A Gravitational Lens need not produce an Odd Number of Images

Given any space-time $M$ without singularities and any event $O$, there is a natural continuous mapping $f$ of a two dimensional sphere into any space-like slice $T$ not containing $O$. The set of future null geodesics (or the set of past null geodesics) forms a 2-sphere $S^2$ and the map $f$ sends a point in $S^2$ to the point in $T$ which is the intersection of the corresponding geodesic with $T$. To require that $f$, which maps a two dimensional space into a three dimensional space, satisfy the condition that any point in the image of $f$ has an odd number of preimages, is to place a very strong condition on $f$. This is exactly what happens in any case where the odd image theorem holds for a transparent gravitational lens. It is argued here that this condition on $f$ is probably too restrictive to occur in general; and if it appears to hold in a specific example, then some $f$ should be calculated either analytically or numerically to provide either an illustrative example or counterexample.Comment: 8 pages, amste

The Effect of Migrant Workers on Employment,Real Wages and Inequality The Case of Israel -1995 to 2000

This paper deals with the impact of migrant workers on the Israeli wage structure, on the chances of being unemployed or out of the labor force and on inequality in gross earnings from work. One of the manifestations of globalization is the movement of migrant workers from low-income to richer countries.The recent increase in living standards in Israel has created significant wage differentials for workers from low-income countries. Paradoxically,an important trigger for this process was also the worsening of Israel’s security situation in 1993,following the Oslo accord between Israel and the Palestinians.Israel responded to the deterioration by closures,which sharply reduced the number of Palestinian workers in Israel,substituting them with migrant workers, mainly from Eastern Europe,South and Central America and the Far East. The rapid inflow of migrant workers,especially since 1995,makes Israel an interesting case study for studying its effects on labor force participation, unemployment,the wage structure and gross earnings inequality.Given the bias in the government’s permit policy in favor of unskilled workers,the paper emphasizes the effects on Israelis with weak economic endowments. The research is based on pooled micro data,combined with data on the number of non-Israeli workers by economic branch.The micro-data is based on the Israeli income survey,including a host of personal characteristics,such as the individual’s education level,labor market status and a model-based calculation of welfare benefits. The research also focuses on government policy issues,such as the effect of the replacement ratio on the rate of labor force participation.For individuals not in the labor force the replacement ratio is defined as the income support payment divided by the potential wage.The inflow of migrant workers affects the potential wage negatively and together with a relatively easy access to income support payments,this policy variable is found to contribute significantly to the explanation of the exclusion from the labor force and the worsening of gross earnings distribution in a statistically significant way.The effect of these variables on unemployment is less clear and the effects on the wage structure are varied,distinguishing between substitutive and complementary effects,depending on the individual’s occupational and educational characteristics as well as on the time perspective. The study also shows that the highly branch-specific Israeli migrant permit policy did not prevent the effects on wages from spreading throughout the economy,thus emphasizing the general-equilibrium nature of these effects.Migrants; Foreign workers; Israel; Income inequality; Employment

Globalization and World financial Turmoil - A Test for Israel's Economic Policy

The World financial turmoil,that beset emerging economies during much of 1997 and culminated after the Russian crisis in the second half of 1998,presents an interesting test case for economic policy in an open economy.Israel's policy response was radical,and -with the benefit of hindsight -successful in maintaining and reinforcing stability,when the odds of many emerging economies,such as Israel,were clearly at risk.Indeed several emerging markets suffered a severe setback in output,a deep and sometimes contagious fall in the value of stocks and a sharp depreciation in their exchange rates,when the world financial crisis evolved.National policy mistakes were punished by rapid capital flight,spearheaded by foreign investors and accompanied by a loss of these countries'international creditworthiness. What can we learn from Israel's experience in the late 1990s? Lesson #1:Macroeconomic stability must be maintained continually. Lesson #2:Enhance the Flexibility of the Exchange Rate Regime Lesson #3:A nominal appreciation can be consistent with a real depreciationFinancial stability; Israel; Financial Vulnerability; Globalization; Sustainable Macroeconomic policy; Financial Liberalization

Eigenbundles, Quaternions, and Berry's Phase

Given a parameterized space of square matrices, the associated set of eigenvectors forms some kind of a structure over the parameter space. When is that structure a vector bundle? When is there a vector field of eigenvectors? We answer those questions in terms of three obstructions, using a Homotopy Theory approach. We illustrate our obstructions with five examples. One of those examples gives rise to a 4 by 4 matrix representation of the Complex Quaternions. This representation shows the relationship of the Biquaternions with low dimensional Lie groups and algebras, Electro-magnetism, and Relativity Theory. The eigenstructure of this representation is very interesting, and our choice of notation produces important mathematical expressions found in those fields and in Quantum Mechanics. In particular, we show that the Doppler shift factor is analogous to Berry's Phase.Comment: 22 pages, also found on http://math.purdue.edu/~gottlie

Social Policy Targeting and Binary Information Transfer between Surveys

This paper deals with the optimal transfer of binary information (BIT) on group membership between different statistical surveys of an identical population, a need arising frequently in socio-economic surveys. The limited number of questions asked in any one survey may necessitate information transfer between surveys. We design a method for a a BIT between a source-survey originally including the information and a target survey in which it is needed. An efficient BIT depends on (1) efficient estimation of the statistical model explaining group-membership as estimated by the ROC-curve, (2) the choice of a cutoff value for translating the forecasted logistic probability back into a binary variable and (3) a statistically testable quality control of the transfer. We suggest an optimal cutoff point that minimizes the sum of squared errors instead of the well-known Hosmer-Lemeshow method. Our application illustrates how survey data can be enhanced, when repeated interviews are expensive or difficult to implement. We enhance the Household Expenditure Survey (HES) by transferring a binary variable of households' religious group membership from the Social Survey to the HES. This helps identify extremely poor groups for poverty calculations and improved targeting of anti-poverty policy.ROC curves; Binary Variables; Logistic Regression; Group Identification; Optimal Cutoff Value; Poverty Targeting; Poverty Mapping; Small Area Estimation

Chapter 8: Issues in Welfare Policy

The incidence of poverty,as measured by the relative index customarily used in Israel,rose in 2005 to a level of 24.7 percent.Some reduction in poverty was evident in 2006,however,and in the year to June 2006 it reached 24.4 percent. Alternative poverty indices which consider a household poor if its income is lower than that required to buy a basic basket of goods,also indicate a decline in poverty in 2005,after rising in the previous three years. Forty percent of the poor manage to consume more than the amount indicated by the poverty line,but the high rates of poverty prevailing for years make it difficult for the weaker sections of the population to maintain a reasonable standard of living,so that the level of consumption of sixty percent of the poor,as well as their income level,is below the poverty line. The incidence of poverty is high and has risen over the years among large families,those with low levels of education,and families with few breadwinners,especially among Arabs and the ultra-orthodox (Haredi). Growth contributes to the reduction of poverty among those well integrated in the labor market,but no such effect is evident among those with low rates of participation. The extent of poverty is a forceful reminder of the need for an ongoing policy of reducing poverty,together with fiscal discipline that supports sustainable growth.The policy should be directed towards encouraging those capable of working to join the labor force,increasing the return to labor for those on low wages,and directly supporting the poor who have low earning power. At the beginning of 2007 the government decided on steps intended to narrow social gaps in Israel and to increase the rate of participation in the labor market.These steps included the introduction of earned income tax credits (EITCs),compulsory pension schemes,increased enforcement of labor laws,and subsidy of day centers and nurseries to enable mothers to go out to work.These measures are intented to be introduced gradually,by 2010.Poverty; Israeli Economy; Consumption poverty