I have been long been confused about the question that how the total market-clearing condition is got. I mean, in some somewhat complex dsge models, the condition is not simply y=c+i+g things, especially when there are financial frictions in the model. Usually, such frictions are also added to the right-hand-side of the total market-clearing condition. However, few papers give details about how to obtain this. I think this is because, according to Walras’ Law, one market-clearing condition should be dropped (usually the household’s budget constraints). Thus, the total market-clearing condition just takes place of the household/s budget constraints, and if we substitute other market conditions or budgets or productive equations in the total market-clearing condition, we can get the household’s budget constraints, and vise versa. Am I right? (I tried a few classic dsge models, and this rule always holds. But still I am not sure about this.) Thanks in advance.
What do you mean with “total market clearing condition”? What you outline is the resource constraint of the economy, which is something else than a budget constraint. But yes, combining the budget constraint with other optimality conditions usually allows recovering the resource constraint.
In the end, how available resources are used depends on your assumptions, e.g. whether you assume adjustment costs that use up resources.
Thank you, professor. Sorry for my unclear description, and yes, I mean to say “resource constraint of the economy”. And your answer is helpful.
When I worked on this part, I realized that even I loss some adjustment costs in the resource constraint (if actually they should, due to assumption), it doesn’t matter because according to the Walras’ Law this means the adjustment costs are afforded by the household. This is also acceptable and reasonable. Thus this is just somewhat description text error, but the model itself can work well.
But new learners often make mistakes when they decide whether one equation should come into the final (non)linear systerm. e.g. they may put both household budget constraint and resource constraint into dynare. In this situation, lossing adjustment costs in the resource constraint may be very dangerous, because dynare may not find out the error by the colinear relationship checking function. (I guess)
All in all, I just want to make sure whether I can obtain the resource constraint more safely and more exactly if I recover it from the household budget constraint. I am also not sure if my understanding of Walras’ Law and dsge model is right. And your reply do help me a lot. Thank you, professor.
Note that quadratic adjustment costs will usually drop out from the resource constraint at first order. So that is often not a reason to worry. But this is not a general results. So you need to be careful.
Oh yes, that’s right. Thanks for your additional advice, professor. It’s helpful.
I’m comparing the MX Model (Textbook SGU, Chapter 7) to Jermann’s model (1998, Asset pricing in production economies). Both use capital adjustment costs, but the definition is different.
In SGU: Capital adjustment costs enter directly the budget constraint. I plug in the law of motion of capital accumulation (which itself does not show any capital adjustment costs) and find the FOCs. In the equilibrium condition (demand for final goods = supply for final goods), I observe again the capital adjustment cost terms (this makes sense).
In Jermann: I find capital adjustment costs directly in the law of motion of capital. In terms of this, I do not have to add them to the budget constraint. --> I don’t understand why they do not show up in the equilibrium condition (resource constraint). Can somebody please explain this? Are they already included in the definiton of ‘i’ (investment)?
Yes, the costs in Jermann are taken out of the capital stock (they essentially change the depreciation). As such, they are covered by investment.