New Unidimensional Indexes for China

A first principal component combines several indicators so as to maximize their internal consistency for measuring a construct. First principal components are extracted here from Swiss Economic Institute and World Bank datasets containing yearly societal indicators for China. These indicators are input to population‐weighted regressions without recourse to survey sampling or probabilistic inference. The results demonstrate Chomskyan globalization and domestic credit as strong exogenous and endogenous predictors of Chinese per capita GDP. These encouraging findings, easily extendable to other nations, are brought by two new societal indexes with assured unidimensionality.


Introduction
Varoufakis [1] portrayed the United States of America as The Global Minotaur, receiving foreign capital and controlling the world economy since the Bretton Woods Conference in 1944, near the end of World War II.(http://en.wikipedia.org/wiki/Bretton_Woods_system).Central to this portrayal is The Swiss Economic Research Institute regards actual flows and low restrictions as economic globalization and personal contact, information flows, and cultural proximity as social globalization.We use KOF's six indicators as proxies for Chomsky's literal globalization, defined as 'international integration-economic, cultural, political' [3] (p. 35).

Domestic Credit
The International Monetary Fund (IMF) observed that the declining surplus in China is due to (a) the collapse of global demand caused by the financial crisis of 2008 and (b) China's steep increase in investment "to prop up domestic demand and offset the large shock emanating from the [ . . .] collapse in external demand" [7].In generating this offset, the IMF noted that "China already has a head start compared with other high-growth economies with regard to financial deepening.Bank deposits and credit as shares of GDP are higher in China than in many other economies" [7].Domestic credit is measured by two indicators monitored by the World Bank: Domestic credit to the private sector (% of GDP) refers to financial resources provided to the private sector by financial corporations.The financial corporations include monetary authorities and deposit money banks.Domestic credit provided by the financial sector (% of GDP) includes all credit to various sectors.The financial sector includes monetary authorities and deposit money banks.
Chinese domestic credit provides a huge potential for kinetic household demand and the business investment that supplies it.

Per Capita GDP
The IMF [7] notes that Chinese government policy is now "designed to accelerate the transformation of the Chinese economic model, improve livelihoods, and raise domestic consumption.[...] If successful, this would ultimately prove to [ . . .] contribute significantly to strong, sustained, and balanced global growth."The importance of sustained GDP growth has also been emphasized by the Leeds UK Steady State Economy Conference [8], the United Nations Division for Sustainable Development [9], and the Annual Forum of The Progressive Economy Initiative [10].This economic consensus points to per capita GDP as a policy objective, rather than the unbridled GDP growth of technical globalization (cf.[3]): GDP per capita is the gross domestic product divided by the midyear population.Data are in constant 2010 U.S. dollars.This World Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's turn from low-cost exports toward domestic services and consumption.

Indicator Weighting
Unidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), which finds optimal indicator weights that maximize internal index consistency.This approach differs from the KOF index and national index theory [12], which weight indicators a priori.It also differs from recent Chinese indexes, which weight their indicators to maximize the prediction of external criteria such as growth.
The theory in Sections 3.2 and 3.3 is written for the six globalization indicators in Section 2.1.Section 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are described in Sections 2.1-2.3.
times its between-year covariance matrix, where
is an unknown positive scalar.
Corollary 1.The total covariance matrix of the vector (G ti1 G ti2 . . .G ti6 ) is (1 + Section 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are described in Sections 2.1, 2.2, and 2.3.
) times its between-year covariance matrix.
Next, we linearly transform G tij to Z tij for j = 1, . . ., 6, such that the distribution of each Z tij has a mean of zero and a variance one over i = 1, . . ., N t and t = 1992, . . ., 2013.This standardizes the different units of G ti1 , G ti2 , G ti3 , G ti4 , G ti5 , and G ti6 .
Lemma 1.The within-year covariance matrix of the vector (Z ti1 Z ti2 . . .Z ti6 ) over i = 1, . . ., N t and t = 1992, . . ., 2013 is also e obtained here by principal components analysis [11] (pp. 536-544), eights that maximize internal index consistency.This approach differs al index theory [12], which weight indicators a priori.It also differs hich weight their indicators to maximize the prediction of external times its between-year covariance matrix, i.e. the multiplicative relation of within-to-between-year covariance matrices is preserved under distinct linear transformations of the six latent globalization impacts.
ry re obtained here by principal components analysis [11] (pp. 536-544), eights that maximize internal index consistency.This approach differs nal index theory [12], which weight indicators a priori.It also differs which weight their indicators to maximize the prediction of external thin-year covariance matrix of the vector (Gti1 Gti2 … Gti6) over i = 1, …, Nt its between-year covariance matrix, where ɷ is an unknown positive scalar.

Indicator Weighting
Unidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), hich finds optimal indicator weights that maximize internal index consistency.This approach differs om the KOF index and national index theory [12], which weight indicators a priori.It also differs om recent Chinese indexes, which weight their indicators to maximize the prediction of external iteria such as growth.
Lemma 2. The latent correlation between Z tij and Z tik may be written as Corollary 3. Individual ti's latent score on the first principal component Z of matrix (r jk ) is where the vector (a 1 a 2 . . .a 6 ) is the first eigenvector of (r jk ) [11] (pp. 536-537).[8], the United Nations Division for le Development [9], and the Annual Forum of The Progressive Economy Initiative [10].omic consensus points to per capita GDP as a policy objective, rather than the unbridled th of technical globalization (cf.[3]): per capita is the gross domestic product divided by the midyear population.Data are in 2010 U.S. dollars.ld Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's low-cost exports toward domestic services and consumption.

ensional Index Theory
tor Weighting imensional indexes are obtained here by principal components analysis [11] (pp. 536-544), ds optimal indicator weights that maximize internal index consistency.This approach differs KOF index and national index theory [12], which weight indicators a priori.It also differs nt Chinese indexes, which weight their indicators to maximize the prediction of external ch as growth.theory in Sections 3. neity Axiom 2. The within-year covariance matrix of the vector (Gti1 Gti2 … Gti6) over i = 1, …, Nt 92, …, 2013 is ɷ times its between-year covariance matrix, where ɷ is an unknown positive scalar.
) −1 , replicates the yearly mean mskyan globalization; domestic credit; latent principal-components and regression; per pulation-weighted indexes and regression slopes; quality assurance; ɷ-homogeneity [1] portrayed the United States of America as The Global Minotaur, receiving foreign rolling the world economy since the Bretton Woods Conference in 1944, near the end .(http://en.wikipedia.org/wiki/Bretton_Woods_system).Central to this portrayal is eynes, who deplored the vindictive Versailles Treaty at the end of World War I and United States in the Great Depression, only to be dismissed at Bretton Woods by ers.Keynes predicted that "a dollar-backed fixed exchange rate system would create ures down the road […] that would […] cause […] trade imbalances to grow with, le effects first upon the deficit countries and then upon everyone else" [2] (p.10).rious misadventure is described by Noam Chomsky as technical globalization, which ure of liberal and protectionist measures and many related to investor rights, not ned to serve the interests of investors, financial institutions, and other centers ) −1 , contains unknowable deviations Z ti − Z t. over i = 1, . . ., N t and t = 1992, . . .,2013.However, the between-year vector Z b is knowable up to an unknown multiplier.We now express this multiple of Z b .

Manifest Principal Components
Definition.Z tj is the N t -weighted standardized value of G tj in axiom 1.
Lemma 5. Due to Lemmas 2 and 4, the latent correlation r jk in lemma 2 between Z tij and Z tik may be expressed as the manifest correlation ce matrix of the vector (Gti1 Gti2 … Gti6) over i = 1, …, Nt ovariance matrix, where ɷ is an unknown positive scalar.
Note that first manifest principal component G is standardized with mean zero and variance of one.Also, manifest index G t is the product of two unobservable factors; the multiplier (1 + ω) 1 /2 and the latent index Z t. .

Latent Regression
Our second index consists of the two indicators in Section 2.2.Therefore, in Sections 3.2 and 3.3 we let j = 1, 2 and overwrite 'globalization' by 'domestic credit', G by D, G by D, and Z by Y.This allows the interpretation of the resulting index as the product of multiplier (1 + ω) 1 /2 and the latent mean impact Y t. of domestic credit for year t.Our final index is the single indicator in Section 2.3.Thus, we set j = 1 in Sections 3.2 and 3.3 and overwrite 'globalization' by 'per capita GDP', G by W, G by W, and Z by X.This permits us to interpret China's manifest index W t = (1 + ω) 1 /2 X t. as the product of unknown factors (1 + ω) 1 /2 and the latent per capita GDP index X t. .Principal components G and D, and indicator W, replicate G t , D t , and W t over i = 1, . . ., N t for t = 1992, . . ., 2013.These replicated manifest indexes are multiples of China's latent indexes of globalization Z t. , domestic credit Y t. , and per capita GDP X t. in year t.The observable sums-of-products matrix of G, D, and W, enables latent regressions involving globalization, domestic credit, and per capita GDP.
The IMF [7] notes that Chinese government policy is now "designed to accelerate the transformation of the Chinese economic model, improve livelihoods, and raise domestic consumption.[...] If successful, this would ultimately prove to […] contribute significantly to strong, sustained, and balanced global growth."The importance of sustained GDP growth has also been emphasized by the Leeds UK Steady State Economy Conference [8], the United Nations Division for Sustainable Development [9], and the Annual Forum of The Progressive Economy Initiative [10].This economic consensus points to per capita GDP as a policy objective, rather than the unbridled GDP growth of technical globalization (cf.[3]): GDP per capita is the gross domestic product divided by the midyear population.Data are in constant 2010 U.S. dollars.This World Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's turn from low-cost exports toward domestic services and consumption.

Indicator Weighting
Unidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), which finds optimal indicator weights that maximize internal index consistency.This approach differs from the KOF index and national index theory [12], which weight indicators a priori.It also differs from recent Chinese indexes, which weight their indicators to maximize the prediction of external criteria such as growth.
The theory in Sections 3.2 and 3.3 is written for the six globalization indicators in Section 2.1.Section 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are described in Sections 2.1, 2.2, and 2.3.
. Bivariate Lemma 6.The manifest regression slope G T D/G T G of domestic credit on globalization equals the latent slope business investment that supplies it.

Per Capita GDP
The IMF [7] notes that Chinese government policy is now "designed to accelerate the transformation of the Chinese economic model, improve livelihoods, and raise domestic consumption.[...] If successful, this would ultimately prove to […] contribute significantly to strong, sustained, and balanced global growth."The importance of sustained GDP growth has also been emphasized by the Leeds UK Steady State Economy Conference [8], the United Nations Division for Sustainable Development [9], and the Annual Forum of The Progressive Economy Initiative [10].This economic consensus points to per capita GDP as a policy objective, rather than the unbridled GDP growth of technical globalization (cf.[3]): GDP per capita is the gross domestic product divided by the midyear population.Data are in constant 2010 U.S. dollars.This World Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's turn from low-cost exports toward domestic services and consumption.

Indicator Weighting
Unidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), which finds optimal indicator weights that maximize internal index consistency.This approach differs from the KOF index and national index theory [12], which weight indicators a priori.It also differs from recent Chinese indexes, which weight their indicators to maximize the prediction of external criteria such as growth.
The theory in Sections 3.2 and 3.3 is written for the six globalization indicators in Section 2.1.Section 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are described in Sections 2.1, 2.2, and 2.3.
for kinetic household demand and the policy is now "designed to accelerate , improve livelihoods, and raise domestic rove to […] contribute significantly to strong, nce of sustained GDP growth has also been nference [8], the United Nations Division for of The Progressive Economy Initiative [10].a policy objective, rather than the unbridled ided by the midyear population.Data are in ://beta.data.worldbank.org)captures China's d consumption.
uge potential for kinetic household demand and the government policy is now "designed to accelerate nomic model, improve livelihoods, and raise domestic ultimately prove to […] contribute significantly to strong, The importance of sustained GDP growth has also been Economy Conference [8], the United Nations Division for nnual Forum of The Progressive Economy Initiative [10].pita GDP as a policy objective, rather than the unbridled [3]): c product divided by the midyear population.Data are in rmance (http://beta.data.worldbank.org)captures China's tic services and consumption.
here by principal components analysis [11] (pp. 536-544), t maximize internal index consistency.This approach differs heory [12], which weight indicators a priori.It also differs ht their indicators to maximize the prediction of external written for the six globalization indicators in Section 2.1.omestic credit, and per capita GDP, whose indicators are alization indicator G tj (j = 1, …, 6) induces a latent idiosyncratic t is China's population size in year t = 1992, …, 2013.variance matrix of the vector (Gti1 Gti2 … Gti6) over i = 1, …, Nt year covariance matrix, where ɷ is an unknown positive scalar.
provides a huge potential for kinetic household demand and the supplies it.
at Chinese government policy is now "designed to accelerate hinese economic model, improve livelihoods, and raise domestic l, this would ultimately prove to […] contribute significantly to strong, al growth."The importance of sustained GDP growth has also been Steady State Economy Conference [8], the United Nations Division for , and the Annual Forum of The Progressive Economy Initiative [10].nts to per capita GDP as a policy objective, rather than the unbridled lization (cf.[3]): oss domestic product divided by the midyear population.Data are in ereign performance (http://beta.data.worldbank.org)captures China's ard domestic services and consumption.ory are obtained here by principal components analysis [11] (pp. 536-544), weights that maximize internal index consistency.This approach differs onal index theory [12], which weight indicators a priori.It also differs which weight their indicators to maximize the prediction of external

ithin-year covariance matrix of the vector (Gti1
Gti2 … Gti6) over i = 1, …, Nt s its between-year covariance matrix, where ɷ is an unknown positive scalar.
mestic credit provides a huge potential for kinetic household demand and the vestment that supplies it.DP [7] notes that Chinese government policy is now "designed to accelerate ion of the Chinese economic model, improve livelihoods, and raise domestic .]If successful, this would ultimately prove to […] contribute significantly to strong, alanced global growth."The importance of sustained GDP growth has also been he Leeds UK Steady State Economy Conference [8], the United Nations Division for elopment [9], and the Annual Forum of The Progressive Economy Initiative [10].onsensus points to per capita GDP as a policy objective, rather than the unbridled chnical globalization (cf.[3]): pita is the gross domestic product divided by the midyear population.Data are in .S. dollars.k index of sovereign performance (http://beta.data.worldbank.org)captures China's ost exports toward domestic services and consumption.
nal Index Theory ighting ional indexes are obtained here by principal components analysis [11] (pp. 536-544), mal indicator weights that maximize internal index consistency.This approach differs dex and national index theory [12], which weight indicators a priori.It also differs nese indexes, which weight their indicators to maximize the prediction of external rowth. in Sections 3.2 and 3.

xiom 2. The within-year covariance matrix of the vector (Gti1
Gti2 … Gti6) over i = 1, …, Nt 2013 is ɷ times its between-year covariance matrix, where ɷ is an unknown positive scalar.
hinese domestic credit provides a huge potential for kinetic household demand and the usiness investment that supplies it.
r Capita GDP he IMF [7] [8], the United Nations Division for nable Development [9], and the Annual Forum of The Progressive Economy Initiative [10].conomic consensus points to per capita GDP as a policy objective, rather than the unbridled rowth of technical globalization (cf.[3]): DP per capita is the gross domestic product divided by the midyear population.Data are in nt 2010 U.S. dollars.
orld Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's rom low-cost exports toward domestic services and consumption.
dimensional Index Theory dicator Weighting nidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), finds optimal indicator weights that maximize internal index consistency.This approach differs he KOF index and national index theory [12], which weight indicators a priori.It also differs recent Chinese indexes, which weight their indicators to maximize the prediction of external a such as growth.he theory in Sections 3. geneity Axiom 2. The within-year covariance matrix of the vector (Gti1 Gti2 … Gti6) over i = 1, …, Nt 1992, …, 2013 is ɷ times its between-year covariance matrix, where ɷ is an unknown positive scalar.
Chinese domestic credit provides a huge potential for kinetic household demand and the business investment that supplies it.

Per Capita GDP
The IMF [7] notes that Chinese government policy is now "designed to accelerate the transformation of the Chinese economic model, improve livelihoods, and raise domestic consumption.[...] If successful, this would ultimately prove to […] contribute significantly to strong, sustained, and balanced global growth."The importance of sustained GDP growth has also been emphasized by the Leeds UK Steady State Economy Conference [8], the United Nations Division for Sustainable Development [9], and the Annual Forum of The Progressive Economy Initiative [10].This economic consensus points to per capita GDP as a policy objective, rather than the unbridled GDP growth of technical globalization (cf.[3]): GDP per capita is the gross domestic product divided by the midyear population.Data are in constant 2010 U.S. dollars.This World Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's turn from low-cost exports toward domestic services and consumption.

Indicator Weighting
Unidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), which finds optimal indicator weights that maximize internal index consistency.This approach differs from the KOF index and national index theory [12], which weight indicators a priori.It also differs from recent Chinese indexes, which weight their indicators to maximize the prediction of external criteria such as growth.
The theory in Sections 3.2 and 3.3 is written for the six globalization indicators in Section 2.1.Section 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are described in Sections 2.1, 2.2, and 2.3.
Chinese domestic credit provides a huge potential for kinetic household demand and the business investment that supplies it.

Per Capita GDP
The IMF [7] notes that Chinese government policy is now "designed to accelerate the transformation of the Chinese economic model, improve livelihoods, and raise domestic consumption.[...] If successful, this would ultimately prove to […] contribute significantly to strong, sustained, and balanced global growth."The importance of sustained GDP growth has also been emphasized by the Leeds UK Steady State Economy Conference [8], the United Nations Division for Sustainable Development [9], and the Annual Forum of The Progressive Economy Initiative [10].This economic consensus points to per capita GDP as a policy objective, rather than the unbridled GDP growth of technical globalization (cf.[3]): GDP per capita is the gross domestic product divided by the midyear population.Data are in constant 2010 U.S. dollars.This World Bank index of sovereign performance (http://beta.data.worldbank.org)captures China's turn from low-cost exports toward domestic services and consumption.

Indicator Weighting
Unidimensional indexes are obtained here by principal components analysis [11] (pp. 536-544), which finds optimal indicator weights that maximize internal index consistency.This approach differs from the KOF index and national index theory [12], which weight indicators a priori.It also differs from recent Chinese indexes, which weight their indicators to maximize the prediction of external criteria such as growth.
The theory in Sections 3.2 and 3.3 is written for the six globalization indicators in Section 2.1.Section 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are described in Sections 2.1, 2.2, and 2.3.
The matrix generalization of Lemma 6 is multivariate Lemma 7.

Multivariate Lemma 7.
The manifest and latent regression slopes of per capita GDP on globalization and domestic credit are equal, i.e., where the manifest 2 × 2 and 2 × 1 matrices are submatrices of the matrix in (1).
The slopes in Lemmas 6 and 7 derive from multi-year population regressions of 28 billion latent impacts over i = 1, . . ., N t and t = 1992, . . ., 2013 (cf.Axiom 1).These slopes are not subject to sampling variation like regression slopes estimated from survey samples.Hence, we are unencumbered by probabilistic inference, estimation, or hypothesis testing (cf.Section 6).The within-year covariance matrix of the vector (Gti1 Gti2 … Gti6) over i = 1, …, Nt times its between-year covariance matrix, where ɷ is an unknown positive scalar.

Sufficiency (but not
-Homogeneity Axioms 1 and 2 imply the manifest indexes G t for t = 1992, . . ., 2013.However, population-weighted principal components analysis produces identical manifest indexes in the presence of other latent multi-year distributions that are not 017, 22 Hopefully, 21st century cooperation among these three global institutions will rejected Bretton Woods proposal: "the creation of a new world currency, a system rates between this world currency and the national currencies, and a world central run the whole system" [2] (p.14).unterweight to technical globalization is developing in China's transition from nvestment, and trade toward growth that is driven by domestic services and

Introduction
Varoufakis [1] portrayed the United States of America as The Global Minotaur, receiving foreign capital and controlling the world economy since the Bretton Woods Conference in 1944, near the end of World War II.(http://en.wikipedia.org/wiki/Bretton_Woods_system).Central to this portrayal is John Maynard Keynes, who deplored the vindictive Versailles Treaty at the end of World War I and who saved the United States in the Great Depression, only to be dismissed at Bretton Woods by American planners.Keynes predicted that "a dollar-backed fixed exchange rate system would create other misadventures down the road […] that would […] cause […] trade imbalances to grow with, ultimately, terrible effects first upon the deficit countries and then upon everyone else" [2] (p.10).
The most serious misadventure is described by Noam Chomsky as technical globalization, which denotes "a mixture of liberal and protectionist measures and many related to investor rights, not trade, all designed to serve the interests of investors, financial institutions, and other centers of concentrated state-private power" [3] (p. 35).Technical globalization has spawned dangerous trade imbalances, along with the North American Free Trade Agreement (NAFTA), the proposed Trans-Pacific Partnership (TPP), and Transatlantic Trade and Investment Partnership (TTIP).The latter proposals reach across both oceans and threaten sovereignty itself.
The pending TPP and TTIP agreements between the United States and its Pacific and European trading partners do not include the emerging BRICS economies, which stand as counterweights to these mutations in technical globalization.The capitalization and currency reserves of the BRICS's New Development Bank in Shanghai dwarf those of the World Bank and the International Monetary Fund combined.Hopefully, 21st century cooperation among these three global institutions will supplant Keynes' rejected Bretton Woods proposal: "the creation of 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" [2] (p.14).
A second counterweight to technical globalization is developing in China's transition from manufacturing, investment, and trade toward growth that is driven by domestic services and -homogeneity is a sufficient, but not necessary, condition for the observation of manifest indexes G t for t = 1992, . . ., 2013.mbines several indicators so as to maximize their internal irst principal components are extracted here from Swiss sets containing yearly societal indicators for China.These ted regressions without recourse to survey sampling or nstrate Chomskyan globalization and domestic credit as dictors of Chinese per capita GDP.These encouraging ns, are brought by two new societal indexes with assured estic credit; latent principal-components and regression; per s and regression slopes; quality assurance; ɷ-homogeneity tates of America as The Global Minotaur, receiving foreign since the Bretton Woods Conference in 1944, near the end wiki/Bretton_Woods_system).Central to this portrayal is vindictive Versailles Treaty at the end of World War I and t Depression, only to be dismissed at Bretton Woods by "a dollar-backed fixed exchange rate system would create hat would […] cause […] trade imbalances to grow with, ficit countries and then upon everyone else" [2] (p.10).cribed by Noam Chomsky as technical globalization, which ionist measures and many related to investor rights, not s of investors, financial institutions, and other centers (p.35).Technical globalization has spawned dangerous merican Free Trade Agreement (NAFTA), the proposed satlantic Trade and Investment Partnership (TTIP).The nd threaten sovereignty itself.ts between the United States and its Pacific and European ing BRICS economies, which stand as counterweights to .The capitalization and currency reserves of the BRICS's rf those of the World Bank and the International Monetary cooperation among these three global institutions will proposal: "the creation of a new world currency, a system currency and the national currencies, and a world central ] (p.14).l globalization is developing in China's transition from ward growth that is driven by domestic services and -homogeneity within and between indexes, imply the manifest regression slopes in Lemmas 6 and 7. Again, population-weighted regression analysis produces identical manifest slopes from other latent multi-year distributions that are not Math.Comput.Appl.2017, 22, 13; doi: 10.3390/mca22010013 www.mdpi.com/journal/mca

Introduction
Varoufakis [1] portrayed the United States of America as The Global Minotaur, receiving foreign capital and controlling the world economy since the Bretton Woods Conference in 1944, near the end of World War II.(http://en.wikipedia.org/wiki/Bretton_Woods_system).Central to this portrayal is John Maynard Keynes, who deplored the vindictive Versailles Treaty at the end of World War I and who saved the United States in the Great Depression, only to be dismissed at Bretton Woods by American planners.Keynes predicted that "a dollar-backed fixed exchange rate system would create other misadventures down the road […] that would […] cause […] trade imbalances to grow with, ultimately, terrible effects first upon the deficit countries and then upon everyone else" [2] (p.10).
The most serious misadventure is described by Noam Chomsky as technical globalization, which denotes "a mixture of liberal and protectionist measures and many related to investor rights, not trade, all designed to serve the interests of investors, financial institutions, and other centers of concentrated state-private power" [3] (p. 35).Technical globalization has spawned dangerous trade imbalances, along with the North American Free Trade Agreement (NAFTA), the proposed Trans-Pacific Partnership (TPP), and Transatlantic Trade and Investment Partnership (TTIP).The latter proposals reach across both oceans and threaten sovereignty itself.
The pending TPP and TTIP agreements between the United States and its Pacific and European trading partners do not include the emerging BRICS economies, which stand as counterweights to these mutations in technical globalization.The capitalization and currency reserves of the BRICS's New Development Bank in Shanghai dwarf those of the World Bank and the International Monetary Fund combined.Hopefully, 21st century cooperation among these three global institutions will supplant Keynes' rejected Bretton Woods proposal: "the creation of 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" [2] (p.14).
A second counterweight to technical globalization is developing in China's transition from manufacturing, investment, and trade toward growth that is driven by domestic services and -homogeneous.Therefore, www.mdpi.com/journal/mca7150, Gainesville, FL 32611-7150, USA; : 24 January 2017 icators so as to maximize their internal ponents are extracted here from Swiss rly societal indicators for China.These ithout recourse to survey sampling or n globalization and domestic credit as per capita GDP.These encouraging two new societal indexes with assured rincipal-components and regression; per opes; quality assurance; ɷ-homogeneity s The Global Minotaur, receiving foreign oods Conference in 1944, near the end ds_system).Central to this portrayal is s Treaty at the end of World War I and to be dismissed at Bretton Woods by ixed exchange rate system would create se […] trade imbalances to grow with, then upon everyone else" [2] (p.10).omsky as technical globalization, which d many related to investor rights, not ancial institutions, and other centers globalization has spawned dangerous de Agreement (NAFTA), the proposed d Investment Partnership (TTIP).The ignty itself.ited States and its Pacific and European ies, which stand as counterweights to and currency reserves of the BRICS's ld Bank and the International Monetary ng these three global institutions will tion of a new world currency, a system national currencies, and a world central developing in China's transition from t is driven by domestic services and -homogeneity is also sufficient, but not necessary, for the observation of manifest slopes identical to those in Lemmas 6 and 7.
The nent combines several indicators so as to maximize their internal struct.First principal components are extracted here from Swiss nk datasets containing yearly societal indicators for China.These n-weighted regressions without recourse to survey sampling or lts demonstrate Chomskyan globalization and domestic credit as ous predictors of Chinese per capita GDP.These encouraging er nations, are brought by two new societal indexes with assured ion; domestic credit; latent principal-components and regression; per indexes and regression slopes; quality assurance; ɷ-homogeneity United States of America as The Global Minotaur, receiving foreign conomy since the Bretton Woods Conference in 1944, near the end dia.org/wiki/Bretton_Woods_system).Central to this portrayal is red the vindictive Versailles Treaty at the end of World War I and he Great Depression, only to be dismissed at Bretton Woods by ted that "a dollar-backed fixed exchange rate system would create ad […] that would […] cause […] trade imbalances to grow with, n the deficit countries and then upon everyone else" [2] (p.10).re is described by Noam Chomsky as technical globalization, which protectionist measures and many related to investor rights, not interests of investors, financial institutions, and other centers er" [3] (p. 35).Technical globalization has spawned dangerous North American Free Trade Agreement (NAFTA), the proposed nd Transatlantic Trade and Investment Partnership (TTIP).The oceans and threaten sovereignty itself.greements between the United States and its Pacific and European e emerging BRICS economies, which stand as counterweights to lization.The capitalization and currency reserves of the BRICS's hai dwarf those of the World Bank and the International Monetary century cooperation among these three global institutions will Woods proposal: "the creation of a new world currency, a system is world currency and the national currencies, and a world central stem" [2] (p.14).technical globalization is developing in China's transition from trade toward growth that is driven by domestic services and ).Central to this portrayal is at the end of World War I and smissed at Bretton Woods by ange rate system would create ade imbalances to grow with, n everyone else" [2] (p.10).s technical globalization, which related to investor rights, not stitutions, and other centers tion has spawned dangerous ment (NAFTA), the proposed ment Partnership (TTIP).The lf. s and its Pacific and European ch stand as counterweights to rency reserves of the BRICS's nd the International Monetary three global institutions will new world currency, a system urrencies, and a world central g in China's transition from en by domestic services and -homogeneous distributions is a canonical subset of the class of latent distributions that give identical population-weighted indexes and regression slopes.

Globalization Index
The six indicators in the following two Stata [13] commands are described in Section 2.1: The option pcf denotes principal components factorization.The optional qualifier [fweight = popt] gives an N t -weighted first principal component 'global' that replicates indexes G t over i = 1, . . ., N t for t = 1992, . . ., 2013.The Stata commands in (2) operate on a 22 × 6 spreadsheet.
Table 1 exhibits the eigenvalues found by our analysis of Chomskyan globalization.The unidimensionality obtained from the first principal component is demonstrated by the dominance of the first eigenvalue over the remaining five eigenvalues.This implies that G extracts the preponderance of information contained in these six indicators, i.e., that these indicators are internally consistent in measuring a single construct.This first principal component accounts for 4.897/6 = 0.816 of the variance in these KOF indicators.Thus, our new index of Chomskyan globalization is quality assured for China.1.Each loading in the loadings eigenvector is the Pearson-product-moment correlation of that indicator with the first principal component over i = 1, . . ., N t and t = 1992, . . ., 2013.Due to Corollary 5, this manifest loading also equals the latent correlation between Z tij and Z ti, i.e., between the individual latent impacts of indicator j (= 1, . . .,6) and those of the first principle component over i = 1, . . ., N t and t = 1992, . . ., 2013.Finally, each coefficient in the scoring eigenvector is the weight of that indicator in individually scoring this first principal component (cf.Corollary 3).The sum of the squared scoring coefficients is the reciprocal of the first eigenvalue in Table 1 (cf.Lemma 3).
The N t -weighted first principal component 'domesticcredit' replicates indexes D t over i = 1, . . ., N t for t = 1992, . . ., 2013.The Stata commands in (3) operate on a 22 × 2 spreadsheet.Tables 3 and 4 exhibit the eigenvalues and eigenvectors for domestic credit.The strong unidimensionality of the first principal component D is seen by the large difference between the two eigenvalues.The first principal component accounts for 1.974/2 = 0.987 of the variance in the two indicators, whose loadings on this factor are also extremely high.This degree of internal consistency quality-assures our new credit index for China.Notes: the sum of the squared loadings equals the first eigenvalue in Table 3.The scoring eigenvector is a scalar multiple of the loadings eigenvector.The sum of the squared scoring coefficients is the reciprocal of the first eigenvalue in Table 3.

The Setup for Regression
Our latent bi-variate and multi-variate regressions run over individuals i = 1, . . ., N t in years t = 1992, . . ., 2013, encompassing 28 billion personal impacts.The regression slopes read out from Lemmas 6 and 7 are computed from manifest principal components G and D and indicator W.These three vectors carry the replicated yearly indexes G t , D t , and W t .The standardizations of the two manifest principal components, and the single indicator, to mean zero and variance one, enables a comparison of the slopes of W on G and D.

Bivariate Regression of Principal Components
The strong exogenous effect of Chomskyan globalization on domestic credit is 0.806 with R 2 = 0.650.This regression slope, derived in Lemma 6, was computed from Stata [13] Command where popt is China's population in year t = 1992, . . . the United States of America as The Global Minotaur, receiving foreign orld economy since the Bretton Woods Conference in 1944, near the end ikipedia.org/wiki/Bretton_Woods_system).Central to this portrayal is deplored the vindictive Versailles Treaty at the end of World War I and s in the Great Depression, only to be dismissed at Bretton Woods by redicted that "a dollar-backed fixed exchange rate system would create he road […] that would […] cause […] trade imbalances to grow with, st upon the deficit countries and then upon everyone else" [2] (p.10).enture is described by Noam Chomsky as technical globalization, which l and protectionist measures and many related to investor rights, not e the interests of investors, financial institutions, and other centers power" [3] (p. 35).Technical globalization has spawned dangerous the North American Free Trade Agreement (NAFTA), the proposed PP), and Transatlantic Trade and Investment Partnership (TTIP).The both oceans and threaten sovereignty itself.TIP agreements between the United States and its Pacific and European de the emerging BRICS economies, which stand as counterweights to globalization.The capitalization and currency reserves of the BRICS's hanghai dwarf those of the World Bank and the International Monetary 21st century cooperation among these three global institutions will etton Woods proposal: "the creation of a new world currency, a system een this world currency and the national currencies, and a world central le system" [2] (p.14).t to technical globalization is developing in China's transition from and trade toward growth that is driven by domestic services and times their between-year covariance matrix.

Multivariate Regression of per Capita GDP on Principal Components
Table 5 exhibits the slopes and R 2 for the regression of per capita GDP on globalization and domestic credit.The multi-year population slopes in Table 5

Introduction
Varoufakis [1] portrayed the United States of America as The Global Minotaur, receiving foreign capital and controlling the world economy since the Bretton Woods Conference in 1944, near the end of World War II.(http://en.wikipedia.org/wiki/Bretton_Woods_system).Central to this portrayal is John Maynard Keynes, who deplored the vindictive Versailles Treaty at the end of World War I and who saved the United States in the Great Depression, only to be dismissed at Bretton Woods by American planners.Keynes predicted that "a dollar-backed fixed exchange rate system would create other misadventures down the road […] that would […] cause […] trade imbalances to grow with, ultimately, terrible effects first upon the deficit countries and then upon everyone else" [2] (p.10).
The most serious misadventure is described by Noam Chomsky as technical globalization, which denotes "a mixture of liberal and protectionist measures and many related to investor rights, not trade, all designed to serve the interests of investors, financial institutions, and other centers of concentrated state-private power" [3] (p. 35).Technical globalization has spawned dangerous trade imbalances, along with the North American Free Trade Agreement (NAFTA), the proposed Trans-Pacific Partnership (TPP), and Transatlantic Trade and Investment Partnership (TTIP).The latter proposals reach across both oceans and threaten sovereignty itself.
The pending TPP and TTIP agreements between the United States and its Pacific and European trading partners do not include the emerging BRICS economies, which stand as counterweights to these mutations in technical globalization.The capitalization and currency reserves of the BRICS's New Development Bank in Shanghai dwarf those of the World Bank and the International Monetary Fund combined.Hopefully, 21st century cooperation among these three global institutions will supplant Keynes' rejected Bretton Woods proposal: "the creation of 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" [2] (p.14).
A second counterweight to technical globalization is developing in China's transition from manufacturing, investment, and trade toward growth that is driven by domestic services and times their between-year covariance matrix (cf.Lemma 7).The beta option standardizes the GDP indicator to mean zero and variance one, and maintains this prior standardization of the principal components for domestic credit and globalization.This option allows a comparison of the two regression slopes delivered by Command (5).
Regressions ( 4) and ( 5) demonstrate that Chomskyan globalization exogenously drives domestic credit which, in turn, endogenously drives per capita GDP.Table 5 shows that Chomskyan globalization also exerts a direct exogenous impact on per capita GDP.A high proportion (R 2 = .689) of the variance in W is accounted for by G and D. These results extend Chomskyan globalization's beneficial impacts on domestic well-being from Europe [5] and the G20 nations [12] to China.

Future Directions
Unidimensional index theory overrides "the central dogma of statistical inference, that there is a component of randomness in data" [14] (p.9)."Neither denying nor quantifying uncertainty, we simply ignore it" [12] (p.9).
The axiomatic approach to sequential human populations in Section 3 brings compelling advantages to the data science of human populations.Probabilistic inference is replaced by parameter computation and random variables give way to real variables.This suggests further "statistical thinking and new foundational frameworks" that help sort out "the many philosophical issues data science presents" [15] (pp.4,5).This call has been echoed by the American National Science Foundation, which has "released a revised version of the solicitation Critical Techniques and Technologies for Advancing Foundations and Applications of Big Data Science" [16] (p. 6).

Advantages of Latent Principal Components and Regression over Sample Surveys
Data definition.Pfeffermann observed that "The use of big data does not require a sampling frame, questionnaires, interviews, and all the other ingredients underlying survey samples.[ . . .] this should be the ultimate target of every country-having sufficiently accurate administrative records so that no population censuses will be needed" [17] (pp.433, 455).Horrigan also views Big Data as nonsampled data "from electronic sources whose primary purpose is something other than statistical inference [ . . .] this type of Big Data typically comprises the universe and, by definition, can represent (nearly) the entire population" [18] (pp.[25][26].As examples of nonsampled universe files, Horrigan mentions daily price indexes, point-of-sale retail databases, universe data on hospitals, and corporate data. The present paper exploits the electronic files of the World Bank and the Swiss Economic Research Institute.Principal-component indexes, directly computed from established macro indicators, are more plausible and palpable than constructs hypothesized to be measured by survey samples of human populations.Latent principle-component scores (cf.Corollaries 3 and 4) are also practical alternatives to questionnaire scores that require the protection of individual privacy.In most countries, self-reported consumption, received services, and well-being are not even available.
Data collection.For almost half a century the interrogation of individuals in survey samples has been shadowed by skepticism about the incremental benefits of subjective indicators over and above objective indicators already in use [19][20][21][22].The problems associated with subjective measurement point up the pitfalls of survey sampling, which may not be needed in the first place (cf.[23,24]).
Population-weighted indexes and regressions evade the host of long-standing, and now acute, issues daunting micro-data collection.First, sampled micro data are beset by the unresolved competition between randomization-based and model-based regression [25][26][27].Second, both types of regression face problems of measurement error [28], sampling error [29,30], unit nonresponse [31], missing data [32], and variance estimation [33,34].Unit nonresponse alone threatens the entire survey industry due to public unwillingness to answer mail, telephone, internet, or face-to-face questions [35].The host of problems associated with survey measurement and process quality were discussed and illustrated almost twenty years ago in the volume edited by Lyberg et al. [23].Today Bradburn [24] (p.94) laments that "the challenges confronting the survey researcher are dominated by the difficulty in locating sample persons and getting them to respond at all."This reluctance to respond has spawned "Suspicious Supervisors and Suspect surveys [ . . .] preventing data fabrication is a widely understood challenge among survey professionals that is seldom discussed publicly" [36].
Data analytics.Here latent regression slopes over 28 billion values are read out in Lemmas 6 and 7 and computed by Stata Commands (4) and ( 5).This computation is justified by the theory in Section 3, which derives latent Chinese indexes as first moments of unobservable yearly distributions.
Lemma 6, implemented by Command (4), reveals the effect of globalization on domestic credit.The slope 0.806 of D on G, with R 2 = 0.650, shows that Chomskyan globalization has exogenously increased Chinese domestic credit over the period from 1992-2013.Table 5 then shows that the endogenous effect of domestic credit and the exogenous impact of Chomskyan globalization account for almost 70% of the variance in Chinese per capita GDP.

Conclusions
Unidimensional index theory weights economic indicators so as to maximize the internal consistency of their societal indexes.This approach differs from indexing that weights indicators a priori or that maximizes the prediction of external criteria such as growth.
The present results demonstrate Chomskyan globalization and domestic credit as strong exogenous and endogenous predictors of per capita GDP in China.These encouraging findings, easily extendable to other nations, are brought by two new macro indexes with assured unidimensionality.In the future, other economic indicators, discovered from Big Data [37][38][39][40], can be input to Commands (2) and (3) to quality assure other indexes.The discovery of new unidimensional indexes, facilitated by cooperating governments, the United Nations, the World Bank, the International

1 .
2 and 3.3 is written for the six globalization indicators in Section 2.1..4 is written for globalization, domestic credit, and per capita GDP, whose indicators are in Sections 2.1, 2In year t, China's globalization indicator G tj (j = 1, …, 6) induces a latent idiosyncratic ij on individual i = 1, …, Nt, where Nt is China's population size in year t = 1992, …, 2013.

Lemma 4 .
Due to Corollary 2, (pp. 536-544), ernal index consistency.This approach differs hich weight indicators a priori.It also differs cators to maximize the prediction of external he six globalization indicators in Section 2.1.t, and per capita GDP, whose indicators are tor G tj (j = 1, …, 6) induces a latent idiosyncratic pulation size in year t = 1992, …, 2013.

. 2
and 3.3 is written for the six globalization indicators in Section 2.1.alization, domestic credit, and per capita GDP, whose indicators are and 2.3.s China's globalization indicator G tj (j = 1, …, 6) induces a latent idiosyncratic , Nt, where Nt is China's population size in year t = 1992, …, 2013.

1 .
2 and 3.3 is written for the six globalization indicators in Section 2.1.n 3.4 is written for globalization, domestic credit, and per capita GDP, whose indicators are bed in Sections 2.1, 2.2, and 2.3.tent Principal Components ntial Axiom In year t, China's globalization indicator G tj (j = 1, …, 6) induces a latent idiosyncratic Gtij on individual i = 1, …, Nt, where Nt is China's population size in year t = 1992, …, 2013.

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homogeneity signifies a broader class of latent multi-year distributions supporting the manifest indexes and slopes in Sections 3.2-3.4.Thus, the class of www.mdpi.com/journal/mcana esville, FL 32611-7150, USA; y 2017 as to maximize their internal re extracted here from Swiss tal indicators for China.These course to survey sampling or zation and domestic credit as ita GDP.These encouraging societal indexes with assured omponents and regression; per lity assurance; ɷ-homogeneity al Minotaur, receiving foreign nference in 1944, near the end , 2013.The optional qualifier [fweight = popt] gives the Nt-weighted slope G T D/G T G.This manifest slope equals the latent slope Z T Y/Z T Z when the within-year covariance matrix of Y and Z is i: 10.3390/mca22010013 www.mdpi.com/journal/mcahomed ccepted: 4 January 2017; Published: 24 January 2017 omponent combines several indicators so as to maximize their internal a construct.First principal components are extracted here from Swiss rld Bank datasets containing yearly societal indicators for China.These ulation-weighted regressions without recourse to survey sampling or results demonstrate Chomskyan globalization and domestic credit as ogenous predictors of Chinese per capita GDP.These encouraging to other nations, are brought by two new societal indexes with assured alization; domestic credit; latent principal-components and regression; per ighted indexes and regression slopes; quality assurance; ɷ-homogeneity [7][7]notes that Chinese government policy is now "designed to accelerate formation of the Chinese economic model, improve livelihoods, and raise domestic tion.[...] If successful, this would ultimately prove to […] contribute significantly to strong, , and balanced global growth."The importance of sustained GDP growth has also been ed by the Leeds UK Steady State Economy Conference 2is the reciprocal of the first eigenvalue of (r jk ), then the first latent principal component Z is also standardized with mean zero and variance one over i = 1, . . ., N t and t = 1992, . . ., 2013.Corollary 4. Z = Z b + Z w , where Z b , with variance (1 +

with variance ensional Indexes for China
[2]lored the vindictive Versailles Treaty at the end of World War I and d States in the Great Depression, only to be dismissed at Bretton Woods by eynes predicted that "a dollar-backed fixed exchange rate system would create down the road […] that would […] cause […] trade imbalances to grow with, fects first upon the deficit countries and then upon everyone else"[2](p.10).misadventure is described by Noam Chomsky as technical globalization, which f liberal and protectionist measures and many related to investor rights, not o serve the interests of investors, financial institutions, and other centers
3 is written for the six globalization indicators in Section 2.1.
notes that Chinese government policy is now "designed to accelerate ansformation of the Chinese economic model, improve livelihoods, and raise domestic mption.[...] If successful, this would ultimately prove to […] contribute significantly to strong, ned, and balanced global growth."The importance of sustained GDP growth has also been asized by the Leeds UK Steady State Economy Conference

Table 2
details the internal index consistency demonstrated in Table

Table 2 .
Components of the first principal component for globalization.Notes: the sum of the squared loadings equals the first eigenvalue in Table1.The scoring eigenvector is a scalar multiple of the loadings eigenvector.The sum of the squared scoring coefficients is the reciprocal of the first eigenvalue in Table1.

Table 3 .
Eigenvalues for domestic credit.

Table 4 .
Eigenvectors of the first principal component of domestic credit.

Table 5 .
Regression effects on per capita GDP.