ABOUT one-third of new widows in the United States experience a substantial reduction - 25 percent or more - in their living standards when their husbands pass on.This is one finding of a study by economists Alan Auerbach of the University of Pennsylvania and Laurence Kotlikoff of Boston University. In a paper for the National Bureau of Economic Research, the authors note that many couples do not purchase adequate life insurance. In their study, Mr. Auerbach and Mr. Kotlikoff analyzed the results of a "retirement history survey" of household heads aged 58 to 63 in 1969. The individuals or their widows were interviewed every two years from 1969 to 1979. This survey provided about 1,300 appropriate examples for examining the incomes of actual widows before and after their husband's deaths. The authors measure the income of wives prior to the death of their husbands as one-half the couple's combined income. Using this measure, they find that 34.8 percent of older wives (over age 65) suffer at least a 25 percent decline in their incomes when their husbands die. Focusing on wives who are "at risk," namely those wives whose husbands account for 62 percent or more of the couple's combined income, the fraction of underinsured wives rises to 36.3 percent. The cut in living standards is often even more severe for both younger widows and widows with greater income prior to their husband's death. Using a calculation that looks at average income for a number of years before and after widowhood, 44 percent of those widows under age 55 lost more than 25 percent of income, compared with 36.7 percent of those aged 55 to 65. Among widows under age 55, (most of whom are at least in their late 40s in this data set), nearly one in four saw income drop more than 50 percent.