nach oben

Erschienen in:

2010 | OriginalPaper | Buchkapitel

22. Classical Dynamics in a General Keynes–Wicksell Model

verfasst von : Prof. Dr. Peter Flaschel

Erschienen in: Topics in Classical Micro- and Macroeconomics

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this chapter, we introduce a general model of monetary growth which contains several existing models as special cases. The model is complete in the sense that it allows for a full interaction among the three major markets (goods, labor and assets), and consistent in that the budget constraints for households, firms and the government are all respected. This gives rise to a four-dimensional differential equation system. The stability properties of some special lower dimensional cases of the model are characterized analytically, and the unrestricted model is then briefly examined numerically. Stein (1982, p. 191) defines a “Keynes–Wicksell model of money and capacity growth” as “one where there are independent savings and investment functions, but output is always at capacity”. The dynamic properties of general models of the Keynes–Wicksell type, consisting of fully interacting money, goods and labor markets, have not been systematically explored in the literature to date. Such models are of a very neoclassical nature with respect to their building blocks. Yet, despite their supply side orientation, our analysis reveals that a monotonic adjustment of real wages to the long-run full employment level cannot be expected to occur once the complexity of the various feedbacks and interactions between the major markets in a capitalist economy are adequately taken into account. This is the main finding of the chapter.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel The Goodwin Distributive Cycle After Fifteen Years of New Observations

In addition, the following notation is adopted: for any variable x, we use \(\dot{x}\) to denote its time derivative, \(\hat{x}\) to denote its growth rate, x ₀ to denote its steady state value, and x′ and x _y to denote total and partial derivatives respectively.

This device saves one further adjustment equation; for an attempt at justification, see Sargent (1973, p. 429).

Real taxes T are calculated net of government interest payments. Taxes are lump-sum and thus do not modify rate of return differentials.

An alternative specification, requiring that the growth rate of the capital stock be consistent with the savings plans of households (rather than the investment plans of firms) is also explored below. Since we allow for goods market disequilibrium through the adjustment of inventories, these two approaches yield different results.

This method of modeling forward-looking expectations appears, for example, in the influential paper by Dornbusch (1976) where, under certain conditions, it yields self-fulfilling forecasts. Gray and Turnovsky (1979) refer to this as “regressive expectations” and we adopt their terminology here. The same rule is referred to by Stein (1982) as “asymptotically rational expectations” and by Groth (1988) as “monetarist expectations”. In the literature on speculative markets, such expectation formation rules are identified as “fundamentalist” (Frankel and Froot 1986; Chiarella 1992). It is important to emphasize that expectations can be forward-looking without being self-fulfilling. There are a number of reasons, such as the costs associated with the expectation calculation technology (Evans and Ramey 1992) or optimization costs in general (Conlisk 1988; Sethi and Franke 1995) why simple forward (or even backward) looking rules might yield higher returns to forecasting than expensive means of obtaining unbiased forecasts. Note that unlike adaptive expectations, a regressive expectations rule does induce instantaneous responses to announcements and news of future events.

Assuming δ₂ Y as inventory accumulation rule instead of δ₂ K would only modify the model slightly; our choice allows us to treat planned inventory accumulation as part of depreciation.

We owe this observation to Reiner Franke, though he is not responsible for this particular solution to the I ≠ S problem. We use α = 0. 2 and q ₀ = 0. 2 in the numerical simulations in Sect. 22.6.

We assume for this categorization of various monetary growth models that the production function is of the CES type so that we can use the constant elasticity of substitution expression ε to denote special cases: ε = 1 corresponds to the Cobb–Douglas case, while ε = 0 represents fixed proportions. Blank entries in the table mean that this parameter does not matter in the considered model, while a + indicates that the parameter is positive and finite. Note finally that β_π ¹ = 0, β_π ² = 0 should be interpreted as π ≡ 0, and r = r ₀ as the prevalence of an infinite interest rate elasticity of money demand (h ₂ = ∞). In the case of the Goodwin model, only its structure is obtained in this way, not its concrete form, since this model relies on Say’s Law in the form I ≡ S.

X _ω ^w = β_w l _ω ∕ l ^s is obviously negative while the sign of X _ω ^p = β_p(i _ω − s _ω) is ambiguous, since i _ω is of ambiguous sign. The partial derivative X _ω ^p will be positive if the production function is approximately characterized by fixed proportions, that is, if f′(l) is sufficiently close to zero, since we would then have i _ω ≈ − r _ω > 0 which is of the same sign as s _ω.

The case of myopic perfect foresight is reconsidered from the viewpoint of nonlinear dynamics in the simple Cagan model of money market dynamics in Flaschel and Sethi (1998). We here extend Chiarella’s (1990, Chap. 7) investigation of this case by including an accelerator term into the price dynamics that is employed by him.

As in earlier situations, stability problems arise if excess demand in the market for goods responds negatively to real wage increases, giving rise to price “decreases” which provide a further stimulus to real wage “increases”.

Of course, the case \(\dot{K} = I\;({\beta }_{k} = 1)\) requires us to keep track of movements in the inventory–capital ratio q; this is done in the next section.

We have already seen that the less extreme assumption β_π ² < ∞ does not make much difference to the results.

Although the figure shows functions that are symmetric, this is not required for the results to follow.

In the case σ_p = 1, the system (22.23)–(22.24) dichotomizes and thus becomes uninteresting from an economic point of view. the case σ_w = 1 leads us back to the Goodwin growth cycle model.

For any given degree of wage flexibility and σ_w < 1 if X _ω ^p < 0 holds.

In our model short-run causality still runs from marginal productivity to real wage determination and not the other way round as was intended by Keynes in his theory of effective demand. Goods demand here only helps to determine the rate of inflation in a Wicksellian fashion.

The constant elasticity of substitution of the production function is given by the term \(\sigma= 1/(1 + \varrho )\).

Among the various nonlinearities that might serve to constrain the dynamics at a distance from the steady state are the liquidity effects modeled in Foley (1987) or the balance of payments effects considered in Sethi (1992).

We do not present an elaborate account of the conditions which establish a Hopf bifurcation here since, as is usually the case, one cannot decide whether the bifurcation occurring in the present model is subcritical, supercritical or of a linear (vertical) type. See Benhabib and Miyao (1981) for further details.

Benassy, J.-P. (1986). A non-Walrasian model of the business cycle. In: R. Day & G. Eliasson (Eds.), The dynamics of market economies. Amsterdam: North Holland.

Benhabib, J., & Miyao, T. (1981). Some new results on the dynamics of the generalized Tobin model. International Economic Review, 22, 589–596.CrossRef

Chiarella, C. (1990). The elements of a nonlinear theory of economic dynamics. Heidelberg: Springer.

Chiarella, C. (1992). The dynamics of speculative behavior. Annals of Operations Research, 37, 101–123.CrossRef

Conlisk, J. (1988). Optimization cost. Journal of Economic Behavior and Organization, 9, 213–228.CrossRef

Dornbusch, R. (1976). Expectations and exchange rate dynamics. Journal of Political Economy, 84, 1161–1176.CrossRef

Evans, G. W., & Ramey, G. (1992). Expectation calculation and macroeconomic dynamics. American Economic Review, 82, 207–224.

Fischer, S. (1972). Keynes–Wicksell and neoclassical models of money and growth. American Economic Review, 62, 880–890.

Flaschel, P. (1993). Macrodynamics. Income distribution, effective demand, and cyclical growth. Bern: Peter Lang.

Flaschel, P., Franke, R., & Semmler, W. (1994). Nonlinear macrodynamics. Stability, fluctuations and growth in monetary economies. Bielefeld: Unpublished manuscript.

Flaschel, P., & Sethi, R. (1998). The Stability of models of money and perfect foresight: Implications of nonlinearity. Economic Modelling, 16, 221–233.CrossRef

Foley, D. (1987). Liquidity-profit rate cycles in a capitalist economy. Journal of Economic Behavior and Organization, 8, 363–376.CrossRef

Franke, R. (1992). Stable, unstable, and cyclical behavior in a Keynes–Wicksell monetary growth model. Oxford Economic Papers, 44, 242–256.

Frankel, J. A., & Froot, K. A. (1986). Understanding the US dollar in the eighties: The expectations of chartists and fundamentalists. Economic Record, 62, 24–38.

Gantmacher, F. R. (1954). Theory of matrices. New York: Interscience.

Goodwin, R. M. (1967). A growth cycle. In: C. H. Feinstein (Ed.), Socialism, capitalism and economic growth. Cambridge, UK: Cambridge University Press.

Gray, M. R., & Turnovsky, S. J. (1979). The stability of exchange rate dynamics under perfect foresight. International Economic Review, 20, 643–660.CrossRef

Groth, C. (1988). IS-LM dynamics and the hypothesis of combined adaptive-forward-looking expectations. In: P. Flaschel & M. Krüger (Eds.), Recent approaches to economic dynamics. Bern: Peter Lang.

Groth, C. (1992). Keynesian-Monetarist dynamics and the corridor: A note. University of Copenhagen: mimeo.

Hirsch, M., & Smale, S. (1974). Differential equations, dynamical systems, and linear algebra. New York: Academic Press.

Keynes, J. M. (1936). The general theory of employment, interest and money. London: Macmillan.

Orphanides, A., & Solow, R. (1990). Money, inflation and growth. In: F. Hahn (Ed.), Handbook of monetary economics. Amsterdam: North Holland.

Rose, H. (1967). On the non-linear theory of the employment cycle. Review of Economic Studies, 34, 153–173.CrossRef

Rose, H. (1990). Macrodynamics. A Marshallian synthesis. London: Basil Blackwell.

Sargent, T. (1973). Interest rates and prices in the long run: A study of the Gibson paradox. Journal of Money, Credit and Banking, 5(1), 385–449.CrossRef

Sargent, T. (1987). Macroeconomic theory. New York: Academic Press.

Sethi, R. (1992). Endogenous growth cycles in an open economy with fixed exchange rates. Journal of Economic Behavior and Organization, 19, 327–342.CrossRef

Sethi, R., & Franke, R. (1995). Behavioral heterogeneity under evolutionary pressure: Macroeconomic implications of costly optimisation. Economic Journal, 105, 583–600.CrossRef

Stein, J. (1971). Money and capacity growth. New York: Columbia University Press.

Stein, J. (1982). Monetarist, Keynesian and new classical economics. London: Basil Blackwell.

Tobin, J. (1975). Keynesian models of recession and depression. American Economic Review, Papers and Proceedings, 55, 195–202.

Tobin, J. (1993). Price flexibility and output stability: An old Keynesian view. Journal of Economic Perspectives, 7, 45–65.

Titel: Classical Dynamics in a General Keynes–Wicksell Model
verfasst von: Prof. Dr. Peter Flaschel
Verlag: Springer Berlin Heidelberg
Buch: Topics in Classical Micro- and Macroeconomics
Print ISBN: 978-3-642-00323-3

Electronic ISBN: 978-3-642-00324-0

Copyright-Jahr: 2010
DOI: https://doi.org/10.1007/978-3-642-00324-0_22