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Capital in Spain, 1850–2019

Abstract

The rising trend in the capital-output ratio and the productivity slowdown have put capital back in the economist’s agenda. This paper contributes to the debate by providing 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, its acceleration was helped by an increase in the “quality” of capital. Capital deepening proceeded steadily, accelerating during 1955–1985 and slowing 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 new capital goods’ relative prices declined due to embodied technological change.

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Notes

  1. 1.

    By consistent and integrated estimates, Oulton and Wallis (2016) mean a common dataset and a common set of assumptions in the construction of long-run estimates of capital stock and capital services.

  2. 2.

    OECD (1993, 2001). For developments and applications of the Jorgenson approach, cf. Jorgenson and Griliches (1967), Hall and Jorgenson (1967), Christensenet al. (1980), Jorgenson et al. (1987), Elías (1978), and Young (1995).

  3. 3.

    Conference Board (2020) follows the same practice. As a sensitivity test, we have replicated the estimates of net capital stock using six, rather than four, types of assets (that is, considering, biological resources and intellectual property products separately) from 1980 onwards. No trend discrepancies are found between the two set of estimates even though the 6 asset estimates exhibit a slightly lower level (see Figures A5 and A10 in Online Appendix C).

  4. 4.

    See Pérez et al. (2019) and Conference Board (2020) for estimates for Spain which distinguish between ICT and non-ICT of assets.

  5. 5.

    The CFM approach is widely used to reconstruct GFCF series in present-day developing countries (Conference Board, 2017). Also, in the Penn World Tables 9.1, in the absence of direct estimates, investment in an asset is assumed to vary with the economy-wide supply (production + imports − exports) (Feenstra et al. 2015, updated).

  6. 6.

    Alternative estimates using the private consumption deflator provide similar results.

  7. 7.

    On the one hand, service lives tend to fall as “product cycles” become shorter and capital goods face higher rates of obsolescence but, on the other, some assets become more durable (OECD 2009). Maddison (1995) used fixed average lives for his historical estimates.

  8. 8.

    These service lives are in line with those used by Pérez et al. (2019). Alternative estimates have been computed with another set of longer average service lives: 70 years (dwellings), 50 years (other construction), and 20 years (transport equipment and machinery). Although longer service lives increase the gross stock and reduce depreciation, and hence, deliver a larger net capital stock, the comparison between the two set of estimates reveals minor differences over time. A third set of estimates has been derived by combining the longer average lives set for 1850-1958 and the shorter average lives set for 1959–2019. Interestingly, the result is lower growth of aggregate capital stock than when the shorter lives set is employed for the entire time span. This finding may be attributed to the fact that the set of average assets lives for the pre-1958 period assigns larger weight to slower growing assets and, consequently, result in lower net capital stock. (See the resulting alternative Net Capital Stock/GDP ratios in Figure A11 in Online Appendix C).

  9. 9.

    Hulten and Wykoff’s (1981) implicit R values were also used in Prados de la Escosura and Rosés (2010). Alternative estimates have been obtained using a double declining balance (T = 2) and the same average service lives, with the resulting depreciation rates of 3.3%, 5.0%, 13.3%, and 13.3% for each of the four asset types. Figure A12 in Online Appendix C compares the net capital stock derived alternatively with the double declining balance and Hulten and Wykoff’s R values, revealing that the net capital stock derived with the double declining balance is lower as the depreciation rates are larger for the same average lives of assets, and so is the consumption of fixed capital (Figure A13).

  10. 10.

    The OLS regression results are (with standard error in parentheses),

    $$\begin{aligned} { \ln }({\text{Dwellings}}) & = - 5. 7 5+ 1. 2 3\;{ \ln }({\text{GDP}}) \\ & \quad (0. 9 9 5)\;(0.0 9 5)\quad {\text{Adj}}.\;R^{ 2} = 0. 70 \\ \end{aligned}$$
    $$\begin{aligned} { \ln }({\text{Other}}\;{\text{Construction}}) & = - 1 1. 2 3+ 1. 70{ \ln }({\text{GDP}}) \\ & \quad ( 1. 2 7 1)\;(0. 1 2 1) \quad {\text{Adj}}.\;R^{ 2} = 0. 7 4\\ \end{aligned}$$
    $$\begin{aligned} { \ln }({\text{Machinery}}) & = - 2 9.0 7+ 3. 1 9 {\text{ ln}}({\text{GDP}}) \\ & \quad ( 1.0 6 2)\;(0. 10 1) \quad {\text{Adj}}.\;R^{ 2} = 0. 9 3\\ \end{aligned}$$
    $$\begin{aligned} { \ln }({\text{Transport}}\;{\text{Equipment}}) & = - 1 7. 1 8+ 2.0 7 {\text{ ln}}({\text{GDP}}) \\ & \quad ( 2. 7 5 5)\;(0. 2 6 3)\quad {\text{Adj}}.\;R^{ 2} = 0. 4 7\\ \end{aligned}$$
  11. 11.

    The yearly rates assumed are −2.75% for other construction and −5.8% for machinery, following Prados de la Escosura and Rosés (2010). Although the destruction, as a share of net capital stock, is lower in the new estimates, 5% versus 7%, a fact that derives from the use of different asset average service lives and from methodological differences in the computation of the capital stock.

  12. 12.

    The formula used is 100 * (natural log X − natural log Y), being X the new estimates and Y, Ivie and INE figures, alternatively.

  13. 13.

    For example, in Myro (1983) and Mas et al. (2000).

  14. 14.

    Cf. Young (1995: 650-1) for similar results in the cases of South Korea and Taiwan.

  15. 15.

    Thus, the endogenous, ex-post rate of return for every period is computed by equating capital compensation Gt plus capital-related taxes on production T tK to the total user costs of capital Ut

    $$G^{t} + T_{K}^{t} = U^{t} = \sum\limits_{k = 1}^{N} {P_{0}^{{k,{\text{tB}}}} } (1 + \rho^{t} )\;[r^{t*} + \delta^{k} (1 + i^{k,t*} ){-}i^{k;t*} ]K^{k,t}$$
    (7)

    From which the ex-post endogenous real rate of return can be derived,

    $$r^{t*} = {{\left\{ {(G^{t} + T_{K}^{t} )\;(1 + \rho^{t} ) - \sum\limits_{k = 1}^{N} {P_{0}^{{k,{\text{tB}}}} [\delta_{0}^{k} (1 + i^{k,t*} ){-}i^{k;t*} ]K^{k,t} } } \right\}} \mathord{\left/ {\vphantom {{\left\{ {(G^{t} + T_{K}^{t} )\;(1 + \rho^{t} ) - \sum\limits_{k = 1}^{N} {P_{0}^{{k,{\text{tB}}}} [\delta_{0}^{k} (1 + i^{k,t*} ){-}i^{k;t*} ]K^{k,t} } } \right\}} {\left\{ {\sum\limits_{k = 1}^{N} {P_{0}^{{k,{\text{tB}}}} K^{k,t} } } \right\}}}} \right. \kern-0pt} {\left\{ {\sum\limits_{k = 1}^{N} {P_{0}^{{k,{\text{tB}}}} K^{k,t} } } \right\}}}$$
    (8)

    Then, the ex-post user cost per unit of capital services for a particular type of asset is obtained as

    $$F_{0}^{t} = P_{0}^{{k,{\text{tB}}}} (1 + \rho^{t} )\;[r^{t*} + \delta_{0}^{k} (1 + i^{k,t*} ){-}i^{k,t*} ]$$
    (9)

    where Gt Non-labour income consists of gross operating surplus and the part of mixed income that can be attributed to capital; T tK taxes on production; P k,tB0 is the purchase price of a new asset at the beginning (B) of year t; ρt is the rate of change of the consumer price index at the beginning of period t; rt* is the real rate of return that applies at the beginning of period t; δk is the rate of depreciation for a new asset k; ik,t* is the ex-post, real rate of asset price inflation for asset k during period t; Kk,t is the productive capital stock of asset k during period t.

  16. 16.

    Upwards biased if coverage is incomplete, since capital income will be compared to an under-valued capital stock and downwards biased if no clear distinction is made between market and government sectors since, probably, only market capital income will be compared to the value of the total capital stock.

  17. 17.

    Nonetheless, capital services have also been derived using an ex-post endogenous rate of return in order to provide a contrast to the ex-ante exogenous estimates. See Online Appendix C.

  18. 18.

    Actually, in Ivie’s estimates 4% real rate of return is chosen for the market sector and 3.5% rate for the non-market sector. The average real rate of return of bank deposits in Spain since 1850 is 4.5% (computed from underlying data in Prados de la Escosura and Rosés (2010), updated to 2019.

  19. 19.

    Similar trends, although less marked, and machinery and equipment never matches other construction, are observed when the ex-post endogenous rate of return is used (Figure A1).

  20. 20.

    Similar results are obtained using the private consumption deflator.

  21. 21.

    The gap is narrower gap when VICS is obtained with an ex-post endogenous, rather than an ex-ante exogenous rate of return. This finding is consistent with the presumed underestimate of capital services derived with an ex-post endogenous rate of return when information on capital assets is incomplete as it is our case (Figure A3).

  22. 22.

    Although the evolution of “quality” of capital using alternatively ex-ante exogenous and ex-post endogenous rates of return share the same tendencies, the level of capital “quality” is lower for the latter as could be anticipated due to the possible underestimate of capital services when they are computed with incomplete information (Figure A6a).

  23. 23.

    See Figure A7 for a comparison that included the new estimates derived with both ex-ante exogenous and ex-post endogenous rate of return.

  24. 24.

    Figure A9 adds up the new estimates of capital quality derived with ex-post endogenous rate of return that exhibits milder gains than when obtained with the ex-ante exogenous rate of return.

  25. 25.

    It is worth stressing that the described patterns for the capital-output ratio and the consumption of fixed capital are confirmed for alternative estimates derived using different average service lives and depreciation rates. Longer lives, by reducing depreciation, increase the level of net capital stock (Figure A11), and the use of the double declining balance implies higher depreciation rates, which increases capital consumption and, hence, reduces the level of net capital stock (Figure A12), while increases the ratio of the consumption of fixed capital ratio to GDP and net capital stock, respectively (Figure A13).

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Acknowledgements

Thanks to Eva Benages, Juan Carlos Robledo, Ezequiel Uriel, and, especially, Matilde Mas and Ilya Voskoboynikov for their most valuable comments and to Juan Carlos Robledo and Eva Benages who kindly provided Ivie’s detailed capital stock and capital services series. A research grant from Fundación Rafael del Pino is gratefully acknowledged.

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Correspondence to Leandro Prados de la Escosura.

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Prados de la Escosura, L. Capital in Spain, 1850–2019. Cliometrica (2021). https://doi.org/10.1007/s11698-020-00221-2

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Keywords

  • Capital stock and services
  • Capital deepening
  • Capital-output ratio
  • Spain

JEL Classification

  • D24
  • E01
  • E22
  • N33
  • N34