Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives

A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a strongly polynomial algorithm for the case when all $C_{ij}$'s are convex quadratic functions, settling an open problem raised e.g. by Hochbaum [1994]. We also give strongly polynomial algorithms for computing market equilibria in Fisher markets with linear utilities and with spending constraint utilities, that can be formulated in this framework (see Shmyrev [2009], Devanur et al. [2011]). For the latter class this resolves an open question raised by Vazirani [2010]. The running time is $O(m^4\log m)$ for quadratic costs, $O(n^4+n^2(m+n\log n)\log n)$ for Fisher's markets with linear utilities and $O(mn^3 +m^2(m+n\log n)\log m)$ for spending constraint utilities. All these algorithms are presented in a common framework that addresses the general problem setting. Whereas it is impossible to give a strongly polynomial algorithm for the general problem even in an approximate sense (see Hochbaum [1994]), we show that assuming the existence of certain black-box oracles, one can give an algorithm using a strongly polynomial number of arithmetic operations and oracle calls only. The particular algorithms can be derived by implementing these oracles in the respective settings

Monetary Policy, Interest Rate Rules, and Inflation Targeting: Some Basic Equivalences

Policymakers increasingly view short-term nominal interest rates as the main instrument of monetary policy, often in conjunction with some inflation target. Interest rates on short-term indexed government debt (i.e., a real interest rate) have also been used as policy instruments. To understand the pros and cons of different policy rules and instruments, this paper derives some basic equivalences among different policy rules. It is shown that, under certain conditions, the following three rules are exactly equivalent: (i) a 'k-percent' money growth rule; (ii) a nominal interest rate rule combined with an inflation target; and (iii) a real interest rate rule combined with an inflation target. These policy rules, however, become increasingly complex: the first rule requires no feedback mechanism; the second rule requires responding to the inflation gap; while the third rule involves responding to both the inflation gap and the output gap. It is also shown that policy rules which respond to the output gap may avoid a deflationary adjustment.

Approximating Minimum-Cost k-Node Connected Subgraphs via Independence-Free Graphs

We present a 6-approximation algorithm for the minimum-cost $k$-node connected spanning subgraph problem, assuming that the number of nodes is at least $k^3(k-1)+k$. We apply a combinatorial preprocessing, based on the Frank-Tardos algorithm for $k$-outconnectivity, to transform any input into an instance such that the iterative rounding method gives a 2-approximation guarantee. This is the first constant-factor approximation algorithm even in the asymptotic setting of the problem, that is, the restriction to instances where the number of nodes is lower bounded by a function of $k$.Comment: 20 pages, 1 figure, 28 reference

How is Tax Policy Conducted over the Business Cycle?

It is well known by now that government spending has typically been procyclical in developing economies but acyclical or countercyclical in industrial countries. Little, if any, is known, however, about the cyclical behavior of tax rates (as opposed to tax revenues, which are endogenous to the business cycle and hence cannot shed light on the cyclicality of tax policy). We build a novel dataset on tax rates for 62 countries for the period 1960-2013 that comprises corporate income, personal income, and value-added tax rates. We find that, by and large, tax policy is acyclical in industrial countries but mostly procyclical in developing countries. Further, tax policy in countries with better institutions and/or more integrated with world capital markets tends to be less procyclical/more countercyclical.

Output Costs, Currency Crises, and Interest Rate Defense of a Peg

Central banks typically raise short-term interest rates to defend currency pegs. Higher interest rates, however, often lead to a credit crunch and an output contraction. We model this trade-off in an optimizing, first-generation model in which the crisis may be delayed but is ultimately inevitable. We show that higher interest rates may delay the crisis, but raising interest rates beyond a certain point may actually bring forward the crisis due to the large negative output effect. The optimal interest rate defense involves setting high interest rates (relative to the no defense case) both before and at the moment of the crisis. Furthermore, while the crisis could be delayed even further, it is not optimal to do so.

Delaying the Inevitable: Optimal Interest Rate Policy and BOP Crises

The classical model of balance of payments crises implicitly assumes that the central bank sits passively as international reserves dwindle. In practice, however, central banks typically defend pegs aggressively by raising short-term interest rates. This paper analyzes the feasibility and optimality of raising interest rates to delay a potential BOP crisis. Interest rate policy works through two distinct channels. By raising demand for domestic, interest-bearing liquid assets, higher interest rates tend to delay the crisis. Higher interest rates, however, increase public debt service and imply higher future inflation, which tends to bring forward the crisis. We show that, under certain conditions, it is feasible to delay the crisis, but raising interest rates beyond a certain point may actually hasten the crisis. A similar non-monotonic relationship emerges between welfare and the increase in interest rates. It is thus optimal to engage in some active interest rate defense but only up to a certain point. In fact, there is a whole range of interest rate increases for which it is feasible to delay the crisis but not optimal to do so.

Living with the Fear of Floating: An Optimal Policy Perspective

As documented in recent studies, developing countries (classified by the IMF as floaters or managed floaters) are extremely reluctant to allow for large nominal exchange rate fluctuations. This 'fear of floating' is reflected in the fact that, in spite of being subject to larger shocks, developing countries exhibit lower exchange rate variability and higher reserve variability than developed countries. Moreover, there is a positive correlation between changes in the exchange rate and interest rates and a negative correlation between both changes in reserves and the exchange rate and changes in interest rates and reserves. We build a simple model that rationalizes these key features as the outcome of an optimal policy response to monetary shocks. The model incorporates three key frictions: an output cost of nominal exchange rate fluctuations, an output cost of higher interest rates to defend the currency, and a fixed cost of intervention.

Segmented Asset Markets and Optimal Exchange Rate Regimes

This paper revisits the issue of the optimal exchange rate regime in a flexible price environment. The key innovation is that we analyze this question in the context of environments where only a fraction of agents participate in asset market transactions (i.e., asset markets are segmented). Under this friction alternative exchange rate regimes have different implications for real allocations in the economy. In the context of this environment we show that flexible exchange rates are optimal under monetary shocks and fixed exchange rates are optimal under real shocks.

Segmented Asset Markets and Optimal Exchange Rate Regimes

This paper revisits the issue of the optimal exchange rate regime in a flexible price environment. The key innovation is that we analyze this question in the context of environments where only a fraction of agents participate in asset market transactions (i.e., asset markets are segmented). Under this friction, alternative exchange rate regimes have different implications for real allocations in the economy. In particular -- and contrary to standard results under sticky prices -- we show that flexible exchange rates are optimal under monetary shocks and fixed exchange rates are optimal under real shocks.