Does raising taxes to fund physical capital in an OLG model make sense?

Sorry to ask a non-DSGE modeling question under this category. My question is rather about General OLG modeling (but still macro, so maybe someone has an idea):

The government in my country (Ghana) introduced educational subsidies in 2017, but it is a public debate among policymakers (since then) if that policy will cause an increase in economic growth. I have read the literature, and this debate is also true among academics.

In the same country, Esther Duflo and her co-authors did a randomized control trial of the policy where they subsidized some students (treatment group) but not others (control group). Aggregate growth effects, however, are inconclusive from the results of the paper. More like we don’t know; we have to wait and see.

Then some authors (Fujimoto et al.) use an OLG model (calibrated to Ghana’s economy) to conclude that the policy will raise steady-state GDP by 7%. However, they exclude physical capital from the model.

So I introduce physical capital into the OLG model (calibrated to Ghana’s economy). The results show that the increase in GDP as a result of the policy is not a guarantee. It depends on the tax rate, subsidy rate, and so on.

Some policymakers say we should use that money elsewhere, like investing in physical capital, which kinda makes sense to me. Because currently, our growth rate of human capital (from the PWT dataset) exceeds the growth rate of physical capital. So if \frac{K}{H} is constant in steady-state as endogenous model posits, then we are kinda approaching a lower \frac{K}{H} steady-state in my country. So perhaps, we should spend that money on physical capital, not human capital.

So I want to do that in the OLG model. That is, take the money the government is using to subsidize human capital and give it to firms to subsidize their physical capital accumulation. Does that make sense in an OLG environment? It makes sense to me, but of course, I could be wrong…:). And although I have searched, I have not found a paper that does that. Thanks for any comments.

A couple of thoughts:

  1. The big question with experimental papers is almost always how to extrapolate results to general equilibrium. That’s where the GE modeling typically comes in.
  2. You did not tell us which frictions need to be addressed by the government. A standard growth model will have the economy move to a steady state with K/H constant. Why do you need to subsidize anything here?

Thanks for the reply, Prof. Pfeifer. Sorry for my long reply below.

I am a little confused about what this statement means. But I guess you mean the frictions in the educational system that the government is trying to address? Let me know if it is something else. So some people are poor and cannot afford education (here, secondary education). So the government wants to eliminate that limitation, thus providing free access for all, irrespective of income. Enrolment was 804974, 851312, 880770 (three years before the policy) and 1013005, 1155841, 1249449 (three years after the policy). So there is a little bit of a jump there following the policy.

Yes, K/H is constant in the steady state, but we want to achieve a higher growth rate of output (Y), which is driven by the growth rate of human capital (H) in the OLG model. The growth rate of human capital (H), in turn, is endogenous and is determined by steady-state K/H and other parameters.

Raising taxes to subsidize H can increase the growth rate of output, but it can also hurt it. For example, if you raise taxes too much or, say, the subsidy rate is not large enough (at least from my simulations so far).

What I want to do next in the model is use those taxes (raised from households) to finance physical capital accumulation and not human capital accumulation and compare results. Some policymakers actually have this view. Like the government should abandon financing human capital and rather finance physical capital with that resource. The motivation here is that physical is already too low relative to human capital.

My concern: I have searched the literature, and also, from my macro classes in the past, there wasn’t actually any endogenous model that said, let’s raise taxes to finance physical capital. It was almost always about financing human capital or, say, R&D. So not sure if my attempt to finance physical capital accumulation with taxes here makes sense. I could elaborate more on how I want to do that, but I wanted to know if, at least, it makes sense in the OLG environment to consider physical capital subsidy as an alternative policy to a human capital subsidy (from the government). The goal is the assess the two policies; how it affects the growth rate of output.

What I am saying is: why is there underinvestment into the various forms of capital that the government needs to address? For human capital, the story is usually one of borrowing constraints: people are unable to borrow against their future earning (returns to human capital), because there is no collateral. For physical capital, the market failure is less straightforward. Why is there underinvestment into capital and how can the government address that?
Also note that investment decisions depend on production functions. Higher human capital usually increases the marginal product of capital, making it more attractive to invest into it. Why do you need additional government incentives? You may have a story of insufficient domestic savings to finance all the necessary capital investment. But that is then mostly a story of borrowing from abroad rather than taxing current income to redistribute it.

Oh yeah, I see your point in the above statement.

I agree here. Many authors in my country have blamed it on several things (for e.g., anti-private capital ethos within the bureaucracy, corruption, the culture of Ghana’s political economy, neoliberal policies, and so forth). But yeah you are right, the savings rate is also low (less than 10%) until we found oil in 2011. It has since jumped to about 18-20% (in WDI dataset). But I am quite sure though that the domestic savings rate is still about the same, i.e., below 10%. In a previous work (following the barrier to physical capital accumulation literature), I actually found that it takes both a low savings rate and a high barrier to physical capital accumulation to match the growth rate of Ghana’s declining capital-output ratio. So the reasons why physical capital is low are numerous, which can be summed up into low savings and other barriers. I agree with your statement though that taxing current income to fund physical capital here is not the best in this case. Regarding borrowing from abroad, our debt is pretty high lately, and Fitch and Moody’s downgraded us to ccc and caa2, respectively. So we got some relief from the IMF instead this year. But that is another story, I guess. I understand your point though.

Let’s say the above statement fails in the real world, then government intervention is needed, right? Actually, there is one paper published in the AER titled “The return to capital in Ghana.” The authors find that return to capital is high in Ghana…thus, creating the puzzle; “why does foreign capital not flow from abroad into Ghana.” The authors make some suggestions like financial market frictions; maybe these factors also contribute to why domestic physical capital accumulation is weak in Ghana. So, in this case, perhaps, we may need a government intervention…for example, through taxes? I mean when firms are not able to borrow due to financial market imperfections (in other words, savings does not transform into physical capital investments due to some financial market frictions). Or, in this case, also borrowing from abroad is most preferable?

Yes, you are right here…so borrowing constraints is a feature in the OLG model I use.

In the end it seems to be a quantitative matter. If there are frictions that inhibit both physical and human capital accumulation, both should be addressed and you should pick the low-hanging fruit first.