Emergent dynamics of a macroeconomic agent based model with capital and credit

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Abstract

In this paper we present and discuss a Macroeconomic Agent-Based Model with Capital and Credit (CC-MABM) which builds upon the framework put forward by Delli Gatti et al. (2011). The novelty of this model with respect to the previous framework consists in the introduction of a stylized supply chain where upstream firms – i.e. producers of capital goods (K-firms) – supply a durable and sticky input (capital) to the downstream firms, who produce consumption goods (C-firms) to be sold to households. Both C-firms and K-firms resort to bank loans to satisfy their financing needs. There are two-way feedbacks between firms and markets which yield interesting emerging properties at the macro level. We show that the interaction of upstream and downstream firms and the evolution of their financial conditions – in a nutshell: Capital and Credit – are essential ingredients of a “crisis” i.e. a sizable slump followed by a long recovery.

Introduction

In macroeconomic model building, very often researchers start from simple models where capital goods are absent. This is the case, for instance, of the simplest New Keynesian DSGE model presented in Clarida et al. (1999) (hereafter CGG) where firms produce only consumption goods using only labor as an input. This is also the case, in the agent based literature, of the Macro Agent Based Model (MABM) developed in Delli Gatti et al. (2011).1

Toy models in which the only final use of goods is consumption and the only input is labor are easier to interpret and sometimes sufficient to answer deep research questions but they are surely inadequate when one wants to replicate empirical business cycle facts. As it is well known, in fact, changes in capital and in inventories play a major role in shaping the dynamic pattern of GDP. The first reason why we want to move up the ladder of complexity in macroeconomic model building, therefore, is simply realism, i.e. the need to reproduce macroeconomic reality as closely as possible.

A second and no less important reason is that the financing decisions of firms enter into the picture in a significant way only when investment is considered. The balance sheet of the firm is, in this case, properly defined: capital and liquidity show up in the assets’ side, external finance (debt) on the liabilities side, equity or net worth being defined by the difference between the two. Decisions concerning investment and decisions concerning financial structure of the investing firm, in fact, are deeply interrelated. Capital should be incorporated into a macroeconomic model if we want to take into account financial factors in an appropriate conceptual setting.2

The NK literature has rapidly gone beyond the simple CGG framework. Starting from the pioneering work of Bernanke et al. (1999) (hereafter BGG), a large literature has developed which takes investment and financing decisions into account in the presence of financial frictions. The architecture of these models is rather sophisticated (even if they retain the representative agent assumption), in some cases so complicated that the overall picture becomes blurred and the interpretation of results difficult.

In the agent based literature, too, macroeconomic models have incorporated capital and investment. For instance, in the EURACE framework (Cincotti et al., 2010, Dawid et al., 2012) firms need heterogeneous capital goods and heterogeneous labor services to produce consumption goods. The use of high quality capital goods requires the employment of skilled workers, hence qualities of capital goods and skills of workers are complements in production. In the Keynes meeting Schumpeter (K&S) framework, Dosi et al. (2010) assume that firms use machine tools of different vintages and with different productivities to produce consumption goods. Also in the computational literature, therefore, the architecture of macroeconomic models is sometimes so complicated that the resulting emerging properties become difficult to explore.

In this paper we present a MABM with Capital and Credit (CC-MABM) which builds upon the MABM developed in Delli Gatti et al. (2011). In the CC-MABM there are four categories of agents: households, firms producing consumption goods (C-firms), firms producing capital goods (K-firms) and banks. The corporate sector describes a stylized supply chain: the upstream sector, consisting of K-firms that supply a durable and sticky input (capital) to the downstream sector consisting of C-firms. Both C-firms and K-firms resort to bank loans to satisfy their financing needs.

The CC-MABM may be considered as a simpler and shorter route (with respect to EURACE or K&S) to introduce capital and investment in a MABM. In our model capital goods (and labor) are not differentiated: the productivity of labor and of capital is uniform across firms and workers. This relatively simple architecture, however, generates two-way feedbacks between markets and sectors which yield interesting emerging properties at the macro level.

The time series of GDP computed on artificial data fluctuates around a “long run mean” for an extended time window which we characterize as normal times. Occasionally, however, GDP falls dramatically bottoming out only after many periods of contraction. At the trough, GDP and employment are at least 15% lower than the pre-recession level. The recovery, then, is slow and painful; it takes a long time for GDP and employment to go back to normal. A dramatic slump followed by a long recovery is a crisis in our terminology.

Where does a crisis come from? We show that the interaction of upstream and downstream firms and the evolution of their financial conditions – in a nutshell: Capital and Credit – are essential ingredients of a “crisis”. If they were absent the volatility of GDP would be limited and no sizable slump would occur.

The paper is organized as follows. Section 2 briefly surveys the literature. In Section 3 we sketch the basic features of the model. In 4 Households, 5 C-firms, 6 K-firms, 8 The bank we present the assumptions concerning the behavior of households, C-firms, K-firms and banks respectively. In Section 7 we define the financing gap and the demand for loans. Section 9 is devoted to a discussion of the accounting framework and the interrelated balance sheets of the main categories of agents. Section 10 is devoted to a discussion of the results of the simulations. Section 11 concludes.

Section snippets

Related literature

The need to move up in the ladder of increasing complexity by incorporating capital and credit in macroeconomic models is evident both in NK and in AB literatures.3

In the NK-DSGE literature, the canonical model popularized by CGG in which there are only consumption goods, the only input is labor and

The model

We consider an economy populated by households, firms and banks. The household sector consists of workers and “capitalists”. Workers supply labor and buy consumption goods. Capitalists are the owners of firms (for simplicity we assume that there is one capitalist per firm). They get dividends and buy consumption goods (therefore they behave as rentiers). Both workers and capitalists save and accumulate financial wealth in the form of deposits at banks.

The corporate sector consists of producers

Households

The household sector consists of workers and capitalists.

C-firms

The ith firm in the C-sector (i=1,2,,Fc) produces a C-good using labor and capital. Imperfect information and transaction costs force the firm to explore a limited portion of the price-quantity territory around the current position – the status quo – in order to adapt to the market environment.

At the beginning of time t the ith firm sets the status quo, i.e. the pair (Pi,t,Yi,t) where Pi,t represents the firm׳s selling price and Yi,t is the firm׳s current production. At the end of period t the

K-firms

In the market for K-goods (K-market for short), C-firms are buyers of capital goods sold by K-firms. We assume imperfect information and the existence of transaction costs also in the K-market so that price and quantity are decided by K-firms following adaptive rules similar to those described above for C-firms (see Section 5.1).

There is a crucial difference, however. Since capital is durable, we assume that K-goods are storable, hence the K-firm can carry inventories over from today to

The financing gap

Each firm has a funding problem, irrespective of the type of goods she produces. If liquid resources, Df,t1,f=1,2F, are in short supply with respect to expenditure Xf,t there is a positive financing gap equal to Ff,t=Xf,tDf,t1 in which the firm tries to fill by asking a loan to a bank. If Ff,t<0 the firm can finance expenditure with internal financial resources and therefore she will not ask for a loan.

Expenditure for a C-firm is the sum of the wage bill wNi,t and investment expenditure Pk,t

The bank

For the sake of simplicity we assume that there is only one commercial bank. Households, capitalists and firms hold deposits at the bank to manage their liquidity. The bank accepts deposits in unlimited amount at zero interest rate. On the other hand, firms demand credit according to their production plans and the resulting financing gaps (as shown above). The bank has to decide both the price (interest rate) and the quantity of loans to be supplied to each firm on the basis of her assessment

Accounting

In this section we will describe the accounting framework of the model, focusing on the system of interrelated balance sheets. We will also show the changes in liquidity generated by the financial structure of the balance sheets. As far as households (workers and capitalists) are concerned, the situation is simple. The hth worker has (non-negative) wealth (Eh,t) which coincides with deposits (Dh,t), i.e. Eh,t=Dh,t, h=1,2,H. Hence, savings are deposited at the bank:Dh,t=Dh,t1+Yh,tCh,tThe same

Simulations

Table 2 reports the numerical values of the parameters used in the simulation and the initial conditions.

We have built a medium sized ABM with 3250 households (3000 workers and 250 capitalists) and 250 firms, of which 1/5 in the K-sector. Transaction costs are high in markets for goods: buyers visit a very small number of sellers (Zc=Zk=2). They are slightly lower on the labor market: an unemployed worker, in fact, can visit Ze=5 firms.

Overall there are 16 parameters, which have been generally

Conclusions

In this paper we have explored the emergent properties of a medium sized MABM with Capital and Credit. The interaction between the upstream and downstream segments of the corporate sector (consisting of K-firms and C-firms respectively) in a setting characterized by a durable and sticky input (capital), evolving financial conditions and limited access to credit are the main ingredients of the economic environment under scrutiny.

The upstream sector is relatively small (there are 50 K-firms) but

Acknowledgments

We would like to thank two anonymous referees for very useful criticisms and suggestions. We thank for insightful comments of the participants to the following conferences and seminars: “Computing in Economics and Finance”, Oslo, June 22–24, 2014; “International Economic Association” world conference, Jordan Dead Sea, June 6–10, 2014; “CESIFO Area Conference on Macro, Money and International Finance, February 21–22 2014; “Complexity Seminar series”, Tinbergen Institute, Amsterdam, February 5,

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