Capital Accumulation

Abstract

This chapter provides and analyses new estimates of net capital stock and services for Spain over the last 170 years. The net capital (wealth) stock-GDP ratio rose over time and doubled in the last half a century. Capital services grew fast over the long run, accelerating in the 1920s and from the mid-1950s to 2007. Until 1975, their acceleration was assisted by an increase in the ‘quality’ of capital. Capital deepening proceeded steadily, accelerating from 1955 to 1985, and slowed down thereafter, for expanding sectors attracted less investment-specific technological progress. Although capital consumption rose over time, the rate of depreciation fell from 1970 to 2007, as the relative prices of new capital goods’ declined due to embodied technological change.

An earlier version was published as L. Prados de la Escosura (2022), “Capital in Spain, 1850-2019”, Cliometrica 16(1): 1–28. The estimates of capital stock and services have been revised and updated.

1 Introduction

Capital is back on the economist’s agenda. Thomas Piketty’s (2014) defence of rising capital-output ratio over time has triggered an interest in historical research. The debate on the productivity slowdown has also stimulated the search for its historical roots and, in particular, the role played by capital accumulation.

Using ‘state of the art’ methodology, this chapter offers consistent and integrated estimates of net capital (wealth) stock and capital services that provide a sound basis to address welfare and growth issues.¹ For example, testing current views about increasing capital/output ratios or investigating the contribution of capital deepening to labour productivity growth (see Chap. 4).

The new set of estimates provides the longest homogeneous historical series of capital stock and services available internationally. This represents an improvement on existing capital estimates for Spain, in particular, the historical series by Prados de la Escosura and Rosés (2010) for 1850–2000, and those for later periods, such as Ivie (Mas and Pérez, 2022), Penn World Tables 10.0 (Feenstra et al., 2015, updated), and Conference Board (2022). Not only by considering a longer time span but, more importantly, by closely following the OECD’s Manual (2009), which provides the latest consensus on capital stock and services estimates. Furthermore, unlike the capital estimates for recent decades, the new estimates employ gross fixed capital formation (GFCF) series obtained through splicing national accounts using the interpolation, rather than backward projection method. This procedure avoids over-exaggerating investment levels and, hence, capital stock.

But why study Spain? The case of Spain is that of a middle-income country (at least, until 1970, according to the World Bank’s definition) that succeeded in joining the upper income countries (Calvo-González, 2021). As most historical research on capital has focused on the pioneers of the first and second industrial revolution, providing long-run estimates of capital stock and services, for a country that carried out a transition from a poor, agricultural economy to a post-industrial advanced one, represents an addition to the research on welfare and growth.

The main findings can be summarised as follows.

• 1. Capital input (namely, the flow of capital services into production) grew at a 3.5% annual rate during the last 170 years, accelerating in the 1920s and especially from the mid-1950s to the onset of the Global Financial Crisis (2008). Until 1975, the acceleration of capital input growth was assisted by an increase in the ‘quality’ of capital, that is, a compositional shift towards more productive assets.

• 2. Capital deepening (that is, capital services per hour worked) grew steadily up to World War I, accelerating in the 1920s and even more so between the mid-1950s and mid-1980s, before slowing down, from 1986 to 2007 and, after a strong recovery during the Global Financial Crisis, stagnating since 2014, as expanding economic sectors attracted less investment-specific technological progress.

• 3. The net capital (wealth) stock-GDP ratio, at current prices, rose over time, with a fourfold increase between the early 1880s and 2020, contradicting one of Kaldor’s (1957) stylised facts, and increased by four-fifths from 1970 onwards, in line with Piketty and Zucman (2014) for Western Europe’s wealth-income ratio.

• 4. The consumption of fixed capital (CFC) in terms of GDP increased over time, shadowing the capital-output ratio but, as a proportion of the net capital stock (that is, the rate of depreciation), only rose up to the 1960s, falling from 1970 to 2007 as embodied technological change led to a decline in the relative prices of new capital goods.

The chapter is organized as follows. Section 3.2 discusses the concepts, method, and sources used and presents new estimates of net capital stock and productive capital stock derived with the Perpetual Inventory Method, testing its sensitivity and comparing the results to available series of capital stock. Section 3.3 provides a volume index of capital services, in which the user cost of capital is derived with an ex-ante exogenous rate of return. The volume index of capital services (VICS) is compared to the productive capital stock (PKS), as a growing gap between the two reveals the shift from low return and long life assets to higher return but shorter life assets, that is, an increase in the “quality” of capital. Next, trends in VICs and capital deepening are presented and weighed against available estimates. Lastly, Sect. 3.4 offers the evolution of the capital-output ratio, as well as the consumption of fixed capital (% of GDP) and the depreciation rate (% net capital stock).

2 Capital Stock

The publication of the OECD Manual in 2009 (OECD, 2009) provided a unified methodology with which to measure capital stock and services, which builds bridges between previous OECD methodology and that pioneered by Jorgenson (1963) and further developed by Jorgenson (1989, 1990) and Hulten (1990).² This chapter follows the OECD approach and distinguishes between net capital stock, also labelled wealth, which measures capital assets at their market price, and productive stock, an intermediate stage to derive a volume index of capital services (capital input), that is, the flow of capital services into production.

In the construction of net capital stock estimates, the Perpetual Inventory Method (PIM) is used, cumulating flows of investment, corrected for retirement and depreciation, for each asset. Implementing the PIM requires, by type of asset, (a) investment volumes and deflators; (b) average service lives; (c) depreciation rates; and (d) an initial benchmark level of capital stock.

• (a) Four different types of asset have been distinguished: dwellings, other construction, transport equipment, and machinery and equipment. Biological resources and intellectual property products have been added to machinery and equipment assets because information on them is only available in national accounts beginning in 1980.³ No distinction has been made between ICT and non-ICT assets, due to the dearth of data in national accounts and the aim of providing homogeneous long-run series of capital stock.⁴

  Gross fixed capital formation (GFCF) volume series for each type of asset are obtained by deflating current values, and expressed in 2010 Euro. GFCF current value and deflator series come from Prados de la Escosura (2017, updated). GFCF series are derived from spliced national accounts for 1958–2020 (see Appendix), and via the commodity flow method (CFM), that is, production and trade data to proxy investment by asset type, for 1850–1958.⁵

  It is worth noting that the GFCF deflator series have been smoothed using a Hodrick-Prescott filter in order to avoid negative values for the unit user costs. The same smoothing procedure has been applied to the general price index, which in our case, is the GDP deflator.⁶

• (b) The choice of average services lives, that is, the length of time that assets are retained in the capital stock, presents a challenge. Although choosing different average lives for different periods represents the usual historical practice (Feinstein, 1988; Prados de la Escosura and Rosés, 2010) a single set of average service lives is used here in order to facilitate comparisons with other estimates, as service lives for each asset type are kept constant in most country studies. Moreover, there is no concluding evidence that service lives fall over the long run, as offsetting tendencies are at work.⁷ Thus, dwellings and other construction are assigned average service lives of 60 and 40 years, respectively, while transport and machinery equipment are attributed 15 years each.⁸ Nonetheless, compositional changes in the capital stock imply that the average service life of total capital varies over time and, in so far as a shift towards more productive assets takes place, it declines.

• (c) As regards depreciation rates, a declining balance is chosen, that is, a geometric rate, δ = R/T, where T is the asset’s average service life and R the selected parameter. Geometric depreciation rates differ across assets but are constant over time. Following the US Bureau of Economic Analysis (Fraumeni, 1997), Hulten and Wykoff’s (1981) directly computed depreciation rates and implicit R values, 1.65 for transport equipment and machinery and 0.91 for structures, have been accepted. The resulting depreciation rates are, thus, 1.52%, 2.28%, 11.0%, and 11.0% for dwellings, other constructions, transport equipment, and machinery and equipment (plus intellectual property and biological resources since 1980), respectively.⁹

• (d) In the absence of an initial stock of capital, two main approaches have been used to derive the latter. One assumes, after Harberger (1978), that the economy is at its steady-state and derives the initial stock for each asset type as,

$$ {W}^{\mathrm{t}0}={I}^{\mathrm{t}0}/\left(\delta +\uptheta \right) $$

(3.1)

• where I is real investment; δ, the rate of depreciation; and θ, the growth rate of investment in early years.

An alternative to the steady state assumption approach is to estimate a functional relationship between real GFCF and GDP and, supposing that such a relationship is stable over time, to derive volume GFCF series for the previous period on the basis of available GDP series. Here the relationship between each asset type and GDP has been estimated for 1850–1920 and the regression coefficients applied to the available real GDP estimates to produce GFCF volume series for each type of asset between 1780 and 1850.¹⁰

The initial (1850) level for each capital asset type has been derived with the PIM and the average lives and depreciation rates accepted for the post-1850 period with each approach. Figure 3.1 compares the results of the two approaches. It can be observed that their difference disappears by 1890. As the alternative option to the steady state approach seems to be less stringent, it has been preferred here.

Fig. 3.1

Initial net capital stock: alternatives estimates, 1850–1900 (2010 Million Euro) (natural logs)

Another important issue is the sensitivity of the net capital stock series to the choice of initial level. Thus, the estimates have been replicated, adopting as initial capital both half and twice the level obtained in the favoured option. Figure 3.2 shows that differences diminish as time goes by and fade away by the 1920s. Thus, the estimates seem to be robust to alternative ways of computing the initial level for the last 100 years at least.

Fig. 3.2

Initial net capital stock: sensitivity to alternative options, 1850–1930 (2010 Million Euro) (natural logs)

Next, the Net Capital Stock has been computed for 1850–2020 using the stock-flow relationship (PIM). If we define the net stock at the beginning (^B) of the first year, 1850, as W^1850,B, end-year (^E) net stocks for each asset in all consecutive years are,

$$ {W}^{\mathrm{t}\mathrm{E}}={W}^{\mathrm{t}\mathrm{B}}+{I}^{\mathrm{t}}\hbox{--} \delta \left({I}^{\mathrm{t}}/2+{W}^{\mathrm{t}\mathrm{B}}\right) $$

(3.2)

where I^t is real yearly gross fixed capital formation and δ, the rate of depreciation. All stocks are valued at average prices of 2010 and by adding them up the Net Capital Stock in 2010 Euro is obtained.

The value of the consumption of fixed capital (depreciation) for each asset at 2010 prices, D^t/P₀^t, results from applying the rate of depreciation to the net stock at the beginning of the period plus half the current period’s investment,

$$ {D}^{\mathrm{t}}/{P_0}^{\mathrm{t}}=\delta \left[{I}^{\mathrm{t}}/2+{W}^{\mathrm{t}\mathrm{B}}\right]. $$

(3.3)

The net (wealth) capital stock at current prices, P₀^tW^t, is obtained by reflating the average of the net capital stock at the beginning and the end of each year with the average yearly price index for each asset, P₀^t and, then, adding them up.

$$ {P_0}^{\mathrm{t}}{W}^{\mathrm{t}}={P_0}^{\mathrm{t}}\left({W}^{\mathrm{t}\mathrm{B}}+{W}^{\mathrm{t}\mathrm{E}}\right)/2 $$

(3.4)

Similarly, the current value of the consumption of fixed capital, D^t, has been derived by revaluing its constant price value with the deflator for each asset, P₀^t.

$$ {D}^{\mathrm{t}}=\delta \left[{I}^{\mathrm{t}}/2+{W}^{\mathrm{t}\mathrm{B}}\right]{P_0}^{\mathrm{t}} $$

(3.5)

A final step is to consider the destruction of capital stock resulting from the Spanish Civil War (1936–1939). Although capital assets in transport equipment and dwellings derived through PIM include war damage, this does not seem to be the case for other construction and machinery, as destruction estimates in the historical literature appear to be larger than those resulting from the PIM exercise. Hence, the historical estimates of asset destruction have been accepted and distributed at constant yearly rates over 1936–1939.¹¹ The resulting figures imply a 4.9% contraction of the total net capital stock between 1935 and 1939 which, by asset type, represents a fall of 2.0% (dwellings), 6.8% (other construction), 13.7% (machinery and equipment), and 30.4% (transport equipment), much lower than Maddison’s (1995: 138) guesstimates for World War II destruction in belligerent European countries, except the UK.

How do the new estimates compare to the recent computations of the net stock of fixed capital by the Spanish official statistical office, Instituto Nacional de Estadística (INE)? Figure 3.3 presents the logarithmic deviations expressed in percentages.¹² The new estimates approximately match the INE’s figures, with lower levels in the 2000s and higher ones in the 2010s, and an average absolute difference of 7.7% (standard deviation 3.9).

Fig. 3.3

New net capital stock: differences from INE estimates, 2000–2020 (natural logs %) (current prices) computed with Interpolated GFCF and declining balance

Moreover, the new net capital stock series are systematically lower than Ivie’s figures (Mas and Pérez, 2022) between 1964 and 2011, and only slightly higher thereafter (Fig. 3.4). Why does such a discrepancy exist? A major difference is that the Ivie’s GFCF series for the period 1965–1995 have been spliced using the retropolation method, not through interpolation as in our case (See Appendix, A.1 A Note on Splicing GFCF Series in Spain’s National Accounts). I have replicated the comparison but the new net capital stock estimates are now computed with retropolated GFCF series. The resulting gap between the two series narrows down remarkably, with the average (absolute) difference shrinking to 6.6% (s.d. 6.6) from 20.4% (s.d. 12.6). Therefore, methodological differences explain most of the discrepancy between the two set of estimates.

Fig. 3.4

New net capital stock differences from Ivie estimates, 1964–2020 (natural logs %) (current prices). Computed alternatively with interpolated and retropolated GFCF series

An interesting contrast results from comparing the estimates obtained with the PIM and the capital stock derived from a wealth survey for 1965 (Universidad Comercial de Deusto, 1968–1972), often used to initialise capital stock series.¹³ It can be observed that the wealth survey exaggerates the size of the capital stock (Table 3.1).¹⁴

Table 3.1 Wealth survey and perpetual inventory method estimates in 1965 (000 million Peseta)

Lastly, productive stock, K^t, has been obtained by adding investment in the latest period to the net capital (wealth) stock,

$$ {K}^{\mathrm{t}}={I}^{\mathrm{t}}/2+{W}^{\mathrm{t}\mathrm{B}} $$

(3.6)

It is worth noting that while in order to derive the net capital stock the cumulating flow of investment is corrected for retirement and depreciation, in the case of productive capital only efficiency losses are subtracted. In practical terms, the difference results from the fact that the net capital is valued at the end of the year and productive capital represents the average value in the year. Moreover, productive stocks for each type of asset are computed at constant prices only and used to derive capital service flows.

How do our results for the productive capital stock (PKS) compare with those already available? Figure 3.5a presents the new estimates together with those provided for Spain by the Penn World Tables 10.0 (PWT 10.01) (Feenstra et al., 2015, updated) and Ivie (Mas and Pérez, 2022) since 1950 and 1964, respectively. Although the three series present similar trends, the new estimates exhibit a steeper trend, that is, grow at a faster pace. The explanation of the differential largely lies in the use of retropolated GFCF series before 1995, since the difference narrows down sharply when the new PKS estimates are replicated with retropolated GFCF series (Fig. 3.5b). However, other elements also contribute to explain this; in the case of Ivie’s figures, for example, the initial level derives from the 1965 wealth survey and uses a more detailed breakdown by asset type.

Fig. 3.5

(a) New productive capital stock, 1950–2020: Comparison with PWT10.01 and Ivie estimates (2010=100) (natural logs). (b) New productive capital stock derived with GFCF retropolated series, 1950–2020. Comparison with PWT10.01 and Ivie estimates (2010=100) (natural logs)

3 Capital Services

We can now proceed to compute the capital input, that is, the flow of capital services into production. To do so, a volume index of capital services is derived as a weighted average of productive stock indices by type of asset, in which each asset’s share in total user cost of capital (that is, the current value of capital services) are the weights. This procedure implies that, for each asset, its flow of capital services is proportional to its productive stock, although the rate of variation of capital services differs across assets (Jorgenson and Griliches, 1967).

Thus, we need to compute the unit user cost of capital for each asset, which represents the marginal return an asset generates during one period of production (OECD, 2009). Once obtained, the unit use cost, F₀^t, is multiplied by the asset’s productive capital stock, K^k,t, to derive the value of its capital services, U^k,t. Adding up the values of all assets we obtain the total value of capital services, U^t.

Different rates of return have been used to compute the unit user cost in empirical studies. The ex-post endogenous rate of return is the realised rate of return and, in principle, preferable. For example, it is used by both the Penn World Tables 10.0 (Feenstra et al., 2015, updated) and Conference Board (2022). An ex-post endogenous rate of return equals the value of capital services to capital compensation in national income (that is, the gross operating surplus plus the capital share in gross mixed income), which is consistent with an economy of perfect competition and constant returns to scale (OECD, 2009).¹⁵ The use of an ex-post endogenous rate of return requires, however, a complete coverage of all assets and a distinction between market and government sectors. Otherwise, the rate of return will be biased.¹⁶ Unfortunately, our data do not meet such stringent requirements.

The alternative is, then, to compute an ex-ante exogenous rate of return, that is, the one expected by the investor.¹⁷ In an ex-ante approach, the rate of return for investment on a given asset should not be higher than in an alternative investment of comparable risk. The OECD Manual (OECD, 2009) recommends working with real rates of return and real changes in asset prices, as they are independent from inflation and less volatile, and, in particular, suggests a 4% real rate of return, which is close to Spain’s historical rate, and has been adopted in Ivie’s estimates (Mas and Pérez, 2022).¹⁸ In fact, assuming a fixed real rate of return on investment matches one of Kaldor’s (1957) stylised facts, namely, that the rate of return on investment is roughly constant over long periods of time. The objection can be raised, however, that when an ex-ante exogenous rate of return is chosen, the resulting value of capital services may not match capital compensation in national income.

The ex-ante unit user cost, or capital service price, F₀^t, can be defined as

$$ {F_0}^{\mathrm{t}}={P_0}^{\mathrm{k},\mathrm{tB}}\left(1+{\uprho}_{\left(\mathrm{tB}\right)}\right)\left[{{\mathrm{r}}_{\mathrm{a}}}^{\ast }+{\delta}_0\left(1+{{\mathrm{i}}_{\left(\mathrm{tB}\right)}}^{\ast}\right)-{{\mathrm{i}}_{\left(\mathrm{tB}\right)}}^{\ast}\right] $$

(3.10)

The ex-ante user cost of an asset,

$$ {U}^{\mathrm{k},\mathrm{t}}={F_0}^{\mathrm{t}}{K}^{\mathrm{k},\mathrm{t}} $$

(3.11)

And the total user cost of capital,

$$ {U}^{\mathrm{t}}={\Sigma}_{\mathrm{k}=1}{U}^{\mathrm{k},\mathrm{t}.} $$

(3.12)

where P₀^k,tB is the purchase price of a new asset at the beginning (^B) of year t,

ρ_(tB) the rate of change of the price index (GDP deflator) at the beginning (^B) of year t,

r_a^* the real rate of return (the nominal rate corrected for inflation), 4%, in this case,

i_(tB)^* the real anticipated change in asset prices at beginning (^B) of year t,

δ₀ the rate of depreciation of a new asset, K^k,t the productive capital stock of asset k during period t.

Furthermore, a simplified ex-ante exogenous rate of return can be derived by setting the anticipated real holding gains term i^*t equal to zero. Although this approach has the advantage that it does not require us to estimate anticipated real holding gains, it is only a reasonable alternative if asset price changes do not deviate significantly from changes in the GDP deflator. The resulting user cost, then, becomes,

$$ {SF_0}^{\mathrm{t}}={P_0}^{\mathrm{k},\mathrm{tB}}\left(1+{\uprho}_{\left(\mathrm{tB}\right)}\right)\left[{{\mathrm{r}}_{\mathrm{a}}}^{\ast }+{\delta}_0\right] $$

(3.13)

Lastly, a Törnqvist index of aggregate capital services is computed as,

$$ \ln \left({KS}^{\mathrm{k},\mathrm{t}}/{KS}^{\mathrm{k},\mathrm{t}-1}\right)=\Sigma {\overline{v}}^{\mathrm{k},\mathrm{t}}\ln \left({K}^{\mathrm{k},\mathrm{t}}/{K}^{\mathrm{k},\mathrm{t}-1}\right) $$

(3.14)

where K^k,t is the productive capital stock of asset k and ${\overline{v}}^{\mathrm{k},\mathrm{t}}=\frac{1}{2}\left({v}^{\mathrm{k},\mathrm{t}-1}+{v}^{\mathrm{k},\mathrm{t}},\right)$ the two adjacent year average share of each asset in total user cost of capital, being v^{k, t} = U^{k, t}/U. Then, the volume index of capital services (VICS) is obtained as the exponential.

It is worth noting the different weighting of the capital stock (the share of assets in its total current value) and the index of capital services (the share of assets in total returns to capital). Figure 3.6 shows the composition of the net capital stock, dominated by structures (dwellings and other construction) that in spite of the long-term fall in the share of dwellings until the early 1990s and the rise of machinery and equipment up to the early 1960s, still contribute four-fifths of the net capital stock value in 2020. A different and more volatile picture results from the composition of capital returns, as assets with lower average service lives (and, hence, higher depreciation rates) are those with higher marginal returns (Fig. 3.7). Thus, machinery and equipment matches the share of other construction since the mid-twentieth century and the share of dwellings declines more than in the net capital stock.¹⁹

Fig. 3.6

Net capital stock composition (current prices) (%)

Fig. 3.7

Capital services’ composition (ex-ante exogenous rate of return) (current prices) (%)

But how different is the composition of capital services when they are obtained with the simplified ex-ante exogenous rate of return, as favoured in Ivie’s estimates (Mas and Pérez, 2022)? Similar but less volatile trends appear, even though machinery and equipment’s remains below the share of other construction (Fig. 3.21), but the validity of the simplified approach depends on the stability of relative GFCF prices.

Figure 3.8 offers the evolution of the price of each type of asset relative to the GDP deflator and shows how they fluctuate.²⁰ For example, the relative price of both machinery and transport equipment experienced a decline between the late 1850s and 1880s, which coincided with railway construction and the early stage of industrialisation, and a sustained fall from the 1950s, which was steeper until the late 1970s. Embodied technological change helps explain these assets’ relative price trends. Thus, assuming that asset prices mimic the general price index is unrealistic and alters the weighting of the volume index of capital services.

Fig. 3.8

GFCF prices relative to the GDP deflator (2010=1) (Hodrick-Prescott smoothed)

The different weighting of the net capital stock and capital services is also reflected in the evolution of productive capital stock and the volume index of capital services, since VICS grows faster than PKS as more dynamic assets are usually those of shorter average service life but higher returns. Figure 3.9 confirms their divergent evolution, which has widened since the 1970s.²¹

Fig. 3.9

Volume index of capital services (VICS) (ex-ante exogenous rate of return) and productive capital stock (PKS), (1850=100) (natural logs)

An index of capital “quality” that measures the capital input’s composition effect can be derived as the ratio between the volume index of capital services and that of productive capital stock,

$$ {KQ}^{\mathrm{k},\mathrm{t}}={KS}^{\mathrm{k},\mathrm{t}}/{K}^{\mathrm{k},\mathrm{t}} $$

(3.15)

Figure 3.10 shows a long-run increase in the “quality” of capital, punctuated by reversals, in which a contraction during the Civil War (1936–1939) and its autarkic aftermath (1939–1953) and a fast increase between the mid-1950s and the late 1970s, followed by deceleration, only broken by the late 1980s spurt, stand out.²² A rise in the index signals a shift towards capital goods with higher unit user costs and, hence, higher marginal productivity.

Fig. 3.10

Capital quality (ex-ante exogenous rate of return) (1850=1). Note: Capital quality = Ratio of volume index of capital services to productive capital stock

A comparison between the new volume index of capital services and earlier estimates is pertinent. In the first place, let us compare the new results with Prados de la Escosura and Rosés’s (2010) estimates, under similar assumptions (namely, Hulten and Wykoff’s declining balance depreciation rates and GFCF series spliced through interpolation). A common pattern is found, but the new VICS presents lower levels, although they tend to converge in the late twentieth century (Fig. 3.11). Such a difference may derive from the lower (and fixed) average service lives used here, while Prados de la Escosura and Rosés employed higher (and variable) average service lives, which, by increasing the gross stock and reducing depreciation, result in a larger net capital stock.

Fig. 3.11

Volume index of capital services (VICS)*: comparison with Prados de la Escosura and Rosés (2010) (1850=100) (natural logs). *Ex-ante exogenous rate of return

The comparison between the new volume index of capital services and those VICS derived by PWT10.01 and Ivie (Mas and Pérez, 2022), to which Conference Board (2022) estimates since 1990 have been added, shows slower growth for the PWT10.01 and Ivie series, but rather similar for the Conference Board series (Fig. 3.12a).²³ The main explanation for the different pace of growth is that both PWT10.01 and Ivie estimates are based on pre-1995 GFCF series spliced through retropolation, unlike the new VICS, which draw on GCFC interpolated series. Figure 3.12b confirms that when VICS are derived using retropolated GFCF series, the gap with PWT10.01 and Ivie narrows sharply, especially from the late 1970s onwards. Moreover, as PWT10.01 estimates are derived with ex-post endogenous rates of return, the differential narrows further when the new VICS are computed with this rate of return (Fig. 3.27).

Fig. 3.12

(a) New volume index of capital services (VICS): Comparison with PWT10.01, Ivie, and conference board (CB) estimates, 1950–2020 (2010=100) (natural logs). (b) New VICS, 1950–2020. Alternative estimates derived with GFCF retropolated series. Comparison with PWT10.01, Ivie, and conference board (CB) estimates (1850=100) (logs)

The comparison in terms of capital quality, that is, the ratio between capital services and productive capital indices, reveals that quality gains are much larger in the new estimates than in the PWT10.01 and Ivie’s (Fig. 3.13).²⁴

Fig. 3.13

Capital quality: comparison with PWT10.01 and Ivie estimates, 1950–2020 (2010=1)

What are the observed trends in capital input? Capital services grew at 3.5% over the last 170 years but at an uneven pace. It is possible to distinguish a period of steady growth, slightly above 2% per year, up to 1920, in which the compositional change of capital (capital quality) represented a minor proportion (Table 3.2). In the 1920s, the growth rate doubled, with nearly a third contributed by capital quality. The slowdown of the early 1930s did not revert to the pre-1920 growth thanks to its compositional change. After shrinking during the Civil War and recovering mildly during the World War II years, capital input growth returned to its pre-1920 growth trend until the mid-1950s when it began an intense acceleration that lasted for half a century and was cut short by the onset of the Global Financial Crisis (2008). During Spain’s delayed and short Golden Age (1959–1975), capital input growth was nearly fourfold that of the pre-1920 era, with capital quality contributing one-fifth of the total. The oil crises that coincided with the decade of ‘transition to democracy’ (1976–1985) represented a substantial slowdown in absolute and per capita GDP but not in terms of capital input that, with hardly any quality improvement, kept growing at 5% yearly during the ‘transition’ decade and after Spain’s accession to the European Union. The Great Recession (2008–2013) nearly halved the post-1975 rate of capital services growth and, since 2014, capital input has been growing at the slowest pace since World War II.

Table 3.2 Capital input growth, 1850–2020 (%) ex-ante exogenous rate of return (annual average logarithmic rates)

If we look now at the volume of capital services per hour worked, that is, capital intensity or deepening, this grew steady up to World War I, intensified in the 1920s and, after nearly stagnating for two decades, expanded at an accelerated pace between the early-mid 1950s and mid-1980s (Table 3.3 and Fig. 3.14). Capital deepening slowed down thereafter, particularly between the mid-1990s and 2007 and, after a spurt during the Great Recession, practically stagnated. A comparison with alternative capital deepening figures for the post-1950 era shows that the new estimates grew faster than PWT10.01 estimates and similarly to the Conference Board’s since 1989 (Fig. 3.15).

Table 3.3 Capital deepening growth, 1850–2020 (%) ex-ante exogenous rate of return (annual average logarithmic rates)

Fig. 3.14

Capital deepening* (2010=100) (natural logs of ×100 level). *Volume index of capital services (VICS) (ex-ante exogenous rate of return) per hour worked

Fig. 3.15

New capital deepening* estimates, 1950–2020: comparison with PWT10.01 and conference board (CB) (2010=100) (natural logs). *VICS (ex-ante exogenous rate of return) per hour worked

It is worth highlighting the inverse association between capital deepening and employment growth in post-Franco Spain (Fig. 3.16). Employment destruction during the decade of ‘transition to democracy’ (1976–1985) and the Global Financial Crisis (2008–2013) contribute to explain capital deepening in those years; conversely, from the accession to the EU to the onset of the Global Financial Crisis (1986–2007), and in the post-2014 recovery, employment creation underlies the deceleration in capital deepening. Thus, capital deepening slowdown since 1986 suggests that expanding sectors have not attracted much investment-specific technological progress.

Fig. 3.16

Growth breakdown of volume index of capital services (VICS)* (ex-ante exogenous rate of return) (%). *VICS = VICS/hour × hours worked

4 Capital-Output Ratio and Capital Consumption

Capital has a dual nature as a storage of wealth and provider of capital services to production (OECD, 2009). So far, the focus has been on capital services. Let us now look at the evolution of wealth or net capital stock.

Piketty’s (2014) identification of a fluctuating capital-output ratio going back to the eighteenth century has challenged one of Kaldor’s (1957) stylised facts. Namely, the stability of the capital-output ratio. Such a claim is hardly news for economic historians, who have long been sceptical about empirical regularities. Prados de la Escosura and Rosés (2010) challenged the long-run stability of the capital-output ratio, and Gallardo-Albarrán and Inklaar (2020) have rejected it for more than 30 countries over the last 100 years.

The evolution of Net Capital Stock ratio to GDP, expressed at current prices, shows that after declining until the early 1880s, a sustained increase took place, with the capital-output ratio rising fourfold between the early 1880s and 2020 (Fig. 3.17). An initial phase of expansion, in which the ratio more than doubled, lasted until the early 1930s, peaking during the Civil War (1936–1939) when economic activity severely contracted. Relative stability from the late 1940s to 1960, with the ratio ranging between 2.0 and 2.5, was followed by a dramatic fall until the mid-1960s, at a time of fast economic growth, and a subsequent recovery that heralded a strong and sustained increase in the capital-output ratio, punctuated by reversals in the late 1980s and, again, in the late 2010s. The sustained rise of the capital-output ratio and capital deepening led to the decline of capital productivity (that is, real GDP per VICS) over the long run (Fig. 3.18).

Fig. 3.17

Net capital stock/GDP ratio (current prices): with and without dwellings

Fig. 3.18

Capital productivity* (ex-ante exogenous rate of return) (2010=100) (natural logs). *Capital productivity: ratio of real GDP to volume index of capital services (VICS)

From the late 1990s, low interest rates and the scarcity of urban land fuelled a boom in the price of dwellings—as the increase in the relative price of dwellings until the mid-2000s confirms (Fig. 3.8)—that contributed to the rise of the capital-output ratio. That is why the capital-output ratio excluding dwellings is also presented in Fig. 3.17. The same trends, but with less intensity, are confirmed.

The evolution of the capital-output ratio in Spain matches the experience of a large sample of countries in which the capital output ratio doubled during the last century (Gallardo-Albarrán and Inklaar, 2020), although the increase seems to have been more intense in the Spanish case, unlike the UK’s, where the capital-output ratio ceased its expansion and declined during the last two decades of the past century (Oulton and Wallis, 2016). By 2013, the capital (wealth)-output ratio at current prices reached a value of 4, when it was just two in 1970, in line with the findings of Piketty and Zucman (2014) for Western European countries. However, this represents practically half the ratio of personal wealth to national income estimated for Spain, although it also doubled over the same time span (Artola Blanco et al., 2020). A necessary caveat is that private wealth estimates add financial assets to the net capital (wealth) stock (that is, non-financial assets) and exclude financial liabilities.

The consumption of fixed capital, expressed as a proportion of GDP, follows the pattern of the capital-output ratio, jumping from 3 to nearly 15% between the 1880s and 2020 (Fig. 3.19). However, when the ratio of capital consumption to net capital stock—that is, the depreciation rate—is considered, it expanded up to the mid-1930s and, again, as of 1950, peaking in the late 1960s, before declining steadily until the mid-2000s, to rebound later. What explains this behaviour? As the composition of capital stock changes towards more productive but higher depreciation assets, one would expect a rise in the depreciation rate. However, new capital goods are more productive as they embodied new vintage technology, so a decline in their relative prices would accompany their expansion (Fig. 3.8) and helps explain the fall in the rate of depreciation between 1970 and 2006.²⁵

Fig. 3.19

Consumption of fixed capital/GDP ratio and depreciation rate (consumption of fixed capital/net capital stock ratio), (current prices)

5 Conclusions

The on-going debate on the rising trend in the capital-output ratio and the productivity slowdown requires long run, consistent, and integrated series of output and production factors. This chapter presents new estimates of net capital (wealth) stock and capital services for Spain during the last 170 years, which allow us to address welfare and growth issues.

Methodological differences matter for the resulting estimates. The new OECD methodology used here clearly differentiates between stock as wealth and capital as an input (that is the flow of services capital provides to production) and represents a major advance in the construction of capital estimates reconciling different approaches, including those previously used by the OECD and those employed by Jorgenson and his school. Most historical estimates, however, are based on outdated methodologies that are not compatible with recent capital stock and services estimates. Consistency with the latest vintage methodology used by international organizations facilitates, for example, testing current views in relation to increasing capital/output ratios or investigating the contribution of capital deepening to labour productivity growth. The chapter also rejects the option of using GFCF series derived by splicing national accounts through backwards projections, as they bias GFCF levels upward and, consequently, capital stock levels too, and adopts GFCF series derived through interpolation of national accounts. These methodological contributions can be applied elsewhere, especially to those developing countries experiencing a deep structural transformation and in the construction of historical series.

The new net capital stock estimates are not off the mark when compared to official national statistical series for the twenty-first century, and the differences over the last half a century when compared with the Penn World Tables 10.0 and Ivie’s figures are largely methodological in nature, mainly splicing available GFCF series through retropolation (backward projection) rather than using interpolation as is the case here.

Capital services expanded over time, accelerating in the 1920s and between the mid-1950s and 2007, with capital ‘quality’ (composition effect) contributing until 1975. Capital deepening increased in the long run, especially from 1955 to 1985, slowing down after Spain’s accession to the European Union, as expanding economic sectors attracted less investment-specific technological progress.

The net capital (wealth) stock-GDP ratio rose over time, contradicting Kaldor’s (1957) stylised fact while confirming Piketty and Zucman (2014) results. Although the consumption of fixed capital (% GDP) shadowed the capital-output ratio, the rate of depreciation fell from 1970 to the onset of the Global Financial Crisis, as new capital goods’ relative prices declined due to embodied technological change.

The inverse association between capital deepening and employment growth in post-Franco Spain mimics the behaviour of labour productivity, which rises when employment falls and declines when employment expands (Prados de la Escosura, 2017). How much did capital deepening contribute to raising labour productivity over the long run? The next chapter provides an answer.

Appendix

1.1 A.1 A Note on Splicing GFCF Series in Spain’s National Accounts

Available national accounts’ series are provided for different and usually short periods on the basis of different benchmark or reference years and different methodologies. In order to present a single homogeneous series, splicing is required. There is no consensus on how to do it. The most frequent splicing procedure has been retropolation in which the value provided by the latest benchmark estimate is projected backward with the rate of variation for previous benchmark series so the earlier series is re-scaled to match the new benchmark level. The practical advantage is that it preserves the rate of variation of the earlier benchmark series. On the downside, however, retropolation tends to overexaggerate past levels since new rounds of national accounts introduce new definitions and classifications and new sources and estimation procedures that usually translate into higher levels for the new benchmark series at the year in which the new and the old benchmark series overlap.

The interpolation method, instead, accepts the levels computed directly for each benchmark-year as the best possible estimates—as they are computed with ‘complete’ information on quantities and prices-, and distributes the gap between the ‘new ‘and ‘old’ benchmark series in the overlapping year at a constant rate over the time span in between the old and new benchmark years. By respecting the levels for the different benchmark years, the interpolation method alters the rate of variation, unlike the retropolation method. The consequence is that earlier levels are usually lower in the interpolated series than in the retropolated series.

In other words, the retropolation method presumes the error lies in the level of the ‘old’ series, but not in its rate of variation. The interpolation method challenges this assumption and deems the cumulative result of the emergence of new goods and services, not considered in the old benchmark series, the source of error.

The interpolation method appears provides a superior alternative, supported by the fact that recent rounds of national accounts have chosen it. In the case of Spain, for 1995–2020, national accounts provide spliced estimates in which, once adjustments are made for methodological changes, the different benchmark series are interpolated (Prados de la Escosura (2016, 2017). Thus, the dilemma about the splicing method refers only to the pre-1995 period (with the exception of 1980–86 in which national accounts were also interpolated).²⁶

More specifically, since the 2000 benchmark (CNE00) the interpolation method was used after adjusting upwards the old benchmark series for methodological changes. Thus, the gap between, say, CNE15 and CNE10 in the year 2015, was decomposed into methodological and statistical plus other differences. Firstly, CNE10 series for 2010–2014 were adjusted upwards for methodological discrepancies with CNE15. Then, the residual gap, due to statistical and other differences, was distributed at a constant rate throughout the in-between benchmarks years, 2011–2014.²⁷ A detailed discussion of the splicing of Spanish national accounts and the available alternatives is provided in Prados de la Escosura (2017, Ch. 9) https://link.springer.com/chapter/10.1007/978-3-319-58042-5_9

See Tables 3.4, 3.5, 3.6, 3.7 and 3.8.

Table 3.4 Net capital stock and consumption of fixed capital 1850–2020 (million Euro)

Table 3.5 Net capital stock/GDP ratio

Table 3.6 Productive capital stock, 1850–2020 (million 2010 Euro)

Table 3.7 Capital input, productive capital stock, and capital quality, 1850–2020 (2010=100)

Table 3.8 Capital deepening^a 1850–2020 (2010=100)

1.2 A.2 Alternative Estimates: Figures

See Figs. 3.20, 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28, 3.29, 3.30, 3.31 and 3.32.

Fig. 3.20

Capital services’ composition (ex-post endogenous rate of return) (current prices) (%)

Fig. 3.21

Capital services’ composition (simplified ex-ante exogenous rate of return) (current prices) (%)

Fig. 3.22

Volume index of capital services (VICS) (ex-ante exogenous and ex-post endogenous rate of return) and productive capital stock (1850=100) (natural logs)

Fig. 3.23

Volume index of capital services (VICS) (ex-ante exogenous and simplified ex-ante exogenous rate of return) and productive capital stock (1850=100) (natural logs)

Fig. 3.24

Volume index of capital services (VICS) with four and six assets, 1980–2020 (2010=100) (natural logs) ex-ante exogenous endogenous rates of return

Fig. 3.25

(a) Capital quality* (ex-ante exogenous and ex-post endogenous rate of return) (1850=1). *Capital quality = Ratio of VICS to productive capital stock. (b) Capital quality* (full and simplified ex-ante exogenous rate of return) (1850=1). *Capital quality = Ratio of VICS to productive capital stock

Fig. 3.26

New VICS*: comparison with PWT10.01, conference board (CB), and Ivie estimates, 1950–2020 (2010=100) (natural logs) ex-ante exogenous and ex-post endogenous rates of return

Fig. 3.27

VICS estimates with GFCF retropolated series, ex-ante exogenous and ex-post endogenous rates of return. Comparison with PWT10.01, conference board (CB), and Ivie (2010=100) (logs)

Fig. 3.28

Capital quality*: comparison with PWT10.01 and Ivie estimates, 1950–2020 (2010=1). *Derived with ex-ante exogenous and ex-post endogenous rates of return

Fig. 3.29

Net capital stock/GDP ratio with four and six assets, 1980–2020 (current prices)

Fig. 3.30

Net capital stock/GDP ratio: estimates with alternative average service lives (current prices). Note: A, longer lives; B, shorter lives; A-B, A up to 1958 and B thereafter

Fig. 3.31

Hulten & Wykoff and double declining balance net capital stock/GDP ratio (current prices)

Fig. 3.32

Double declining balance consumption of fixed capital/GDP ratio and depreciation rate (consumption of fixed capital/net capital stock ratio), (current prices)