Equality of the bulk and edge Hall conductances in a mobility gap

We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate definition of the edge conductance may be obtained through a suitable time averaging procedure or by including a contribution from states in the localized band. In a further result on the Harper Hamiltonian, we show that this contribution is essential. In an appendix we establish quantized plateaus for the conductance of systems which need not be translation ergodic.Comment: 38 pages, LaTeX, uses svjour class. Corrected a number of typos and an error in proof of Lemma four. The latter correction appears as a separate erratum in the published version. Additional typos corrected in v

Aspects of the Optimal Management of Exchange Rates

This paper analyzes aspects of the economics of the optimal management of exchange rates. It shows that the choice of the optimal exchange rate regime depends on the nature and the origin of the stochastic shocks that affect the economy. Generally, the higher is the variance of real shocks which affect the supply of goods, the larger becomes the desirability of fixity of exchange rates. The rationale for that implication is that the balance of payments serves as a shock absorber which mitigates the effect of real shocks on consumption. The importance of this factor diminishes the larger is the economy's access to world capital markets. On the other hand, the desirability of exchange rate flexibility increases the larger are the variances of the shocks to the demand for money, to the supply of money, to foreign prices and to purchasing power parities. All of these shocks exert a similar effect and their sum is referred to as the "effective monetary shock." It is also shown that the desirability of exchange rate flexibility increases the larger is the propensity to save out of transitory income. When the analysis is extended to an economy which produces traded and non-traded goods it is shown that the desirability of exchange rate flexibility diminishes the higher is the share of non-traded goods relative to traded goods and the lower are the elasticities of demand and supply of the two goods.

Sectorial Wages and the Real Exchange Rate

Consider a multi-sector economy subject to an exogenous demand shock that alters the equilibrium structure of relative prices. How should the structure of sectorial wages adjust in response to such a shock? This question is addressed in the context of a multi-sector model of an open-economy producing internationally tradable and non-tradable goods. In order to focus on intersectorial wage structure without abandoning the competitive neoclassical paradigm we assume that workers differ from each other in their absolute and relative skills. Such differences result in equilibrium wage differentials which are affected by the exogenous real shock. Cost of negotiations result in labor market contracts which set nominal wages in advance of the realization of the stochastic shocks. The analysis provides formulae for the optimal sectorial wage-indexation rules. The optimal rules alter both the absolute and the relative structure of sectorial nominal wages. We examine the dependence of the optimal wage adjustments on the degree of heterogeneity of the skill distribution and on the degree to which the economy is open to international trade; we also study the effects of various shocks and policies on the real exchange rate, real wages and the distribution of income.

Optimal Wage Indexation, Foreign-Exchange Intervention and Monetary Policy

This paper deals with the design of optimal monetary policy and with the interaction between the optimal degrees of wage indexation and foreign exchange intervention. The model is governed by the characteristics of the stochastic shocks which affect the economy and by the information set that individuals possess. Because of cost of negotiations, nominal wages are assumed to be precontracted and wage adjustments follow a simple indexation rule that links wage changes to observed changes in price. The use of the price level as the only indicator for wage adjustments may not permit an efficient use of available information and, may result in welfare loss. The analysis specifies the optimal set of feedback rules that should govern policy aiming at the minimization of the welfare loss. These feedback rules determine the optimal response of monetary policy to changes in exchange rates, interest rates and foreign prices. The adoption of the optimal set of feedback rules results in the complete elimination of the welfare cost arising from the simple indexation rule and from the existence of nominal contracts. Since optimal policies succeed in the elimination of the distortions, issues concerning the nature of contracts and the implications of specific assumptions about disequilibrium positions become inconsequential. The analysis then proceeds to examine the interdependence between the optimal feedback rules and the optimal degree of wage indexation. It is shown that a rise in the degree of exchange rate flexibility raises the optimal degree of wage indexation. One of the key conclusions is the proposition that the number of independent feedback rules that govern a policy must equal the number of independent sources of information that influence the determination of the undistorted equilibrium. Thus, it is shown that with a sufficient number of feedback rules for monetary policy there may be no need to introduce wage indexation. It is also shown that an economy that is not able to choose freely an exchange rate regime can still eliminate the welfare loss by supplementing the(constrained) monetary policy with an optimal rule for wage indexation. The paper concludes with an examination of the consequences of departures from optimal policy by comparing the welfare loss resulting from the imposition of alternative constraints on the degree of wage indexation, on foreign exchange intervention and on the magnitudes of other policy feedback coefficients.

Supply Shocks, Wage Indexation and Monetary Accommodation

This paper develops a unified framework for the analysis of wage indexation and monetary policy in the presence of supply shocks. We first present simple formulae for the optimal wage indexation rule and for the optimal money supply rule. In order to set the stage for an evaluation of departures from the optimal policy rules we first analyse two extreme cases -- a rule that stabilizes employment and a rule that stabilizes the real wage. The analysis of these two extreme cases provides the ingredients for the evaluation of various rules for wage indexation and for monetary targeting. We examine the implications of indexing wages to (i) nominal GNP, (ii) the CPI and (iii) the value-added price index, as well as the implications of targeting the money supply to these alternative three indicators. It is shown that, the various indexation rules bear a dual relation to the various monetary targeting rules. The welfare ranking of the various rules depends on whether the elasticity of the demand for labor exceeds or falls short of the elasticity of labor supply. If the demand for labor is more elastic than the supply, then policy rules that stabilize employment produce a smaller welfare cost than policy rules that stabilize the real wage. In that case, indexing wages to nominal GNP results in a smaller welfare cost than indexing to value-added price index which, in turn, produces a smaller cost than indexation to the CPI. Because of the dual relation between monetary policy and wage indexation, it follows that under the same circumstances, monetary policy that targets nominal GNP produces a smaller welfare cost than policy that targets the value-added price index which, in turn, results in a smaller cost than the policy that targets the CPI. This ranking is reversed when the elasticity of the supply of labor exceeds the elasticity of demand.

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates on fractional moments of the matrix elements of $U_\omega(U_\omega -z)^{-1}$, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of $S$. Such estimates imply almost sure localization for $U_\omega$

Exponential dynamical localization for the almost Mathieu operator

We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency

The collection efficiency of the Value Added Tax: Theory and international evidence

This paper evaluates the political economy and structural factors explaining the collection efficiency of the Value Added Tax (VAT), where the collection efficiency is determined by the probability of audit and by the penalty on underpaying, and implementation lags imply that the present policy maker determines the efficiency of the tax system next period. Theory suggests that the collection efficiency is affected by political economy considerations - greater polarization and political instability would reduce the efficiency of the tax collection, and collection is impacted by structural factors affecting the ease of tax evasion (such as urbanization, agriculture share, openness). We evaluate the VAT collection efficiency (VAT revenue over the aggregate consumption divided by the standard VAT rate) in a panel of 44 countries over 1970-99. A one standard deviation increase in durability of political regime, and in the ease and fluidity of political participation, increases the VAT collection efficiency by 3.1% and 3.6%, respectively. A one standard deviation increase in urbanization, trade openness and the share of agriculture, changes the VAT collection efficiency by 12.7%, 3.9% and -4.8%, respectively. Qualitatively identical results apply for the ratio of VAT revenue to GDP divided by the standard VAT

Decay Properties of the Connectivity for Mixed Long Range Percolation Models on Zd\Z^d

In this short note we consider mixed short-long range independent bond percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge $(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity $\tau_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.Comment: 6 page

Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.Comment: 29 pages, 1 figure, to appear in AH