## Japanese Convergence and Non-Convergence and the Financial Crisis of the Early 1990s

Suppose that you believed in the Solow long-run growth model—that economies converge over time to steady-state growth paths with a speed of convergence determined by the factor shares in the production function, and that the different steady-state growth paths of developed economies at least have different levels determined by accumulation rates and population growth rates but all have a constant growth rate given by the world’s frontier rate of labor-augmenting technological progress.

What can we say about the long-run consequences of the Japanese financial crisis as viewed through this particular lens?

Before the financial crisis that hit the Japanese economy at the start of the 1990s, the simplest possible post-World War II convergence regression, starting with the advent of the Korean War in 1950[1], shows Japan converging to a relative GDP per capita level of 1.05 times the U.S. level with a convergence speed of 0.074/year—closing 7.4% of the gap vis-a-vis the U.S. in an average year.

Growth = 0.0774 − 0.0738(YJ/YUS)

Adding in the years since the financial crisis and rerunning the regression with a post-financial crisis (0,1) dummy variable shows Japan before the crisis behaving the same: converging to a relative GDP per capita level equal to 1.028 of the U.S. at a convergence speed of .077/year—closing 7.7% of the gap vis-a-vis the U.S. in an average year.

With the financial crisis, however, the dummy variable causes the growth regression intercept to shift: Japan is no longer converging to a GDP per capita level of 1.03 times the U.S.. Instead, Japan appears to be converging to a level of 0.77 times the U.S.: Japan appears to be losing ground. At any given relative level of GDP per capita, post-financial crisis Japan’s growth rate is 2.81%/year slower, with a t-statistic of −3.08 and a corresponding marginal significance level of 0.0010.[2]

Growth = 0.0792 − 0.0771(YJ/YUS) - 0.0281(Post-Financial Crisis)

Do we take seriously—or half seriously—what this regression is telling us: that the financial crisis destroyed 25% of Japan’s long-term potential wealth and shifted its long-run Solow steady-state growth path down by that amount (or, alternatively, 29% in the specification that allows not just the intercept but the slope to change with the crisis)?

Do we take serially—or half seriously—the alternative: that Japan was on the path to convergence to U.S. levels of average productivity, that something happened at the start of the 1990s to knock Japan off of convergence to that long-run steady-state growth path and onto convergence to a much lower steady-state growth path, and that the financial crisis was simply the recognition by asset markets that previous expectations of Japan’s convergence to the U.S. growth path were overoptimistic?

Or do we simply abandon the Solow growth model as our lens through which we try to make sense of the long-run growth destinies of different national economics?

If that, what framework do we use to try to organize and make sense of the long-run growth destinies of different national economies, or do we simply retreat into ignorance?

[1] Using annual Penn World Table 7.1 chained real GDP per capita data. https://pwt.sas.upenn.edu/php_site/pwt_index.php

[2] Allowing the slope as well as the intercept of the convergence regression to change with the financial crisis produces a pre-financial crisis equation of

Growth = 0.0773 − 0.0738(YJ/YUS)

with long-run convergence to 1.05 times the U.S. level, and an imprecisely-estimated post-financial crisis convergence equation of:

Growth = 0.1122 − 0.1537(YJ/YUS)

with long-run convergence to 0.73 of the U.S. level.