High-Dimensional Menger-Type Curvatures - Part I: Geometric Multipoles and Multiscale Inequalities

We define a discrete Menger-type curvature of d+2 points in a real separable Hilbert space H by an appropriate scaling of the squared volume of the corresponding (d+1)-simplex. We then form a continuous curvature of an Ahlfors d-regular measure on H by integrating the discrete curvature according to the product measure. The aim of this work, continued in a subsequent paper, is to estimate multiscale least squares approximations of such measures by the Menger-type curvature. More formally, we show that the continuous d-dimensional Menger-type curvature is comparable to the ``Jones-type flatness''. The latter quantity adds up scaled errors of approximations of a measure by d-planes at different scales and locations, and is commonly used to characterize uniform rectifiability. We thus obtain a characterization of uniform rectifiability by using the Menger-type curvature. In the current paper (part I) we control the continuous Menger-type curvature of an Ahlfors d-regular measure by its Jones-type flatness.Comment: 47 pages, 13 figures. Minor revisions and the inclusion of figure

Mixed Dynamics in a Parabolic Standard Map

We use numerical and analytical tools to demonstrate arguments in favor of the existence of a family of smooth, symplectic diffeomorphisms of the two-dimensional torus that have both a positive measure set with positive Lyapunov exponent and a positive measure set with zero Lyapunov exponent. The family we study is the unfolding of an almost-hyperbolic diffeomorphism on the boundary of the set of Anosov diffeomorphisms, proposed by Lewowicz.Comment: laTeX, 31 pages, 15 figure

RURAL LIVELIHOODS IN ARMENIA

In this paper the structure of the rural economy in Armenia is explored from a household perspective. The paper draws on the livelihoods framework, recognizing the different capitals and activities that support rural households' livelihood strategies. Ownership of capitals and access to activities are examined in relation to the incidence of poverty on the basis of data from a recent large-scale survey of rural households in Armenia. Different measures for the outcome of livelihood strategies in terms of well-being are observed, which are consistently linked to income levels across poor and other households. Income-poor households are found to be less well-endowed especially with financial and social capital. They derive smaller income shares from economic activities, and more from dissaving and social payments. The findings are relevant to policies aimed at alleviating rural poverty.Community/Rural/Urban Development, Labor and Human Capital,

Productivity and Efficiency of Corporate and Individual Farms in Ukraine

The paper presents a comparative analysis of the productivity of corporate and individual farms in Ukraine based primarily on cross-section data from a farm survey conducted by FAO in 2005. We calculate partial land and labor productivity, total factor productivity, and technical efficiency scores (using Stochastic Frontier Analysis) for farms of different organizational forms. Our results demonstrate with considerable confidence that, contrary to established convictions among the Ukrainian decision makers, the large corporate farms are not more productive than the smaller family farms. This finding is not restricted to Ukraine, as a similar result has been obtained by in Moldova, Russia, and the U.S. Policies encouraging a shift from large corporate farms to smaller individual farms, rather than the reverse, can be expected to produce beneficial results for Ukrainian agriculture and the economy in general. The government of Ukraine should abandon its inherited preference for large-scale corporate farms and concentrate on policies to improve the operating conditions for small individual farms. At the very least, the government should ensure a level playing field for farms of all sizes and organizational forms, and desist from biasing its policies in favor of large farms.family farms, corporate farms, comparative performance, technical efficiency, total factor productivity, agrarian reforms, transition countries, Farm Management, Productivity Analysis, D24, J24, P27, P31, P32, Q12, Q15, R14,

Promoting Economic Mobility by Increasing Postsecondary Education

Explores policy options for expanding educational opportunities for low-income students to enhance upward economic mobility. Examines the effectiveness of student aid in promoting college completion and proposes a plan for better guidance and preparation

Least squares approximations of measures via geometric condition numbers

For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine subspace. Such approximations are given by averaging real-valued multivariate functions which are typically scalings of squared (d+1)-volumes of (d+1)-simplices. Specifically, we show that such averages are comparable to the square of the d-dimensional least squares error of that measure, where the comparison depends on a simple quantitative geometric property of it. This result is a higher dimensional generalization of the elementary fact that the double integral of the squared distances between points is proportional to the variance of measure. We relate our work to two recent algorithms, one for clustering affine subspaces and the other for Monte-Carlo SVD based on volume sampling

Farm debt in transition countries: Lessons for Tajikistan

Farms in Tajikistan currently face a severe debt crisis that has been caused by a combination of two factors typical of such situations in many countries: (a) the inability of the farms to make a profit under current conditions and (b) continued lending by the banks to cotton producers regardless of reduced payment capacity and lack of credit-worthiness. The paper traces the accumulation of farm debt in Tajikistan to pervasive government intervention in both financing and production decisions, which has led to soft budget constraints and moral hazard behavior. The purpose of the paper is to inform the debate around the issue of cotton farm debt in Tajikistan by studying the experience of other countries that had to contend with farm debt overhangs in the 1980s and the 1990s. Five CIS transition countries (Belarus, Kazakhstan, Moldova, Russia, and Ukraine) and one market economy (Israel) are studied using time series of aggregate financial reports of the farm sectors. The comparative analysis shows that the farm debt issue is not strictly a transition economy phenomenon. The problem can occur in market economies (e.g., Israel) if the state pursues policies directed toward the expansion of farm production without heed to creditworthiness of the farms and if the farm structure is incompatible with profitability and efficiency criteria. The basic reasons that led to debt accumulation in CIS and in Israel remain valid to this day, and the policy solutions implemented in these countries are relevant for Tajikistan.Farm debt, transition economies, Tajikistan, CIS, Israel, farm restructuring, agricultural reforms, Agricultural Finance, Institutional and Behavioral Economics, Q140, P210, P320, G300,

Rethinking agricultural reform in Ukraine

Land reform and farm restructuring have always been a major component of the transition from plan to market in all formerly socialist countries, and especially in the 12 former Soviet republics forming the Commonwealth of Independent States (CIS). Ukraine, the second most populous country in CIS (after Russia) and the third largest by area (after Russia and Kazakhstan), began the process of agrarian reform in March 1991, six months before the declaration of independence from the Soviet Union. However, all through the 1990s international organizations berated Ukraine for its slow and insufficient reforms. Derogatory phrases like "one step forward, two steps back", "changing the sign on the door", "disappointing performance", "lack of vigorous progress" were universally (and justifiably) used to describe the Ukrainian reforms during the presidency of Leonid Kravchuk (1991-1994) and then (perhaps with less justification) under Leonid Kuchma (1994-2004). Evaluating the outcomes of nine years of reforms through 1999, World Bank experts summarized the conclusions of their continuous monitoring efforts in the following uncomplimentary language (CSAKI, LERMAN, 2001): In Ukraine, land reform has been mostly limited to transforming state ownership into collective ownership⦠The weak reforms have failed to radically change the traditional collective organization of Ukrainian farms⦠Break-up and internal restructuring of large farms has been very limited. Hence it should not be a surprise that the transition process is not delivering in terms of increased profitability and efficiency. The "big bang" came in December 1999 in the form of Presidential Decree No. 1529/99 "On immediate measures to accelerate the reforms in the agricultural sector". By this decree Ukraine made the momentous decision to complete land privatization through conversion of the "land shares" â paper certificates of landownership previously distributed to the rural population â into demarcated and titled physical plots. This decision, long advocated by international donors, set Ukrainian land policies sharply apart from the policies of other large CIS countries (Russia, Kazakhstan, Belarus), and put Ukraine roughly on the same land reform path as the two smallest CIS members, Moldova and Azerbaijan. January 2005 marked the five-year anniversary of this landmark decree. FAO accordingly launched a monitoring study to assess the outcomes of reform since 2000 and to formulate a set of policy recommendations based on the post-2000 reality in the rural sector.1 The overall purpose of the study was to determine to what extent and in what ways there had been fundamental changes in land and farm policy after 2000. The methodology included a structured questionnairebased survey of three constituencies representing the Ukrainian farm structure: The managers of large corporate farms, individual peasant farmers, and operators of rural household plots (this survey is referred to as the 2005 FAO farm survey). Interviews were also conducted with regional agricultural officials to get a view of farm-level changes "from the outside". Official national statistics were used to construct a picture of sectoral changes. The survey was designed to conduct a comparative analysis of land rights, management structure, and economic performance in the two main sectors of Ukrainian agriculture â corporate farms and individual farms. We were also planning to collect information that would enable us to detect significant differences between the "new wave" corporate farms created on the basis of the new legislation in the post-2000 period and the "old wave" descendants of the traditional collective and state farms. The study is a collaborative effort of three institutions: The Policy Assistance Branch of FAOâs Regional Office for Europe and Central Asia (REUP) in Rome, the UNDP-sponsored Agricultural Policy for Human Development (APHD) project in Kiev, and the Institute of Sociology, also in Kiev. David Sedik as the Head of REUP was responsible for the overall design, management, and coordination of the study. Vladimir Artyushin and Nikolai Pugachev from the APHD project were in charge of the local implementation of the study in Ukraine, including collection and analysis of sectoral data. Yurii Privalov, Aleksandr Goncharuk, and Maria Olenina from the Institute of Sociology were responsible for the survey field work and oversaw the construction of the computer database with the survey data. Zvi Lerman from the Hebrew University of Jerusalem provided overall scientific guidance for the survey and, together with David Sedik, carried out the final analysis on which the study is based. This book is organized in two parts. Part I presents a brief overview of the agricultural policy environment in Ukraine before and after 2000, followed by a detailed discussion of the legal foundations of land and farm reform and an overall picture of the impacts of reform on the farm sector since 1990. Part II presents the findings of a survey of nearly 1,400 individual and corporate farms conducted in the spring of 2005 in eight oblasts. The survey has been designed to provide focused information highlighting the changes that occurred at the farm level since the 1999 Presidential Decree. The Executive Summary at the beginning of the volume contains the main findings of the study and some policy recommendations. The last chapter (Chapter 16) brings together our main conclusions in a more detailed format. The main literature and data sources used in the study are given in the list of references at the end. Tables and figures without references to a specific source are based on the 2005 FAO farm survey.Agricultural Finance, Community/Rural/Urban Development, Consumer/Household Economics, Farm Management, Industrial Organization, Labor and Human Capital, Land Economics/Use,

Sources of Agricultural Productivity Growth in Central Asia

The paper examines agricultural production and productivity growth in two Central Asian countries – Tajikistan and Uzbekistan. Both countries are characterized by a significant shift of resources from the traditional Soviet model of collective agriculture to more market-compliant individual and family farming. In both countries, the beginning of the policy-driven switch to family farming around 1997 coincided with the beginning of recovery in agriculture, namely resumption of agricultural growth after a phase of transition decline since 1991. In addition to growth in total agricultural production, we also observe significant increases in productivity of both land and labor since 1997. These observations suggest that productivity growth may be attributable to the changes in farming structure in Central Asia. To check this conjecture we assess the sources of growth by applying the standard Solow growth accounting methodology. Using time series of country statistics for farms of different organizational forms, we decompose the growth in output into growth in the resource base (extensive growth) and growth in productivity (intensive growth). Solow growth accounting clearly shows that, first, much of the growth at the country level is attributable to increases in productivity rather than increases in resources and, second, the increases in productivity in family farms (especially household plots) outstrip the increases in productivity in former collective and state farms. These findings confirm that the recovery of agricultural production in Central Asia has been driven largely by productivity increases, and it is the individual farms that are the main source of agricultural productivity increases.agricultural productivity, agricultural growth, family farms, corporate farms, comparative performance, agrarian reforms, transition countries, Central Asia, Tajikistan, Uzbekistan, Agricultural and Food Policy, Institutional and Behavioral Economics, Land Economics/Use, Productivity Analysis, P27, P31, P32, Q15, R14,