Dynamic Savings Choices with Disagreements

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=AM_HTMLorMML-full"></script>We study a flexible dynamic savings game in continuous time, where decision makers rotate in and out of power. These agents value spending more highly while in power creating a time-inconsistency problem. We provide a sharp characterization of Markov equilibria. Our analysis proceeds by construction and isolates the importance of a local disagreement index, `beta(c)`, defined as the ratio of marginal utility for those in and out of power. If disagreement is constant the model specializes to hyperbolic discounting. We also provide novel results for this case, offering a complete and simple characterization of equilibria. For the general model we shoe that dissaving occurs when disagreements are sufficiently high, while saving occurs when disagreements are sufficiently low. When disagreements vary sufficiently with spending, richer dynamics are possible. We provide conditions for continuous equilibria and also show that the model can be inverted for primitives that support any smooth consumption function. Our framework applies to individuals under a behavioral interpretation or to governments under a political-economy interpretation