Factor shares and returns

In the country-specific files we provide detailed decomposition of corporate product and national income into labor and capital components. The analysis of factor shares in the corporate sector is standard and does not raise any particular difficulty. At the national level, however, there are a number of issues. The main difficulty is how to deal with self-employment. Other issues include whether one should attribute some capital income to the government sector, and difficulties in the measurement of housing capital income. We deal with each of these issues in turn.

A.7.1 Capital shares in the non-corporate business sector

There are three main ways to estimate factor shares in the non-corporate business sector: (i) assign the self-employed 100% of the average wage of salaried workers; (ii) apply some capital returns to the capital stocks of self-employed individuals; (iii) assume the same factor income decomposition in the non-corporate and corporate business sectors.

Most estimates of the shares of labor and capital in national income try to impute a wage to the self-employed (see Glyn, 2009). This is for instance the method that Ameco retains to com-pute its own adjusted wage series.⁸³ One problem, however, is that there is no particular reason why we should attribute 100% of the average wage of salaried workers to the self-employed.

The self-employed have historically been concentrated in sectors where average incomes have been much lower than the national average, such as agriculture; today, on the contrary, many of them are in relatively high-paying sectors, such as health. One way to deal with this issue is to use data on income and employment at the sectoral level to assign the self-employed imputed sectoral wages, correcting for part-time work when possible.⁸⁴

The method that consists in applying rates of return to the capital stock of the self-employed is rarely used, as until recently comprehensive balance sheets for the non-corporate sector were

83Series ALCD0 (adjusted wage share in market price GDP) and ALCD2 (adjusted wage share in factor-cost GDP).

84This is the what is usually done in productivity studies (see for instance EU KLEMS). This is also the method used by Jorgenson and Landefeld (p. 34) to form their estimate of total capital income in the U.S.

economy (Table 1.6, p. 54-55) which also includes imputed values of the services of consumer durables as well as the net rent on government tangible assets.

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not available.

In practice, estimates that apply average wages to the hours worked by self-employed persons (or capital returns to their capital stocks) often result in negative returns to either capital or labor. As Jorgenson and Landefeld (2006, p. 33) discuss, the reasons for this problem are not entirely clear. Explanations include the possibility that mixed income may be under-estimated in national accounts, and issues in the measurement of the numbers of hours worked by self-employed (or the capital stocks they use). Mixed income can be under-estimated for a number of reasons: the self-employed may underreport income to tax and statistical authorities; some of the earnings of small business owners that should logically be recorded as mixed income are also sometimes treated as corporate dividends in the national accounts. The latter problem occurs when small businesses are included in the corporate sector but the partners are counted as self-employed in labor force surveys (e.g., because they choose to be paid in the form of dividends only). This problem is particularly acute in countries that have a vast network of small and medium enterprises, such as Germany. In this case, too much corporate dividends tend to be recorded, and too little mixed income compared to the the number of self-employed identified in surveys.⁸⁵

In view of the many issues raised by the methods that impute wages or returns to the self-employed, in our database, whenever possible, we have opted for the third method: we assume that the capital share is the same in the non-corporate as in the corporate business sectors.⁸⁶ One drawback is that this method cannot always be applied: we need to know the net-product of the non-corporate business sector, and in some cases national accounts are not detailed enough.

But one advantage of the method, when the data exist, is that we can check the plausibility of the results by computing the average wage of self-employed individuals which is consistent with

85Only non-corporate businesses can be the source of mixed income. But the distinction between corporate and non-corporate activity is far from being always clear. In the 2008 SNA (4.155-4.156), the main criterion is whether the liability of the partners is limited (corporation) or unlimited (un-incorporated enterprise). However, some un-incorporated enterprises are to be treated as “quasi-corporations” in the SNA if they have complete sets of accounts, many partners, and behave like corporations.

86Specifically, we compute factor income in the non-corporate sector by multiplying the net product of the non-corporate business sector by the factor shares that prevail in the corporate sector. A number of estimates of factor shares deal with self-employment by applying the corporate sector’s factor shares to mixed income (rather than to the overall net product of the non-corporate business sector). This way of doing things necessarily results in higher labor shares in the non-corporate sector than in the corporate sector, since total labor income in the non-corporate sector is then equal to wages paid to non-corporate salaried workers plus the imputed labor component of mixed income. The problem is that there is no clear reason why the labor share should necessarily always be higher in the non-corporate sector, so overall it seems to us that our method is somewhat more consistent.

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identical factor shares in the corporate and non-corporate business sectors.

In the country-specific appendices, we precisely explain how we estimated factor shares in the non-corporate sector given available data, and the robustness checks that we were able to conduct. We also describe on a case-by-case basis the way we have obtained historical estimates of factor shares for the 19th century, at times when all standard methods raise formidable difficulties because of the high share of agriculture in output.⁸⁷

A.7.2 Housing capital income

An important part of the economy’s capital income – though one which unfortunately tends to be disregarded in standard measures of factor shares – is housing capital income. However, it is not always straightforward to properly isolate this income in published national accounts.

In principle, things are quite simple: housing capital income is equal to the net product of the housing sector, which by convention is measured in the SNA as the net operating surplus of the household sector.

There are two main issues here. First, home-owners who have contracted mortgages consume financial intermediation services. These services, called “financial intermediation services indi-rectly measured” (FISIM), are conventionally defined as the margin between mortgage interest rates and a reference rate (such as the rate at which banks can refinance themselves with the central bank). In the national accounts, FISIM consumed by home-owners are treated as inter-mediate consumption, so that they are excluded from the value added of the household sector, hence from the net product of the housing sector. Because there is substantial cross-country heterogeneity in the way FISIM are measured,⁸⁸ comparisons of housing products across coun-tries are rendered somewhat difficult. One solution would be to add FISIM on mortgages to net housing product; however in many countries FISIM on mortgages are not isolated.

The second issue that affects the comparability of housing capital income is the following. By definition, the net operating surplus of the household sector only captures the income generated

87There are three main issues. First, there is no particular reason why the distribution of factor shares should be the same in agriculture as in the corporate sector, so the method we generally use for 1970-2010 makes relatively little sense before. Second, attributing an average agricultural wage to peasant farmers often faces important data constraint. Lastly, there is the very tricky issue of how to deal with unpaid family workers, historically quite important in many countries, in some cases through to the mid-twentieth century. Attributing those workers the average wage often results in labor share exceeding 100% in the whole economy (see Glyn, 2009, p. 109).

88In particular, statistical agencies often use ad hoc methods to smooth variations in FISIM that occur when central banks set extremely low refinancing rates (as has been the case since 2008).

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by households’ housing activities. But households do not own 100% of the housing stock, and there is some variation in the share of houses owned by corporations. In Germany and France, households own about 85% of the dwelling stock and non-financial corporations almost all the rest, while in the U.K. the household share is 95%. In the country-specific appendices, we precisely describe how we have estimated housing capital stocks and income given available data, and what scopes the estimates cover.

A.7.3 Should the government earn capital income?

By convention, in the SNA the net return to government capital is implicitly assumed to be zero.

The SNA estimates the value of government (and other non-market producers) output by costs.

The only cost measured for the use of capital inputs in the production of government services is depreciation. In principle a financing opportunity cost – i.e., a rate of return on government non-financial assets – should also be included. This rate of return cannot be directly observed, but one natural candidate would be the interest rate that the government pays on its debt. Doing so, however, would raise the issue that GDP would rise when interest rates for government debt increase. And it is also unclear what exact interest rate should be picked – short term, long term, etc. This seems to be the main reasons why the SNA prefers to retain in practice the assumption of zero net return on government assets, although capital income imputations are routinely made for owner-occupied dwellings (a task, however, made easier by the fact that market rents are readily available).⁸⁹ In this research we have not attempted to correct the official data and so there is no capital income in the government sector.

A.7.4 Alternative measure of the capital share: the concept of capital services In our database, we measure capital income, consistent with standard practice, as the sum of net operating surplus (net corporate profits and housing capital income), the fraction of mixed income that can be attributed to capital, and net foreign capital income. However, there is no strong reason why this should always be equal to the contribution made by capital to production.

One can for instance imagine that corporate profits are generated by imperfect competitions, so that the net operating surplus of the corporate sector is not strictly speaking a return to

89Jorgenson and Landefeld (2006) propose to include the net return to government capital in GDP. They find that the gross return is about 3.5% of GDP (“services of durables, structures, land, and inventories held by government”: $340bn in 2002, see Table 1.5 p.51). This gross return includes depreciation which is already counted in GDP ($178bn) so that the net return is about $162bn, i.e. a bit less than 2% of national income.

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capital.

Independently from the SNA, however, there is a rich tradition of productivity analysis that attempts to isolate the contribution to production of capital, labor, and multi-factor productivity at the industry level.⁹⁰ A number of statistical agencies are currently devoting substantial effort into integrating these productivity accounts to the standard national accounts and making the two consistent.⁹¹ This is recognized in the 2008 SNA, which proposes that “for those offices interested, a table supplementary to the standard accounts could be prepared to display the implicit services provided by non-financial assets.” (SNA 2008, 20.1).

There are two ways to measure the contribution of capital to production, what is known as “capital services”: (i) using observed rental prices (to be then multiplied by the quantities of capital used), (ii) imputing those prices. Since in practice rental markets do not exist for a number of capital goods (or relevant rental prices are not collected), in productivity studies, rental prices are routinely imputed on the basis of the famous Hall and Jorgenson (1967) user cost formula. That is, the rental price p_k of a capital good k, also known as the user cost (i.e., the unit cost for the use of k for one period), is computed on the basis of k’s estimated price, P^k, a reference rate of return equal to the opportunity cost of money, r, a depreciation rate, δ (estimated from age-efficiency profiles etc.) and asset price inflation, ˆP^k:

p_k =P^k[r−Pˆ^k+ (1 + ˆP^k)δ]

Neglecting the small δPˆ^k term, this formula can be simplified as pk =P^k(r−Pˆ^k+δ) and has a straightforward interpretation: the rental price is equal to the real opportunity cost of an investment of value P^k plus the loss in asset value as the asset ages (economic depreciation).⁹² In practice, as discussed for instance in Hsieh (2002, pp. 507-508), the literature uses a variety of methods to compute the real interest rate r−Pˆ^k.

When there is a discrepancy between operating surplus and the value of capital services, it can be that not all operating surplus is a payment made to capital (e.g., monopoly rents) or

90Productivity data are produced by the BLS in the U.S. (http://www.bls.gov/bls/productivity.htm) and the EU-KLEMS consortium in the European Union.

91See in the U.S. Jorgenson and Landefeled (2006) and Jorgenson (2009). There are several inconsistencies between the SNA and productivity accounts. E.g., the former value industry and sectoral output at market price while the latter use basic prices, i.e., deduct taxes on products (net of subsidies), such as value-added taxes, excise duties, import taxes, etc. (code D21 for taxes and D31 for subsidies in ESA95 classification).

92This formula excludes the treatment of taxes. See for instance Jorgenson and Landefeld (2006, pp. 76 sqq) for an introduction to the user-cost formula, the effect of introducing taxes, the methods use to compute the real interest rate, etc.

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that some assets used in production have not been well identified (e.g., intangible capital) or that their value or depreciation has not been well estimated. Conversely one can compute the discount factor that equates the value of capital services with operating surplus.

As we explain in the main text of the paper, our overall conclusion is that capital shares α are in many ways more difficult to measure than wealth-income and capital-output ratiosβ. So far the economics literature has mostly focus upon the study of α. We argue in this research that the study of β should rank highly in future research agendas. Ideally one would obviously like to make progress on both fronts.

A.7.5 Computing the average return on wealth

Using national account data, one can compute the economy-wide average rate of return on wealth r by dividing the capital share α by the wealth-income ratio β: r = α/β. In practice, there are slightly different ways to proceed.

The simplest way is to set α equal to the share of capital in factor-price national income, i.e. α =YK/(Y −Tp), where YK is the sum of all capital income earned by domestic residents as identifiable in national accounts (housing capital income, corporate capital income, imputed capital income in the non-corporate business sector, and net foreign investment income), and Y −T_p is factor-price national income (i.e., national income net of production taxesT_p), and to set β equal to the private wealth-national income ratio W/Y. This formulation assumes that product taxesT_p are split between labor and capital in equal proportions and is straightforward to implement. It is the one we use for the computation of the average rate of returns series presented in Table A145 and displayed in Figure 14 of the main paper. This formulation has also the advantage that the capital share and the labor share (defined as the sum of all labor income as identifiable in national accounts: wage and salaries, imputed labor income in the non-corporate business sector, and net foreign labor income) sum to 1.

A problem, however, is that this procedure is slightly inconsistent in the sense thatβincludes government debt whileαexcludes government interest payments. So in effect the average rate of return is under-estimated. The consistent formula includes government interest payments (net of government interest receipts) in the capital share. In Table US.11, JP.11, etc., of the country-specific files, we report detailed computations of the standard capital shareαand the augmented capital share α^∗ including net government interest payments (the results are summarized in

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Appendix Table A48 and A48b). One problem is that the sum of α^∗ and the labor share now exceeds one. The corrected rate of return r^∗ =α^∗/β turns out to be qualitatively similar to the return r=α/β.⁹³

Another consistent way to proceed would be to exclude net government interest payments from the numerator, but to include the return earned by government on its assets, and to divide this economy-wide flow of capital income by the national-wealth income ratioβ_n= (W+W_g)/Y. This is probably the most consistent way to proceed – it would deliver the average return on national wealth, as opposed to the average return on private wealth only in the above computations. But as we have seen, government capital income is not measured yet in national accounts, so this procedure cannot be implemented easily.