Saturday, September 28, 2013

Capital in the Penn World Table 8.0

This is another tricky issue with the new Penn World Table (PWT 8.0). In principle it is easy to compute a capital series if we know the level of investments each year, have estimates of the depreciation rate and the initial capital stock. The latter is the most difficult to obtain and cross-country datasets make essentially arbitrary decisions to estimate these starting stocks. The usual approach is to assume that the economy is in the steady state of the Solow model and compute the initial stock from the current level of investment, some growth rate of the economy or capital stock and the rate of depreciation. We are using that for the paper we are writing on the stylized facts of energy and growth. PWT 8.0 instead assumes that all countries had a capital/GDP ratio of 2.6 expressed in units of the local currency in the first year that data is available for that country, which could be anywhere from 1950 to 1990... There is some rationale for this. A regression analysis shows that there is no relation between the level of GDP and capital/GDP ratios in 2005 (Because of depreciation capital stocks in 2005 are not that sensitive to the initial values) and the average is about 2.6.

The interesting thing is that they have separate price series for each country for (output side) GDP (pl_gdpo) and for capital stock (pl_k). These show that in developing countries capital is much more expensive relative to output than it is in the US and other developed countries. This means that a common ratio of 2.6 translates into a real capital/GDP ratio where capital and GDP are both aggregated using US prices that varies across countries and is lower in developing and higher in developed countries. You can compute this as CK/CGDPO. Also, this will mean that there is an extra term in a cross-country Solow growth model which is the capital/output price ratio:

where Y is GDP, K capital, delta is the depreciation rate, s is the saving rate, and pY/pK is the ratio of output to capital prices. In developing countries saving buys less new capital stock per Dollar than it does in developed countries. This would be another reason in the Solow framework for why developing countries are poorer than developed countries. At least, that's what I'm understanding at the moment.

Here are the three different capital-output ratios for China:

The blue line is the ratio at international prices and the red line at constant national prices. These are equal by construction in 2005. The green line is the nominal ratio of dollar values of capital and GDP. This is equal to 2.6 in 1952. The blue line shows the strong capital deepening in China since the late 1980s. The other series do not indicate any capital deepening at all. The discrepancy between the blue and green lines is easy to explain. The price of capital/output relative to the US ratio has fallen from 2.77 in 1952 to 0.74 in 2011 (capital cost 1.39 times the US price in 1952 and 0.46 times in 2011 while output's price changed from 0.5 to 0.61 times the US level). By assumption capital and output have the same price in the US.

So what does the red "constant national prices" series mean? It will deviate from the blue line to the extent that the prices of different types of capital deviate in the country in question from the international price vector. It seems that the two lines tend to track each other much better in developed countries than developing, though India is a clear exception to that rule. For example, if structures are relatively undervalued in China (as would make sense as structures are non-traded) and the capital deepening in China is heavily driven by structures (as the data in this article by Wang and Szirmai support) then the red line will show a much slower increase in capital per unit of GDP than the blue line. 

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