some notes on discount factor restrictions for dynamic optimization problems

We consider dynamic optimization problems on one-dimensional state spaces. Un- der standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1 = h(xt) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.

Time-consistent Monetary Policy Rules

A monetary policy rule is a function mapping any given output level of the economy to a corresponding rate of inflation. Such a rule is time-consistent if the central bank has no incentive to deviate from it. Within a simple dynamic model combining an output-inflation trade-off with rational private-sector expectations we study existence and properties of time-consistent monetary policy rules. It is shown that such rules exist only if (i) the central bank gives relatively high weight to price stability and relatively low weight to output stabilization and if (ii) the random shocks to the economy are not too strong. If time-consistent monetary policy rules exist, they are generically non-unique.Monetary policy, Time-consistency, Policy rules, Inflation

Inflation Forecast Targeting in an Overlapping Generations Model

In the framework of a standard overlapping generations model, it is shown that active inflation forecast targeting reinforces mechanisms that lead to indeterminacy of the monetary steady state and to countercyclical behavior of young-age consumption. The inflation forecast targeting rule which minimizes the volatility of inflation can be active or passive, depending on the characteristics of shocks and the risk aversion of households. Inflation forecast errors are always greater under active inflation forecast targeting than under passive inflation forecast targeting or strict money growth targeting. The monetary steady state is more likely to be indeterminate under an active rule of inflation forecast targeting than under the corresponding backward-looking rule (inflation targeting), but backward-looking rules can render the monetary steady state unstable.Monetary policy, Inflation forecast targeting, Overlapping generations model

A dynamic pricipal-agent problem as a feedback Stackelberg differentioal game

We consider situations in which a principal tries to induce an agent to spend e®ort on accumulating a state variable that a®ects the well-being of both parties. The only incentive mechanism that the principal can use is a state-dependent transfer of her own utility to the agent. Formally, the model is a Stackelberg di®erential game in which the players use feedback strategies. Whereas in general Stackelberg di®erential games with feedback strategy spaces the leader's optimization problem has non-standard features that make it extremely hard to solve, in the present case this problem can be rewritten as a standard optimal control problem. Two examples are used to illustrate our approach.

Insecure Property Rights and Growth: The Roles of Appropriation Costs, Wealth Effects, and Heterogeneity

We extend the model of insecure property rights by Tornell and Velasco (1992) and Tornell and Lane (1999) by adding three features: (i) extracting the common property asset involves a private appropriation cost, (ii) agents derive utility from wealth as well as from consumption, and (iii) agents can be heterogeneous. We show that both an increase in the appropriation cost and, when appropriation costs vary across agents, an increase in the degree of heterogeneity of these costs reduce the growth rate of the public capital stock. We also show that, in the interior equilibrium, the private asset can have either a lower or a higher money rate of return than the common property asset.corruption, property rights, growth, appropriation cost

Hirarchical Growth: Basic and Applied Research

We develop a model that incorporates salient features of growth in modern economies. We combine the expanding-variety growth model through horizontal innovations with a hierarchy of basic and applied research. The former extends the knowledge base, while the latter commercializes it. Two-way spillovers reinforce the productivity of research in each sector. We establish the existence of balanced growth paths. Along such paths the stock of ideas and the stock of commercialized blueprints for intermediate goods grow with the same rate. Basic research is a necessary and sufficient condition for economic growth. We show that there can be two different facets of growth in the economy. First, growth may be entirely shaped by investments in basic research if applied research operates at the knowledge frontier. Second, long-run growth may be shaped by both basic and applied research and growth can be further stimulated by research subsidies. We illustrate different types of growth processes by examples and polar cases when only upward or downward spillovers between basic and applied research are present.

Optimal Fiscal and Monetary Policy Without Commitment

This paper studies optimal fiscal and monetary policy in a stochastic economy with imperfectly competitive product markets and a discretionary government. We find that, in the flexible price economy, optimal time-consistent policy implements the Friedman rule independently of the degree of imperfect competition. This result is in contrast to the Ramsey literature, where the Friedman rule emerges as the optimal policy only if markets are perfectly competitive. Second, once nominal rigidities are introduced, the Friedman rule ceases to be optimal, inflation rates are low and stable, and tax rates are relatively volatile. Finally, optimal time-consistent policy under sticky prices does not generate the near-random walk behavior of taxes and real debt that can be observed under optimal policy in the Ramsey problem. A common reason for these results is that the discretionary government, in an effort to asymptotically eliminate its time-consistency problem, accumulates a large net asset position such that it can finance its expenditures via the associated interest earnings.

Intergenerational equity and stationarity

We consider quasi-orderings of infinite utility streams satisfying the strong Pareto axiom (i.e., Paretian quasi-orderings) and study the question of how strong a notion of intergenerational equity one can impose on these quasi-orderings without generating an impossibility theorem. Building on a result by Mitra and Basu (2007), we first show that there exist many possible extensions of the finite anonymity axiom that are satisfied by some Paretian quasiordering. Then we study how the additional requirement of stationarity `a la Koopmans (1960) affects this result. After proving a possibility theorem for this case, we demonstrate that stationarityimposes strong restrictions on the extendability of the finite anonymity axiom.

Inflation dynamics under optimal discretionary fiscal and monetary policies

We examine the dynamic properties of inflation in a model of optimal discretionary fiscal and monetary policies. The lack of commitment and the presence of nominally risk-free debt provide the government with an incentive to implement policies which induce positive and persistent inflation rates. We show that this property obtains already in an environment with flexible prices and perfectly competitive product markets. Introducing nominal rigidities and imperfect competition has no qualitative but important quantitative implications. In particular, with a modest degree of price stickiness our model generates inflation dynamics very similar to those experienced in the U.S. since the Volcker disinflation of the early 1980s.