The Distribution of Human Capital in Sweden, ch. 5

5. Estimations of human capital

The results of the human capital estimations are based on a fixed effect wage regression applied to panel data spanning 14 years from 1992 to 2005, covering roughly 300 000 individuals each year. The methodology is described in detail in chapter 2, and the data is discussed in chapter 3. This chapter will now present novel estimates of the distribution of human capital in the Swedish economy.

5.1 Probability densities and descriptive statistics

In Figure 5.1 below the probability density distributions of human capital (hit) and person effects (Θi) are plotted using a Gaussian kernel to estimate the densities.1 As we can see they are both roughly bell shaped, but with the person effect having thicker tails.

Figure 5.1 [Figure not shown]

From Figure 5.1 we can also see that human capital is slightly shifted to the right compared to the person effect. Underlying this relation is the effect that the experience component of xitβ has on human capital. By and large, the traits of the distributions in Figure 5.1 correspond quite well to those estimated in Abowd et al. (2005) .

To complement the distribution plot, some descriptive statistics of the measures are provided in Table 5.1 below.

Table 5.1 [Table not shown]

As we saw in the distribution plot, hit has a slightly larger mean while the dispersion of Θi is larger. The perceptible symmetry of the distributions is also reflected in the percentiles, indicating only a slight negative skewness for hit and a slight positive skewness for Θi. The overall impression is that the two measures have quite similar distributions, which of course is not surprising since hit is the sum of Θi and the experience component of xitβ. Nevertheless , the absence of anomalies in the measures does indicate that the model specification has been successfully implemented.

5.2 Components of human capital

It was mentioned in the introductory chapter that the person effect would be decomposed into one observable and one unobservable part. This has been done by running an OLS regression on Θi using a fully interacted specification with the time-invariant variables gender, immigrant, and education level in the variable vector zi (see equation (1.3)).2 The reason for doing this decomposition is that it can tell us something about the presumed advantage of our specification. Recall that the aim of the specification is to capture unobservable components of human capital in the person effect Θi. This implies that if the explanatory power of the person effect is mostly attributable to its observable component, then our specification has not really added much in terms of explaining the variation of wages. If, on the other hand, the explanatory power of Θi largely stems from its unobservable component, it would indicate that our specification has succeeded in estimating something of importance, which would have remained omitted in a rudimentary wage equation. And so, a series of crude correlations between ln_wage and the different components of human capital is presented in Table 5.2 below.

Table 5.2 [Table not shown]

An interesting feature of the human capital components is that the person effect and the experience component are negatively correlated. This result was also obtained in Abowd, Lengermann and McKinney (2003), though not in Abowd, Kramarz and Margolis (1999). The implication of the negative correlation is that older individuals generally carry a lower person effect, probably reflecting that younger generations of employees born in the 1970s and 1980s  have unobservable abilities that are better adapted to production in the modern knowledge economy.

Now, the correlation between ln_wage and the different components of human capital can be seen in the first correlation column. And as is obvious from the calculations, the unobservable part of the person effect is a lot more important and more highly correlated with wages than the observed part! Not only is this result imperative for the justification of this study, it also, in my opinion, speaks volumes against the baseline wage equation where unobserved characteristics are omitted. Furthermore , this result is very similar to that obtained by Abowd, Lengermann and McKinney (2003) and in line with the result in Abowd, Kramarz and Margolis (1999), thereby confirming the importance of accounting for unobserved characteristics in a wage model.

A different way of gauging the impact of the estimation strategy is to add the obtained estimates of the human capital components to a baseline wage equation and see what happens with the explanatory power of the model. The result from such an exercise is presented in Table 5.3 below.

Table 5.3 [Table not shown]

The explanatory power of the baseline wage model is about 0.50. Upon adding the person effect to the specification, the explanatory power leaps to 0.78! To investigate the powers at play, only the observable part of the person effect is added to the baseline model in the next specification. As a consequence , the explanatory power plunges back down to 0.50. And as we would expect after observing this behavior, upon only adding the unobservable part of the person effect to baseline model, the explanatory power soars back up to 0.78. In the last specification , the human capital measure is added to the baseline model whereby an explanatory power at about 0.85 is obtained, the highest of all specifications.

Just as the results in Table 5.2 hinted, the unobserved component of the person effect appears to have captured a source of variation in wages that the observed variables are unable to account for. Although the specification scheme presented above is not precisely the same as the one in Abowd, Lengermann and McKinney (2003), to the extent that a comparison allows itself to be made, our results are very much in line with what they previously found. Now that the impact of the unobserved characteristics on explaining the variation in wages has been explored, we will shift focus and in the next section compare levels of human capital in different branches of industry to their respective productivity growth.

5.3 Human capital and productivity growth

The comparison between different compositions of human capital and the corresponding productivity growth in various branches of industry in this section should be viewed as a, hopefully intriguing, example of the kind of relationships that are possible to study using the human capital estimates obtained in this paper. However , the example does by no means exhaust the analytical tools made available by obtaining the human capital estimates. That would have required far more time and effort, and is consequently outside the scope of this thesis.

All the data and indexes used for the productivity growth measure in this section have been gathered from the National Accounts at SCB. Productivity is defined as value added divided by hours worked, whereby the value-added series, spanning from 1994 to 2005, has been deflated by means of volume based indexes specifically designed for this purpose by SCB. Hence , the calculated average annual growth rate only covers the period 1994–2005, while the human capital and person effect estimates are based on the period between 1992–2005. Although Sweden did experience a detrimental financial crisis in 1992, it seems unlikely that the effect it had on the levels of human capital in the economy were contemporaneous. Rather, they will have operated on a long-term basis, when those affected by the decrease in public spending (pupils, children of parents who receive welfare, people in labor market programs, etc.) entered the labor market. Therefore I do not think that the slight difference in time periods is a major problem for our analysis. But the financial crisis in 1992 does suggest that the productivity growth calculations might be sensitive to the choice of benchmark time period.

The share of employees with an estimated human capital above the 75th percentile within different industrial branches is presented in column (1) in Table 5.4 below. Column (2) presents the share of employees with an estimated person effect above the 75th percentile. The corresponding estimates for the share of employees below the 25th percentiles are presented incolumns (4) and (5), while the average annual productivity growth can be read in column (3).

Table 5.4 [Table not shown]

The percentile distributions contain all available observations in the analysis sample. As a consequence , the obtained percentiles for each branch of industry should be interpreted as the mean percentile value over time. At first glance, there does not appear to be any discernible patterns relating the labor force composition to the level of productivity growth. However , previous studies have indicated that the relationship between human capital and productivity is stronger in the service sector than in the manufacturing sector (Abowd et al. 2005). Hence , in an investigative effort, the branches of industry that to varying extents can be classified as Knowledge Intensive Business Services (KIBS) (Brandén, Lindmark and Sandqvist, 2010) (Nählinder, 2005) have been colored blue in Table 5.4, while the more traditional parts of the manufacturing sector have been colored red.

Now, from this exercise we can observe that the KIBS industries, with the exception of financial intermediation, follow a general tendency where increased shares of top percentile employees are associated with higher levels of productivity growth. And similarly that increased shares of bottom percentile employees are associated with lower levels of productivity growth. For the traditional manufacturing sector, however , the occurrence of high shares of top percentile employees, or low shares of bottom percentiles, does not seem to have any clear association to the level of productivity growth.

The implication of the enigmatic result for the financial intermediation branch is very difficult to assess. Previous research indicates that it is notoriously difficult to accurately calculate the value-added measure of that particular branch, a perception that has become abundantly clear since the financial turmoil of 2008 started (Turner et al. 2010). But whether it can explain the results we find here, I simply do not know. And since the results in this section are merely based on quite crude comparisons, it would be imprudent to draw far-reaching conclusions on the matter.

Last but not least, in the event that the reader is interested in further descriptions of the distribution of human capital, Table A.2 in the appendix will present the mean and standard deviation of the human capital and person effect estimates by industry, county, and sector. Furthermore, Table A.3 in the appendix will present percentile calculations analogous to those in Table 5.4 above, but in different sectors of the economy. Similarly, Table A.4 in the appendix contains the percentile calculations by county.


1 The reader might think it is odd that the probability density functions take values greater than one. The explanation is that the probability densities are measured in the reciprocal units of their corresponding variable’s range, and are thus not measured on a probability scale.
2 Table A.5 in the appendix contains the results from estimating this model.