Electrical tree structures generated by the ab-initio discharge-avalanche model

Initially the discharge-avalanche model for electrical tree formation treated the local Poisson fields as being derived from the applied Laplace field via a modification factor that was regarded as a random variable in time and space. Recently we have removed this approximation by calculating the local Poisson fields from the space charge arrangement produced by discharges in the tree tubules and avalanches in the surrounding polymer. This “ab-initio” version of the model has now been fully implemented. The ac-cycle is divided into 16 time segments. In each time segment tube-discharges are allowed to occur if the potential difference along a tube is greater than an onset threshold. Positive space charge is regarded as being deposited on the tube walls in the form of positive ions. Negative charge is allowed to penetrate the polymer where it can be used to initiate avalanches and thereby generate damage. The avalanches compete with a field dependant mobility in rearranging the charge around the tree tips

Labor Compensation and the Structure of Private Pension Plans: Evidence for Contractual Versus Spot Labor Markets

Distingiishing "spot" versus "contract" views of the labor market is of critical importance to a host of economic issues ranging from wage flexibility over the business cycle to firm financial valuation. The structural features of U.S. private pension plans permit surprisingly strong inferences concerning the incentive effects of private pension plan provisions and the contractual nature of the U.S. labor market. This paper examines the accrual of vested pension benefits of a nation-wide sample of pension plans. We find strikingly larged is continuities in the profile by age of the ratio of annual accrued pension benefits to the standard wage. These discontinuities primarily occur at the ages of full vesting and early retirement. Representative plans often exhibit absolute changes in accrual ratios of 20 to 30 percentage points at these ages.The provisions of many plans imply large negative accruals after the age of early retirement. Job change typically involves a large loss in pension wealth as well. Since the average worker's marginal product presumably changes smoothly as he or she ages, these pension data can only be reconciled with spotmarket clearing if age wage profiles within a firm exhibit exactly offsetting discontinuities at key ages. Casual inspection of firm wage setting behavior rules out this requirement of spot market clearing. In our view the magnitude,patterns, and variations in pension accrual ratios are strikingly at odds with spot market equilibrium. While market clearing in longer term contracts seems the only equilibrium theory consistent with these findings, it also strains our credulity to ascribe optimizing behavior to the pension accrual profiles chosen by a vast array of U.S. businesses. In the process of presenting these profiles we also consider the following questions concerning U.S. pensions. What are the incentive effects of private pension plans? What is the cost in pension benefits of job turnover? How important is vesting? Is there a cost in pension benefits of foregoing the early retirement option? Do pension stipulations encourage early retirement? While the considerable heterogeneity of pension plan provisions permits no simple or single answer to these questions, the data suggest that pensions can have major incentive effects on job turnover and retirement. In general pensions represent a very significant factor, and at certain ages, a dominant factor in employee compensation.

Pension Backloading, Wage Taxes, and Work Disincentives

The Federal Government is actively involved in encouraging the formation and growth of private pensions and in regulating their behavior. The primary form of encouragement is the government's tax subsidization of pensions. A primary attribute of pension plan provisions is an implicit tax on employment after certain ages. The primary form of pension regulation is through ERISA, the Employee Retirement Income Security Act. The government's involvement in encouraging and regulating private pensions appears to reflect its desire that workers have a secure source of old age income which will lessen their reliance on Social Security. In recent years the government has reacted to demographic changes, and their effects on Social Security funding, and the increase in early retirement by also using its pension and Social Security tax and regulatory policies to encourage workers to delay their retirement decision. This paper examines the structure of pension plans with two questions in mind. First have government pension backloading regulations aimed at assuring future pension benefits been effective? and, second, has the structure of old age pension accrual at the end of the workspan, an implicit tax, greatly limited the effectiveness of government policy in reversing the trend to early retirement? The answers to these questions are important for assessing the benefits of the government's tax subsidization of pensions, as they are currently structured. The principal findings of this study are: (1) ERISA regulations notwithstanding, a significant proportion of defined benefit plans exhibit severe backloading. Indeed, backloading is an inherent property of defined benefit pension plans. (2) A large fraction of defined benefit plans embed very substantial old age work disincentives, through an implicit tax on wage earnings. (3) These pension retirement incentives are often much greater than Social Security's retirement incentives. (4) Evidence from one large Fortune 500 firm indicates that pension retirement incentives can greatly increase the extent of early retirement.

Employee Retirement and a Firm's Pension Plan

The provisions of the pension plan in a large corporation are described in detail. The implications of the provisions are indicated by pension accrual profiles. These profiles are set forth, together with standard age-earnings and Social Security accrual profiles, in the form of life-time budget constraints. The plan provided very strong incentives to retire beginning at age 55. After age 65, negative pension and negative Social Security accruals effectively impose almost a 100 percent tax rate on wage earnings for many employees of the firm. Departure rates from the firm are compared with economic incentives inherent in the plan provisions. The inducements in the plan provisions to retire early have had a very substantial effect on departure rates from the firm. Over 50 percent of those employed by the firm at age 50 leave before 60 and 90 percent before age 65. The jumps in departure rates at specific ages coincide precisely with the discontinuities and kink points in the worker compensation profiles that result from the pension plan provisions together with wage earnings profiles and Social Security accrual.

The Incentive Effects of Private Pension Plans

The proportion of workers covered by pensions has increased very substantially over the past two or three decades, and in particular the number of older workers with pensions continues to increase. During the same period,and especially in the past decade, the labor force participation of older workers has declined dramatically. These two trends may well be related. This paper examines the incentive effects of private pensions. We find that the provisions of pension plans provide very substantial incentives to terminate work at the current job after the age of early retirement and even greater incentives to leave after the age of normal retirement. It is not unusual for the reduction in pension 'benefit accrual after these retirement ages to equal the equivalent of a 30 percent reduction in wage earnings. In addition to a potentially large impact on labor force participation of older workers, pension plan provisions are likely to have important effects on labor mobility of younger workers.