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Nonlinear dynamics of educational choices under social influence and endogenous returns

Andrea Caravaggio, Marco Catola, Silvia Leoni

Abstract

Decisions to pursue higher education are not fully explained by economic incentives, with social influence and peer effects playing a crucial, yet dynamically understudied, role. This paper develops a theoretical non-linear dynamics model analysing the interplay between economic returns and social pressure. We model a heterogeneous population of "Followers" who exhibit imitative behaviour, and "Positional Agents" who display counter-adaptive behaviour. Agents' preferences for education evolve endogenously, reacting to both aggregate enrolment and an endogenous wage premium that declines with the supply of educated workers. The aggregate dynamics are governed by a one-dimensional non-linear map. By assuming fixed population structure. we show that the social conflict between pro-cyclical imitative forces and counter-cyclical positional forces can destabilize the steady state, generating a period-doubling route to chaos. These complex, endogenous fluctuations in enrolment emerge only for intermediate, heterogeneous population mixes, while homogeneous populations remain stable. We argue that this instability represents a significant coordination failure, scrambling economic signals and hindering rational long-term planning for both students and institutions, making it a key policy concern. Finally, we also extend the result to the case where the population structure is endogenous.

Nonlinear dynamics of educational choices under social influence and endogenous returns

Abstract

Decisions to pursue higher education are not fully explained by economic incentives, with social influence and peer effects playing a crucial, yet dynamically understudied, role. This paper develops a theoretical non-linear dynamics model analysing the interplay between economic returns and social pressure. We model a heterogeneous population of "Followers" who exhibit imitative behaviour, and "Positional Agents" who display counter-adaptive behaviour. Agents' preferences for education evolve endogenously, reacting to both aggregate enrolment and an endogenous wage premium that declines with the supply of educated workers. The aggregate dynamics are governed by a one-dimensional non-linear map. By assuming fixed population structure. we show that the social conflict between pro-cyclical imitative forces and counter-cyclical positional forces can destabilize the steady state, generating a period-doubling route to chaos. These complex, endogenous fluctuations in enrolment emerge only for intermediate, heterogeneous population mixes, while homogeneous populations remain stable. We argue that this instability represents a significant coordination failure, scrambling economic signals and hindering rational long-term planning for both students and institutions, making it a key policy concern. Finally, we also extend the result to the case where the population structure is endogenous.

Paper Structure

This paper contains 15 sections, 5 theorems, 57 equations, 7 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. Dynamic Trajectories with fixed population structure
  4. No preference for wage premium
  5. Preference for wage premium
  6. Effects of sensitivity to increases of supply of educated workers
  7. Dynamic Trajectory with endogenous population structure
  8. Conclusion
  9. Local derivations and proofs
  10. Primitive objects and basic derivatives
  11. Individual demands and indirect utility
  12. Aggregate map and composition dynamics
  13. Jacobian, Schur conditions, and bifurcation curves
  14. A sufficient $\ell_1$-type bound and a threshold on $\mu$
  15. Conservative computable bounds for $g^\star$ and $h^\star$

Key Result

Proposition 1

Let $\Gamma$ be the function defined in (eq:mappa) and assume for simplicity that $\rho=\rho_\pi$ and $\sigma=\sigma_\pi$. Then: $\blacktriangleleft$$\blacktriangleleft$

Figures (7)

  • Figure 1: Bifurcation Diagrams of behavioural reactivity. Parameter set: $\rho = 0.98$, $I = 1.0$, $p_e = 1.2$, $p_c = 0.53$, $\lambda = 0.5$, $\kappa = 0.3$, $\overline{\Pi}= 100$.
  • Figure 2: Time series of $E$. Parameter set: $\rho = 0.98$, $I = 1.0$, $p_e = 1.2$, $p_c = 0.53$, $\lambda = 0.5$, $\kappa = 0.3$, $\overline{\Pi}= 100$, $\sigma = 16.5$.
  • Figure 3: Cobweb Diagram of $E_t$
  • Figure 4: Bifurcation Diagram with respect to $\lambda$. Parameter set: $\rho = 1.18$, $I = 1.0$, $p_e = 1.2$, $p_c = 0.53$, $\kappa = 0.3$, $\overline{\Pi}= 100$, $\sigma = 17.9$.
  • Figure 5: Bifurcation Diagrams of behavioural reactivity. Parameter set: $\rho = 0.98$, $I = 1.0$, $p_e = 1.2$, $p_c = 0.53$, $\lambda = 0.5$, $\kappa = 0.3$, $\overline{\Pi}= 100$.
  • ...and 2 more figures

Theorems & Definitions (11)

  • Proposition 1: Existence of the fixed point
  • proof
  • Proposition 2: Absorbing interval for $\Gamma$
  • proof
  • Proposition 3
  • proof : Proof
  • Remark 1
  • Proposition 4
  • proof : Proof
  • Proposition 5
  • ...and 1 more