1. We note in passing here that for both countries there are several 'mini-breaks' that suggest the possibility of re-calibration of the model parameters. This leads, in practice, to a series of 'mini-models' covering as few as 20 or 30 years. However, an obvious constraint that is impossible to incorporate explicitly in the mathematical optimization process is the need for each variable to be continuous across breaks. Ignoring that condition leads to extremely implausible results.

2. However, the very long-run relationship, as reflected by the error-correction term, might be interpreted in this way (Stern 2000).

3. The literature of Granger-causation includes studies for a number of other countries, such as Taiwan, Korea, Singapore and the Philippines. However, the developmental history of those countries is so different from the US and Japan that we hesitate to draw any conclusions from them.

4. One reason for the surge in private savings was the traditional 13th month end-of-year 'bonus', much of which went into the postal savings system, despite low interest rates. More important was the role of the Japan Development Bank, which provided cheap capital to industry - especially coal, electric power, steel and ship-building - from the Fiscal Investment and Loan Plan (FILP), which controlled the postal savings as well as other pools of capital. FILP controlled more than four times the capital of the world's largest private bank at one time. Perhaps the most important device was the policy, begun in 1954, of 'over-loaning', which enabled many firms to borrow more than their net worth from local banks, which in turn over-borrowed from the Bank of Japan (Wikipedia 2006). This gave the Bank of Japan total control over the entire financial system of the country. A further partial explanation of the phenomenon was the tremendous increase in Tokyo land prices, followed by the painful collapse in 1992. Land values were included as part of companies' capital assets, and of course many loans were secured by land values. The over-loaning policy was unsustainable, of course, and it led to a huge non-performing loan 'overhang' that was never accurately measured (because of leverage effects), but was still estimated to be in excess of $500 billion, as of 2005. Economic growth in Japan averaged only 1 percent per year from 1993 through 2005, largely because of the banks' reluctance to make new loans.

5. There is an extensive literature on this issue, covering a number of different countries and time periods. The older literature has been summarized by Stern (1993) and reviewed again by Stern in a more recent paper (2000). The earlier papers, mainly based on bi-variate models, were generally inconclusive or the results were not statistically significant. Stern's (1993) paper reached a more robust conclusion, based on a multivariate analysis in which energy quality was taken into account (based on prior work by several authors: Jorgenson 1984; Hall et al. 1986; Kaufmann 1994). Energy quality, as defined by Hall et al., defines a hierarchy of qualities, with firewood and coal at the bottom, followed by crude oil, refined petroleum products, natural gas, and electricity, rated by relative price per unit of heat production. This scheme resembles our term 'useful work' insofar as it gives electricity a much higher quality rating than coal or crude oil. Using this scheme, Stern (1993) found that Granger-causality ran from energy consumption to GDP.

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