I’m facing an issue with NLSolve. I have two interacting functions that are working well, and I need to adapt them. Let me briefly summarize how the functions are currently set up and what I’m aiming to achieve.
Firstly, I have a function that calculates the government deficit:
function deficit(t) tax_h, tax_l = t, t # Lots of calculations dif_tax = (ep_h * wp_h * tax_h - (eg_h * wg_h)) + (ep_l * wp_l * tax_l - (eg_l * wg_l)) F = [dif_tax] return F end
Then, I’m using another function that incorporates the
deficit function within it, like this:
function solvemodeltax(chute_param, chute_th, chute_tl) chute_t = [chute_th, chute_tl] taxopt = nlsolve(x -> deficit(x), chute_t).zero tax_h = taxopt tax_l = taxopt # Lots of calculations return output end
And this is working fine. However, I’m aiming to perform a counterfactual exercise where the government needs to balance the budget for each specific sector (noting that H represents high skill and L represents low skill). Consequently, I’ve modified the code as follows
function deficit_separatesector(t) tax_h, tax_l = t, t # Lots of calculations dif_taxh = ep_h * wp_h * tax_h - (eg_h * wg_h) dif_taxl = ep_l * wp_l * tax_l - (eg_l * wg_l) F = [dif_taxh, dif_taxl] return F end
In this case, the return is no longer a one-element array, but a two-element collection representing the deficit for each type of worker. Consequently, I adapted the solving function as follows (with a focus on the relevant parts):
function solvemodeltax_v2(chute_param, chute_th, chute_tl) chute_t = [chute_th, chute_tl] taxopt = nlsolve(x -> deficit_separatesector(x, kappa_h=kappa_h, kappa_l=kappa_l, b_h=b_h, b_l=b_l, y_h=y_h), chute_t).zero tax_h = taxopt tax_l = taxopt # Lots of calculations return output end
In this last part, this final NLSolve is where the code encounters issues. The dimensions seem correct, and everything else appears fine, but I’m uncertain why it’s unable to find a solution. Is this an error within the code or a theoretical problem? Is there anything I can do to improve it?
From my perspective, it should work since the deficits are interlinked, suggesting that it’s possible (due to function continuity) to find a rate that optimally combines both sectors.
Note: I haven’t provided the entire function details, only the main aspects, as they are quite extensive. I believe this should give you an understanding of my point and the challenges.