners who will almost certainly be
- missed. This would lead to underestimating total variance and thus overestimating the contribution of within
firm differences, which is calculated as a residual in the studies mentioned above. This is one reason that as matched firm-worker data has been made available it has been used to directly estimate the contribution of within firm inequality to overall inequality, rather than estimate it as a residual after estimating overall and between firm inequality, as in Davis and Haltiwanger (1991). Lazear and Shaw (2009) give estimates from matched firm-worker data in a number of EU countries and the USA. They find that the between firm contribution to overall variance in log earnings is around 20-40% in the countries they study. Song et al. (2015) used matched firm and worker data from the US to examine the changes in the relative importance in between firm and within firm contributions to overall dispersion in 3
SLIDE 4
- earnings. They find that between firm differences have become larger, but that within firm differences have
been stable. Benguria (2015) explores the evolution of earnings inequalities in Brazil from 1999 to 2013. He shows that both the variance of log wages and the part explained by the difference between firms decrease during the period, but that it was an average of 66%, much higher than for the sample of countries in Lazear and Shaw (2009). The comparison between Brazil and South Africa has been studied by Lam et al. (2015). These two countries were competing for the title of the most unequal country in the world, but Brazil saw its level
- f inequality decreasing during the past decade, while no such trend was observed in South Africa. This is
another reason to examine the structure of inequalities on the firm side in South Africa.
2.3 Inequality between firms in South Africa
The ILO 2016/2017 Global Wage report (ILO 2016) focuses on inequality between and within firms. Most
- f the analysis of between firm wage inequality is on European countries but there is some analysis for a few
developing countries, including South Africa. The firm data that was used for South Africa was the Survey
- f Employers and Self-employed (SESE) conducted by Statistics South Africa in 2013. This is actually a
survey of non-VAT registered firms that are identified through a 30 000 household survey - where the owners
- f such firms are identified and a follow up survey of them is conducted. These are thus mostly unregistered,
informal firms (see Fourie and Kerr (2017) for further details) and are thus relatively small - nearly 80% are
- wn account workers and the total employment in the firms (employees and owners) is around 2.4 million,
when total employment was around 15 million in 2013. This is thus not really a useful sample to explore inequality in average earnings between firms. Nevertheless, the ILO report uses this data to estimate various measures of inequality in the average earnings between firms. One important finding is that the P90/P10 ratio of average earnings in these firms was 12 in South Africa, much higher than in Chile (2), Vietnam (8) and a number of developed countries where the ratio was generally between 2 and 5. In the analysis below we compare our findings with those in the ILO report.
3 Data
In order to estimate the contributions of within and between firm variation in earnings to overall earnings we use two sources of data. The first is data from the 1999 October Household Survey, and two Labour Force Surveys, which have been harmonised as part of the PALMS dataset (Kerr and Wittenberg 2016). 4
SLIDE 5 The second is the Regional Services Council (RSC) firm census for the City of Cape Town 1. All our data are for the period of 1999-2000. The main reason is that the RSC, the only source of information about firms, is from 2000. We also use the 2001 census data as a check on the employment information from the household surveys and the RSC Data.
3.1 Household surveys : PALMS data
From the PALMS data we use only the household surveys around 2000 (the year of the RSC firm data) which are the October Household Survey (OHS) 1999, Labor Force Survey pilot (LFS) 2000 (February) and LFS 2000 (September). We are interested in those who are living in Cape Town but by restricting to this area we ended with three fairly small samples. Furthermore, we are interested in workers in the formal sector and so we ignore workers in the informal sector. Since the formally self-employed are likely to appear in a firm’s wage bill we included them with the wage earners. This means that for OHS 99 we have 530 observations; for LFS 00-1, 365 observations and for LFS 00-2, 1125 observations. We combine the observations across these three surveys for our analysis below. One problem with household surveys is the earnings non-response rate. People with high earnings are
- ften likely not to respond or to respond less often than the others. We cannot correct for item non-response
to the earnings question although we follow Wittenberg (2008) in using bracket weights to correct for those individuals reporting their earnings in brackets. If we are missing relatively high earners due to item non- response we can reasonably assume that we are underestimating the total variance of the earnings in the population.
3.2 The RSC Data
The RSC data was created by the city of Cape Town. Each formal and registered firm was taxed by the city (until 2006) and this provided the basis of the administrative data contained in the RSC data. This is thus a census of all registered, formal firms, and DataFirst provides this admin data for 2000-2006. In addition to the information that came from the administration of the tax, there was also a survey done of all the firms in the RSC database in 2000. We use the data from the survey on employment in each firm, as well as the total wage bill from the administrative data. Kerr (2015) provides a more detailed description of the data. Since this data set gives us the number of workers and the wage bill of each firm, it allows us to estimate the variance in earnings between firms, and to use this, along with an estimate of the overall variance in
1Both of them are available on the DataFirst portal- datafirst.uct.ac.za
5
SLIDE 6 earnings from the household surveys, to estimate the variance in earnings within firms. In the RSC the number of workers given is the number of permanent workers but the wage bill given is likely to include the wages of the temporary workers, this means we may be overstating the average earnings in each firm. What effect this may have on inequality measures is not so clear. 3.2.1 Correction for employment non-response Since this is a census and not a survey, there are no weights for the administrative data. But since the number of permanent workers is not administrative data and stems from the survey part, there are some missing values- around one third of the firms did not respond. We need then to correct for this non-response. To do this we weighted the observations with employment information by the inverse of the probability of response to the survey within groups. We create these groups from quartiles of revenue and wage bill, the main product produced2 and the type of business.
3.3 2001 Census Data
We use the information from the 2001 Census as a check on both the household survey data and the RSC data estimates of total employment in Cape Town. Note that there is here a distinction to be kept in mind between people living in Cape Town and those who are working in Cape Town. For the census data we are looking at the main place of work. The RSC employment information includes individuals who live
- utside Cape Town and the household surveys only include individuals who live in Cape Town (they may
work outside Cape Town and there will be others who live outside Cape Town but work in Cape Town). Unfortunately, we cannot use the census data to calculate the variance in earnings because income is only given through bracket responses.
3.4 Consistency across the datasets
3.4.1 Employment numbers As we can see from table 1, even if there is some variation across the three household surveys, we can say that it is likely that there are more than 800 000 workers in Cape Town around 2000. The 2001 Census gives 850 000 which is consistent with the OHS and LFS household surveys. However the RSC data has
- nly about 550 000 workers. There are several possible reasons for the difference between the estimates.
Firstly the census number, which is thought to be the more reliable one, includes both temporary and informal workers. In the 2001 census only 2.5% people working in Cape Town stated they were informally
2Using SIC code
6
SLIDE 7 employed (Kerr 2015), so this cannot be the explanation for the differences. The RSC survey asked about the number of permanent workers, and the household survey data shows that approximately 75% of employees are permanently employed. This means that the census and household survey data gives approximately 600 000 formal permanent workers. Also, the city of Cape Town suspects some tax evasion so that the RSC data, which is supposedly a census, probably misses some firms. This suggests that our data sets are fairly consistent as regards the number of workers and we can point out explanations for the differences that exist. Table 1: Employment in the RSC and Household Surveys Data set Total Employment Median Employment RSC 570k 130 RSC (1 outlier) 550k 112 OHS 1999 810k X LFS 2000 -1 905k 20-49 LFS 2000 -2 805k 20-49 Census 2001 850k X Note : The RSC firms total employment is 570 000 when weighted to take account of non-response, although this includes one firm with 20 000 employees. Thus row 2 excludes this firm and thus the RSC estimates give 550000 permanent workers. The text points out that this is approximately correct once we account for the fact that 25% of workers from the household survey and census totals are not permanent, and a small fraction are in informal firms and thus excluded from the RSC.
4 Descriptive data from the RSC
In this section we provide a description of the firms in the RSC data. We document information from the size distribution of firms and also the proportion of workers employed in firms of different sizes. We also describe mean wage bill per worker. Table 2 shows that 48% of firms employ between 1 and 3 workers, whilst the median firm in the RSC has between 4-7 employees. Firms with more than 200 workers are only 1% of all firms but employ 39% of workers. Not shown is that the median firm has 4 employees, the mean is 17 whilst the median worker works in a firm
- f size 100. These results suggest that the median and mean firm in Cape Town is somewhat smaller than
the nationally representative data used in Kerr et al. (2014) -the Quarterly Employment Statistics Survey from Statistics South Africa- and Kerr (2017) using the South African Revenue Service tax data. Mean earnings per worker are highest in firms with between 4-7 employees, the next highest is those with between 31-50 employees. The largest firms have the lowest mean earnings per worker, a result that contradicts findings from most other countries, where earnings rise with firm size, but is consistent with other work on firm size and earnings in South Africa using the tax data (Bhorat et al. 2017). There does however seem to be a positive relationship between the age of the firm and mean earnings per worker- workers in 7
SLIDE 8
- lder firms have higher average earnings. From the standard deviation within each size category we note
a negative relationship between the standard deviation and the size. The smaller the firm the higher the variance in this category. More precisely, among the firms with between 31 and 200 employees, we find both the highest mean log wage and the lowest standard deviation - after the biggest firm’s standard deviation. We also note that age and size seem to imply effects of the same order. Indeed, the range for the age categories is from 8.03 to 8.23 when with the size it is from 8.03 to 8.26. Ignoring the oldest firms category gives us another fact : the age categories demonstrate lower standard deviations among the cate- gories than with the size ones. The standard deviations seem to be decreasing with age within the categories. Table 2: Descriptive Statistics from the RSC data
- Prop. firms
- Prop. Workers
- Nbr. Workers
mean wage Mean wage diff Size ∈ [1, 3] 48% 5.2% 22k 5478 483 ∈ [4, 7] 22% 6.5% 28k 7991 2296 ∈ [8, 15] 14% 9.3% 39k 4839
∈ [16, 30] 8% 10.5% 44k 5550 555 ∈ [31, 50] 3% 8.5% 36k 6113 1118 ∈ [51, 200] 4% 21.5% 92k 4751
> 200 1% 38.5% 163k 4193
Age ∈ [0, 2] 18% 11.5% 49k 6939 1944 ∈ [3, 7] 30% 19% 80k 4861
∈ [8, 15] 20% 14% 59k 4377
∈ [16, 30] 12% 15.5% 65.5k 4309
∈ [31, 100] 7% 21% 89k 5173 178 > 100 0% 7% 30k 3988
Missing 13% 12% 51.5k 5206 210 Note : The mean wage differential is the difference between the mean of the group (weighted by the weights and number of workers : mean*) and the mean of the whole population.
5 Various Measures of Overall and Between firm inequality
We can use the RSC data to explore the extent of inequality in average earnings between firms and the household survey data to measure overall earnings inequality, using several inequality measures. The first measure is the deciles of the two distributions and the P90/P10 ratio. Figure 1 shows the deciles of average monthly earnings in the RSC firms, weighted by firm size as well as accounting for non-response of some firms, as discussed above. It also shows the deciles for individual monthly earnings from the household survey
- data. The mean earnings per worker is around 33% higher than the household surveys, and the median is
around 15% higher than the household surveys. One obvious explanation is that only permanent workers 8
SLIDE 9 are included in the employment number, but their earnings are included in the wage bill data in the RSC. Overall inequality is somewhat higher than average wage between firms inequality, as measured by the p90/p10 ratios- these ratios are 8.4 in the RSC and 9.5 in the household survey data. An alternative measure
- f inequality is the Gini coefficient. The Gini coefficient in the household survey data is 0.7 (recall this is for
Cape Town only). In the RSC data a Gini coefficient can be calculated for average earnings by firm. This would be the overall earnings Gini if all workers had the average earnings in the firm they work for. In the RSC data this is 0.47, suggesting that between firm inequalities are very substantial. For example this Gini is higher than the overall labour income Gini coefficients for all the 32 countries considered by Koske et al. (2012), except Brazil. In the following sections we focus specifically on one further measure of inequality- the variance of log earnings, estimating this using the average earnings by firm in the RSC and earnings in the household survey data and then using these estimate to decompose overall variance in log earnings into between and within components.
6 Variance Decomposition Method
Since the variance is defined as the mean of the squared distance to the mean, it characterizes the dispersion
- f the wages and the higher the variance, the higher the inequality. But only looking at the variance cannot
give us an idea of how this variance is explained or distributed, as we do not have any idea how these inequalities can be decomposed between groups. This question matters a lot for an understanding of the South African labour market. If wages inequalities can only be partly explained by workers’ characteristics, this suggests that firm characteristics have an important impact on inequality. Following Davis and Haltiwanger (1991), consider a random variable X, the log of earnings, and N, the number of units (individuals in this case), with indicator i and K the number of groups (firms) with indicator
- j. The mean is ¯
- X. Then it is possible to write3 :
V(X) = 1
N
N
i=1(Xi − ¯
X)2 = 1
N
K
j=1 nj( ¯
Xj − ¯ X)2 + 1
N
K
j=1 njVj(X)
= Vbetween(X) + Vwithin(X) This is a classical decomposition of the variance between variance between the groups (Vbetween(X)) and
3See section A for the proof
9
SLIDE 10 the variance within the groups (Vwithin(X)). More precisely, the term
1 N
K
j=1 nj( ¯
Xj − ¯ X)2 is the variance between the firms. It is as if each worker in the firm has the same wage (equal to the mean wage of the firm) and then we measure the variance across the mean wage of the firms weighting by the size of each firms in order to keep the proportion between small firms workers and bigger firms workers. The other term
1 N
K
j=1 njVj(X) is simply the weighted4 mean of variances of the wages inside the firms. In order to esti-
mate such things, ideally we would like to have a data set where for every worker we have the income and the firm in which he is working, that is to say a matched employer-employee data set. But since this is not read- ily available in South Africa, we need to estimate the different elements from different sources of information. It is of interest to recall that the unbiased estimator of the variance5 in the population is : S2 = 1 n − 1
N
(Xi − ¯ X)2 As we noted above, our strategy is to estimate the different elements of this decomposition through different data sets. Estimating two of the three elements allows us to obtain an estimate of the third. Thus we are going to estimate the total variance, V(X), using household survey data, and the variance between firms, Vbetween(X), using the RSC data, to estimate the variance within firms.
7 Within-Firm Inequality Estimates from the Variance Decompo- sition Method
In this section we estimate within firm inequality, using the variance of log earnings in the household surveys and the variance of log mean wage bill from the RSC firm data and employing the decomposition method described above. We find reasonable estimates of the proportion of the total variance explained by the variance across firms, though missing temporary workers in the RSC employment data and some outliers in the RSC may be affecting our results.
7.1 Results
Using the RSC we are able to calculate the following terms : Vb(X) = 1
K
wjnj( ¯ Xj − ¯ X)2 (1)
4By the number of workers in the firm 5See section A.1 for details about this estimator
10
SLIDE 11 where ¯ X is the weighted mean. But with this data, the weighted mean is the following : ¯ X = 1
njwj ¯ Xj (2) Then, several things should be checked: do the number of workers and the mean wage correspond in the two data sets? If the data sets were perfectly representative of the wage dispersion and of the work force employment then we would have the data sets figures very close in terms of mean of wages and employment. We have seen that the employment numbers are fairly close. Table 3 shows the mean, median and variance
- f earnings and log earnings in the household survey data, as well as in the RSC data. This shows the mean
earnings per worker in the RSC is 21% higher than the mean earnings for formal employees in the household surveys. Table 3: The earnings distribution in the household and firm surveys
Household Surveys mean median Variance Wage / month / worker 4117 2380 63842 Log wage / month / worker 7.84 7.65 0.88 RSC firm survey mean median Variance Wage / month / worker 4995 3420 418752 Log wage / month / worker 8.11 8.04 0.53
The variance between firms is given by equation (1). This is the figure that we have to compare with the variance of log of earnings in the PALMS data sets : we need to look at6 varbtwn vartot 2 . Table 3 shows that this is 0.53. We can then compare this with the variance of log earnings from the household survey data, which table 3 shows is 0.88. This means that varbtwn vartot
0.53 0.88
Thus 60% of the total variance is explained by the variance between firms. This is higher than most
- f the estimates found in the literature from developed countries except France (Lazear and Shaw 2009).
It is very similar to the estimate for Brazil of 56% by Benguria (2015) in 2001, using matched worker-firm
- data. The finding that 60% of total variance is explained by between firm variation in earnings means that
the other 40% of the variance is explained by within firm variation. Thus we have the perhaps surprising result that in South Africa a much lower proportion of the variation in earnings is explained by within firm
6It stems simply from the fact that if a = b + c then b a is the part of a explained by b.
11
SLIDE 12 variation than many of the more equal developed countries discussed in Lazear and Shaw (2009). 7.1.1 By sector It is also possible to examine how much of the total variation in earnings is explained by between firm variation across different sectors. Table 4 shows the results by sector. Unfortunately this results in some sectors having relatively few observations. Of those with more than 100 earners the percentage of the variance that can be explained by between firm variance is 49% in manufacturing, 47% in construction, 86% in trade, 54% in finance and 100% in services. Clearly some of these suffer from a small sample size problem, particularly in the household survey data. Table 4: Results by sector
Sector Data Nbr.obs Nbr.Wkrs Mean(logy) S.d. % var. explned % perm. Wkrs Agricul., hunting, HH data 90 19k 6.88 0.96 70% foresting & farming RSC 172 5.5k 8.11 0.92 92% Manufacturing HH data 533 136k 7.86 .89 80% RSC 2366 132k 8.09 0.62 49% Construction HH data 208 60k 7.55 0.93 49% RSC 864 21k 7.98 0.64 47% Trade HH data 434 122k 7.65 .83 61% RSC 5856 107k 8.08 0.77 86% Transport HH data 121 40k 8.16 0.76 87% RSC 581 15k 8.25 0.70 85% Finance HH data 216 77k 8.05 1.03 74% RSC 3321 108k 8.22 0.76 54% Services HH data 365 185k 8.08 0.87 86% RSC 1823 35k 8.18 0.87 100%
8 Conclusion
In this paper we have used an underutilised source of firm data, the RSC data, to estimate the variance
- f log earnings per worker between firms, and to use a variance decomposition to estimate the residual as
the variance of log earnings within firms. This means we can calculate the proportion of the total variation in log earnings that comes from within firm differences and the proportion that comes from between firm differences. We have also used a new source of firm data to provide some descriptive statistics which are of some
- interest. Regarding the age and the size of the firms, it seems that the older the firm is, the higher its mean
wage is. It is not true that larger firms have higher average wages- a finding that is at odds with findings from many other countries, but that has been found in other South African data. Between firm inequality has not been studied in South Africa. The RSC data shows that the Gini coefficient if each worker earned the average earnings of their firm would be 0.47, a massive level of inequality. 12
SLIDE 13
This result is also in line with our result that 60% of the variance of log earnings is explained by between firms differences in Cape Town in 2000. This is a similar level to Brazil but much smaller than many developed countries, which also have lower levels of inequality. The proportion of the variance of log earnings explained by between firm variation differs across sectors. The limitations of this study are data related. Firm data in South Africa is scarce and we have had to make do with a less than ideal data set. The RSC survey asked only about permanent workers, whilst the wage bill is for all employees. Because it also covered only Cape Town, the sample from the household surveys we used was also quite small, possibly resulting in errors in the measurement of total variation in earnings per worker, which would then affect estimates of the proportion of the total variance explained by within firm variation. The newly available tax data from the South African Revenue Services is a census of tax paying firms and their employees. This data can be used to estimate the within and between contributions to total variation in log earnings much more accurately, which we hope to undertake in future work. 13
SLIDE 14 A Variance Decomposition
V(X) = 1
N
N
i=1(Xi − ¯
X)2 =
j nj N 1 nj
Xj + ¯ Xj − ¯ X)2 =
j nj N 1 nj
Xj)2 + 2
j nj N 1 nj
Xj)( ¯ Xj − ¯ X) +
j nj N
1 nj ( ¯
Xj − ¯ X)2 But since we have : 2
nj n 1 nj
(Xi − ¯ Xj)( ¯ Xj − ¯ X) = 2
j nj n 1 nj
Xj − Xi ¯ X − ¯ X2
j + ¯
Xj ¯ X) = 2
j nj n
nj
Xj −
1 nj
X −
1 nj
X2
j + 1 nj
Xj ¯ X
j nj n
¯ X2
j − ¯
Xj ¯ X − ¯ X2
j + ¯
Xj ¯ X
We can then write : V(X) = 1
N
K
j=1 nj( ¯
Xj − ¯ X)2 + 1
N
K
j=1 njVj(X)
= Vwithin(X) + Vbetween(X)
A.1 Estimator of Variance
One can show that the variance of this estimator is the following : V(S2) = N (N − 1)2 (µ4 − σ4) − 2 (N − 1)2 (µ4 − 2σ4) + 1 N(N − 1)2 (µ4 − 3σ4) (3) We can see that it is convergent and can be estimated by :
N (N − 1)2 ( ˆ µ4 − S4) − 2 (N − 1)2 ( ˆ µ4 − 2S4) + 1 N(N − 1)2 ( ˆ µ4 − 3S4) (4) Where ˆ µ4 = 1
N
X)4 14
SLIDE 15 Figure 1: Deciles of overall individual labour earnings and average earnings by firm
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Decile 1 Decile 2 Decile 3 Decile 4 Decile 5 Decile 6 Decile 7 Decile 8 Decile 9
Monthly Earnings
Earnings deciles for firms and workers
Earnings per employee PALMS individuals Mean earnings per employee RSC firms weighted by number of workers
Source: Own calculations from RSC firm data, 2000, and PALMS household surveys 1999-2000.
15
SLIDE 16
References
Benguria, F., “Inequality Between and Within Firms: Evidence from Brazil,” 2015. Bhorat, Haroon, Morn Oosthuizen, Kezia Lilenstein, and Franois Steenkamp, “Firm-level deter- minants of earnings in the formal sector of the South African labour market,” Technical Report 2017. Chennells, Lucy and John Van Reenen, “Establishment Level Earnings, Technology And The Growth Of Inequality: Evidence From Britain,” Economics of Innovation and New Technology, 1998, 5 (2-4), 139–164. Davis, S. and J. Haltiwanger, “Wage Dispersion Between and Within U.S. Manufacturing Plants 1963- 86,” Brooking Papers : Microeconomics, 1991. Fourie, Fredrick and Andrew Kerr, “Informal sector Employment Creation in South Africa: What can the SESE Enterprise Survey tell us,” REDI Working Paper Series 32, REDI, University of Cape Town 2017. ILO, “Global Wage Report 2016/2017, Wage Inequality in the workplace,” Technical Report, ILO 2016. Kerr, A, “The Life Cycle of South African Manufacturing Firms,” Data First Technical Paper, 2015, 33. Kerr, Andrew, “Job Flows, Worker Flows And Churning In South Africa,” South African Journal of Economics, 2017. and Martin Wittenberg, “A Guide to version 3.1 of the Post-Apartheid Labour Market Series (PALMS),” Technical Report, DataFirst, University of Cape Town 2016. , , , and Jairo Arrow, “Job Creation And Destruction In South Africa,” South African Journal of Economics, 2014, 81 (1), 1–18. Koske, Isabell, Jean-Marc Fournier, and Isabelle Wanner, “Less Income Inequality and More Growth Are They Compatible? Part 2. The Distribution of Labour Income,” OECD Economics Department Working Papers 925, OECD Publishing January 2012. Lam, D., A. Finn, and M. Leibbrant, “Schooling Inequality, Returns to Schooling and Earnings In- equality,” Wider Working Paper 050, 2015. Lazear, E. and K. Shaw, “Wage Structure, Raises and Mobility: An Introduction to International Com- parisons of the Structure of Wages Within and Across Firms,” 2009. 16
SLIDE 17
Leibbrandt, M., I. Woolard, A. Finn, and J Argent, “Trends in South African Income Distribution and Poverty since the Fall of Apartheid,” OECD Social, Employment and Migration Working Paper, 2010, 101. Song, Jae, David J. Price, Fatih Guvenen, Nicholas Bloom, and Till von Wachter, “Firming Up Inequality,” NBER Working Papers 21199, National Bureau of Economic Research, Inc May 2015. Wittenberg, Martin, “Nonparametric estimation when income is reported in bands and at points,” Work- ing Papers 94, Economic Research Southern Africa 2008. , “Wages and Wage Inequality in South Africa 19942011: Part 1 Wage Measurement and Trends,” South African Journal of Economics, June 2017, 85 (2), 279–297. , “Wages and Wage Inequality in South Africa 19942011: Part 2 Inequality Measurement and Trends,” South African Journal of Economics, June 2017, 85 (2), 298–318. 17
