# Keeping up with the Joneses

Household borrowing and insolvency has been on the rise lately. This is yet another phenomenon that could not have happened according to baseline neoclassical economic theory, so we need some innovations to explain it.

This post looks at the effect of the “keeping up with the Joneses” phenomenon on excessive borrowing, how borrowing constraints can protect households, and what macroeconomic effects these micro decisions can entail.

So how does borrowing work in the standard theory of lifecycle consumption behavior? Households simply maximize their discounted sum of lifetime utility. When they cannot afford their desired consumption level (because of negative income shocks) they borrow money, when they have leftover cash they invest it in some asset. The no Ponzi-game condition assumed in these models ensures that at the end of their lifetimes households – roughly speaking – leave the world with a zero borrowings/savings balance.

So borrowing is a temporary phenomenon that helps smooth out consumption, which is preferred by the risk-averse households. It sort of protects against income risk.

How can this break down in the real world? What if households face borrowing constraints for instance? I.e. they cannot always borrow as much as they’d like to. This could lead to the rejection of the above model. And indeed there is a classic study by Zeldes (1989) that confirms that borrowing constraints do matter.

The topic of this article is a paper by Koenig and Groessl (2014). They examine how keeping up with the Joneses can lead to excessive borrowing. In the presence of this excessive borrowing, they look at how borrowing constraints can help protect households. Finally, they check whether any macroeconomic changes can be triggered by this kind of behavior. They use an agent-based computational model, which I think could have great potential in the field of heterogeneous agent macroeconomics, but to date these models are rarely used there as far as I know.

The model is set up as follows. Households have a wage income, which has some degree of uncertainty to it. They can then use this income to finance their desired consumption. If the income exceeds desired consumption, households save excess income as deposits in banks. If the income is less than desired consumption, then households can take out a loan from the same banks to finance it. The next period wage income will be increased (decreased) by these accumulated deposits (loans) and the respective interest payments.

The first priority of an indebted household is always to repay the loan. Only the income that remains after fulfilling one’s obligations can be used to finance consumption. Households that cannot pay back the loan in full (in the period when the loan matures) are considered insolvent. All but a small “non-pledgable” part of their disposable income is taken as a partial loan repayment and they are forbidden from taking out a new loan the next period. Insolvent households thus have a guaranteed minimum income in the form of this non-pledgable income, which is used for consumption.

The desired consumption level of households consists of two main components. First, it depends on their income. I.e. households wish to consume a certain portion of their income as opposed to saving it (marginal propensity to consume). Second, desired consumption also depends positively on the mean consumption in the economy in the previous period. This captures the Joneses effect.

The other main agent in the model is the commercial bank. There is only one commercial bank (henceforth “the bank”) for simplicity. The commercial bank takes the deposits of households, and uses it to satisfy the loan demands of the households and the government. If the bank cannot meet all the demands for loans it can borrow money from the central bank to have enough resources.

Obviously, the interest rate charged by the central bank for these loans exceeds the interest paid on deposits, and is less than the interest households need to pay on loans. The government pays the central bank interest rate on its loans though.

The commercial bank is owned by the central bank. Any profits the bank makes is transferred to the government. Any losses are transferred to the central bank, which satisfies them by printing out money. Money supply is therefore directly tied to a potential negative cash flow at the commercial bank, which can happen if for instance too many households default on their loans.

The commercial bank would have no incentive to lend carefully and reasonably if all its losses are taken over by the central bank. Therefore, the central bank can set a policy parameter, which determines the maximum line of credit the commercial bank can extend to a particular household. This is the borrowing constraint of the households.

If Y is net income for the household, L is the loan cap, and i is the interest on the loan, then if the bank wants to avoid all losses it must set the loan cap so that

$L(1+i) = Y,$

that is the loan (including both principal and interest payments) cannot exceed the net income. Note that loans are given for one period only. One problem of course is that if loans are given in period t, then they are to be repaid in period t+1. Since income is somewhat stochastic, this could have some unexpected problems. The banks just use the assumption though that income won’t change, which is true in expectation in this model (as income shocks have a zero mean).

The actual loan cap is spiced up with the borrowing constraint feature mentioned above. Solving the above equation for L, and adding an additional parameter yields

$L = \lambda \frac{Y}{1+i},$

where lambda is the policy parameter set by the central bank. It determines the severity of the borrowing constraint. The authors actually assume that there are two lambdas: one for above mean income individuals, one for below mean income individuals. Both lambdas are between 0 and 1.

Besides the households, commercial bank, and central bank, the last actor in this model is the government. The government does not seem to be doing much here. They get some revenue in the form of a tax from household income, and as mentioned they get all the positive cash flows from the commercial bank. Furthermore, these sources can be extended by borrowing (i.e. debt-financing or bonds). These revenues are then spent on some exogenous (fixed) government expenditure and to service interest payment on any previous government debt.

Government expenditure doesn’t seem to have any particular role, it just augments GDP. It must be noted though that it is actually GDP that determines the wages of households as well. So this is how government expenditures are related to household finances. I wonder though if this mechanism is somewhat oversimplified. Perhaps, government expenditures could also be used to finance the aforementioned minimum income of insolvent households. On the other hand, this complication may not add much value to the model.

This finishes our discussion of the basic set-up of the model. The authors now run a couple of scenarios. They run the model for three Joneses effects (nonexistent, some, strong), and three borrowing constraints (nonexistent, some, severe). This leaves us with nine combinations of parameters.

In the cases when there is no Joneses effect, households can always fulfill their desired level of consumption (since it’s just a certain percentage of their net income). Well, at least as long as the marginal propensity to consume is less than one, which it is by assumption in the numerical analysis. Therefore, households take out no loans, and any fluctuations in the economy come from the (assumed) randomness of incomes. Consequently, the existence and severity of borrowing constraints do not have an effect on the outcomes of the model.

Introducing the Joneses effect, but having no borrowing constraints changes things predictably. First, the Joneses effect induces below mean income households to consume more, above mean income households to consume less. This is because the target consumption level of the Joneses effect is merely the mean consumption in the economy. So on average, one should expect that aggregate consumption doesn’t change. The problem is that now poor households often need to borrow to achieve their desired level of consumption. Consequently, they go bankrupt sometimes. And then in the next period, they cannot borrow again, so they cannot reach their desired consumption. This results in a lower aggregate consumption. The size of this drop depends on the strength of the Joneses effect. The stronger the effect, the larger the drop.

Moreover, the fact that poor households’ consumption fluctuates due to the mechanism described above, we have a higher aggregate fluctuation in consumption and GDP. We can see below that a stronger Joneses effect leads to higher fluctuations in GDP.

Introducing a loose borrowing constraint into the picture changes things slightly. Obviously, the amount of private debt goes down, and the number of bankruptcies as well. Volatility decreases somewhat, and the mean consumption and GDP are roughly unchanged for the moderate Joneses effect, and decrease somewhat for the strong Joneses effect (both compared to the no-borrowing-constraints case with the same Joneses effect).

A tight credit constraint does not change much. For the moderate Joneses effect, it further decreases volatility, and keeps GDP and consumption roughly constant. For the strong Joneses effect, we have effectively the same result as with the loose credit constraint.

We know that the Joneses effect exists in the real world. So the general result seems to be that introducing credit constraints can potentially help. It can decrease bankruptcies and volatility (both generally desirable) without hurting GDP and aggregate consumption much. The severity of the credit constraints does not seem to matter much, at least not in this model. While stricter constraints strengthen the effects of the constraint, they only do so marginally.

The model lacks certain important features though, which prevents us from making serious policy recommendations based on it.

First, the authors also mention that the Joneses effect is rather oversimplified (which is all the more unfortunate because it is supposed to the central theme of this analysis). It has the same magnitude for all income levels, furthermore it assumes everyone wants to get closer to the mean consumption. This latter fact is especially worrying, as I am not really aware of a Joneses effect which induces one to adjust one’s consumption downwards. In the model, the Joneses effect actually acts negatively on the desired consumption of above mean income households, which I find grossly unrealistic. This is a major flaw in my opinion. I feel it could alter the results of the numerical analysis dramatically if we were to change this assumption.

Second, income distribution is not fit to any real world data. My understanding is that the authors assume a uniform income distribution, but in reality they do not really talk about how they initialize the income distribution. Even if they use a normal distribution assumption, fitting the income inequality to data would be important. A very key part of the numerical analysis is that certain households are credit constrained. How volatile GDP and consumption is, and how much credit constraints matter depend sensitively on the actual number of low income people relative to middle and high income people, i.e. on the exact distribution of income. So this should not be overlooked.

Third, and this is just a subjective opinion, agent-based models are good in part because one doesn’t necessarily have to make so many simplifying assumptions. In the end, we’re not after analytical but numerical results. For this reason, I think the authors are way oversimplifying their model. They could get away with modeling things much more realistically and add more complexity into their model. This could remedy most if not all of the biggest concerns with this model.

Taking these and some other limitations into account and correcting for them could make this a decent paper. There is quite a bit of work remaining until then though. Anyways, I find the general direction of this research quite interesting even if it’s still in its infancy, so I thought it was worth a post.