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There doesn't appear to be any empirical justification for anything the author has done here. Does anyone really believe that 1/ the "stock' of ideas can be measured by a real number and 2/ national output is proportional to some power of the "stock" of ideas?

Like, how do you even measure an idea? The paper feels like the author has done a load of maths and shoehorned one particular interpretation onto his equations.






That's exactly what he has done and there is nothing wrong with that when it's done right (Charles I. Jones is a top man).

>Does anyone really believe that 1/ the "stock' of ideas can be measured by a real number and 2/ national output is proportional to some power of the "stock" of ideas?

System dynamics can be modeled with numbers that can never be measured or are hard to measure. The exact number of working hours and capital spend to produce innovation is hard to measure and approximations (like what companies announce or number of patents) don't capture the whole picture. It's still reasonable to assume that the number exists.

Optimal taxation and economic growth are big subjects and this paper is not trying to solve it or propose a policy. The paper explores the dynamics of taxation and growth under three conditions mathematically ignoring the rest. Trying to see how big effects small changes can have is interesting.


> That's exactly what he has done and there is nothing wrong with that when it's done right (Charles I. Jones is a top man).

That sounds like an argument from authority to me. If he decides to use the form Y = A^b L and I decide to use, say, a confluent hypergeometric function, who's to say who is correct?


> who's to say who is correct?

Nobody. My friend studied econometry. I was appaled to hear that they just take some real process, assume it's governed by some equation then massage all the maths they can out of it.

They consider different equation for the same process (although they usually have favorite one) and never bother themselves with proving if any of them is actually reflected in reality of said process.

It's basically philosophy for people that can do some math.

They also use the math without deep understanding of it (sort of cargo cultishly). That I know because I worked for a prof and a post docs of econonometry on some project later.


> who's to say who is correct?

Someone who knows the economic growth theory better than I do. I have studied growth theory maybe 16-20 hours total. I'm not humble guy but I know I don't have the ability to join the debate and argue against. My hope is to learn the gist of the paper. In my comments I didn't try to argue for or against, I was trying to describe what the article is about.

Assuming that you are random guy in the internet who suffers from insomnia, I think your level of knowledge is even smaller than mine.

> If he decides to use the form Y = A^b L

That form is not his idea. It's very basic for all steady-state growth models. These models require strong assumptions like Cobb-Douglas production function, labor-augmenting technological growth and linear differential equation (only asymptotic requirement). To go trough all the assumptions would require a seminar.


Ok, let me try this again. Have you, (presumably) an economics student, ever seen an empirical justification for a Cobb-Douglas production function? Would I see such a justification if I opened, say, Mankiw's textbook?

If not, how do you know the assumptions are reasonable?


> Would I see such a justification if I opened, say, Mankiw's textbook?

Yes. Starting page 58. Cobb–Douglas was derived to match empirical observations (constant factor share, constant capital and labor share) and it was proved to have some nice properties.

Note that Cobb–Douglas only approximately true starting point. It does not capture everything. For example capital and labor shares are not completely constant. The simplicity of the function makes it useful and it's taught in basic econ. classes because it holds true well enough. You need slightly more complex models or relax the function for some stuff.


Ok, now we're getting somewhere. Mankiw says [0]:

Paul Douglas was a U.S. senator from Illinois from 1949 to 1966. In 1927, however, when he was still a professor of economics, he noticed a surprising fact: the division of national income between capital and labor had been roughly constant over a long period. In other words, as the economy grew more prosperous over time, the total income of workers and the total income of capital owners grew at almost exactly the same rate.

Douglas' evidence isn't actually presented in Mankiw, it's just stated as fact: do note that I asked for empirical evidence in my earlier post. The observations are over 90 years old, and the government didn't even collate national statistics in the 1920s. Do they still hold? Do they hold in non-US countries?

I'm not these modelling choices (cobb-douglas above, and the assumptions in TFA) are wrong, I'm saying that they're unjustified.

[0] http://irfanlal.yolasite.com/resources/N.%20Gregory%20Mankiw...




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