A little evidence against the AR(1) growth model

My last few posts have complained about the AR(1) lagged growth model (that's the one that says
income per person this year = a * income last year + b * other terms + error term,
a and b being constants) on theoretical grounds. I said that stability might be a problem. Here's a little evidence that it is.

I ran estimates for Niger (a low income country), China (a rapidly growing country), and the US (a large economically leading country) on a growth model like the one above. Income was measured as log of gdp per person, and there was one other term, log of capital investment. I used five year growth periods since 1959, so had ten data points for each. I used OLS to make the whole process quick and easy, so there are bias issues discussed below.

Niger had an autoregressive 'a' coefficient of 0.22, China had 1.04, and the US had 0.84. I Chow-tested the equality of the Niger and US values, getting a p-value of .06. The equality of the US and China means had a p-value of 0.001.

Now using OLS to estimate AR(1) should bias down the coefficients in these small samples, with the US affected more than Niger, and China affected more than the US since closeness to unity increases bias. So the range of 'a' coefficients is likely to be even larger.

I am not sure of the direction of standard deviation bias, and the t-test might not be entirely correct for estimation, but the Chow values are large enough to be confident that the true tests would indicate that the autoregressive parameters are not stable from country to country. Yes, there are a lot of caveats, but my point holds. In fact, inspecting several countries, it doesn't seem that the parameters are stable within countries over time either.