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Volume 9 Issue 3 - July 2008

Research Brief: Adequacy of Resources and Returns-to-Scale in Retirement

by Michael Hurd and Susann Rohwedder

A common metric for retirement well-being is the income replacement rate, the amount of retirement income expressed as a percentage of preretirement income. Some fixed fraction, such as 80 percent, is often put forward as the amount needed to ensure a comfortable retirement. In prior work, we have argued that it makes more sense to consider consumption in retirement as an indicator of adequacy of resources. This is primarily because retirees can spend out of their wealth and other resources. Our earlier work considered all sources of wealth that could potentially support the path of consumption from the beginning of retirement to the end of life (Hurd and Rohwedder, 2006).  In that paper, we argued that a more informative measure of resource adequacy is “necessary” wealth, or the minimum level of wealth necessary to carry out a life-cycle consumption plan. This measure reflects potential adjustments to a household’s consumption that would prevent it from running out of wealth late in life. 

Another important consideration is the fact that, among couples, a substantial fraction of the total retirement years will be spent by the surviving  spouse  living  as  a  single  person.  The old saying that “two can live as cheaply as one” is a concept economists refer to as “returns-to-scale.” It refers to the ability of a couple to spend less than twice what a single spends to achieve the same level of well-being. Accurately quantifying this concept has important policy implications: to the extent that singles need less than couples to maintain the same standard of living, assessments of the adequacy of resources that make no adjustment for widowing will misstate economic preparation. We estimate returns-to-scale parameters in spending by older households, using data from the Consumption and Activities Mail Survey (CAMS) and the Health and Retirement Study (HRS) and apply these to assessments of adequacy of retirement resources.  This research brief summarizes this work. 

What are Returns-to-Scale?

Returns-to-scale arise in several ways. For example, a couple may share a car or other good; meals require about the same amount of work and cost for two as one and may involve less waste.  Returns-to-scale can vary between complete and none.  If the couple spends the same amount as a single yet each spouse achieves the same level of well-being as the single, returns-to-scale are complete, and, indeed, two can live as cheaply as one.  If the couple requires twice the spending of a single for each to achieve the same well-being, there are no returns-to-scale.  Policymakers often use a returns-to-scale parameter. If there are no returns-to-scale, the parameter is 2.0: a couple requires twice the spending to achieve the level of well-being of a single person, and consumption per person is half that of the couple. If there are complete returns-to-scale, the returns-to-scale parameter is 1.0, and consumption per person is the same as consumption by the couple.

Estimates of returns-to-scale have implications for Social Security and other government programs that define their benefits in relation to the poverty line. For example, Social Security benefits of a widow amount to two-thirds of the benefit that the couple was receiving prior to the husband’s death. The implicit returns-to-scale parameter is 1.5; that is, to achieve the same level of well-being as a single person, a couple is deemed to require 1.5 times that person’s income. However, the poverty line implicitly defines the returns-to-scale parameter to be 1.26. As a consequence, a couple whose only income is Social Security benefits will experience a decline in income at widowing that is greater than the decline in the poverty line. Our results provide estimates of realistic returns-to-scale parameters to use in the design of government programs.

The present study focuses on returns-to-scale among older couples, comparing their total spending as a couple with the spending of the widowed spouse. The objective of the couple is to choose consumption during retirement before and after widowing to maximize the sum of the utility of the couple and of the widow.  In this context, an important determinant of consumption is mortality risk, which we account for in this work.

Estimates of Returns-to-Scale

We find a median drop in spending at widowing of about 25 percent. Alternative estimates of returns-to-scale based on the raw data come from the differential drop in spending observed among widowed households and simultaneous drops in spending among households where marital status and household size did not change. We consider two such control groups: (a) single households living alone; and (b) couple households living alone. The rationale for taking the differential is that spending might have dropped even in the absence of widowing and we want to identify that portion of the drop in spending that is due to widowing. We find spending changes for singles of about 8 percent. Differencing with the drop observed among widowed households, we find that widowing appears to lead to a drop in spending of about 16 percent. For couples living alone we find declines in spending of 3.5 percent so that the differential drop for widowed households is 21 percent.

Consumption-based Assessments of Adequacy

In this work, we propose a consumption-based replacement rate as a measure of the adequacy of retirement resources. We observe the resources at retirement of a single person. We ask: can the resources support the projected consumption path? The consumption path is anchored at the initial post-retirement consumption level and follows the path given by the slopes of consumption paths that we have estimated from the CAMS panel. If the consumption path cannot be supported by the economic resources, we find the initial level of consumption that would permit the person to follow the life-cycle path. The consumption replacement rate is the ratio of the affordable consumption to the actual consumption. If the replacement rate is greater than one, economic resources are more than sufficient to finance the actual consumption path. If it is less than one, there is a shortfall in resources.

Because lifetime is uncertain, and wealth is not typically annuitized, we also ask whether the observed initial consumption level permits the person to follow the lifecycle path with a high degree of probability. Here the uncertainty is length of life, so the question is equivalent to finding whether the resources will sustain the path until advanced old age where the probability of survival is very small. For couples the basic method is similar. The couple will follow the consumption path as long as both spouses survive, and then the surviving spouse will switch to the consumption path of a single person. The shape of the single’s path is estimated as described above, but the level will depend on returns-to-scale in consumption by the couple. At the death of the first spouse, the surviving spouse reduces consumption to the level specified by the returns-to-scale parameter. Knowing the consumption path of the surviving spouse, we find the expected present value of consumption for the lifetime of the couple and the surviving spouse. We also determine the fraction of households that can finance their expected consumption path with, say, 95% probability, and by how much a household would have to adjust consumption to keep the chances of running out of wealth towards the end of the life cycle reasonably small.


Our individual-level metric for adequate preparation is based on the following concept.

By how much does the household have to adjust initial consumption compared with actual initial consumption to keep the probability of running out of wealth at the end of  life below a desired threshold?

We set our adjustment threshold to -15%. That is, in a particular simulation, someone is adequately prepared if he can afford initial consumption that is at least 85% of actual initial consumption. Overall we say that the individual is adequately prepared if the chances are 95% or greater that he can afford this initial adjusted level of consumption. For couples we mean the consumption by the couple as long as both spouses survive and the subsequent consumption by the survivor.

Among singles, consumption could be increased on average at all education levels. For example, among those with less than a high school education, average actual initial consumption is $19,100 whereas average affordable consumption is $23,000. At the individual level actual initial consumption is generally consistent with the available resources - 74 percent are adequately prepared according to our definition. However, just a little more than half of those in the lowest education band are adequately prepared.

We have chosen a required reduction of initial consumption by 15 percent or more to signal inadequate preparedness. We have tested the sensitivity of our results with respect to these cut off points. The results are surprisingly insensitive to these definitions, especially with respect to the cut-off for the probability of having to reduce consumption. The reason is that most households either fall substantially short of the thresholds of adequacy or they exceed them by a large margin.

Our baseline simulations for couples use the returns-to-scale parameter implicit in the poverty line; that is, a couple needs 26 percent more than a single person to achieve the same level of well-being, which implies that widows or widowers will consume 79.4 percent as much as the couple did prior to widowing. We actually observed in the data a median drop of 21.1 percent which is not materially different from the drop implied by the poverty line. The average affordable consumption is $98,500, yet average initial consumption is just $43,000. Thus on average couples could increase their consumption substantially. Even the median of the individual ratios of affordable consumption to actual consumption is 1.84. Although there is a gradient by education level, among those lacking high school graduation, the median of the ratio of affordable to actual consumption is 1.55.

For married persons, about 87 percent are adequately prepared, and females and males are about equally likely to be prepared. As with singles our overall results are not sensitive to the cut-off points we have used in our definitions of adequate preparation.  When we run these analyses using different values of the returns-to-scale parameter, we find that the fraction of couples adequately prepared for retirement is not very sensitive to the amount of returns-to-scale.


This work takes a novel approach to estimating returns-to-scale in household spending by using the event of widowing for identification. From raw data, we find drops in spending from 16 to 25 percent at widowing, which is close to the returns-to-scale implied by the difference in the poverty lines for couples and singles. From model-based estimations we found the importance of accounting for uncertainty of survival.

Using consumption-based replacement rates, we assess the adequacy of financial preparation for retirement of households shortly after retirement. We conduct simulations for several different values of the returns-to-scale parameter. Results were not very sensitive to this parameter, because most couples are well prepared for retirement in that their retirement resources exceed what they need to maintain their consumption path into advanced old age.


Hurd, M. and Rohwedder, S. “Alternative Measures of Replacement Rates” MRRC Working Paper WP 2006-132.

This Research Brief is based on MRRC Working Paper WP 2008-174. View the full paper here. WP2008-174

Michael Hurd is Director of the RAND Center for the Study of Aging. Susann Rohwedder is an Economist at RAND.