Discussion Paper

No. 2019-51 | October 21, 2019
A note on observational equivalence of micro assumptions on macro level


The author sets up a simplistic agent-based model where agents learn with reinforcement observing an incomplete set of variables. The model is employed to generate an artificial dataset that is used to estimate standard macro econometric models. The author shows that the results are qualitatively indistinguishable (in terms of the signs and significances of the coefficients and impulse-responses) from the results obtained with a dataset that emerges in a genuinely rational system.

Data Set

JEL Classification:

B41, C63, D83


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Cite As

Alexey A. Ponomarenko (2019). A note on observational equivalence of micro assumptions on macro level. Economics Discussion Papers, No 2019-51, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2019-51

Comments and Questions

Anonymous - Referee report 1
October 28, 2019 - 08:52

see attached file

Alexey Ponomarenko - Response to Referee 1
November 03, 2019 - 14:24

Please see the file attached

Anonymous - Referee´s response on author´s comment
November 21, 2019 - 13:52

I take the author’s comment that since the reinforcement learning algorithm used in thepaper does not produce expected values for demand, cost etc. there is no straightforwardmeasure of forecast error in the learning case. I would insist however that comparing thesigns of the GMM coefficients and the general ...[more]

... shapes of the IRFs is not sufficient to claimthat results are ‘indistinguishable’. One relatively easy thing to do would be to look atconfidence intervals for the IRFs and the GMM coefficients for the different cases. Dothey overlap? In that case it could indeed be claimed that results are not distinguishable.Otherwise one could only say that results are qualitatively similar. In that latter case,however, the contribution of the paper would be somewhat unclear as I do not think any-one would dispute that rational and non-rational behaviour can produce similar-lookingIRFs.

I am happy with the author’s replies to my other comments and the way they plan toaddress the issues I raised.

Anonymous - Referee report 2
November 26, 2019 - 10:41

The paper enters the debate between theoretical and empirical application of microfounded modelling. The paper develops a simple and effective modelling to understand to what extent different micro-assumptions differently influence macro-level analysis.

The findings highlight that a set of macroeconomic variables obtained by aggregation of rational agents correlates to ...[more]

... those obtained by aggregation of bounded-rational agents that learn with reinforcement.

A simplified ABM simulates the behaviour of individuals that decide whether or not to enter a market depending on profitability gains: the difference between the firm’s specific unit production costs and the market price.
Five systems are considered for simulation to obtain micro-level datasets that are econometrically investigated at the macro-level.
The first three datasets are ‘pure’ strategy systems: (i) rational agents that know everything about the data generating process of the involved quantities; (ii) bounded-rational agents with full information that know time series of profitability gains, aggregate trend costs and demand; (iii) bounded-rational agents with limited information that consider profitability gains only. A dataset involves (iv) ‘mixed strategies’ (in equal proportions) and the last one (v) considers agents that decide ‘randomly’.

Simulation outcomes give evidence that the market participation rate is higher in systems with learning agents –either (ii) fully informed or with (iii) limited information- rather than the one with (i) rational agents. In contrast, the per-capita profit is higher and less volatile in the rational agents’ system.

GMM regressions on the five databases explain output as depending on costs and demand: parameters are statistically significant and their sign is coherent. Nevertheless, except the case of the ‘mixing strategies’ system, fitting capabilities are not satisfactory and do not help to distinguish between rational and learning agents’ systems.

To shed more light on this point, VAR estimation informs that correlations between endogenous (output and price) and exogenous (costs) variables emerge both in systems with rational or learning agents and, more interestingly, that such correlations are almost indistinguishable in the following sense. For each of the five experiments the IR-functions are obtained. By comparison of the rational agents’ system IR-function with those of the other four systems it is shown that (a) output is affected by exogenous innovations and (b) the IR-functions perform almost the same shape. Therefore, this finding seems to explain that, once compared to rational agents, those who do not know the data generating process can anyway adapt through learning as well.

Even though it is hard to imagine how a large number of micro-strategies superimpose in the formation of macro-quantities, while it has been clearly explained how the macro-outcomes influence micro behaviors, the econometric exercises developed on different systems lead to supporting the hypothesis that microfoundation in terms of rational expectations generates aggregate outcomes that are not so different from those generated by learning agents, with full or limited information. If, by considering more sophisticated models, it were proved that learning agents’ systems aggregate outcomes are still not so different from rational agents’ systems ones, then one may consider dealing with the former microfoundation to overcome some of the not so realistic assumptions of the latter. Of course, the described experiments are simple enough to prepare the analysis: the behaviour of individuals has been voluntarily maintained at the simplest level, the result is interesting and promising but, at the same time, more sophisticated modelling of individual behaviour is needed for a possible generalization. For instance, the micro-level modelling essentially is characterized by heterogeneity while interaction is absent: differently said, agents live within a system and sense the environment but operate in isolation. A possible extension may consider the possibility to introduce a network of interactions through which agents exchange information about what they expect the near future will be.