John Maynard Keynes deplored the vindictive Versailles Treaty ending World War I, saved the United States in the depth of the Great Depression, and went on to construct our gross domestic product (GDP). This paper views his three classic GDP constituents as separate time-varying indicators.

Keynes [1] introduced household expenditure and domestic savings as elements of GDP in 1936 in his General Theory of Employment, Interest and Money. In 1940 he added government expenditure to GDP in How to Pay for the War [2]. Near the end of World War II in 1944 Keynes proposed “a new world currency, a system of fixed exchange rates between this world currency and the national currencies, and a world central bank that would run the whole system” [3] (p. 14). This proposal was dismissed at the Bretton Woods Conference by American planners who insisted on a dollar-backed fixed exchange-rate system which has since controlled the global economy (http://en.wikipedia.org/wiki/Bretton_Woods_system).

“Shortly before his death on 21 April 1946, Keynes persuaded the powers at the University of Cambridge to create a new Department of Applied Economics. […] the Cambridge department along with Harvard University’s Development Advisory Service would together […] incubate the first set of ideas around what GDP would look like, and then help to export them to the four corners of the world” [4] (p. 32). American planners then used the Keynesian GDP formula to measure the effect of American aid and to manage European economies. In 1999, mindful of Simon Kuznets’ original accounting of distinct goods like cars and cereal boxes by their dollar values [4] (Introduction), the United States Commerce Department proclaimed the GDP formula as the US government’s greatest invention of the 20th century.

The severest criticism of GDP has been that it does not measure well-being. “[…] after the end of World War II, […] Amartya Sen and Mahbub ul Haq would openly revolt against the idea of organizing economies according to GDP. And Haq […] would lead the design of the United Nations’ Human Development Index, which has so far come closest to dethroning GDP” [4] (p. 41). In 1989, Haq’s UN team settled on life expectancy, education, and per capita income as the components of the HDI. The last component was insisted on by the “formidable Sen”, who resolved the measurement of life expectancy and education in years and income in dollars [4] (pp. 93-95). However, “The HDI, for all its successes, had no discernable impact on the dominance of GDP as the world’s principal and most sought-after measure of economic well-being” [4] (p. 101).

Despite GDP’s dominance of global economic measurement, in 2008 French president Nicholas Sarkozy railed, “For years people whose lives were becoming more and more difficult were being told that living standards were rising. How could they not feel deceived?” [5] (p. viii). “Mis-Measuring Our Lives: Why GDP Doesn’t Add Up […] argues for a ‘dashboard’ of indicators that together paint a more accurate picture of a society’s well-being. […] the report makes clear to its readers that HDI […] was ‘the simplest representation’ of a broader human development approach that sparked a global revolution in how we measure well-being” [4] (p. 159).

In Spain, Marchante, Ortega, and Sánchez found that an augmented HDI regionally converged over 1980-2001, whereas regional disparities in per capita income remained constant [6]. The HDI measures a nation’s health and educational results rather than expenditures, along with its standard of living calibrated by gross per capita income. Resting on Marchante et al., the OECD [7], and the Sarkozy report, Ferrara and Nisticò [8] constructed a well-being index containing another augmented HDI, along with indicators measuring equal opportunity in the labor market, competitiveness, and quality of the socio-institutional context. They found that regional convergence in Italy over 2004-2010 ordered as: their augmented HDI alone, their entire well-being index, and per-capita GDP.

Due to the dominance of GDP across the world’s economies, this paper analyses its internal consistency and external relation to HDI, which is the most established indicator in Stiglitz, Sen, and Fitoussi’s “dashboard” of well-being indicators [5]. Sections 2 and 3 describe GDP and The United Nation’s Human Development Index. Section 4 posits the perfect internal consistency and perfect external prediction of any unidimensional index such as GDP. Under this postulation, equally-weighted GDP and differentially-weighted GDP are perfectly correlated and perfectly predict any external criterion variable such as HDI. Section 5 empirically demonstrates the internal consistency of GDP indicators and confirms their precise prediction of HDI in the USA and China. Section 6 discusses the added value that GDP theory, as a special case of unidimensional index theory, brings to the treatment of data from sequential populations. Section 7 emphasizes the value of these newly discovered properties of GDP to developed and developing economies in the 21^st century.

Simon Kuznetz originally formulated national accounts in terms of summative ratio-scaled money. He added up various American income sources and reported his result to the United States Senate in January, 1934 [4] (Prologue, Chapters 2 and 3). “In 1940, six years after Simon Kuznetz had presented his national income estimates to the Senate, Keynes had written down in a table the basis for what today is the formula for GDP” [4] (p. 26). This formula adds up GDP’s three macro indicators, which are described by the World Bank as follows (http://beta.data.worldbank.org):

Household final consumption expenditure (current US$): “Household final consumption expenditure (formerly private consumption) is the market value of all goods and services, including durable products (such as cars, washing machines, and home computers), purchased by households. It excludes purchases of dwellings but includes imputed rent for owner-occupied dwellings. It also includes payments and fees to governments to obtain permits and licenses. Here, household consumption expenditure includes the expenditures of nonprofit institutions serving households, even when reported separately by the country. Data are in current US dollars.”

Gross domestic savings (current US$): “Gross domestic savings are calculated as GDP less final consumption expenditure (total consumption). Data are in current US dollars.”

The World Bank’s update of Keynes’ final indicator, added prior to World War II [2] [4] (Chapters 2 and 3), is:

General government final consumption expenditure (current US$): “General government final consumption expenditure (formerly general government consumption) includes all current government expenditures for purchases of goods and services (including compensation of employees). It also includes most expenditures on national defense and security, but excludes government military expenditures that are part of government capital formation. Data are in current US dollars.”

The dollar denomination of variables counted in different units (automobiles, cereal boxes, etc.) allows the ratio scaling of GDP up to a multiplier calibrating GDP in single, thousands, millions, billions, or trillions of current US dollars. This ratio scaling also allows daily exchange-rates to multiply one nation’s currency into another’s (e.g. dollars into yen, etc.).

The HDI comprises macro indicators that are described by the United Nations Development Program (http://hdr.undp.org/en/data): “The HDI is a summary measure of average achievement in key dimensions of human development: a long and healthy life, being knowledgeable and having a decent standard of living. The HDI is the geometric mean of normalized indices for each of the three dimensions.

The health dimension is assessed by life expectancy at birth; the education dimension is measured by mean of years of schooling for adults aged 25 years and more and expected years of schooling for children of school entering age. The standard of living dimension is measured by gross national income per capita.”

In non-UN data life expectancy has been found to correlate positively with education, occupational class, and income from 1971-75 to 2011-14. Gross National Income is also the preponderant correlate of life satisfaction in the 2009-2012 Gallup World Poll data [10]. The United Nations, like Gallup, uses the logarithm of income to reflect the diminishing importance of income with increasing GNI. The UN then computes its HDI composite as the geometric mean of these three dimensions of well-being.

The United Nations Development Program (http://hdr.undp.org/en/data) continues:

“The normalized [0, 1] scale for health and education (in years) and standard of living (in logarithm-of-dollar-units) is obtained as follows:

Minimum and maximum values (goalposts) are set in order to transform the indicators expressed in different units into indices on a scale of 0 to 1. These goalposts act as the “natural zeros” and “aspirational targets,” respectively, from which component indicators are standardized … Having defined the minimum and maximum values, the dimension indices are calculated as the ratio of actual value minus minimum value to maximum value minus minimum value.

For the education dimension, this ratio is first applied to each of the two indicators, and then the arithmetic mean of the two resulting indices is taken…

Because each dimension index is a proxy for capabilities in the corresponding dimension, the transformation function from income to capabilities is likely to be concave—that is, each additional dollar of income has a smaller effect on expanding capabilities. Thus, for income, the natural logarithm of the actual, minimum and maximum values is used”.

The conversion of HDI’s three dimensions to a common [0, 1] scale was accomplished by Amartya Sen [4] (pp. 93-95) [5] (p. xxix). Sen’s natural zeros and aspirational targets are calibrated in years for life span and lifetime schooling. For standard of living these goalposts are measured in logarithm-of-dollar-units. The above ratio then places health, education, and standard of living in [0, 1]. The geometric mean of these three points is the HDI, which is also in [0, 1].

Sen’s conceptualization of the HDI is based upon national policy results rather than goals. The linkage among HDI’s dimensions has recently been supported by van Raalte et al. [11], who report that life expectancy (average at death) ranks perfectly with Finnish educational level and occupational class for nine successive time points over 1970-2015. These authors also found that Finnish life expectancy ranks perfectly with the Finnish income quintile for four successive time points over 2000-2015.

Our first theoretical goal is to provide an internal quality assurance of GDP. This is especially important in light of the trade war between the United States and China and the resulting slowdown in global GDP growth. Our second goal is to externally relate GDP to welfare by posing HDI as a fractional polynomial regression function of GDP. The closeness of this function of GDP to HDI allows us to assert that GDP is well-being.

Linearity of M and K. The perfect internal consistency of N_t-weighted indicators G_t1, G_t2, and G_t3 guarantees a perfect correlation between a nation’s manifest principal component M in definition 2 and its Keynesian GDP K in definition 4. Thus, the actual internal consistency of N_t-weighted indicators G_t1, G_t2, and G_t3 governs the actual correlation between M and K. Table 1 shows that near-perfect indicator correlations in China produce a correlation of 1.0000 between M and K. The slightly lower American correlation 0.9998 is due to the somewhat lower indicator correlations in the USA.

Country Specificity of M. The first principal component M in definition 2 has maximum variance among all linear combinations of population-weighted GDP indicators whose squared coefficients sum to one. This conditional maximum variance equals the first eigenvalue of the population-weighted covariance matrix of the three indicators in Section 2.

Lemma 3. The sum of the three eigenvalues of the indicators’ covariance matrix equals the sum of the three indicator variances. Thus, the ratio of the first eigenvalue to the sum of the three eigenvalues is the proportion of the total variance of the three indicators accounted for by the first principal component M [13] (pp. 536-538).

Note that in the present application of principal components analysis we are only concerned with the first component. Accordingly, our focus is on the first eigenvalue and the first eigenvector of the covariance matrix of the three GDP indicators described in Section 2. The eigenvalues and eigenvectors of the American and Chinese covariance matrices are exhibited in Table 2 and Table 3. They are produced from the first Stata command [16] in Appendix A1. The second Stata command gives our first principal component M.

The second line in Table 2 shows that principal component M accounts for 99.5436406% of the variance in the three American GDP indicators. This demonstrates that these three classic indicators possess almost perfect internal consistency in measuring Keynesian GDP in the American economy. The eigenvector in the second line of Table 3 contains the optimal national weights for GDP’s three indicators in the USA (cf. Section 2). These Eigen weights demonstrate that household consumption most heavily drives M in the American economy.

The third line in Table 2 demonstrates that 99.8561065% of the variance in China’s GDP indicators is attributable to M, giving nearly perfect internal consistency. However, the eigenvector in the third line of Table 3 shows a very different profile for these indicators in China than in the USA. American national weights reveal that M is primarily driven by household consumption, with gross domestic savings and government consumption having far lower weights in M. In contrast, Chinese national weights show that M is primarily driven by gross domestic savings, with household and government consumption exhibiting much lower weight in M (cf. Section 4.1). The values of the first eigenvectors in Table 3 demonstrate the country-specificity of weighted GDP in the USA and China.

Fractional Polynomial Regressions of H on K. The correlations between M and K in Table 1, and the results in Section 5, support our hypothesis that fractional polynomial regressions of H on X (=M, K) give nearly perfect predictions of H by both M and K. Due to K’s global accessibility, Equation (1) and Equation (2) use K in our fractional polynomial functions. f(K) and g(K) approximate H without measuring it directly:

USA: H ≈ f(K) = 0.0317122K^0.5 + 0.7856233 (1)

Note. The sum of the three eigenvalues is the total variance in the three GDP indicators. This is 7.5672036 in the USA and 4,790,141.19 in China. The percent of indicator variance accounted for by the first principal component is 99.5436406% in the USA and 99.8560963% in China. Each percent is 100 × the ratio of the first eigenvalue to the sum of that nation’s three eigenvalues [13] (pp. 536-538).

Note. The squared scoring coefficients in each row sum to one. The tabled values weight each nation’s three indicators in computing that nation’s first principal component M [13] (pp. 536-538).

China: H ≈ g(K) = 0.2622926K^0.5 − 0.057356K^0.5lnK + 0.3135376 (2)

The bivariate regression of H on K^0.5 (not shown) for the USA has intercept 0 and slope 1. The trivariate Chinese regression of H on K^0.5 and K^0.5lnK (not shown) has an intercept and slope closely approaching 0 and 1. Thus, f(K) and g(K) are virtually identical to H in the USA and China.

g(K) in Equation (2) is a fractional polynomial function quite distinct from f(K) in Equation (1). Both functions give close empirical support to our hypothesis in Section 4.2. They also validate the country specificity of f(K) and g(K) in the world’s two largest economies. The fitted R²s for f(K) and g(K) are 0.9862 and 0.9924 in the USA and China. The larger R² for China comports with its higher indicator correlations in Table 1. Interestingly, comparably high Chinese R²s attend several other fractional polynomial functions of K, which also closely approximate H. These ancillary functions, although more unsightly than g(K) in (2), are equally useful in approximating well-being in the absence of UN human development data. Thus, the approximation of H by a function of K is not unique in the class of fractional polynomial transformations of K. We also note that these other approximating functions are invariant up to multiplication of K by a positive constant, i.e. these functions are independent of the scaling of K.

Figure 1 and Figure 2 plot H on K. Figure 1 shows only slight downward concavity, indicating American household and government spending that is well beyond people’s needs. This result reiterates American insistence upon “the almighty dollar” as the global standard at Bretton Woods in 1944 [3] [4]. In contrast, Figure 2 demonstrates a sharply diminishing marginal utility for money in Chinese society, with little change in H beyond its sizable increases driven by initial increments in K. The fitted plots of H on K in Figure 1 and Figure 2 are virtually identical to those for H on M (not shown).

As already noted, the extremely close fit of both functions in Figure 1 and Figure 2 strongly supports our hypothesis in Section 4.2, and validates the country specificity of f(K) and g(K). These results demonstrate that Keynesian K is a near perfect proxy for well-being H. Thus, K can replace the UN’s HDI in the USA and China. It remains to be shown if GDP proxies HDI in the other 18 nations of the G20.

Equally weighted and Eigen weighted GDP are perfectly correlated in China and nearly perfectly in the USA. Eigen-weighted GDP signals a nation’s economic profile, while equally-weighted GDP remains in place for conventional analysis of economic data. Equally-weighted GDP will be preferred due to its availability in most national accounts.

These new properties of equally-weighted and Eigen-weighted GDP are also useful in a more general theory of national constructs. In this article GDP and HDI are aggregated from national indicators correlated over time. In other applications constructs may be correlated over, say, the G20 nations at a single time point to take a snapshot of cross-national differences among developed and developing countries [22]. Moreover, constructs may be geographical, bio-medical or socio-political as well as the GDP and HDI indexes treated here.

Finally, Keynes’ equally-weighted GDP remains a nation’s dominant policy informant. For some years now the USA Federal Reserve’s Board of Governors has been negotiating with the Congress in order to add a third mandate to their long-standing missions of reducing unemployment and inflation. Fed Chairman J. Powell described this new mandate as the mitigation of falling GDP (www.reuters.com/video/2019/07/10/powells-testimony-raises-hopes-of-rate-c?videoId=572792782). In view of the broad agreement that the transpacific trade war reduces GDP worldwide (https://www.federalreserve.gov/newsevents/testimony/powell20190710a.htm), as well as our finding that GDP is well-being, it follows that economic turbulence lowers human development everywhere. The world and its data call on the United States and China to stop their trade war. The consequent well-being of nations will affect the 21^st century more than Keynesian GDP influenced the 20^th century in which it was born.

This article is dedicated to my best critic, Maria Cohn Bechtel. The author thanks Dr. Bethany Bechtel for her gift [4] that alerted him to the importance of GDP to us all, and for her insistence on monitoring a nation’s economic indicators over time.

This adaptation of [12] [35] improves upon [35] by parsimoniously linking GDP to the United Nation’s Human Development Index.

The author declares no conflicts of interest regarding the publication of this paper.

Bechtel, G. (2019) GDP Is Well-Being! Results in the USA and China. Open Journal of Social Sciences, 7, 189-204. https://doi.org/10.4236/jss.2019.712014

Axiomatic computation (rather than estimation) of population parameters is carried out on the three time-series of indicators for the USA and China supplied by the World Bank (http://beta.data.worldbank.org). The findings in Table 2 and Table 3 are brought by 2-level principal components theory in Section 4.1 and its empirical application in Section 5:

The first of the following two Stata commands [16] lists the three dollar-denominated GDP indicators in Section 2:

pca hhspend savings govspend [fweight = popt], covariance

predict M

The first Stata command operates on 26 × 4 American and Chinese spreadsheets with rows labeled 1990 … 2015 and columns labeled population, household expenditure, gross domestic savings, and government expenditure. popt is population size, calibrated in millions, over 26 successive American and Chinese populations in years 1990 … 2015. The optional qualifier [fweight = popt] popt-weights variables hhspend, savings, and govspend, expanding them to run over i = 1, …, pop_t for t = 1990, …, 2015. The option covariance calls for a 2-level principal components analysis of the covariance matrix of these three expanded variables in the USA and China. These expanded variables are measured in trillions of current US dollars.

The second Stata command gives the first 2-level principal component M of hhspend, savings, and govspend in the USA and China.

The UN time series H, described in Sections 3 and 4.2, is obtained from the United Nations Development Program (http://hdr.undp.org/en/data). The time-series K of Keynesian GDP is supplied by the World Bank (http://beta.data.worldbank.org). Fractional polymonial functions of H on K are returned by the following bivariate and trivatiate regression commands:

USA: fracpoly, degree(1) noscaling adjust(no): regress H K [fweight = popt]

China: fracpoly, degree(2) noscaling adjust(no) powers(.5, .5): regress H K [fweight = popt]

These Stata commands [16] operate on a 26 × 3 spreadsheet with rows labeled 1990 … 2015 and columns labeled population, H, and K. popt is population size, calibrated in millions, over 26 successive American and Chinese populations in years 1990 … 2015. The fracpoly optional qualifiers retain the calibration of K in trillions of current US dollars. The three fracpoly qualifiers for the USA command return the fractional polynomial function in Equation (1). The four fracpoly qualifiers for the China command return the fractional polynomial function in Equation (2). The optional qualifier [fweight = popt] for the regress command popt weights variables H and K, expanding them to run over i = 1 … pop_t for t = 1990 … 2015. The expanded variable K is measured in trillions of current US dollars. The expanded variable H is measured on Sen’s [0, 1] scale described in Section 3 [4] (pp. 93-95) [5] (p. xxix).