# Accounting For Cross-Country Income Di erences

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1 Accounting For Cross-Country Income Di erences January 2011 () Aggregation January / 10

2 Standard Primal Growth Accounting Aggregate production possibilities frontier: where Change in output is ) output growth: Y t = F (T t, K t, L t ) K t = capital services L t = labour services (total hours?) T t = total factor productivity (residual) Ẏ Y = FK K Y Ẏ = F K K + F L L + F T Ṫ K K + FL L Y L L + FT T Ṫ Y T () Aggregation January / 10

3 Assuming perfect competition and CRS: ) GDP growth: F K = q and F L = w Ẏ Y = α K t K + (1 where α t = q tk t Y t So TFP growth is measured as α t) L L + FT T Ṫ Y T = capital share g = Ẏ Y α t K K (1 α t ) L L,! estimate is only as good as measures of Y, K, L and α () Aggregation January / 10

4 Measuring Capital Growth Capital stock estimates typically use perpetual inventory method: K t = I t + (1 δ)k t 1, where I t = real investment δ = rate of depreciation Successive iteration ) K t = t 1 s=0 where initial capital stock is proxied by (1 δ) s I t s + (1 δ) t K 0 K 0 = I 0 δ () Aggregation January / 10

5 Accounting for self employment To compute labour share, 1 α, National Accounts data on employee compensation are used BUT what about self employment income?,! large component of income in developing countries (Gollin, 2002) Correcting for this, yields estimates across countries that average 0.65 and are not systematically related to income level () Aggregation January / 10

6

7 TFP Growth vs. Factor Accumulation Are di erences in output per worker the result of di erences in costly capital formation or due to di erences in total factor productivity? Early estimates suggested most came from TFP, but others have argued that we should include human as well as physical capital But how do we measure human capital across countries? () Aggregation January / 10

8 Why do Some Countries Produce So Much More Output per Worker than Others? (Hall and Jones, 1999) Aggregate production function for country i: Y i = K α i (A i H i ) 1 α Can be re written as where Y i L i = κ i h i A i, h i = H i κ i = L i Ki Y i = average human capital α 1 α = capital intensity" How much of the cross-country variation in Y i L i by each component can be accounted for () Aggregation January / 10

9 Index of Human Capital Wage per unit of human capital is v i = (1,! wage of indvidual j in country i is H i α)y i w ij = v i h ij,! in logs: log w ij = log v i + log h ij Mincerian wage regressions log w ij = a i + b i s ij + c i X ij + ε ij, () Aggregation January / 10

10 Hall and Jones use index of average human capital: where E i = average schooling. h i = e b i E i Use Mincerian return estimates to capture diminishing returns: b i = 0.13 for average schooling < 4 years = years = 0.07 over 8 years () Aggregation January / 10

11 Table 1: Productivity Calculations: Ratios to U.S. Values Contribution from Country Y/L (K/Y ) α/(1 α) H/L A United States Canada Italy West Germany France United Kingdom Hong Kong Singapore Japan Mexico Argentina U.S.S.R India China Kenya Zaire Average, 127 Countries: Standard Deviation: Correlation w/ Y/L (logs) Correlation w/ A (logs) Note: The elements of this table are the empirical counterparts to the components of equation (3), all measured as ratios to the U.S. values. That is, the first column of data is the product of the other three columns.

12 Figure 1: Productivity and Output per Worker Harrod Neutral Productivity, 1988, U.S.= PRI ITA HKG SAU JOR SGP ESP FRA LUX YEM SYR CAN AUTBEL GBR USA MEX ISLNLD SWECHE DEU BGD VEN AUS ISR GTM MUS BRA DZAPRTBRB OANTTO EGY MLT TUN IRL DNK SYC SURIRN ARG OMN GRC FIN NOR CYP JPN NZL SLE COL PAK URYKOR MAR SLV TUR REUCRI DOM ZAF SUN SWZ MYS FJI COG LKA PERCHL PRY ECU SEN HND THA PAN YUG MOZ NAM RWA BEN CIV BOL GAB HUN MDGGMBHTI CMR NIC IND UGA SDN IDN JAM CSKPOL TCD GHA PNG PHL MLI GIN LSO SOM ROM BWA ZAR CAF KENZWE CPV BDI AGO GUY GNB NGA NER MRT TZA BUR TGO BFA MWI CHN COM ZMB Coeff = StdErr= R2 = Output per Worker, 1988 (in 1985 U.S. Dollars)

13 Main Findings Strong positive correlation between output per worker and TFP Strong positive correlation between average human capital and TFP Most of the di erence between developed and less developed countries is due to TFP di erences,! typical nding of most cross-country accounting exercises () Aggregation January / 10

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