Abstract
From the very beginning macroeconomics analysis tried to understand aggregate relationships (GDP, Consumption, Investments, etc.). The most famous one is the Keynesian relation between aggregate consumption at time t, \(C_t\) and aggregate income, \(Y_t\)
where \(\bar{C}\) is the autonomous component of consumption and c is the marginal propensity to consume.
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Notes
- 1.
These aggregate relation was later modified by Friedman (1957) and Ando and Modigliani (1963) in \(C_t = F(Y_{pt})\) where \(Y_p\) is permanent income.
- 2.
In Keynes’ words (Keynes 1936) a “psychological law of consumption”.
- 3.
The field of Experimental Economics aims at investigate individual behaviors. In this field data are collected through laboratory or field controlled experiment as in physic or biology in which the phenomenon under observation is the choices of human beings. Running an experiment means to create a controlled environment to examine some questions of interest. This method has a great advantage with respect to the use of existing data set, i.e. researchers are able to isolate the impact of the variable under investigation and, most important, they are able to observe real individual’s choices or preferences.
- 4.
Think about the importance, of inter-bank networks or firm-bank credit networks today.
- 5.
The Nobel Price in 2002 for his research in experimental economics.
- 6.
A famous example of the importance of point 2 is the aggregate relation between output and inputs in the basic modern new-keynesian models with sticky prices in a monopolistic competition environment. Because of firms setting different prices the aggregate relation between output and input is different from the micro one. Thanks to the Calvo price setting mechanism it is possible to compute the macro function depending also on a price dispersion (see Christiano et al. 2010).
- 7.
This approach needs well defined optimization problems; concave objecting functions evaluated on a convex support.
- 8.
The above derivation exploits the fact that the production function has CRS (\(\lambda _i\) can be factor out) and the sum of the fractions \(\lambda _i\) sum to 1; that is \(\sum _i \lambda _i = 1\).
- 9.
The indirect utility function, say \(v_i\) is the utility function, say \(u_i\), evaluated at the optimal solution, \(c_i^*(p,a_i)\); that is \(v(p,a_i) = u(c_i^*(p,a_i))\).
- 10.
By definition quasi-homothetic preferences generate affine Engel curves in wealth or income. The mathematical definition of an homothetic function f(x) where x is a vector is the following: given two vectors \(x_1\) and \(x_2\), if we have that they obtain the same value \(f(x_1)=f(x_2)\) then they produce the same value when multiplied by the same positive number k, i.e. \(f(kx_1)=f(kx_2)\). The economical intuition is that consumption of any good is always a given fraction of wealth or income independent of its level.
- 11.
See below the comparison between agents’ behavioral rules in standard macroeconomics and in the agent based literature.
- 12.
Like in the famous 1983 movie “Trading Places” with Eddie Murphy!
- 13.
A deep analysis of the aggregation problem can be found in Browning et al. (1999), Heathcote et al. (2009), and Guvenen (2011).
- 14.
An example of an agent-based model analyzing firm-bank network using a Japanese dataset is Catullo et al. (2015).
- 15.
Note that, to simplify the analysis, we assume a constant level of labor.
- 16.
The complexity of an Economic System and the necessity to build the model as an evolving comprehension of it by the agents is expressed with the notion of the Economy as an Evolving Complex System in Arthur et al. (1997), Blume and Durlauf (2005), Arthur (2006) and with the Bottom-up Adaptive Macroeconomics in Delli Gatti et al. (2011).
- 17.
Nevertheless, there are agent-based models in which agents derive the behavioral rules optimizing. Examples are the works of Delli Gatti et al. (2003, 2005a) analyzing the macroeconomic consequences of the heterogeneity implied by the framework in Greenwald and Stiglitz (1993). In this line of research, firms maximize profits considering the expected cost of the bankruptcy event.
- 18.
This is a standard assumption for adjacency matrices in graph theory, meaning that agents have no self-loops. A more detailed analysis, with self loops, is in Palestrini (2013).
- 19.
Specifically, expectations and adaptive behaviors described in the Chapter 2.5 are driven from financial models (Brock and Hommes 1998).
- 20.
When a modeler wants to create a multi-markets model, where agents act in different environments, such as, for instance, the consumption or the stock market, it is useful to remember that we are dealing with the same individual which, although in a market is a consumer and in the other one an investor, should have consistent and coherent strategies and behavioral rules in the two different systems. In other words, if an agent is “rational” in a market, he must apply the same behavior in all the other environments where he operates.
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Catullo, E., Palestrini, A., Tedeschi, G. (2016). Getting Started: The Aggregation Conundrums and Basic Toolkits of Agent Based Modeling. In: Caiani, A., Russo, A., Palestrini, A., Gallegati, M. (eds) Economics with Heterogeneous Interacting Agents. New Economic Windows. Springer, Cham. https://doi.org/10.1007/978-3-319-44058-3_1
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DOI: https://doi.org/10.1007/978-3-319-44058-3_1
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