The Solow Model 3 – Taking the Model to Data
The Solow model is consistent with some aspects of the data on growth but not with other aspects. What do we learn from the consistencies and the inconsistencies?
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So the point about increasing savings rate ought to be really powerful - that's linked to the Big Push theory, isn't it?
I think the Big Push theory is linked to the so-called Poverty-Traps. A poverty-trap in the Solow-Swan model can occur when the production function is somewhat different from the one that we have studied now (the simple k^a). Consider instead a production function that has 3 regions. Region 1, for small levels of k, presents decreasing returns to capital, region 2 (for medium levels of k) presents increasing returns to capital and region 3 (for big levels of k) again decreasing or constant returns. With this production function there can be more than one steady state, in this case, we could have two steady states, one that gets us stuck in region 1 and another somewhere in region 3. If a poor country has this function, the most likely is that they're going to get stuck in the lower steady-state, and the only way that they are going to make it past it is if they receive a massive influx of capital (Big Push) that allows them to escape from this poverty trap. You can find more information in Sala-i-Martin's "Lecture Notes on Economic Growth". http://www.nber.org/papers/w3563.pdf?new_window=1
So at 10:15 you assume that there are competitive markets - (in particular competitive Labour Markets) to compare US and Zambia. NOw to have competitive Labour Markets wouldn't you need to have free movement of labour between the two markets? or Does this w = MPL only require localised competitive labour markets?
The US is notoriously strict about labour movement so this seems to be a dubious assumption to make at this stage.
If I understand the model for individual output correctly reducing n, the number of workers, reduces depreciation and thus output shifts to the right. Does this make sense?
I do not quite understand the very last point of the lecture "If poor countries are poor because they lack capital and skilled labour, then return on capital and skilled labour should be much higher in poor countries."
1. Firstly, I found it hard to find how this assumption comes from the Solow model : in the previous equations, the case is made for the marginal return on skilled labour ( dy/dL = (1 - alpha) * (K/L)^alpha ), that you might find at 11:30 on the video ; but with rather strong assumptions. The case for capital is more straightforward.
2. More importantly, it seems to me that you equate the return in social utility that a country might gain from an extra unit of skilled labour, and the return in cash that this extra skilled unit which happens to be a human being might expect from his job. In your words : Wage = marginal return on extra skilled labour. In my opinion, that is obviously not the case. Take the example of physician in Malawi : in a poor country, he might save valuable lives by hundreds in a year, thus adding huge return ; but his own monetary return will be incomparably low, if you think he might have practised plastic surgery in California... Hence the incentive, not to stay in Malawi.
But maybe is it the main weakness of the Solow model (or at least this version) : not taking into account that capital K as well as skilled labour L might flee from one country to another - that is to say, in poor countries, K is increased by only a fraction of i (= saving rate * production), and L diminishes over time.
Your conclusion here seems a bit broad given that you were specifically looking into whether savings rate could be responsible for differences in GDP per Capita. You had already assumed that A, n, alpha, delta and n were equal for US and Z. But there was no logical or a priori basis for that general assumption.
Yes, if you are looking to see how much of a difference savings rate could make, then you control for the other factors. What the analysis shows is that the savings rate contribution depends on alpha. We can extract real-world alpha examples and these do not appear to allow sufficient flexibility for savings rates to be the majority contributor to the observed real-world differences in GDP per capita. Hence the assumption (or the model) must be incorrect.