# Market Clearing Conditions

I have a simple question. For example, when we have 2 types of households such as savers and borrowers, we end up with 2 different budget constraints. At the end of the model, we sum the budget constraints and impose market-clearing conditions. It generally gives us a typical resource constraint. However, when we take the equations to Dynare, we exclude some of the market-clearing conditions and one of the budget constraints.
To illustrate:

why do we exclude the household budget constraint, bond market clearing condition and labor market clearing condition when we take the FOCs to Dynare?

Hi lexsp,

This is due to the fact that all equations in the system need to bring valuable information to the system.
But since Walras’ Law posits the presence of an equilibrium in the nth market given the equilibrium in the other n-1 markets, specifying an equation that imposes equilibrium in the nth market adds a redundant equation, i.e. an equation that adds no valuable information to the solution of the system.

Hi Camilo,

Thank you for the answer. In this example, there are 4 markets,
1-Labor Market
2-Bond Market
3-The Real Estate Market
4-Good Market
According to the Walras Law, we need to take any 3 of these conditions, however just 2 of the conditions take place in the model. This is what makes me confusing actually.

Hello, following what Camilo says, my recommendation when replicating any model in the MOD file is to write down all the budget constraints of all agents, and then omit the general market clearing condition.
For the labour market, perhaps you can use only one labour variable, instead of defining supply and demand, L and L’, hence, you don’t need to specify the labour market clearing condition. The same can apply to the bonds market. However, in the case for the real estate market, you need to specify the clearing condition because both variables (following the notation in the equation you posted) are demands. I hope I did explain myself.

Hi Fernando,

Hi everyone, I have a similar question on that.

@lexsp mentioned that

If I understand correctly, scholars often call it “Aggregate Budget Constraint” (ABC hereafter), or in the open economy literature “current account equation”.

Then @cmarch stated that

I know Walras’ Law, and usually people ignore the labor market clearing condtion. And I agree with what @fernando said:

BUT let’s come back to ABC.
ABC =
Household’s budget constraint+
Profits of firms+
bond market clearing condition (if applicable)+
something else.

So all the information in ABC has already been involved in the RHS of the above equality, does it mean ABC itself is redundant?

I find some papers do not have ABC, some have, and even some authors say those who missed ABC are incorrect. Really confused.

Does ABC relate with the decision of the CENTRAL planner?
Suppose it does, then CENTRAL corresponds to ABC, but due to ABC has already reflected the information of budget constraints of private sectors, so we delete the one of households??

In contrast, if decentralized economy is ok for our purpose, does it mean we don’t need add constraints at all. We do not need ABC in this case??

Sorry for bothering!

Hi Fernando,

So using one variable for both labor supply and labor demand kinda means the labor market clearing condition has implicitly been captured in the model? Something like that?

If you have two household types and hence two types of labor- savers (ls) and borrowers (lb), how about specifying this equation ‘Ls + Lb = L’ as part of the equilibrium equations of the model? ‘L’ here is both aggregate labor demand and aggregate labor supply though.

Yes, if one is demand and the other is supply, then by using the same notation the demand equals the supply implicitly.

In such case you are declaring a new variable `L` which is aggregate supply of labour. Then the equation you specify is just the definition of aggregate supply of labour.

Ok, I see. Thanks for the reply.

Sorry Fernando, I did something wrong again. Specifically, I try to replicate “Banking Competition, Housing Prices and Macroeconomic Stability”. It is a kind of Iacoviello type model extended with banking system. In the paper, there is a counter-cyclical spread between deposit rate and loan rate, and this spread is the source for Banks’ accumulated profits. These profits are transferred to savers, therefore included on the income side of the savers’ budget constraint. Here I have 3 budget constraints and 4 market clearing condition.
A-Savers’ budget constraint
d(t)+cs(t)+Ph(t)*[hs(t)-hs(t-1)]=f(t)+div(t)+w(t)Ls(t)+Rd(t-1)d(t-1)/infl(t)
B-Borrowers’ budget constraint
cb+Ph(t)[hb(t)-hb(t-1)]+Rb(t-1)b(t-1)/infl(t)=y(t)/x(t)-w(t)Ld(t)+b(t)
C-Banks’ budget constraint
div(t)+Rd(t-1)d(t-1)/infl(t)+b(t)=Rb(t-1)b(t-1)/infl(t)+d(t)
Market Clearing Conditions:
D-Labor Market
Ls(t)=Ld(t)
E-Financial Market
d(t)=b(t)
F-The Real Estate Market
hs(t)+hb(t)=1
G-Good Market
cs(t)+cb(t)=y(t)

When I sum A+B+C and impose D+E+F, it yields G. In this case, which equations I should take into Dynare? Is it okay if I exclude G and take the rest? Thank you once more time.

I will leave out one of the budget constraints for the 2 household types. By the way, I think Ls(t)=Ld(t) is not market-clearing. Maybe you can replace that equation with an aggregate labor equation (L = Ls(t)+Ld(t)) where L is aggregate labor supply. And as Fernando said, you can assume that the aggregate labor market clears implicitly in the model. Thus, we need only an aggregate labor supply variable (L) together with Ls(t) and Ld(t) in the model. Aggregate labor demand implicitly equals aggregate labor supply in the model (i.e., market clearing in the aggregate labor market), and hence we donot need another variable for aggregate labor demand.

Hi Kofiemma,

Actually Ld stands for Labor Demand as borrowers are entrepreneurs in the model. They produce intermediate good using a fraction of total real estate and labor supplied by savers.

I think that by summing up all assets and liabilities in the model, you will end up with Y_t=Y_t.

Following your example, I would leave out equation G. Using A and B implies G. However, you could use either “A and G” or “B and G”, because in the former “B” is implied, and in the latter “A” is implied.
It is a good exercise to always check the summation of all assets and liabilities to see whether all markets clear.

Oh I see, so you don’t actually need both Ls(t) and Ld(t) in the equilibrium equations of the model. You can replace both Ls(t) and Ld(t) with L(t) in equations A and B, and assume that the labor market clears implicitly. So market clearing in the labor market gets dropped. Other equations can remain.

@HelloDynare If done correctly, then using the respective budget constraints and market clearing conditions will return the resource constraint of the economy (e.g. Y=C+I+G+NX), which is probably what you mean with ABC. Conceptually, it is stricter than a budget constraint. Economic agents can sometimes live beyond their means (e.g. government violating their intertemporal budget constraint). But you cannot violate a resource constraint: you can only use up the goods and services that have actually been produced. But as I said, it is usually implied by the respective other constraints and therefore often not explicitly put in models. It does not add additional information per se.

I agree. I believe @fernando has the identical thought.

I think because for the intertemporal budget constraint, agents can allocate their consumption between two periods, they have some flexibility. But for the resource constraint, agents have to comply with per period.

Your explanation confirms my hunch! Thank you!