The main organizing principle in growth economics over the last sixty years :
“balanced growth path”
“Kaldor Facts” 
- The growth rate of output per worker is constant over time
- The rate of return on capital is constant over time
- The share of output paid to capital is constant over time
But not every country has such a consistent trend line.
- a BGP is really a statement about what happens in the long run. Like Germany or Japan, you could be off of the BGP, but will eventually settle into a situation of constant growth rates.
France shows a further departure, not only a shift in the level of the BGP, like Japan, but also a change in the slope,meaning the growth rate was permanently higher.
A paper recently checks 26 countries whether their path of GDP per capita follows a strict BGP:
- a strict BGP is only for the US and Canada
- no for the rest of the OECD and the other Asian countries
If return to capital is measured by take total payments to capital ratio (dividends, rents, or interest)
If measured by bond yields
40-year deviation from 5% between about 1970 and 2010 seems like an abuse of the word “tendency”
Or stock earnings yield.
It looks like a tendency to be around 6-8% over the long run, with a distinct dip in the recent few years.
But for UK and France, return to capital shows some stability over long periods of time.
This looks as if the capital share is rising over the last 40 years for all these countries
The inverse of this is the decline in labor shares. A paper has investigated both if and why this is occurring.
If an economy has a BGP, then what Uzawa indicates is that it either has a very specific production function (Cobb-Douglas) or a very specific rate of progress in capital-augmenting technology (zero)
It feels implausible that the real world actually would have the exact right conditions
GHOS suggest is that human capital growth may be sufficient to break the strict nature of Uzawa’s conditions.
a model of economic growth that doesn’t require Cobb-Douglas production, has a positive growth rate of capital-augmenting technological change, and yet still has a BGP.
A different approach establishes conditions by which the aggregate production function may be Cobb-Douglas, even though the underlying technical production functions of firms are not.
There has been significant shifts of labor between sectors (generally, ag to manufacturing to services) over time in most economies.
For those countries appeared to go from one BGP to another, the existing models are good at capturing the dynamics within each BGP,
but they have no way of explaining why it was that South Korea took off for a different BGP in about 1960, or why France’s growth rate shot up after World War II. These shifts are completely exogenous in these models.
These three conditions are part of the the “Kaldor Facts” established in by Nicolas Kaldor in 1957. These facts were supported by relatively sparse information gleaned from the period running from the late 19th century up to the 1920’s, and for most of them Kaldor ignored major changes that occurred in the Great Depression.
They establish conditions for preferences or production functions that allow for economic activity to wax and wane in different sectors, but in aggregate continues to be consistent with Kaldor’s facts.