Capital in the Twenty-First Century

by Thomas Piketty

  4. From Old Europe to the New World

  1. In order to concentrate on long-run evolutions, the figures accompanying this chapter indicate values by decade only and thus ignore extremes that lasted for only a few years. For complete annual series, see the online technical appendix.

  2. The average inflation figure of 17 percent for the period 1913–1950 omits the year 1923, when prices increased by a factor of 100 million over the course of the year.

  3. Virtually equal to General Motors, Toyota, and Renault-Nissan, with sales of around 8 million vehicles each in 2011. The French government still holds about 15 percent of the capital of Renault (the third leading European manufacturer after Volkswagen and Peugeot).

  4. Given the limitations of the available sources, it is also possible that this gap can be explained in part by various statistical biases. See the online technical appendix.

  5. See, for example, Michel Albert, Capitalisme contre capitalisme (Paris: Le Seuil, 1991).

  6. See, for example, Guillaume Duval, Made in Germany (Paris: Le Seuil, 2013).

  7. See the online technical appendix.

  8. The difference from Ricardo’s day was that wealthy Britons in the 1800s and 1810s were prosperous enough to generate the additional private saving needed to absorb public deficits without affecting national capital. By contrast, the European deficits of 1914–1945 occurred in a context where private wealth and saving had already been subjected to repeated negative shocks, so that public indebtedness aggravated the decline of national capital.

  9. See the online technical appendix.

  10. See Alexis de Tocqueville, Democracy in America, trans. Arthur Goldhammer (New York: Library of America, 2004), II.2.19, p. 646, and II.3.6, p. 679.

  11. On Figures 3.1–2, 4.1, 4.6, and 4.9, positive positions relative to the rest of the world are unshaded (indicating periods of net positive foreign capital) and negative positions are shaded (periods of net positive foreign debt). The complete series used to establish all these figures are available in the online technical appendix.

  12. See Supplemental Figures S4.1–2, available online.

  13. On reactions to European investments in the United States during the nineteenth century, see, for example, Mira Wilkins, The History of Foreign Investment in the United States to 1914 (Cambridge, MA: Harvard University Press, 1989), chap. 16.

  14. Only a few tens of thousands of slaves were held in the North. See the online technical appendix.

  15. If each person is treated as an individual subject, then slavery (which can be seen as an extreme form of debt between individuals) does not increase national wealth, like any other private or public debt (debts are liabilities for some individuals and assets for others, hence they cancel out at the global level).

  16. The number of slaves in French colonies emancipated in 1848 has been estimated at 250,000 (or less than 10 percent of the number of slaves in the United States). As in the United States, however, forms of legal inequality continued well after formal emancipation: in Réunion, for example, after 1848 former slaves could be arrested and imprisoned as indigents unless they could produce a labor contract as a servant or worker on a plantation. Compared with the previous legal regime, under which fugitive slaves were hunted down and returned to their masters if caught, the difference was real, but it represented a shift in policy rather than a complete break with the previous regime.

  17. See the online technical appendix.

  18. For example, if national income consists of 70 percent income from labor and 30 percent income from capital and one capitalizes these incomes at 5 percent, then the total value of the stock of human capital will equal fourteen years of national income, that of the stock of nonhuman capital will equal six years of national income, and the whole will by construction equal twenty years. With a 60–40 percent split of national income, which is closer to what we observe in the eighteenth century (at least in Europe), we obtain twelve years and eight years, respectively, again for a total of twenty years.

  5. The Capital/Income Ratio over the Long Run

  1. The European capital/income ratio indicated in Figures 5.1 and 5.2 was estimated by calculating the average of the available series for the four largest European economies (Germany, France, Britain, and Italy), weighted by the national income of each country. Together, these four countries represent more than three-quarters of Western European GDP and nearly two-thirds of European GDP. Including other countries (especially Spain) would yield an even steeper rise in the capital/income ratio over the last few decades. See the online technical appendix.

  2. The formula β = s / g is read as “β equals s divided by g.” Recall, too, that “β = 600%” is equivalent to “β = 6,” just as “s = 12%” is equivalent to “s = 0.12” and “g = 2%” is equivalent to “g = 0.02.” The savings rate represents truly new savings—hence net of depreciation of capital—divided by national income. I will come back to this point.

  3. Sometimes g is used to denote the growth rate of national income per capita and n the population growth rate, in which case the formula would be written β = s / (g + n). To keep the notation simple, I have chosen to use g for the overall growth rate of the economy, so that my formula is β = s / g.

  4. Twelve percent of income gives 12 divided by 6 or 2 percent of capital. More generally, if the savings rate is s and the capital/income ratio is β, then the capital stock grows at a rate equal to s / β.

  5. The simple mathematical equation describing the dynamics of the capital/income ratio β and its convergence toward β = s / g is given in the online technical appendix.

  6. From 2.2 years in Germany to 3.4 years in the United States in 1970. See Supplemental Table S5.1, available online, for the complete series.

  7. From 4.1 years in Germany and the United States to 6.1 years in Japan and 6.8 years in Italy in 2010. The values indicated for each year are annual averages. (For example, the value indicated for 2010 is the average of the wealth estimates on January 1, 2010, and January 1, 2011.) The first available estimates for 2012–2013 are not very different. See the online technical appendix.

  8. In particular, it would suffice to change from one price index to another (there are several of them, and none is perfect) to alter the relative rank of these various countries. See the online technical appendix.

  9. See Supplemental Figure S5.1, available online.

  10. More precisely: the series show that the private capital/national income ratio rose from 299 percent in 1970 to 601 percent in 2010, whereas the accumulated flows of savings would have predicted an increase from 299 to 616 percent. The error is therefore 15 percent of national income out of an increase on the order of 300 percent, or barely 5 percent: the flow of savings explains 95 percent of the increase in the private capital/national income ratio in Japan between 1970 and 2010. Detailed calculations for all countries are available in the online technical appendix.

  11. When a firm buys its own shares, it enables its shareholders to realize capital gains, which will generally be taxed less heavily than if the firm had used the same sum of money to distribute dividends. It is important to realize that the same is true when a firm buys the stock of other firms, so that overall the business sector allows the individual sector to realize capital gains by purchasing financial instruments.

  12. One can also write the law β = s / g with s standing for the total rather than the net rate of saving. In that case the law becomes β = s / (g + δ) (where δ now stands for the rate of depreciation of capital expressed as a percentage of the capital stock). For example, if the raw savings rate is s = 24%, and if the depreciation rate of the capital stock is δ = 2%, for a growth rate of g = 2%, then we obtain a capital income ratio β = s / (g + δ) = 600%. See the online technical appendix.

  13. With a growth of g = 2%, it would take a net expenditure on durable goods equal to s = 1% of national income per year to accumulate a stock of durable goods equal to β = s / g = 50% of national income. Durable goods need to b
e replaced frequently, however, so the gross expenditure would be considerably higher. For example, if average replacement time is five years, one would need a gross expenditure on durable goods of 10 percent of national income per year simply to replace used goods, and 11 percent a year to generate a net expenditure of 1% and an equilibrium stock of 50% of national income (still assuming growth g = 2%). See the online technical appendix.

  14. The total value of the world’s gold stock has decreased over the long run (it was 2 to 3 percent of total private wealth in the nineteenth century but less than 0.5 percent at the end of the twentieth century). It tends to rise during periods of crisis, however, because gold serves as a refuge, so that it currently accounts for 1.5 percent of total private wealth, of which roughly one-fifth is held by central banks. These are impressive variations, yet they are minor compared with the overall value of the capital stock. See the online technical appendix.

  15. Even though it does not make much difference, for the sake of consistency I have used the same conventions for the historical series discussed in Chapters 3 and 4 and for the series discussed here for the period 1970–2010: durable goods have been excluded from wealth, and valuables have been included in the category labeled “other domestic capital.”

  16. In Part Four I return to the question of taxes, transfers, and redistributions effected by the government, and in particular to the question of their impact on inequality and on the accumulation and distribution of capital.

  17. See the online technical appendix.

  18. Net public investment is typically rather low (generally around 0.5–1 percent of national income, of which 1.5–2 percent goes to gross public investment and 0.5–1 percent to depreciation of public capital), so negative public saving is often fairly close to the government deficit. (There are exceptions, however: public investment is higher in Japan, which is the reason why public saving is slightly positive despite significant government deficits.) See the online technical appendix.

  19. This possible undervaluation is linked to the small number of public asset transactions in this period. See the online technical appendix.

  20. Between 1870 and 2010, the average rate of growth of national income was roughly 2–2.2 percent in Europe (of which 0.4–0.5 percent came from population growth) compared with 3.4 percent in the United States (of which 1.5 percent came from population growth). See the online technical appendix.

  21. An unlisted firm whose shares are difficult to sell because of the small number of transactions, so that it takes a long time to find an interested buyer, may be valued 10 to 20 percent lower than a similar company listed on the stock exchange, for which it is always possible to find an interested buyer or seller on the same day.

  22. The harmonized international norms used for national accounts—which I use here—prescribe that assets and liabilities must always be recorded at their market value as of the date of the balance sheet (that is, the value that could be obtained if the firm decided to liquidate its assets, estimated if need be by using recent transactions for similar goods). The private accounting norms that firms use when publishing their balance sheets are not exactly the same as the norms for national accounts and vary from country to country, raising multiple problems for financial and prudential regulation as well as for taxation. In Part Four I come back to the crucial issue of harmonization of accounting standards.

  23. See, for example, “Profil financier du CAC 40,” a report by the accounting firm Ricol Lasteyrie, June 26, 2012. The same extreme variation in Tobin’s Q is found in all countries and all stock markets.

  24. See the online technical appendix.

  25. Germany’s trade surplus attained 6 percent of GDP in the early 2010s, and this enabled the Germans to rapidly amass claims on the rest of the world. By comparison, the Chinese trade surplus is only 2 percent of GDP (both Germany and China have trade surpluses of 170–180 billion euros a year, but China’s GDP is three times that of Germany: 10 trillion euros versus 3 trillion). Note, too, that five years of German trade surpluses would be enough to buy all the real estate in Paris, and five more years would be enough to buy the CAC 40 (around 800–900 billion euros for each purchase). Germany’s very large trade surplus seems to be more a consequence of the vagaries of German competitiveness than of an explicit policy of accumulation. It is therefore possible that domestic demand will increase and the trade surplus will decrease in coming years. In the oil exporting countries, which are explicitly seeking to accumulate foreign assets, the trade surplus is more than 10 percent of GDP (in Saudi Arabia and Russia, for example) and even multiples of that in some of the smaller petroleum exporters. See Chapter 12 and the online technical appendix.

  26. See Supplemental Figure S5.2, available online.

  27. In the case of Spain, many people noticed the very rapid rise of real estate and stock market indices in the 2000s. Without a precise point of reference, however, it is very difficult to determine when valuations have truly climbed to excessive heights. The advantage of the capital/income ratio is that it provides a precise point of reference useful for making comparisons in time and space.

  28. See Supplemental Figures S5.3–4, available online. It bears emphasizing, moreover, that the balances established by central banks and government statistical agencies concern only primary financial assets (notes, shares, bonds, and other securities) and not derivatives (which are like insurance contracts indexed to these primary assets or, perhaps better, like wagers, depending on how one sees the problem), which would bring the total to even higher levels (twenty to thirty years of national income, depending on the definitions one adopts). It is nevertheless important to realize that these quantities of financial assets and liabilities, which are higher today than ever in the past (in the nineteenth century and until World War I, the total amount of financial assets and liabilities did not exceed four to five years of national income) by definition have no impact on net wealth (any more than the amount of bets placed on a sporting event influences the level of national wealth). See the online technical appendix.

  29. For example, the financial assets held in France by the rest of the world amounted to 310 percent of national income in 2010, and financial assets held by French residents in the rest of the world amounted to 300 percent of national income, for a negative net position of −10 percent. In the United States, a negative net position of −20 percent corresponds to financial assets on the order of 120 percent of national income held by the rest of the world in the United States and 100 percent of national income owned by US residents in other countries. See Supplemental Figures S5.5–11, available online, for detailed series by country.

  30. In this regard, note that one key difference between the Japanese and Spanish bubbles is that Spain now has a net negative foreign asset position of roughly one year’s worth of national income (which seriously complicates Spain’s situation), whereas Japan has a net positive position of about the same size. See the online technical appendix.

  31. In particular, in view of the very large trade deficits the United States has been running, its net foreign asset position ought to be far more negative than it actually is. The gap is explained in part by the very high return on foreign assets (primarily stocks) owned by US citizens and the low return paid on US liabilities (especially US government bonds). On this subject, see the work of Pierre-Olivier Gourinchas and Hélène Rey cited in the online technical appendix. Conversely, Germany’s net position should be higher than it is, and this discrepancy is explained by the low rates of return on Germany’s investments abroad, which may partially account for Germany’s current wariness. For a global decomposition of the accumulation of foreign assets by rich countries between 1970 and 2010, which distinguishes between the effects of trade balances and the effects of returns on the foreign asset portfolio, see the online technical appendix (esp. Supplemental Table S5.13, available online).

  32. For example, it is likely that a significant part of the US trade deficit simply c
orresponds to fictitious transfers to US firms located in tax havens, transfers that are subsequently repatriated in the form of profits realized abroad (which restores the balance of payments). Clearly, such accounting games can interfere with the analysis of the most basic economic phenomena.

  33. It is difficult to make comparisons with ancient societies, but the rare available estimates suggest that the value of land sometimes reached even higher levels: six years of national income in ancient Rome, according to R. Goldsmith, Pre-modern Financial Systems: A Historical Comparative Study (Cambridge: Cambridge University Press, 1987), 58. Estimates of the intergenerational mobility of wealth in small primitive societies suggest that the importance of transmissible wealth varied widely depending on the nature of economic activity (hunting, herding, farming, etc.). See Monique Borgerhoff Mulder et al., “Intergenerational Wealth Transmission and the Dynamics of Inequality in Small-Scale Societies,” Science 326, no. 5953 (October 2009): 682–88.

  34. See the online technical appendix.

  35. See Chapter 12.

  6. The Capital-Labor Split in the Twenty-First Century

  1. Interest on the public debt, which is not part of national income (because it is a pure transfer) and which remunerates capital that is not included in national capital (because public debt is an asset for private bondholders and a liability for the government), is not included in Figures 6.1–4. If it were included, capital’s share of income would be a little higher, generally on the order of one to two percentage points (and up to four to five percentage points in periods of unusually high public debt). For the complete series, see the online technical appendix.