Should production function parameters be time-varying?

[jdebacker]

Several users of OG-Core have been interested in simulating structural transformation. That is somewhat difficult in a stationarized model like OG-Core. But it might help if we could allow time-varying parameters in the production function which could account for a transition to greater capital intensity in production (for example).

@SeaCelo Does this seem reasonable from the perspective of someone who's thought more about models of structural transformation?

[marcelolafleur]

@jdebacker This is a great issue to work on. My understanding of the literature is that there are basically four mechanisms for modeling structural transformation:

1. Differential sectoral TFP growth: reallocation across sectors driven by uneven productivity growth and elasticities of substitution in demand.
2. Differential sectoral capital intensity, where when sectors have different gamma and economy-wide capital deepening reallocates factors toward the less capital-intensive sector.
3. Non-homothetic preferences where demand composition shifts as income grows.
4. Factor-biased technical change within a sector, where capital-augmenting productivity rises relative to labor-augmenting productivity, making capital share trend up (if epsilon>1).

1, 2, 3 seem to have some mechanisms in og-core. 4 seems more difficult because we don't have industry factor productivity variables. I think?

But there are some interpretation problems that arise. The one that seems to matter most is that if we go away from a cobb-douglas form, gamma is read as a distribution parameter, not capital share. So maybe this would need to be limited to epsilon=1 to make the calibration interpretable. Otherwise we would need to create factor-specific productivity variables (A_k and A_L).

I would start to think to start with a sectoral story before adding production parameters, leaning on the industry structure and working on time-varying Z_m, alpha, and different gamma_m. This is a bit of what we simulated in OG-ETH, but we can try to add these, push the limits and see how the model behaves.

Then I think it makes sense to vary gamma, gamma_g, epsilon with time as you propose. This is flexible and lets us fit to a country calibration of a rising capital share, etc. I dont' know what it means for the expressions in firm.py? get_KLratio for example uses gamma and epsilon, so they need to get indexed for each period? Not sure how feasible this is but tax rates already do that.

A deeper and more correct theoretical change would be to create three new productivities per industry and time: A_k, A_L, and A_Kg. Probably a big change?

But then we can also do a demand-side channel by varying alpha_c? And/or vary the IO matrix (exogenously), though I don't know how that would mirror/conflict with the factor changes above.

Not sure how to go from here. Probably needs some careful look at the theory?