# Modeling diversity in Macroeconomics

Until the 70’s of the last century there was a great divide in Economics. On the one hand, Microeconomics studied the individual economic behavior, whether of a firm or a consumer, and was able to construct a General Equilibrium Theory that explained remarkably well (at least, for a social science) many economic regularities like market behavior, the effect of taxes on prices and consumer welfare, and the merits of open markets vs. protectionism, among many others. Macroeconomics, on the other hand, dealt with aggregate behavior and focused on problems like growth, inflation, the level of employment, and economic cycles. But the divide was not so much about the kind of problems as it was about methodology: Micro and Macro models were based on different principles.

To be sure there is nothing wrong with two sciences or two branches of a science to have different sets of primitive assumptions as long as they are not contradictory. After all, not every science can hope to describe and analyze its object of study in terms of the physical elementary particles. Macroeconomics could be based on aggregate statistical behavior. The problem was that Macroeconomics was too aggregated and that some of its assumptions were at odds with the better founded microeconomic analysis. A great part of the history of Macroeconomics in the last decades is the history of overcoming these two problems.

One of the most controversial issues was the use of a representative agent (RA). Macroeconomics, included the prevalent Keynesian models of the time, needed this simplification for computational purposes. A good economic model needs to take into account the complete cycle of all variables or be doomed. For instance, if the government increases public expenditure one needs to clarify how it is financed and to analyze the consequences not only on the side of the public expenditure, but also on the side that collects the money. Models that tried to do this properly became complicated and impossible to compute. One way to deal with the problem was to simplify the consumption side of the economy with a RA. This does not mean that one assumes that there is only one consumer in the economy, but that there can be many as long as they can be modeled as one. Economists found several conditions for this exercise to be legitimate that served as a guide as to when to trust this kind of models.

However, in a work known as *Lucas critique*, Lucas (1976) ^{1} pointed out the abuses of Macroeconomic models using too aggregated or historic data, and his critique served as the starting point to the development of more detailed models. New studies on the microfoundations of Macroeconomics and mathematical computation as well as the availability of more powerful computers helped in this development.

Next is a sample of the advances in Macroeconomics that came after the introduction of heterogeneous agents (HA) in its models. Perhaps an example will help explaining the importance of this. Suppose that you have a model with variables *x*, *y* and *z* that define some characteristics of agents in the model, and that you know that *z *= *x*+*y*. Now, if you have two agents for which the variables take the values (*x*_{1 }= 3, *y*_{1 }= 3) and (*x*_{2 }= 7, *y*_{2 }= 7) respectively then you can have a representative agent with (*x *= 5, *y *= 5). Notice that the value of *z* for the representative agent is 10, the same value you get if you average *z*_{1 }=* x*_{1}+*y*_{1 }= 6 and *z*_{2 }=* x*_{2}+*y*_{2 }= 14. However, if you have another variable, say *r *= *xy*, then the average of *r*_{1 }= 3×3 = 9 and *r*_{2 }= 7×7= 49 is 29 while the value of *r* for the representative agent will be 25. Thus, the appropriateness of a RA depends on the way variables interact. RA models may be adequate to study some aspects of the economy, but their methodology is clearly limited.

One obvious source of heterogeneity among consumers is income. Inequality is absent in representative agent models, which implies that any redistribution effect after a particular economic policy will be overlooked.

Macroeconomic models serve to understand the interaction among the different macroeconomic variables and, thus, orient economic policy. When a model captures these interactions and is calibrated to reflect the idiosyncrasies of a particular economy it may also serve to make quantitative predictions. In this respect there was a particular problem with RA models. When calibrated with the observed parameters for risk aversion and discount factors they yielded interest rates too high when compared with the actual ones. This is known as the “risk-free rate puzzle”. HA models, however, can take into account different income risks for different income groups. If individuals cannot buy complete insurance against these risks (as it is usually the case) then they will save more, which in turn, gives a lower interest rate than the one implied by the RA models, thus solving the puzzle. Zeldes (1989) ^{2} provides a theoretical model and Carroll and Samwick (1998) ^{3} some empirical evidence.

Another consequence of introducing income heterogeneity is that the estimations of the welfare effects of inflation change. In addition to the classical costs of being a tax of money holding, a burden for price adjustments and a discouragement for market activity, HA models add a new possible cost of inflation. The reason is that the precautionary savings discussed above suffer a cost, and then the individual’s consumption volatility increases. Imrohoroglu (1992) ^{4} shows that, in the USA, the welfare loss of the volatility created by a 10% inflation is equivalent to a 1% loss of income. However, when new analyses incorporated other possibilities for precautionary savings, like the use of government bonds, the results changed. The works by Akyol (2004) ^{5}, Algan and Ragot (2010) ^{6} and Chiu and Molico (2010) ^{7} show that HA models imply that inflation may have a redistributive effect. This, together with the fact that individuals with different income typically face different financial constrains, has an interesting consequence. The redistribution from the old and rich to the young and poor due to inflation may mitigate the costs faced by the financially constrained individuals and opens the door for an estimation of an optimal level of inflation. The cited works present different models (some of them introduce age as another source of heterogeneity, for instance) and give different estimates for the USA, an indication that this line of research is still in progress. The future will say if these promising studies lead to an acceptable theory.

Of course, income and age are not the only sources of heterogeneity. Researches have studied models with consumers having different preferences (mostly about risk attitudes and the discount of future income) and expectations (about the value future macroeconomic variables). On the side of firms, the most important sources of heterogeneity are about productivity and financial position. Besides the insight about the costs of inflation and the solution to the “risk-free rate puzzle”, HA models are proving useful in understanding the transmission of monetary shocks, the redistributive effects of monetary policy and of financial frictions and the costs of economic cycle fluctuations, to mention only money related problems. Brzoza-Brzezina *et al*. (2013) ^{8} surveys the advances in HA models in the last twenty five years in the understanding of monetary policy.

## References

- Lucas, R. 1976. Econometric policy evaluation: A critique.
*Carnegie-Rochester Conference Series on Public Policy***1**, 19-46. ↩ - Zeldes, S. P. 1989. Optimal consumption with stochastic income: Deviations from certainty equivalence.
*The Quarterly Journal of Economics***104**, 275–98. ↩ - Carroll, C. D. and Samwick, A. A. 1998. How important is precautionary saving?
*The Review of Economics and Statistics***80**, 410–419. ↩ - Imrohoroglu, A. 1992. The welfare cost of inflation under imperfect insurance.
*Journal of Economic Dynamics and Control***16**, 79–91. ↩ - Akyol, A. 2004. Optimal monetary policy in an economy with incomplete markets and idiosyncratic risk.
*Journal of Monetary Economics***51**, 1245–1269. ↩ - Algan, Y. and Ragot, X. 2010. Monetary policy with heterogeneous agents and borrowing constraints.
*Review of Economic Dynamics***13**, 295–316. ↩ - Chiu, J. and Molico, M. 2010. Liquidity, redistribution, and the welfare cost of inflation.
*Journal of Monetary Economics***57**, 428–438. ↩ - Brzoza-Brzezina M., Kolasa M., Koloch G., Makarski K. & Rubaszek M. (2013). MONETARY POLICY IN A NON-REPRESENTATIVE AGENT ECONOMY: A SURVEY, Journal of Economic Surveys, 27 (4) 641-669. DOI: 10.1111/j.1467-6419.2011.00710.x ↩