This paper analyzes optimal paths in a one-sector growth model when the technology is not convex. In such a case, we prove that optimal paths converge to the upper steady state iff the initial wealth is above a critical level. Then, we first show that, thanks to debt and/or R&D, the poverty trap may be avoided. Second, we introduce a distortion: corruption that mostly has dramatic consequences on growth, but may have a beneficial effect if it is not high and if it improves productivity (incentive effect).

It is common to interpret rejections of the unit-root null hypothesis in favor of a trend stationary process with possible trend breaks as evidence that the data are better characterized as stationary about a broken trend. This interpretation is valid only if the model postulated under the alternative hypothesis is the only plausible alternative to the model postulated under the null. We argue that there are economically plausible models that are not well captured under either the null hypothesis or the alternative hypothesis of these tests. We show that applied researchers who ignore this possibility are likely to reject the unit-root null with high probability in favor of a trend stationary process with possible breaks. Our evidence shows that this potential pitfall is both economically relevant and quantitatively important. We explore the extent to which applied users may mitigate inferential errors by using finite-sample and bootstrap critical values.

This paper examines the quantitative implications of government fiscal policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits local indeterminacy, we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10-cycles, quasiperiodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability, suggesting a unique equilibrium, whereas the true nonlinear model exhibits global indeterminacy. This result implies that stabilization policies designed to suppress sunspot fluctuations near the steady state may not prevent sunspots, cycles, or chaos in regions away from the steady state. Overall, our results highlight the importance of using a model's nonlinear equilibrium conditions to fully investigate global dynamics.

We investigate the optimal path of the primary surplus that a government will choose to minimize costs that derive from exceeding the Maastricht criteria and generally of a “stability pact,” where we assume three components of costs that are related to (1) the debt-to-GDP ratio, (2) the overall deficit-to-GDP ratio, and (3) the acceptance level of savings in the economy. We show that various political-economic settings can result in completely different equilibrium strategies of the debt-to-GDP ratio and the primary deficit. The spectrum of possible optimal strategies ranges from no stationary solutions to multiple equilibrium and cyclical solutions and from positive to negative levels of the optimal debt-to-GDP ratio. Our results emphasize the importance of macroeconomic and behavioral (acceptance rate of a policy) variables in order to explain complex economic time series.

The paper studies multivariate non linear economic dynamical systems with an expectations feedback subjected to exogenous perturbations. In these systems, agents form expectations on future variables based on subjective transition probabilities given by a Markov kernel. The notion of a perfect Markov kernel that generates rational expectations along all orbits of the system is proposed. Conditions are provided under which perfect Markov kernels exist. Applications are given to models of the Cobweb type, to multivariate affine-linear systems, and to the stochastic OLG model of economic growth. For the latter two models, it is shown when a globally attracting random fixed point with rational expectations exists.

Taken literally, the concept of “stabilization policy” implicitly assumes that the macroeconomy is unstable without imposition of a policy. Hence, selection of a “stabilization policy” can be viewed as selection of a policy to bifurcate the system from an unstable to a stable operating regime. The literature on dynamics of high-dimensional systems suggests that successful bifurcation selection is challenging. As an experiment to investigate this point of view, we use the continuous-time UK dynamic macroeconometric model. Under assumptions designed to be most favorable to stabilization policy, we find that policies that would produce successful bifurcation are very complicated. We also find that less complicated policies based upon reasonable economic intuition can be counterproductive, since such policies can contract the size of the stable subset of the parameter space. In fact, an economy that is dynamically stable without policy, but subject to stochastic shocks, could be bifurcated to instability with imposition of a poorly designed “stabilization” policy.

It has been argued that a clear understanding of the stochastic growth model can best be achieved by working out an approximate analytical solution. This paper follows that idea but streamlines the presentation of the loglinear approximate solution for the neoclassical model of capital accumulation. By focusing on the partial elasticity of capital stock with respect to its lag term, this paper is able to confirm analytically some conclusions based on numerical calculations in previous papers, and to clarify why a simpler solution arises in several special cases.