Hobsbawm (1963): pessimist — living standards fell or stagnated during industrialisation (Hobsbawm 1963)
Lindert & Williamson (1983): optimist — real wages roughly doubled 1780–1850 (Lindert and Williamson 1983)
Feinstein (1998): pessimist — Lindert & Williamson’s price index understated inflation; real wages stagnated (Feinstein 1998)
The debate turns on measurement: which nominal wage series? which price index?
Practical: how do you actually build a real wage index?
Conceptual: what does a real wage index tell us about welfare?
Focus today: the practical question
Building a real wage index requires two components:
Nominal wage: wage measured in £ — “what the labourer was actually handed”
Real wage: what those £ can buy
Example: a Lindert & Williamson farm labourer earns £21 in 1781 and £29 in 1851
We need a way to convert nominal £ into purchasing power
Wages are typically observed as weekly rates
We don’t know weeks worked per year
Annual wage \(= w^k_t \times H\) where \(H\) = weeks worked — unknown
Index approach: divide all dates by base year, \(H\) cancels if stable over time
\[\mathcal{W}_t = \frac{\bar{W}_t}{\bar{W}_0} = \frac{\sum_k s^k_t\, w^k_t}{\sum_k s^k_0\, w^k_0}\]
Single-sector wages give a partial picture
Weight sector wages by employment share \(s^k_t\) (from census or other sources)
Weighted average nominal wage:
\[\bar{W}_t = \sum_k s^k_t\, w^k_t\]
\(w^k_t\) = nominal wage in sector \(k\) at time \(t\); \(s^k_t\) = employment share of sector \(k\) at time \(t\)
Caveat: regional relocation of industries can bias the average
Wages are conditional on employment; the unemployed earn \(w = 0\)
One option: add an “unemployment” sector with weight = unemployment rate and wage = 0
But: unemployment \(\neq\) not working
Keep analytically distinct: involuntary unemployment vs non-participation
To convert £ into purchasing power we need a consumption basket
Record what fraction \(\omega^j\) of income is spent on each good \(j\)
Multiply consumption shares by prices to get cost of basket
Two main index approaches: Laspeyres and Paasche
Both express the cost of the basket relative to a base year \(t_0\)
\[\mathcal{P}^L_t = \sum_j \omega^j \frac{p^j_t}{p^j_0}\]
Holds consumption shares \(\omega^j\) fixed at base year \(t_0\)
Easy to compute: you only need to collect consumption data once
Bias: assumes households keep buying expensive goods even as prices rise
Tends to overstate increases in the cost of living
\[\mathcal{P}^P_t = \sum_j \omega^j_t \frac{p^j_t}{p^j_0}\]
Re-samples the consumption basket \(\omega^j_t\) each period
If households switch from beef (expensive) to chicken (cheap), records no welfare loss
Bias: treats all price-induced substitution as welfare-neutral
Tends to understate increases in the cost of living
Fisher ideal index: geometric mean of Laspeyres and Paasche — rarely done in historical work due to data requirements
Chained index (modern practice): compute a Laspeyres index from \(t\) to \(t+1\), then multiply the period-by-period changes:
\[\mathcal{P}^C_T = \prod_{t=0}^{T-1} \mathcal{P}^L_{t \to t+1}\]
Updates basket each period but avoids full Paasche substitution bias
Sensitive to base year when price changes are large
Nominal wage \(\bar{W}_t\) measured in £
Cost-of-living index \(\mathcal{P}_t\) measured in £/basket
Divide to get real wage measured in baskets:
\[\mathcal{R}_t = \frac{\mathcal{W}_t}{\mathcal{P}_t}\]
\(\mathcal{R}_t > 1\): higher purchasing power than base year
\(\mathcal{R}_t < 1\): lower purchasing power than base year
This is why Feinstein’s revision matters: a higher \(\mathcal{P}_t\) mechanically lowers \(\mathcal{R}_t\)
Real wages measure purchasing power of market wages
What they miss:
Even if all these were measurable — how do we combine them into a single “standard of living”?