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Expectations and industry location: a discrete time dynamical analysis

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Abstract

The new economic geography (NEG) aims to explain long-term patterns in the spatial allocation of industrial activities. It stresses that endogenous economic processes may enlarge small historic differences leading to quite different regional patterns—history matters for the long-term geographical distribution of economic activities. A pivotal element is that productive factors move to another region whenever the anticipated remuneration is higher in that region. Given the long-term nature of NEG analyses and the crucial role of expectations, it is astonishing that most of the existing models assume only naïve or myopic expectations. However, a recent stream of the literature in behavioral and experimental economics shows that agents often use expectational heuristics, such as trend extrapolating and trend reverting rules. We introduce such expectations formation hypotheses into a NEG model formulated in discrete time. This modification leads to a system of two nonlinear difference equations (corresponding, in the language of dynamical systems theory, to a 2-dimensional piecewise smooth map) and thus enriches the possible dynamic patterns: with trend extrapolating (reverting) the symmetric equilibrium is less (more) stable; and it may lose stability only via a flip bifurcation (or also via a Neimark–Sacker bifurcation) giving rise to a period-doubling cascade (or also to quasi-periodic orbits). In both cases, complex behavior is possible; multistability, that is, the coexistence of locally stable equilibria, is pervasive; and border-collision bifurcations are also allowed. In this sense, our analysis corroborates some of the basic insights of the NEG.

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Notes

  1. Specifically, Ottaviano (2001) considers the original Krugman’s (1991a) CP model in which the mobile factor, labor, enters in the representative firm’s cost function both as a fixed and as a variable component; Baldwin’s (2001) footloose entrepreneurs (FE) model is an analytically solvable version of the CP model in which the mobile factor, entrepreneurs or human capital, enters in the cost function only as a fixed component. Oyama (2009a, b) extends Baldwin’s analysis to the case of an economy with two or more asymmetric regions (i.e. with different market sizes or degrees of trade openness).

  2. In the case of two asymmetric regions, self-fulfilling prophecies may also re-direct the economy from one CP equilibrium to the other (see Oyama 2009a).

  3. Compared to the standard CP model or to the FE model, the FC model is analytically much simpler. The mobile factor, physical capital, enters only as a fixed component in the cost function as in the FE model; moreover, shifting capital units from one region to the other does not alter the relative market size of the two regions as it occurs for the other two kinds of NEG models after workers or entrepreneurs migration.

  4. Let us note that, strictly speaking, the equilibria \(P^{0}\) and \(P^{1}\) are one-side saddles whose stable sets are reached by some trajectories.

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Acknowledgments

The authors are grateful to the anonymous referees for their useful comments.

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Authors and Affiliations

  1. Department of Scienze Economiche e Sociali, Catholic University, Piacenza, Italy

    Anna Agliari

  2. Department of Economics, University of Naples ‘Federico II’, Naples, Italy

    Pasquale Commendatore

  3. Department of Statistica e Metodi Quantitativi, University of Milano-Bicocca, Milan, Italy

    Ilaria Foroni

  4. Department of Economics, WU Vienna University of Economics and Business, Vienna, Austria

    Ingrid Kubin

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  1. Anna Agliari
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  2. Pasquale Commendatore
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  3. Ilaria Foroni
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  4. Ingrid Kubin
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Correspondence to Ilaria Foroni.

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Agliari, A., Commendatore, P., Foroni, I. et al. Expectations and industry location: a discrete time dynamical analysis. Decisions Econ Finan 37, 3–26 (2014). https://doi.org/10.1007/s10203-012-0139-1

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