A. Cuñat 1 R. Zymek 2

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1 1 2 1 University of Vienna and CESifo, alejandro.cunat@univie.ac.at 2 University of Edinburgh and CESifo, robert.zymek@ed.ac.uk

2 and Outline accounting: quantitative assessment of the contribution of measurable production factors and unmeasurable productivity to income. Benchmark aggregate production/income function: Y n = A n K α n H 1 α n Main result: cross-country variation in aggregate productivity (A n ) much more important than factor endowments (K n, H n ) for understanding the cross-country variation in incomes.

3 and Outline As of now, the answer to the development-accounting question do observed differences in the factors employed in production explain most of the cross-country variation in income is: no, way no. Francesco Caselli, 2005, for Cross-Country Income Differences, Handbook of Economic Growth

4 and Outline Aggregate income function in the open economy: Y n = F n A n K α n H 1 α n F n captures the price of n s output relative to the price of all outputs absorbed in n s final consumption. Depends on bilateral trade determinants : {γ n n} n,n all countries factor endowments: {K n, H n } n distribution of expenditure: {T n } n Picture We calibrate a many-country trade model with data from the world input output database (WIOD) to back out F n across 40 major economies. We perform counterfactuals illustrating the effect on countries real incomes (via F n ) of changes in {T n } n and {γ n n} n,n.

5 and Outline Preview of Results: 1 The standard development accounting framework attributes approx. 25% of the variation in incomes among our sample economies to measurable production factors, {K n, H n } n. 2 Our augmented framework attributes at least 50% of the variation in incomes to measurables, {K n, H n, F n } n. It reduces reliance on implied TFP, {A n } n, by more than half. 3 Counterfactuals consistent with earlier studies: small transfer effects. (Dekle et al. 2007, 2008) sizeable gains from trade. (Waugh, 2010)

6 and Outline Related Literature: 1 accounting: Hall and Jones (1999), Hsieh and Klenow (2010), Caselli (2005, 2015). 2 Factor bias of technology in open economies: Fadinger (2011), Morrow and Trefler (2014). 3 trade and income: Eaton and Kortum (2002), Dekle et al. (2007, 2008), Waugh (2010), Feenstra et al. (2009, 2015). 4 Income differences from domestic input-output structure: Jones (2011), Fadinger et al. (2015), Grobovšek (2015). 5 input-output linkages and business cycles: Bems, Johnson and Yi (2011), Johnson and Noguera (2012), Johnson (2013), Bems (2014), Duval et al. (2015).

7 and Outline and Outline 4 1 Special Case (θ 0) 2 General Case (θ > 0)

8 Static many-country quantitative trade model: 1 Gains from trade due to Ricardian comparative advantage (productivity differences): 1 Armington model Details 2 Eaton-Kortum model Details 2 Production of goods is Cobb-Douglas in physical and human capital (physical capital share α). 3 Constant elasticity of trade flows with respect to trade costs (trade elasticity θ). 4 Country-n trade deficit is captured by transfer T n ; n T n = 0. Real GDP in country n (at consumer prices): Y n r nk n + w n L n P n.

9 1) From Cobb-Douglas production: r n K n + w n L n = 2) From Armington/Eaton-Kortum trade: ) 1 α 1 ( rn ) ( α wn hn 1 α Kn α Hn 1 α α 1 α. }{{} f n Share of country-n value added in country-n consumption: v n n Consumer prices: γ n nf θ n n γ n nf θ γ n n > 0, γ n n = 1, n n P n = 1 A n ( n γ n nf θ n ) 1 θ, where {γ n n} n n captures determinants of bilateral trade.

10 Expression for development accounting: ln y n = ln k α n h 1 α n }{{} ln y ED n f n + ln ( n γ n nf θ n ) 1 θ }{{} ln F n }{{} ln y EL n + ln A n where y n = Y n /L n, k n = K n /L n.

11 Value-added linkages: Then: v n n γ n nf θ n n γ n nf θ n. (1) f n Kn α Hn 1 α = ( v nn fn Kn α H1 α n + T ) n. (2) n Choosing the factor cost of country N as the numeraire, f N = 1. (3) Given (1)-(3); values for α, θ; data {K n, H n, {v n n} n, T n } n, we can: solve for {f n } n, find {γ n n} n,n such that {v n n} n,n matched perfectly.

12 Data Sources: Incomes and production factors, {Y n, K n, L n } n : Penn World Tables 9.0, methodology as in Caselli (2005). Labour productivity, {h n } n : Barro and Lee (2010), methodology as in Caselli (2005). VA linkages, {v n n} n,n, trade balances {T n} n World Input-Output Database: Timmer et al. (2012). international input-output table covering 40 broad use categories (35 industries, 5 final sectors) Example 17 years: economies (plus Rest of the World ): Australia, Austria, Belgium, Brazil, Bulgaria, Canada, China, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, India, Indonesia, Ireland, Italy, Japan, Korea, Latvia, Lithuania, Luxembourg, Malta, Mexico, Netherlands, Poland, Portugal, Romania, Russia, Slovak Republic, Slovenia, Spain, Sweden, Taiwan, Turkey, UK, US.

13 : Year Country n' AUS AUT BEL BGR BRA CAN CHN CYP CZE DEU DNK ESP EST FIN FRA GBR GRC HUN IDN IND IRL ITA JPN KOR LTU LUX LVA MEX MLT NLD POL PRT ROU RUS SVK SVN SWE TUR TWN USA RoW Country n AUS AUT BEL BGR BRA CAN CHN CYP CZE DEU DNK ESP EST FIN FRA GBR GRC HUN IDN IND IRL ITA JPN KOR LTU LUX LVA MEX MLT NLD POL PRT ROU RUS SVK SVN SWE TUR TWN USA RoW Share of country-n' value added in country-n final use (''v_n'n'') Off-diagonal entries: - min = med = max =.121 Diagonal entries: - min = med = max =.895

14 : Years Year Share of country-n' VA in country-n final use Year 1996 Year Share of country-n VA in country-n final use Year 1996

15 4 : θ 0 ln y n ln k α n h 1 α n }{{} + ln [ ( ) α ( ) ] 1 α vn n u n (t) Kn Hn u n n (t) K n H n }{{} Details + ln A n ln y ED n ln F n }{{} ln y EL n Var (ln y n ) = Var ( ) ln yn E + Var (ln An ) + 2Cov ( ) ln yn E, ln A n Discuss success Var ( ) ln yn E Var (ln y n ) ignorance Var (ln A n) Var (ln y n )

16 4 : θ 0 Year 2006: 1996 Graph D L (θ 0) (θ 0) Var (ln y n ) Var ( ) ln yn E Var (ln A n ) success ignorance Caselli (2005) finds values of success ranging from.23 (Europe) to.47 (Americas) in different subsamples for the year Magnitudes are similar for other years between 1995 and 2011.

17 4 : θ 0 Year 2006: 1996 Graph D L (θ 0) (θ 0) Var (ln y n ) Var ( ) ln yn E Var (ln A n ) success ignorance Caselli (2005) finds values of success ranging from.23 (Europe) to.47 (Americas) in different subsamples for the year Magnitudes are similar for other years between 1995 and 2011.

18 4 : θ 0 Log factor cost (numeraire: USA = 0) IND IDN CHN Country factor cost BRA BGR ROU PRT LUX IRL DNK FIN FRA USA GBR AUT AUS BEL CAN ITA JPN SWE NLD ESP DEU CYP GRC TUR MLT MEX SVN KOR TWN EST LTU LVA POL HUN SVK CZE RUS Log source factor cost index Weighted source factor costs IRL USA LUX DNK FRA GBR JPN FIN CAN ITA SWE AUT AUS BEL ESP DEU CYP NLD GRC PRT MLT MEX SVN TUR TWN EST KOR LVA POL LTU HUN SVK CZE ROU BGR BRA RUS IDN CHN IND Log GDP per worker theta -> Log GDP per worker theta -> 0

19 4 : θ 0 IND CHN IDN BRA BGR RUS ROU LVA EST CZE SVK HUN MEX POL SVN LTU KOR JPN PRT MLT GRC DEU SWE DNK CAN ESP FIN AUS CYP TUR BEL ITA FRA NLD AUT GBR USA TWN IRL LUX Implied log TFP Dom. factors only Dom. factors and VA linkages

20 4 : θ > 0 What is the right value for θ? The development-accounting expression above is derived from standard quantitative trade models. In these models, the parameter θ corresponds to the gross trade elasticity. Armington (Backus et al., 1994): subst. elasticity - 1 = θ = 1.5 Eaton and Kortum (2002): θ = 8 Simonovska and Waugh (2014): θ = 4. We present results for different values of θ (with θ = 4 as our preferred value).

21 4 : θ > 0 Year 2006: 1996 success ignorance theta theta Dom. fact. only...and VA links Dom. fact. only...and VA links

22 4 : θ > 0 Log factor cost (numeraire: USA = 0) IND Country factor cost LUX IRL DNK FIN FRA USA GBR AUT AUS BEL CAN ITA JPN SWE NLD ESP DEU CYP GRC PRT TUR MLT MEX SVN KOR TWN EST LTU LVA POL HUN SVK CZE ROU BRA BGR RUS IDN CHN Log source factor cost index Weighted source factor costs IND IDN CHN BRABGR ROURUS MEX LVA EST POLPRT LTU HUN TUR SVKSVN CZE KOR MLTNLD GRC JPN ESP DNK FIN DEU CAN ITA SWE CYP FRA AUT GBR TWNUSA AUS BEL IRL LUX IRL USA LUX DNK FRA GBR JPN FIN CAN ITA SWE AUT AUS BEL ESP DEU CYP NLD GRC PRT MLT MEX SVN TUR TWN EST KOR LVA POL LTU HUN SVK CZE ROU BGR BRA RUS IDN CHN IND Log GDP per worker Log GDP per worker theta -> 0 theta -> theta -> 0 theta ->

23 4 : θ > 0 IND CHN IDN BRA BGR RUS ROU LVA EST CZE SVK HUN MEX POL SVN LTU KOR JPN PRT MLT GRC DEU SWE DNK CAN ESP FIN AUS CYP TUR BEL ITA FRA NLD AUT GBR USA TWN IRL LUX Implied log TFP Dom. factors only Dom. factors and VA linkages

24 4 : CGDP e n/cgdp o n Feenstra et al. (2015) suggest that for open economies: ln y n = ln G n + ln k α n h 1 α n + ln A n, where G n CGDP e n /CGDP o n, and CGDP e n is expenditure side real GDP (= Y n ). CGDP o n is output side real GDP (new since PWT 8.0!). They find little improvement in success and ignorance. Based on the PWT definition of CGDP o n, our model implies: G n = γ 1 θ nn F n, where F n f n / ( n γ n nf θ ) 1 θ n ; and γ 1 θ nn > 1 represents the wedge between the consumer and producer price of country-n output. Comparison

25 4 : Summary Incorporating international linkages into development accounting reduces our reliance on unmeasured TFP in explaining income differences between countries. Instead, we rely on broadly defined trade determinants : {γ n n} n,n, where {γ n n} n,n technology, preferences, trade costs. 2...variation in {γ n n} n,n across countries can be disciplined with (trade) data! New focus (for the future!): Given value-added linkages, international income differences are easier to explain. What are the fundamental forces, captured by {γ n n} n,n, which shape value-added linkages?

26 (θ = 4.0) 1 Balanced Trade 1 Impact on per-worker real income Show 2 Impact on per-worker real consumption Show 2 Autarky 1 Impact on per-worker real income Show 2 Autarky losses vs. relative factor costs Show

27

28 and Outline c " (2), q " (2) Production Consumption c " (1), q " (1) Back

29 2 Armington Model There are N countries, each producing a unique good. Representative agent in n maximises: s.t. C n = A n [ n ω 1 1+θ n n c θ 1+θ n n ] 1+θ θ n p n nc n n r n K n + w n L n + T n, Country n produces its good with the technology: q n = Z n K α n (h n L n ) 1 α. θ > 0, ω n n 0. T n = 0. n Back Goods and factor markets are perfectly competitive. trade barriers lead to price wedges: τ n n 1.

30 2 Eaton-Kortum Model There are N countries. Representative agent in n maximises: s.t. 1 0 C n = A n [ 1 0 ] σ c n (i) σ 1 σ 1 σ di p n (i) c n (i) di = r n K n + w n L n + T n, σ 0. T n = 0. Country n can produce good i for n with the technology: { q n n (i) = Z n n (i) (1 β n) 1+θ [K 1 n n (i) α H n n (i) 1 α] 1+θ θ + β n 1 1+θ n where Q n n(i) has same form as C n ; and Z n n (i) is drawn from: Pr(Z n n Z) = e ω n n Z θ ω n n 0 θ > 0. Back } 1+θ Q n n (i) 1+θ θ θ, Goods and factor markets are perfectly competitive. trade barriers lead to price wedges: τ n n 1.

31 World Input-Output Table for a given year: Supply from countryindustries Country 1 Country N Gross output Value added Industry 1 Industry S Industry 1 Industry S Industry 1 Country 1 Use by country-industries Industry S Industry 1 Country N Industry S Final use by countries Country Country 1 N Back

32 Global Value-Chain Table for a given year: Value added from countries Country 1 Country N Gross output Value added Country 1 Final goods shipped by country-industries Industry Industry 1 S Country N Country 1 Country N Final use by countries Country Country 1 N Back

33 : Year Country n' AUS AUT BEL BGR BRA CAN CHN CYP CZE DEU DNK ESP EST FIN FRA GBR GRC HUN IDN IND IRL ITA JPN KOR LTU LUX LVA MEX MLT NLD POL PRT ROU RUS SVK SVN SWE TUR TWN USA RoW Country n AUS AUT BEL BGR BRA CAN CHN CYP CZE DEU DNK ESP EST FIN FRA GBR GRC HUN IDN IND IRL ITA JPN KOR LTU LUX LVA MEX MLT NLD POL PRT ROU RUS SVK SVN SWE TUR TWN USA RoW Share of country-n' value added in country-n final use (''v_n'n'') Off-diagonal entries: - min = med = max =.128 Diagonal entries: - min = med = max =.923

34 4 : θ 0 We can write as where f 1 K α 1 H1 α 1. f N 1 K α N 1 H1 α N 1 V = and we define f n Kn α Hn 1 α = ( v nn fn Kn α H1 α n + T ) n n = (I V ) 1 [(V v.n 1) t + v.n ] K α N H 1 α N, v 11 v 1N v N 1,1 v N 1,N 1 v.n = v 1N. v N 1,N 1 as an N 1 row vector of ones t = { }. T 1 /KN αh1 α N,..., T N 1 /KN αh1 α Back N

35 4 : success and ignorance ln y n = ln yn ED + ln F n +ln A n }{{} ln A ln y ṅ n ln yn E. Var (ln F n ) > 0 ln yn EL success: Var ( ln y EL n ) = Var ( ln yn ED ) + Var (ln Fn ) + 2Cov ( ln yn ED ), ln F n Including F n will raise success unless Cov ( ) ln yn ED, ln F n is too negative! ignorance: Var ( ln A L ) n = Var (ln yn ) + Var ( ln yn ED ) + Var (ln Fn ) +2Cov ( ln yn ED ) (, ln F n 2Cov ln yn, ln yn ED ) 2Cov (ln yn, ln F n ) Including F n will lower ignorance only if: Cov ( ) ln yn ED, ln F n is low Cov (ln y n, ln F n ) is high Back

36 4 : θ 0 Year 1996: 2006 D L (θ 0) (θ 0) Var (ln y n ) Var ( ) ln yn E Var (ln A n ) success ignorance Caselli (2005) finds values of success ranging from.23 (Europe) to.47 (Americas) in different subsamples for the year Magnitudes are similar for other years between 1995 and 2011.

37 4 : θ 0 Log GDP per worker Domestic factors only IND BRA CHN IDN LUX USA IRL TWN ITA GBR NLD AUT FRA CYP CAN AUS BEL FIN DNK DEU SWE MLT ESP GRC JPN SVN KOR PRT CZE TUR HUN SVK LTU POL EST MEX LVA RUS ROU BGR Explained component Slope = 1.9 (.08) Log GDP per worker Domestic factors and VA linkages (theta -> 0) IND CHN IDN LUX USA IRL TWN CYP ITA FRA GBR NLD CAN AUT AUS BEL FIN DEU DNK SWE MLT GRC ESP JPN SVN KOR PRT CZE TUR HUN SVK POL LTU EST MEX LVA RUS ROU BGR BRA Explained component Slope = 1.3 (.04) Back

38 4 : θ > 0 Year 1996: 2006 success ignorance theta theta Dom. fact. only...and VA links Dom. fact. only...and VA links

39 4 : CGDP e n/cgdp o n Corr. PWT/FIT CZ (θ = 4.0) lng n lnf n lng n PWT/FIT lng n 1.00 lnf n CZ (.26) PWT/FIT (θ = 4.0) lng n.52*** (.00) (.85) PWT/FIT Dev. Acc. ln G n ln F n PWT/FIT CZ (θ = 4.0) CZ (θ = 4.0) Var (ln y n ) ) ) Var ( ln yn E Var ( ln A E n success ignorance Back

40 : No Trade Imbalances (θ = 4.0) Log change in real GDP (PPP) Back CYP LVA GRC BGR ROU LTU MLT PRT TUR EST ESP USA HUN RoW IND ITA MEX SVK SVN GBR FRA POL AUS JPN CAN CZE AUT BRA DNK KOR IDN FIN BEL TWN CHN DEU SWE NLD IRL RUS LUX

41 : No Trade Imbalances (θ = 4.0) Log change in real consumption (PPP) Back CYP LVA GRC BGR ROU LTU MLT PRT TUR EST ESP USA HUN RoW IND ITA MEX SVK SVN GBR FRA POL AUS JPN CAN CZE AUT BRA DNK KOR IDN FIN BEL TWN CHN DEU SWE NLD IRL RUS LUX

42 : Autarky (θ = 4.0) Log change in real GDP (PPP) Back LUX MLT IRL SVK HUN CZE BEL EST BGR SVN NLD LTU TWN AUT LVA SWE DNK POL FIN RoW DEU KOR ROU CAN CYP PRT RUS CHN IDN GBR ITA ESP FRA TUR AUS MEX GRC IND BRA JPN USA

43 : Autarky (θ = 4.0) Log change in real GDP (PPP) as a result of autarky Back IND CHN IDN BGR RUS RoW BRA USA JPN MEX TUR GRC ESP AUS FRA ITA GBR PRTCYP ROU KOR CAN DEU POL FIN SWE DNK LVA AUT LTUTWN NLD EST SVN BEL CZEHUN SVK Log >relative factor cost< term MLT IRL LUX

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