China’s Growth: Convergence Plus

China has been enjoying growth rates near 10% for several years as compared the U.S. growth rates over the past five years, which have averaged less than 3%. Anyone who accepts the premise of the convergence hypothesis might not be surprised:

The absolute convergence hypothesis, posits the following: consider a group of countries, all of which have access to the same technology … the same population growth rate (n) and the same savings propensity (s), and only differ in terms of their initial capital-labor ratio, k. Then, we should expect all countries to converge to the same steady-state capital-labor ratio, output per capita and consumption per capita (k*, y*, c*) and, of course, the same growth rate (n) … Notice that this means that the poor country will grow relatively fast (capital and output grow faster than n), while the rich nation will grow quite slowly (capital and output grow slower than n).

Modern growth economists will argue that we have deepened our understanding of growth since Robert Solow proposed his seminal model almost 50 years ago. I’ll go through a simple exercise of the Solow model in a moment – but let me thank Mark Thoma for pointing out something interesting from Robert Shiller:

The saving rate in China is the highest of any major country. China’s gross saving rate (the percentage of GDP that is not consumed immediately), which includes both public and private saving, is around 50 percent. By contrast, the saving rate in the United States is the lowest of any major country – roughly 10 percent of GDP. Differences in saving rates must be a major reason that China’s annual economic growth rate is a full six percentage points higher than in the US … the uptrend in saving in China began at around the same time as its family planning policy was implemented in 1979. This prevented the birth rate from rebounding after the Cultural Revolution of 1966-76.

Shiller also tries to explain the observed difference in savings rates, but he also predicts that the Chinese savings rate will eventually decline.

But suppose we calibrated a classroom exercise with two nations: A (America) and C (China). We shall assume both have a savings rate = 9% and growth in effective labor (population growth plus technological growth) = 3%, which would imply a steady state capital-output ratio = 3. Our model is calibrated such that A’s output = $12.6 trillion with a capital stock = $37.8 trillion such that its 300 million citizens supply 300 billion of labor hours (half of the population working 2000 hours per year). The model also assumes a Cobb-Douglas production function with the capital share being 30%. The model for A predicts current output per person = $42,000 per year and output growth also equals 3% per year. Taking the same model for C, let assume population = 1305 million with labor hours supplied = 1.305 trillion but have a capital stock of only $380 billion – which would imply output = $8.87 trillion or $6800 per person with a capital-output ratio equal to 0.0428. This model also has A’s wages being $29.40 per hour, while C’s wages would be $4.76 per hour.

Now if we consider the implications of this model for growth over the next decade, we would see A’s growth staying at 3% per year, while B’s growth would start 43% for the first year, still be as high 11.8% by year 5, and tampering to something over 7% by the end of the decade. The capital-output ratio would have risen to 0.565 by the end of the decade with output per person exceeding $20,000 per year and wages exceeding $14 an hour.

As Shiller notes, the reported savings rate for China is even higher and its population growth has been kept low. The U.S., on the other hand, has suffered from a reduction in its national savings rate. There may be a host of reasons why China’s economy failed to generate increases in output per person that were as high as the simple convergence hypothesis would have predicted. Shiller is pointing out, however, that China is enjoying the benefits of a high savings rates, which could imply even faster convergence.