2.1. Reduced capital deepening in a growth accounting exercise

Table 1 summarises a growth accounting exercise for the UK’s market sector since 1970. As usual, estimates of TFP in such decompositions are derived as a residual and in the short run can reflect labour hoarding and other cyclical influences.

Table 1.

A growth accounting exercise

Note: UK market sector

• • Average annualised compound growth per period $ g=100.\left(\frac{\mathit{\ln}{X}_t-\mathit{\ln}{X}_{t-n}}{n}-1\right) $

• • Output growth (col 1) = Growth in hours worked (col 6) + Labour productivity growth (col 3)

• • Labour productivity growth (col 3) = TFP growth (col 2) + Contribution of K/L to productivity growth (col 4) + Contribution of labour composition (not shown).

Source: ONS, own calculations.

We draw attention to the following facts from Table 1:

• • In each of the four economic cycles before the GFC, average peak-to-peak labour productivity growth had been in the region of 2% p.a. with differences in average output growth across the cycles being reflected in differences in labour input growth.

• • The post-GFC cycle from 2008 to 2019 was unusual in that while output growth was weaker than usual, at 1.34% p.a., its composition was skewed towards growth in labour input (1.07% p.a.) rather than growth in labour productivity (0.27% p.a.).

• • The 2.13 pp fall in labour productivity growth from 2.4% p.a. in 2001–2007 to 0.27% p.a. in 2007–2019 is largely accounted for by a fall in TFP growth of 1.74 pp, from an above average rate of 1.69% p.a. in 2001–2007 to virtually zero (−0.05% p.a.) in 2007–2019. Standard neoclassical economics offers little explanation for long-term movements in TFP beyond attributing it to technical progress.Footnote ³

• • Capital deepening was unusually weak in 2007–2019. In the run-up to the GFC, capital deepening had accounted for 0.41 pp of average annual labour productivity growth during 2002–2007. By contrast, there was little change in the aggregate capital/labour ratio after 2008. Overall, the turn-around in capital deepening between 2001–2007 and 2007–2019 (0.4 pp) accounted for around a fifth of the slowdown in labour productivity growth (2.13 pp).

2.2. A sector-level perspective

More light can be shed on the drivers of the overall productivity slowdown by looking at changes in trends in the different market sectors of the economy.Footnote ⁴ Coyle and Mei (Reference Coyle and Mei2023) and Riley et al. (Reference Riley, Rincon-Aznar and Samek2018) have also investigated sectoral patterns in productivity growth using earlier vintages of ONS data.

While labour productivity stagnated in the post-GFC period, there was widely different experience in the various industrial sectors comparing 2001–2007 with 2007–2019. Labour productivity growth fell in seven of the 15 market sectors under consideration; these are mining and quarrying (B, −1.82 pp), manufacturing (C, −6.00 pp), wholesale and retail (G, −1.94 pp), transport and storage (H, −2.80 pp), information and communication (J, −4.65 pp), financial and insurance (K, −8.22 pp) and professional and scientific (M, −2.73 pp). This group includes the external-facing trading sectors. Productivity growth rose in agriculture (A, 0.91 pp), electricity (D, 2.80 pp), water (E, 0.19 pp), construction (F, 2.56 pp), accommodation and food (I, 0.07 pp), administration and support (N, 1.13 pp) and other services (RSTU, 0.55 pp) and was unchanged in the public sector (OPQ). This group includes mainly the internal-facing non-traded sectors.

There is a strong positive correlation between the change in labour productivity growth within the different sectors between 2001–2007 and 2007–2019 and the change in output growth within those sectors. Demand weakness may have contributed to the productivity slowdown, though such an interpretation would have to explain why businesses in these sectors did not cut back employment to a larger extent.Footnote ⁵

As also noted by Coyle and Mei (Reference Coyle and Mei2023) and Riley et al. (Reference Riley, Rincon-Aznar and Samek2018), the decline in labour productivity growth mainly reflects lower productivity growth within sectors rather than reallocation across sectors. The decline in the ‘within’ contribution, obtained by weighting industry labour productivity growth by each sector’s beginning of period current price output share, is also 2.13 pp. The 2.13 pp fall in labour productivity growth from 2001–2007 to 2007–2019 is largely accounted for by the slowdown in productivity growth in manufacturing (contributing −0.95 pp), wholesale and retail (−.26 pp), information and communication (−0.30 pp) and financial and insurance (−0.60 pp).Footnote ⁶ Other sectors made small positive or close-to-zero contributions. It is worth noting that in four of these sectors (B, D, E and I) productivity growth remained negative in 2008–2019.

Table 2 reports ONS estimates of labour productivity growth and its decomposition into TFP change and capital deepening over the pre- and post-GFC economic cycles. Accounting for growth at the industrial sectoral level indicates a reduction in the contribution of capital deepening throughout the economy. We interpret this as evidence of the effect of a common labour supply shock.

Table 2.

Sectoral productivity decompositions

Note:

$ {\displaystyle \begin{array}{cc}\mathrm{Labour}\ \mathrm{productivity}\ \mathrm{growth}=& \hskip-1em \mathrm{TFP}\;\mathrm{growth}+\mathrm{Contribution}\ \mathrm{of}\;\mathrm{K}/\mathrm{L}\;\mathrm{to}\ \mathrm{productivity}\ \mathrm{growth}\\ {}& \hskip-5em +\mathrm{Contribution}\ \mathrm{of}\ \mathrm{labour}\ \mathrm{composition}\;\left(\mathrm{not}\ \mathrm{shown}\right)\end{array}} $

Bold signifies table headings

The sectoral decompositions highlight two factors about the productivity slowdown:

1. 1) With the exception of the professional and scientific sector, each of the sectors that made a material negative contribution to the change in labour productivity growth between 2001–2007 and 2008–2019 (C, G, H, J, K and M) experienced both weaker TFP growth and a lower contribution from capital deepening.

2. 2) Nearly all sectors that benefitted from higher TFP growth in the post-GFC cycle also experienced a lower contribution from capital deepening.

This suggests to us that while certain key sectors experienced an unexplained negative TFP shock, there was a common shock that caused the contribution of capital deepening to decline throughout the economy. A positive labour supply shock would help explain such capital shallowing.

A typical feature of the UK economy is that there is a negative correlation between a sector’s labour expansion and capital deepening that we attribute to slow adjustment of capital to shocks. To illustrate this relationship, we compare average growth in hours worked and the capital deepening contribution, averaged within five distinct business cycles since 1971 for each sector. Figure 2 suggests those sector/period averages with larger labour expansions were associated with a significantly lower capital deepening contribution. Plotting the relationship separately for each business cycle suggests a broadly similar relationship in each period. At a descriptive level, larger labour input expansions are associated with a lower contribution from capital per worker to productivity growth.

Figure 2.

The relationship between growth in hours worked and the capital deepening contribution within business cycles.

Note: Each dot shows a sector’s labour expansion plotted against its capital deepening contribution, with the colour of the dot indicating the business cycle it is drawn from. The lines show the best fit drawn through the scatter for each business cycle. These are all negatively sloped, as is the overall line of best fit through the scatter of all observations.

2.3. Capital/labour substitution

In simple theory, a labour supply shock would be transmitted to the economy through downward pressure on wages causing businesses to substitute labour for capital. Consistent with a labour supply shock, ONS data suggest that the relative price of labour fell quite substantially, by around 20%, in the post-GFC period.Footnote ⁷ The aggregate capital/labour ratio declined from the mid-2000s and, especially, post-crisis.

If capital and labour are gross complements (and the elasticity of substitution σ < 1), an increase in the supply of labour raises the demand for capital. While there is no consensus about the precise value of σ, published estimates in the Constant Elasticity of Substitution (CES) framework using aggregate US or sector-level data suggest σ < 1. This suggests we should expect the capital/labour ratio to fall less than proportionately with the fall in the relative price of labour. That applies in the long run and especially in the short run. Adjustment of the aggregate capital stock plays a key role in transmitting the benefits of a larger labour force through the economy, but this takes time. More generally, a slower adjustment of capital will weigh on the capital/labour ratio (and productivity) in response to a rise in labour supply.

4.1. The long run

One possible interpretation of our aggregate growth accounting exercise is that the observed reduced rate of capital deepening is a response to the slowdown in TFP growth associated with the financial crisis. This is a natural interpretation in a standard growth model in which the capital stock is determined by the usual first order condition requiring the marginal product of capital to equal the real interest rate. Under constant returns to scale, both productivity and the capital/labour ratio are independent of the size of the labour force.Footnote ¹⁰

To illustrate this point, consider a Cobb–Douglas production function which implies the following for labour productivity (y − l).

(1) $$ y-l=a+b\left(k-l\right) $$

where y = log output, l = log labour force, k = log capital stock, a = log TFP, b = capital share. This has the following first-order condition.

(2) $$ \left(1-b\right)\left(l-k\right)=\mathit{\log}\left(r/b\right)\hbox{--} a $$

with r = discount rate. This leads to:

(3) $$ y-l=a+\left[b/\left(1-b\right)\right]\left[a-\mathit{\log}\left(r/b\right)\right]=a/\left(1-b\right)-\left[b/\left(1-b\right)\right].\mathit{\log}\left(r/b\right) $$

implying that labour productivity (y − l) is independent of the quantity of labour supplied (l). In the long run, and given diminishing marginal returns to labour (and capital), rises in the size of the labour force do not affect labour productivity as the optimum capital stock will increase in line with labour supply in equilibrium.

From Equation (2), a negative TFP shock (a) also implies reduced capital deepening. This could mean that the turnaround in aggregate capital deepening we have observed is due to reduced TFP growth and not to a labour supply shock. This argument has been made by Fernald and Inklaar (Reference Fernald and Inklaar2022). In the long run, as Prescott (Reference Prescott1998, p. 526) puts it, ‘TFP determines labour productivity, not only directly but also indirectly by determining capital per worker.

Our interpretation is that this only applies after the economy and labour market have fully adjusted to higher labour supply. The role of stronger domestic labour supply is, therefore, best seen as a view of the ‘medium run’.Footnote ¹¹ But this is important because adjustment does not occur instantaneously. Moreover, the evidence in Section 2 suggests that while some sectors experienced both lower TFP growth and capital shallowing, consistent with a TFP shock, others experienced higher TFP growth and capital shallowing, a combination that is not consistent with a TFP shock alone. We suggest instead that this was due to a common positive labour supply shock that overlay a more heterogeneous, but primarily negative, TFP shock.

In standard macroeconomic analysis, a positive labour supply shock shifts the long-run aggregate supply curve ‘to the right’ and causes actual output to rise in line with increased potential. In the short run, greater availability of labour pushes down on real wages and, by reducing marginal costs, encourages imperfectly competitive firms to lower prices and thereby stimulate demand, output and employment. With capital tending to be slow to adjust, higher employment is associated initially with reduced capital deepening and lower labour productivity. Yet, with a lower capital/labour ratio pushing up the marginal product of capital, firms have an incentive to increase investment until the capital/labour ratio rises back to its original level and the economy returns to its balanced growth path.

In the new, long-run equilibrium, output and the capital stock will have risen proportionately to increased labour supply and labour productivity will ultimately be unaffected by the labour supply shock (e.g. Borjas, Reference Borjas2019).

The key practical question is how long this adjustment process takes to complete and relatedly its impact on labour productivity in the meantime. In an influential analysis of immigration in the United States, Ottaviano and Peri (Reference Ottaviano and Peri2012) explicitly took capital adjustments into account. They noted that ‘the recent growth literature usually estimates a 10% speed of convergence of capital to the own balanced growth path for advanced (OECD) economies (Islam, 1995; Caselli et al 1996)’. They estimate a similar rate of convergence based on US data, 1960–2004.

According to Dustmann et al. (Reference Dustmann, Glitz and Frattini2008), this adjustment speed means that, instead of reducing the capital/labour ratio by 11% and consequently average real wages by 3.6%, the immigrant inflows to the United States between 1990 and 2004 only reduced the capital/labour ratio by 3.4%, which in turn implies a much smaller negative effect of only 1.1% on average wages in the economy. Basically, the faster capital is able to adjust, the smaller will be the effect on average wages in the economy.

Our own assessment is that adjustment could be considerably slower than this in the recent UK context, resulting in an extended period of weaker productivity. Evidence for a substantial elasticity of investment with respect to the cost of capital is sparse (Chirinko et al., Reference Chirinko, Fazzari and Meyer1999) and aggregate relationships typically suggest slow adjustment of fixed investment to its determinants. Moreover, some of the key channels of adjustment may have been especially impaired in the aftermath of the financial crisis.

In order to quantify the possible effects of increased labour supply on productivity over this adjustment period, we employ an empirically-based macroeconomic model that has been calibrated to recent UK quarterly national accounts data.Footnote ¹² The model highlights the possibility of an extended period of weak productivity growth following an increase in labour supply and illustrates the key channels involved. We also show the simulated impact of a reduction in TFP growth for an extended period. Together these shocks can account for the stylised facts of the UK experience following the GFC.

4.2. Simulation results

We use the model (outlined in an Annex) to simulate the effects of a 12.5% increase in the population of working age, corresponding roughly to the increase in UK labour supply that occurred between the GFC that began in 2007 and 2019. In the main case, we allow for an increase that occurs smoothly over a 12-year period (labelled ‘staggered labour supply’). We contrast this with a variant where the increase occurs smoothly over 3 years (‘frontloaded labour supply’).

Employment increases quickly in response to the rise in labour supply (Figure 4). This owes to the extra labour supply pushing down initially on wages and domestic prices leading to increased demand for UK output, and hence employment via the production function. The demand increase is driven by the internationally traded sectors, manufacturing, financial services and other private traded services, where exports rise sharply in response to increased competitiveness. It spills over to other sectors via greater demand for intermediate outputs and as domestic output expands. But domestic demand rises quite sluggishly in comparison. This is partly because of short-term yet persistent weakness in real household income reflecting lower real wages weighing on consumers’ expenditure.

Figure 4.

The simulated macroeconomic effect of increased labour supply.

Domestic-facing, non-traded sectors such as construction and private non-traded services thereby respond more weakly than the internationally traded sectors. The marginal product of capital increases as output rises ahead of the capital stock and this leads to higher fixed investment (Figure 4). But fixed investment increases only moderately leading to a slow expansion in the capital stock. The net effect is that the capital–labour ratio declines and labour productivity is lowered by around 4% at its peak effect (Figure 5).

Figure 5.

The simulated macroeconomic effect of increased labour supply.

The model simulations show that the faster the labour supply shock occurs the larger the short-run adjustment will be, particularly for wages and prices, but the ultimate adjustment is broadly the same.

In summary, the simulation evidence suggests that a labour supply shock of a similar size to the labour supply increase observed in the UK between 2007 and 2019 could reduce the level of labour productivity temporarily by around 4%. This effect is close to the size of the reduced contribution of capital deepening to the productivity slowdown over that period.

As highlighted earlier in this paper, the evidence suggests that the major part of the productivity slowdown was due to a reduction in TFP. Figure 6 compares the effect on key macroeconomic aggregates of the labour supply shock with a reduction in TFP that is sufficient to reduce labour productivity by 16 log points over 50 quarters. This is achieved in the model by reducing the growth rate of technical progress in the different sectors by 0.5 pp for 6 years.

Figure 6.

The simulated macroeconomic effect of increased labour supply (front-loaded) and reduced TFP.

The top left panel of Figure 6 shows that the negative effect on GDP of the TFP shock would dominate the positive effect of the labour supply shock, so that GDP would be reduced by a combination of these shocks, consistent with the evidence of a lower average growth rate over this period.

The top right panel of Figure 6 shows a similar pattern for fixed investment with the negative effect of the TFP shock dominating the positive effect of the labour supply shock, again consistent with the evidence of weak investment over this period.

The middle-left panel of Figure 6 shows that the positive labour supply shock is required to account for higher employment after the GFC. In this case, the positive effect of the labour supply shock dominates the negligible effect of the TFP shock on employment, consistent with the strong pick-up in employment after the GFC.

The middle-right panel of Figure 6 shows that the positive labour supply shock and the negative TFP shock reinforce each other in their negative effect on the capital/labour ratio. The most significant impact in the short run is that of the positive labour supply shock in bringing about capital shallowing. As discussed earlier this negative effect should wear off in time, but the negative effect of the TFP shock will then become more dominant.

The bottom panel of Figure 6 shows the reinforcing effects of the two shocks on labour productivity. At its peak, the positive labour supply shock would reduce labour productivity by about 4 log points, accounting for around one-fifth of the decline.

How plausible is this simulation evidence? Inevitably, the modelled effect is sensitive to the various assumptions underlying the empirical relationships in the model. Of key importance are the investment relationships that lie behind the small adjustment of fixed investment and the capital stock to an increase in the marginal product of capital. Greater investment sensitivity would reduce the estimated effect on labour productivity, but there is little empirical evidence of such an effect. In fact, as documented in Section 2, recent trends at the aggregate level and in individual sectors support a reduction in capital intensity since the financial crisis, consistent with the simulation evidence. Impaired capital markets following the financial crisis could have made capital adjustment more difficult than implied by the model.

4.3. Cross-country evidence

We now complement our previous analysis with cross-country evidence on productivity growth, population growth and rates of productivity convergence.

We confront two hypotheses with cross-country evidence: (i) countries with higher population growth experience lower productivity growth and (ii) rates of productivity convergence have slowed over time, in particular since the great financial crisis. We then assess how those links vary across countries and how the UK compares in these two respects.

We use data from the Conference Board’s Total Economy Database. From that database, we select its 25 countries in Western Europe, North America, Oceania and Japan for the period from 1960 to 2019, thereby spanning a set of developed market economies over a long period that ended pre-Covid.

As a starting point, average productivity growth correlates negatively with (average annual) population growth in the 60-year period (Figure 7). Lower productivity growth economies over this extended period have tended to have higher population growth. This echoes the cross-country relationship highlighted by Beaudry and Collard (Reference Beaudry and Collard2002) for the period up to 2002.Footnote ¹³

Figure 7.

Labour productivity growth and population growth.

Source: Conference Board, Total Economy Database and Authors’ calculations.

We exploit the cross-country variation in the data by regressing country-level average productivity growth (in a 20-year window) on its population growth and the initial level of productivity which allows for convergence effects. The higher the initial level of labour productivity (20-years earlier), the weaker should be expected productivity growth. This involves estimating:

$$ \Delta \log {\left(\frac{Y}{L}\right)}_{it}={\alpha}_{0,t}+{\alpha}_{1,t}\log {\left(\frac{Y}{L}\right)}_{i0}+{\alpha}_{2,t}\Delta {Pop}_{it}+{e}_{it} $$

Where ‘i’ indexes countries, ‘i’ = 1, 2…, 25, and ‘t’ indexes years, t = 1980, 1981…, 2019. We exploit this variation in 40 years of data on labour productivity growth across 25 countries.

As in the study by Beaudry and Collard (Reference Beaudry and Collard2002), we show the evolution of the rolling coefficients on population growth (α₂) and those coefficients capturing convergence (α₁) (Figure 8 and Figure 9 respectively). These allow us to assess our two hypotheses.

Figure 8.

The evolving relationship between labour productivity growth and population growth.

Source: Conference Board, Total Economy Database and Authors’ calculations.

Figure 9.

The evolving relationship between labour productivity growth and estimated rate of convergence.

Source: Conference Board, Total Economy Database and Authors’ calculations.

Our estimates indicate that the inverse cross-country relation between productivity growth and population (shown in Figure 7) was driven by the experience up to the 1980s and mid-1990s, supporting our first hypothesis for that period. Yet, there is evidence that this estimated relationship has since changed sign. More recently, higher productivity growth economies have tended to have higher population growth, also controlling for convergence.

Regarding convergence itself, the estimated rate of convergence has slowed notably since the early-2000s and in the post-crisis period. Compared with an estimated 2.5% p.a. annual speed of convergence in productivity growth up to the 1980s, this has slowed down to a little over 1% p.a. by 2019, across the sample as a whole (Figure 9). It is natural to think of the financial crisis as having impaired the reallocation of capital, and perhaps labour, in such a way as to have slowed down convergence for countries away from the productivity frontier.

Beaudry and Collard (Reference Beaudry and Collard2002) argued that productivity growth in the 1970s was slower in economies where and when labour force was high, specifically after the adoption of a general purpose technology, and this owed to reduced capital deepening. They also suggest that this relationship was changing by the end of their sample which ran to 1997. Our evidence is consistent with, and extends, that view.

With UK experience since the financial crisis in mind, this cross-country evidence points to a slower pace of convergence as a factor weighing on UK productivity growth. Yet, prima facie, it struggles to reconcile weaker productivity growth with the UK’s increased population growth in this more recent period.

How can we reconcile the UK’s underperformance in the more recent period with its increased population growth – in particular, given the finding that an earlier inverse relationship between productivity growth and population growth has faded and may have even changed sign?

4.3.1. How the UK Compares

Our cross-country panel allows us to explore how these links have varied by country, shedding further light on how UK experience has compared.

Figure 10 shows that UK productivity growth was in a minority of countries for which productivity growth varied inversely with population growth over the whole period. This retains the approach of looking at productivity growth over a 20-year interval with its population growth in that 20-year window. In the UK, we estimate a coefficient (standard error) of −1.42 (0.24). UK experience has in general seen higher population growth associate with weaker productivity growth. In our sample of countries, about as many countries saw their productivity growth vary positively with population growth, including the United States.

Figure 10.

UK productivity growth has moved inversely with its population growth.

The fact that we found cross-country evidence that higher productivity growth countries tended to have higher population growth by the end of the period might have posed a puzzle for understanding UK experience. Our finding that the UK has in general been in a minority of countries with a more negative relation between its productivity growth and population growth may help account for some of this. There is clearly a need for further work to understand these evolving links.

What of the UK’s estimated convergence speed? Our results summarised by the range of country-level coefficients (Figure 11) indicate that the UK witnessed a more modest pace of convergence, estimate at −0.90% p.a. (standard error = 0.14). This may also be a factor that has weighed on UK productivity growth. Our data do not realistically allow us to explore how these links evolved separately for each country and over time.

Figure 11.

The UK’s estimated rate of productivity convergence has been slower than most.

Our cross-country evidence together with our assessment of UK-specific performance suggests: (i) Over time, and across countries in general, the tendency for population growth to weigh on productivity growth that was evident in the 1980s and 1990s has since weakened. (ii) Yet, the UK has had a stronger tendency than most advanced economies for population growth to go hand in hand with weaker productivity growth; (iii) a slower pace of cross-country convergence followed the financial crisis and may have slowed productivity growth; and (iv) slower convergence also applies in the UK, in a feature could have owed to impaired capital markets slowing adjustment of its capital stock to an increase in its labour force.

The natural explanation for these findings is that there is no general relationship between a country’s productivity and population growth, as would be consistent with long-run theory. But in the medium term, the relationship will depend on the causes and nature of population change. Countries at the technological frontier that have a high demand for labour that is met partly from highly-skilled workers from the rest of the world are likely to see faster productivity growth than countries that experience a positive labour supply shock that is accommodated by slow wage and productivity growth.