Abstract
In this paper we set up a baseline, but nevertheless advanced and complete model representing detailed goods market dynamics, heterogeneous labor markets, dual and cross-dual wage-price adjustment processes, as well as counter-cyclical government policies. The cyclical movements of output generate, through Okun’s law, employment variations in the heterogeneous labor market. The core of the resulting Keynesian macrodynamics is however given by credit-financed investment behavior and loan-rate setting by credit suppliers. The framework is constructed in such way that simplified, lower dimensional versions of the model can be obtained by setting parameters describing specific feedback effects from one sector to another equal to zero. Starting from such low dimensional sub-dynamics, we show the local stability of the full 7D model through a “cascade of stable matrices” approach if the feedback chains are sufficiently tranquil in their transmission mechanisms. However, local stability is the point of departure for the numerical investigation of local explosiveness and the forces that can bound such a behavior.
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Notes
We exclude the interest payments of the government as exercising a feedback on consumption by the assumed taxation rules (a standard assumption in macroeconomic theorizing) and reserve this feedback channel for a later extension of the model.
It should be clear that if the two labor markets were not interconnected, the number of both types of workers would grow at an exogenous rate, given by the trend growth term in investment
We note the assumption that investment is not influenced by the state of Tobin’s \(q=p_k/p,\) i.e., the asset markets, see e.g. Charpe et al. (2011), do not yet exercise an influence on the behavior of the real sector of the economy, which only depends on the loan rate setting of the banks run by the asset holders.
KMG stands for Keynes–Metzler–Goodwin and describes the three components of this family of model. Keynes for the aggregate demand principal, Metzler for the inventories adjustment and Goodwin for the wage-price income distribution feedback channel.
We implicitly use the variable \(L^w_1\) for the workforce of firms in order to define the rate of employment as \(e_1=L^w_1/L_1,\) but avoid to use as state variable the rate of utilization of this workforce by \(L^d_1/L^w_1,\) an expression which is here proxied by the variable \(u.\)
It is beyond the scope of this paper to provide theoretical grounds to \(\gamma \), the animal spirits term, especially considering the role of (pure) uncertainty over the longer run in the future development of capitalism.
Of course, global boundedness and thus the persistency of oscillations can be further ensured by adding appropriate behavioral nonlinearities to the model as in Chiarella and Flaschel (2000) and later related work.
This tool for the numerical analysis of dynamic period models as well as continuous-time ODE systems can be downloaded from the webpage of the CeNDEF.
We have added a \(sinh\)-nonlinearity to both the fiscal and the monetary policy rule which are thus assumed to be weak around the steady state, but gather force the more the system departs from it. This is the basis of the persistent fluctuations the chosen numerical example creates.
In order to present the four variables on the same figure, the employment series were scaled up as follow: \((e+.16), (e_1+.086)\) and \((e_2+.38)\).
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Charpe, M., Flaschel, P., Krolzig, HM. et al. Credit-driven investment, heterogeneous labor markets and macroeconomic dynamics. J Econ Interact Coord 10, 163–181 (2015). https://doi.org/10.1007/s11403-014-0126-4
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DOI: https://doi.org/10.1007/s11403-014-0126-4
Keywords
- Macroeconomic stability/instability
- Segmented labor markets
- Business cycles
- Fiscal and monetary policy rules