1. Capital and global productivity comparisons
Pieter Woltjer*
Robert Inklaar
Daniel Gallardo Albarran

2. Background and objectives
Development Accounting
Proximate Causes  Physical Capital, Human Capital, TFP (Maddison)
Role of inputs in accounting for income differences across countries
Current state of debate:
Physical Capital accounts 10-20% income differences
TFP accounts 50-70%

3. Limited role physical capital?
Weakness in development accounting
Capital assumed to be homogenous unit
Lessons from growth accounting:
Different assets have different user costs and marginal products
I.e. for an identical stock value, a Computer will generally add more to output than a Building (in a single year)
Capital service measure will give greater weight
short-lived assets
assets with rapidly falling prices
both characteristics will drive up cost to hire the asset

4. Update to Penn World Table
New estimates of starting stocks of capital
3 methods: PIM, t*, average
38 countries: long-run investment series <1900
92 countries: investment series >1950 & <1970
77 countries: investment series >1970
Estimates of physical capital
Capital stocks
Capital services

5. Starting stocks: PIM PWT 9.0
1950: Assume Capital/Output (K/Y) ratio of 2.6
PWT 9.1
38 countries  historical investment (I) series from <1900
Use Perpetual Investment Method (PIM) to estimate Capital Stock (K) in 1950
𝐾 𝑖𝑡 = 𝐾 𝑖𝑡−1 1− 𝛿 𝑖 + 𝐼 𝑖𝑡

6. Starting stocks: PIM

7. Starting stocks: t* PWT 9.0
1950-…: Assume Capital/Output (K/Y) ratio of 2.6
PWT 9.1
92 countries  investment from 1950/1970 onwards
Use (arbitrary) K/Y ratio for first year (t0)
Lower bound: 0.5
Upper bound: 4.0
Define t* as year that lower and upper bound converge
Extrapolate K/Y at t* back to t0

8. Example of t* estimate starting K/Y

9. Example of t* estimate starting K/Y

10. Time trend in K/Y ratio Linear regression model
ky ~ 1 + year + countrycode
Estimated Coefficients:
Estimate SE tStat pValue
_______ _______ _____ ___________
(Intercept) e-215
year e-243
Number of observations: 2445, Error degrees of freedom: 2406
Root Mean Squared Error: 0.432
R-squared: 0.701, Adjusted R-Squared 0.697
F-statistic vs. constant model: 149, p-value = 0

11. Example of t* estimate starting K/Y

12. K/Y ratios: new estimates

13. TFP: PWT 9.0 vs 9.1 (Capital Stocks)

14. Capital Services (1)
As opposed to capital stocks, which measure the total value, or wealth of all capital equipment and structures in place, our measure captures the capital service flows derived from these capital assets.
Capital services weight the growth of capital assets by their respective rental prices, whereas capital stocks weight assets by their asset price.

15. Capital Services
User Cost of Capital (UCC) reflects the fact that in equilibrium, an investor is indifferent between two alternatives: either buying a unit of capital at time t-1, collecting a rental fee and then selling the depreciated asset in the next period, or earning a nominal rate of return on a different investment opportunity.
The UCC thus depend on the asset-specific depreciation rates ( 𝛿 𝑖 ), the rate of return ( 𝑟 𝑡 ) and the capital gains or losses from price changes in an alternative investment ( 𝑝 𝑖,𝑡 𝐼 ).

16. Median UCC by asset

17. TFP: PWT 9.0 vs 9.1 (Capital Services)

18. Development Accounting: Contributions of capital, labor and TFP (in 2011)