Is growth due to productivity improvement or factor accumulation?

There is an empirical debate whether developing country growth is mainly caused by productivity improvement or factor accumululation. Some of the evidence, theory, and opinions are given in the document here (for example in Table 1 on page 8).

Here is a small theoretical argument why the contributions of both are likely to be of comparable magnitude. It is not complicated but I haven't seen it from anyone else. Suppose output = A.K where A is productivity and K is capital (possibly aggregated across physical and human and other capitals), and A + a.K = b is a budget constraint where a and b are constants. Suppose also that capital suppliers and productivity suppliers are paid roughly the amount they contribute to growth. Then a equals one since A and K are symmetric in the production function so A and K must cost the same. Then output = A.(b - A), and maximising gives A = b/2 (= K). Taking differences over time, the growth contributions of productivity growth and factor accumulation should be the same.

The argument works if the country pays for their productivity improvements. But even if they don't (in the absence of IPRs for example), the costs of technology transfer can be considerable (a famous estimate from the 1970s due to Teece is over half the cost of innovating in the first place if I recall correctly). So even in this case, the costs are comparable to those of renting, and the contribution of productivity improvements will not be far higher.