Fallacious convergence? Williamson’s real wage comparisons under scrutiny

Abstract

The idea of manifest real-wage convergence for unskilled workers in the latter half of the nineteenth century stems from an article from 1995 by Jeffrey G. Williamson. That article presented real wage comparisons of unskilled urban workers for seventeen countries. Sweden, along with the rest of Scandinavia, is found to be an influential case in accounting for much of the alleged factor price convergence taking place. This paper takes a closer look at all the three steps that have to be taken in order to establish real wage comparisons, focusing on Sweden in relation to the US and the UK. The most important findings are twofold. First, that the US–Sweden wage gap is considerably smaller for manufacturing than for building workers, and second, that the rate at which Sweden’s real wages approached the American and the British has been grossly overestimated. Swedish real wages did grow rapidly, but not as rapidly as Williamson’s comparison will have us to believe, because his real wage series does not constitute a representative account of the Swedish unskilled real wage experience. It is argued that, as we suffer from a serious paucity of data for narrow and comparable samples of late nineteenth century unskilled workers, resorting to more encompassing wage measures is a more viable option. That also implies a questioning of the American unskilled wage series, which makes considerably slower progress than the wage series for manufacturing workers.

Appendix1: Real wage series

Table 5 Real wage series for the US, the UK and Sweden, 1860–1913 (1900 = 100)

1.1 Appendix 2: New wage series for Swedish manufacturing

Since official wage statistics for manufacturing workers did not appear before World War I, our wage evidence comes from Bagge et al.’s (1933) detailed investigation based on archival sources. The usual reference point to the movement of pre-World War I Swedish wages is their index of average wages in manufacturing based on averages for iron and steel, mining, metal manufacturing and engineering, sawmills, wood-pulp mills, paper mills, food products, textile industry and leather, rubber goods and chemical industries (Bagge et al. 1933, pp. 43–44). The authors do not give any precise information on the assigned weights but list the factors they consider most important in assigning to each industry an appropriate weight. Those factors are, for instance, the quality of the wage material, the size of the firm from which the pay record was taken and the number of workers in that industry. Quality seems to have mattered most (pp. 38–39): ‘The greatest attention, then, has been paid to the quality of the series, though, to some extent the relative size of the occupations and concerns have also been considered’. The lack of detailed insights into the process of aggregation frustrates any attempt to replicate their average series of manufacturing. This is unfortunate inasmuch as Schön’s (1988) revisions of output, within the context of Swedish historical national accounts, and the corresponding adjustments of the number of workers for the period 1868–1912 (Prado 2008), justify a closer look at what a different weighting scheme, based on the wage bill, may bring about. In the following attempt to assign to each series a new weight, based on the new information on output and employment for 1868–1912, the quality factor attributable to each series is left out of consideration. Instead, the recorded growth rates of wages implied by each of the series are taken at face value.

The starting point is the wage material for different industries, or groups of industries, which underlie the computation of Bagge et al.’s series of average wages. At times, these series have been complemented with the wage material presented in the monographs section to create as many industry-specific wage series as their investigation permits. Furthermore, to avoid the potential influence of reductions in working hours on the movement of wages, hourly earnings are the preferred wage measure. When hourly wages are not available daily wages are the second best option, and annual wages a last resort. When an industry-specific series of wages is not at hand I use the wage series of the most closely related industry, or the series representing the group of industries to which that industry belongs.

Two factors put the construction of wage relatives in favour of the compilation of actual wage levels: first, instead of establishing the average wage level in a particular firm or industry, Bagge et al. track the wage record for a sample of representative workers. They may, therefore, have been more successful in their attempt to picture the movement of wages than establishing actual levels. Second, there is an unfortunate mixture of hourly, daily and annual wages which makes it difficult to establish a representative level of any kind. Nonetheless, the actual wage levels have a bearing on the weights used to combine the different wage relatives into an aggregate series for manufacturing. The starting point is therefore to establish the wage levels for a reference year, in this case 1912. The wage level is derived from the public investigation of cost shares which gives the share of wages in gross output, equivalent to the wage bill (SOU 1923). Dividing the wage bill by the number of workers yields the average annual wage for each industry. Once we have pinned down the annual industry-specific wage levels for 1912, we can proceed by scaling the wage relatives and then weighting the resulting series of annual wages by number of workers as in formula 1, where W and N are average wages and number of employed in year t and industry i, respectively.

$$ \frac{{\sum\nolimits_{i = 1}^{n} {\left( {\frac{{W_{t,i} }}{{W_{1912,i} }}W_{1912,i} } \right)N_{t,i} } }}{{\sum\nolimits_{i = 1}^{n} {N_{t,i} } }} $$

(1)

The series so constructed pave the way for further developments into series that satisfy the requirements of different forms of index numbers. In the following formula 2 the series has been transformed into a Laspeyres index number where the wage relatives are weighted by the wage bill in the base year b. It shows how wages would have progressed had the sectoral structure become set in a fixed mould (Table 5).

$$ \frac{{\sum\nolimits_{i = 1}^{n} {\left( {\frac{{W_{t,i} }}{{W_{b,i} }}} \right)W_{b,i} N_{b.i} } }}{{\sum\nolimits_{i = 1}^{n} {W_{b,i} N_{b,i} } }} = \frac{{\sum\nolimits_{i = 1}^{n} {W_{t,i} N_{b,i} } }}{{\sum\nolimits_{i = 1}^{n} {W_{b,i} N_{b,i} } }} $$

(2)

The normal convention is to measure the intra-sectoral wage movement by choosing an early base year, but, as Table 6 shows, the difference between early and late base years is negligible. Annual weights also allows the computation of a chained Fisher index which records a somewhat slower growth, though again the difference between it and fixed early or late base year is quite insignificant. It bears noting that Bagge et al.’s wage series of average hourly earnings for manufacturing grew considerably faster than my new series, no matter which of the index formula are in use. The gap appears at the end of the 1870s, is widened up to the turn of the century, and maintained until 1913. This is an expected result considering the larger weight given to the wage series for sawmill workers, which grew appreciably slower than the average. The rapid expansion in the sawmill industry was brought to a halt in 1874, and the drop from the peak in 1874 to the trough in 1891 cut the wage level by half. Between 1870 and 1912 the series grew on average 0.37% annually, which was an 80 percent slower progress than for manufacturing as a whole. Since Schön adjusted the level of output for sawmills upwards, and Prado (2008) attempted to make the number of workers correspond with that higher level, the wage bill, and thereby the weight assigned to the wage series have inevitably been augmented significantly. The results in Table 6 show the visual impact that Fig. 11 assesses and confirms that the new weighting scheme applied here changes the colours of the Swedish wage picture. It now looks paler. The difference between the old and the new series is large enough to warrant more attention than there is scope for in this minor investigation. It may have been that Bagge et al. did not assign the series of wages for sawmill workers the large weight it has been assigned here for reasons they did not communicate to their readers. Perhaps they deemed bizarre the behaviour of the wage series of sawmill workers and therefore degraded the quality and the importance of it. What speaks in favour of the reliability of the series is that there is corroborative evidence of the sluggish growth rate of wages for sawmill workers relative to the average of manufacturing (Cornell 1982). As long as no further evidence defies its usefulness the average should include sawmill workers’ wages, weighted with due respect to its great importance in the Swedish economy.

Fig. 11

Hourly wages for male manufacturing workers, 1868–1912 (1868 = 100). Note: the series titled new contains sawmill workers’ wages and computed as a Laspeyres index with 1868 as base year. Sources: the series titled Bagge et al (1933, Table 26); the series titled new is set out in Appendix 1

Table 6 Average percentage growth rates of nominal wages in the manufacturing industry, 1868–1912