Young Widow(er)s, Social Security, and Marriage
ORES Working Paper No. 103 (released March 2004)
Michael J. Brien is with Deloitte & Touche LLP. Stacy Dickert-Conlin is with Syracuse University. David A. Weaver is with the Division of Economic Research, Office of Research, Evaluation, and Statistics, Office of Policy, Social Security Administration.
Acknowledgments: The authors would like to thank Ben Bridges, Joyce Manchester, Sheila B. Kamerman, and participants at the annual meetings of the Population Association of America for helpful comments. The research reported herein was performed pursuant to a grant from the U.S. Social Security Administration funded as part of the Retirement Research Consortium.
Working papers in this series are preliminary materials circulated for review and comment. The findings and conclusions expressed in them are the authors' and do not necessarily represent the views of the Social Security Administration.
Summary
Upon a worker's death, Social Security pays benefits to each minor or disabled child and to the worker's widow(er), provided a child of the worker is in his or her care. Although remarriage has no effect on a child's eligibility for benefits, the benefit going directly to the widow(er) terminates if he or she remarries. One policy rationale for the marriage termination provision is to ensure a well-targeted and less expensive Social Security program. That is, a widow(er) who remarries has access to his or her new spouse's income and is in less need of support from a public program. On the other hand, the termination provision may affect marriage decisions, with some widow(er)s not remarrying and others postponing marriage.
In the income tax literature, when a couple faces a higher (lower) tax bill as a married couple than as two single individuals, it is said that the couple, in effect, faces a marriage penalty (marriage subsidy). We use this terminology for this paper; the amount of Social Security that would be lost if a widow(er) remarries is referred to as the "marriage penalty." We show that the dollar amount of the penalty depends on the primary insurance amount of the deceased worker, the number of children in the family, and the widow(er)'s earnings. The median penalty faced by widow(er)s receiving benefits in 2001 is found to be large (around $4,100 per year). However, the penalty varies substantially across widow(er)s. While more than 20 percent of widow(er)s face no penalty, 10 percent face an annual penalty in excess of $10,920 per year.
We review several studies from the income tax literature and conclude that the Social Security marriage penalties are large relative to penalty amounts found in that literature. In addition, we note that studies have found that the tax code has small but statistically significant effects on marriage decisions; it is possible, therefore, that Social Security marriage penalties, given their size, also affect some marriage decisions. However, a complete analysis of marriage, which would consider a large set of financial, sociological, and demographic variables, is beyond the scope of this paper.
The focus of this paper is on describing and measuring marriage penalties faced by widow(er)s caring for children. Specific options to remove or modify the current law provision that terminates benefits upon remarriage are not addressed here. Such options, which would increase program expenditures, would have to be considered in the broader context of the solvency of the overall Social Security system. Finally, this paper does not address the equity issues that inevitably arise when considering program rules involving marriage.
Introduction
Although there has been a recent policy focus on marriage penalties in the income tax system, researchers have also documented penalties associated with other government policies. Historically, for example, a large literature developed focusing on the marriage penalties in the old Aid to Families with Dependent Children (AFDC) program.1 Concerns over how marriage penalties might affect the well-being and development of children motivated this literature. Despite concerns regarding the well-being of children, researchers have virtually ignored marriage penalties in the Social Security program for families with widow(er)s caring for minor or disabled children.2 Social Security pays benefits to each minor or disabled child and to the worker's widow(er) provided a child of the worker is in his or her care. Although remarriage has no effect on a child's eligibility for benefits, the benefit going directly to the widow(er) terminates if he or she remarries. We find that the median marriage penalty faced by widow(er)s is large (around $4,100 per year).
The child-in-care program affects a sizable number of survivors. At the start of 2001, there were 240,000 persons entitled to child-in-care widow(er) benefits, with over 400,000 children in their care. There is a substantial amount of turnover in the entitled population, such that during the 5-year period 1996 through 2000, about 500,000 widow(er)s were entitled at some point to benefits on the accounts of deceased workers. These 500,000 widow(er)s cared for a substantial number of children—more than a million children had established entitlement to benefits on these accounts by the end of 2000.3
Unlike private insurance, social insurance systems such as the U.S. Social Security program often have provisions that limit or stop payments based on beneficiaries' ability to support themselves. Widow(er)s who remarry presumably receive economic support from their new spouses and are in less need of support from a public program. In this regard, the termination provision is similar to another feature of Social Security, namely, the earnings test. Widow(er)s (and other beneficiaries) who are under the full retirement age and who earn above exempt amounts specified in the law have some or all of their Social Security benefits stopped.4 Provisions such as the termination rule and the earnings test help ensure a well-targeted Social Security program, but they may have the unintended consequence of distorting marriage and work decisions.5
Overall, our work focuses on describing and measuring the marriage penalties associated with the termination provision. We do not address equity issues (that is, should married persons with deceased spouses receive Social Security while other married persons do not), nor do we address the overall treatment of marriage by the Social Security program.6 In addition, we do not offer specific options to modify or eliminate the termination provision. Such options would increase program expenditures and would have to be evaluated in the larger context of Social Security's long-run solvency.7
Institutional Details: Marriage Penalties in the Child-in-Care Program
Social Security calculates benefits based on primary insurance amounts (PIAs)—a figure based on a worker's average lifetime monthly earnings in Social Security-covered employment. A person's PIA increases with earnings, but the PIA formula favors low earners. A widow(er) caring for a deceased worker's child who is under age 16 or disabled is eligible for a monthly benefit potentially equal to 75 percent of the deceased worker's PIA. Each child who is under age 18, disabled, or aged 18 to 19 and attending high school is also eligible for a benefit potentially equal to 75 percent of PIA. The widow(er)'s eligibility ends when he or she remarries or when the youngest child reaches age 16, whichever comes first. However, the children's benefits continue as long as they are categorically eligible.
Although each survivor is potentially eligible for 75 percent of PIA, two provisions of Social Security—the family maximum and the earnings test—can reduce this amount. Thus, the monthly marriage penalty faced by a child-in-care widow(er) is not necessarily equal to 75 percent of the PIA.8
The family maximum of Social Security limits the total amount that can be paid on a given worker's record and is a function of the worker's PIA. To illustrate this provision, consider a worker who died in 2001. Monthly family benefits to the widow(er) and children in that year cannot exceed:
- 150 percent of the first $717 of the worker's PIA, plus
- 272 percent of the worker's PIA over $717 through $1,034, plus
- 134 percent of the worker's PIA over $1,034 through $1,349, plus
- 175 percent of the worker's PIA over $1,349.
Social Security determines the initial maximum in the year the worker dies or, if it is earlier, the year the worker is first eligible for Social Security benefits (that is, age 62 or disabled). From the date it is determined, Social Security annually adjusts the maximum and the PIA for inflation. The dollar bend points of the formula used to determine the initial family maximum benefit adjust each year for wage growth in the economy.9 The family maximum is never below 150 percent of PIA and is never above 187.5 percent of PIA.10
To see how the family maximum affects marriage penalties, consider a family of three (a widow(er) and two children) whose maximum is 187.5 percent of PIA. Although each family member's original benefit amount is 75 percent of PIA, the family maximum will allow each member to be paid only 62.5 percent of PIA (for a total of 187.5 percent). If the widow(er) remarries, his or her benefit stops but the two children then receive their full original benefit amounts of 75 percent of PIA. The family's total benefit following remarriage would be 150 percent of PIA. The actual monthly marriage penalty to the family, therefore, is 37.5 (that is, 187.5 − 150) percent of PIA.
We calculate the penalty at the family level for two reasons. First, the widow(er) probably controls the family's Social Security payments regardless of whether he or she receives a benefit himself or herself. Second, measures of economic well-being, such as the U.S. poverty measure, are typically based on family income.11
In general, we write the monthly marriage penalty as the difference between the family benefits when the widow(er) and the children are eligible, BU, and the family benefits when only the children are eligible, BM:
where N denotes the number of children and FMAX is the family maximum that applies. The formula indicates that, in addition to PIA, the number of children present is a major determinant of the penalty size. Chart 1 depicts this relationship in monthly dollars for 2001. When only one child is present, BU is 150 percent of PIA and BM is 75 percent of PIA. Since the family maximum is never below 150 percent of PIA, it is not a factor in the penalty calculation in this case, and, consequently, the monthly penalty is always 75 percent of PIA. When three or more children are present, the family maximum binds regardless of whether the widow(er) receives benefits, that is, BU and BM both equal the family maximum. Therefore, the penalty is always zero when three or more children are present. When two children are present, the penalty depends on the PIA. One interesting result in the case of two children is that if the PIA is low (that is, below the first bend point in the family maximum formula), the marriage penalty is zero because whether the widow(er) is eligible or not the family benefit will be 150 percent of PIA. In general, the family maximum provisions cause the dollar value of the monthly marriage penalty to be negatively related to the number of children and positively related to the size of the PIA.
Actual marriage penalties for families of workers who died in 2001 and had one, two, or three children
2001 PIA (dollars per month) |
1 child | 2 children | 3 children |
---|---|---|---|
1 | 1 | 0 | 0 |
2 | 2 | 0 | 0 |
3 | 2 | 0 | 0 |
4 | 3 | 0 | 0 |
5 | 4 | 0 | 0 |
6 | 5 | 0 | 0 |
7 | 5 | 0 | 0 |
8 | 6 | 0 | 0 |
9 | 7 | 0 | 0 |
10 | 8 | 0 | 0 |
11 | 8 | 0 | 0 |
12 | 9 | 0 | 0 |
13 | 10 | 0 | 0 |
14 | 11 | 0 | 0 |
15 | 11 | 0 | 0 |
16 | 12 | 0 | 0 |
17 | 13 | 0 | 0 |
18 | 14 | 0 | 0 |
19 | 14 | 0 | 0 |
20 | 15 | 0 | 0 |
21 | 16 | 0 | 0 |
22 | 17 | 0 | 0 |
23 | 17 | 0 | 0 |
24 | 18 | 0 | 0 |
25 | 19 | 0 | 0 |
26 | 20 | 0 | 0 |
27 | 20 | 0 | 0 |
28 | 21 | 0 | 0 |
29 | 22 | 0 | 0 |
30 | 23 | 0 | 0 |
31 | 23 | 0 | 0 |
32 | 24 | 0 | 0 |
33 | 25 | 0 | 0 |
34 | 26 | 0 | 0 |
35 | 26 | 0 | 0 |
36 | 27 | 0 | 0 |
37 | 28 | 0 | 0 |
38 | 29 | 0 | 0 |
39 | 29 | 0 | 0 |
40 | 30 | 0 | 0 |
41 | 31 | 0 | 0 |
42 | 32 | 0 | 0 |
43 | 32 | 0 | 0 |
44 | 33 | 0 | 0 |
45 | 34 | 0 | 0 |
46 | 35 | 0 | 0 |
47 | 35 | 0 | 0 |
48 | 36 | 0 | 0 |
49 | 37 | 0 | 0 |
50 | 38 | 0 | 0 |
51 | 38 | 0 | 0 |
52 | 39 | 0 | 0 |
53 | 40 | 0 | 0 |
54 | 41 | 0 | 0 |
55 | 41 | 0 | 0 |
56 | 42 | 0 | 0 |
57 | 43 | 0 | 0 |
58 | 44 | 0 | 0 |
59 | 44 | 0 | 0 |
60 | 45 | 0 | 0 |
61 | 46 | 0 | 0 |
62 | 47 | 0 | 0 |
63 | 47 | 0 | 0 |
64 | 48 | 0 | 0 |
65 | 49 | 0 | 0 |
66 | 50 | 0 | 0 |
67 | 50 | 0 | 0 |
68 | 51 | 0 | 0 |
69 | 52 | 0 | 0 |
70 | 53 | 0 | 0 |
71 | 53 | 0 | 0 |
72 | 54 | 0 | 0 |
73 | 55 | 0 | 0 |
74 | 56 | 0 | 0 |
75 | 56 | 0 | 0 |
76 | 57 | 0 | 0 |
77 | 58 | 0 | 0 |
78 | 59 | 0 | 0 |
79 | 59 | 0 | 0 |
80 | 60 | 0 | 0 |
81 | 61 | 0 | 0 |
82 | 62 | 0 | 0 |
83 | 62 | 0 | 0 |
84 | 63 | 0 | 0 |
85 | 64 | 0 | 0 |
86 | 65 | 0 | 0 |
87 | 65 | 0 | 0 |
88 | 66 | 0 | 0 |
89 | 67 | 0 | 0 |
90 | 68 | 0 | 0 |
91 | 68 | 0 | 0 |
92 | 69 | 0 | 0 |
93 | 70 | 0 | 0 |
94 | 71 | 0 | 0 |
95 | 71 | 0 | 0 |
96 | 72 | 0 | 0 |
97 | 73 | 0 | 0 |
98 | 74 | 0 | 0 |
99 | 74 | 0 | 0 |
100 | 75 | 0 | 0 |
101 | 76 | 0 | 0 |
102 | 77 | 0 | 0 |
103 | 77 | 0 | 0 |
104 | 78 | 0 | 0 |
105 | 79 | 0 | 0 |
106 | 80 | 0 | 0 |
107 | 80 | 0 | 0 |
108 | 81 | 0 | 0 |
109 | 82 | 0 | 0 |
110 | 83 | 0 | 0 |
111 | 83 | 0 | 0 |
112 | 84 | 0 | 0 |
113 | 85 | 0 | 0 |
114 | 86 | 0 | 0 |
115 | 86 | 0 | 0 |
116 | 87 | 0 | 0 |
117 | 88 | 0 | 0 |
118 | 89 | 0 | 0 |
119 | 89 | 0 | 0 |
120 | 90 | 0 | 0 |
121 | 91 | 0 | 0 |
122 | 92 | 0 | 0 |
123 | 92 | 0 | 0 |
124 | 93 | 0 | 0 |
125 | 94 | 0 | 0 |
126 | 95 | 0 | 0 |
127 | 95 | 0 | 0 |
128 | 96 | 0 | 0 |
129 | 97 | 0 | 0 |
130 | 98 | 0 | 0 |
131 | 98 | 0 | 0 |
132 | 99 | 0 | 0 |
133 | 100 | 0 | 0 |
134 | 101 | 0 | 0 |
135 | 101 | 0 | 0 |
136 | 102 | 0 | 0 |
137 | 103 | 0 | 0 |
138 | 104 | 0 | 0 |
139 | 104 | 0 | 0 |
140 | 105 | 0 | 0 |
141 | 106 | 0 | 0 |
142 | 107 | 0 | 0 |
143 | 107 | 0 | 0 |
144 | 108 | 0 | 0 |
145 | 109 | 0 | 0 |
146 | 110 | 0 | 0 |
147 | 110 | 0 | 0 |
148 | 111 | 0 | 0 |
149 | 112 | 0 | 0 |
150 | 113 | 0 | 0 |
151 | 113 | 0 | 0 |
152 | 114 | 0 | 0 |
153 | 115 | 0 | 0 |
154 | 116 | 0 | 0 |
155 | 116 | 0 | 0 |
156 | 117 | 0 | 0 |
157 | 118 | 0 | 0 |
158 | 119 | 0 | 0 |
159 | 119 | 0 | 0 |
160 | 120 | 0 | 0 |
161 | 121 | 0 | 0 |
162 | 122 | 0 | 0 |
163 | 122 | 0 | 0 |
164 | 123 | 0 | 0 |
165 | 124 | 0 | 0 |
166 | 125 | 0 | 0 |
167 | 125 | 0 | 0 |
168 | 126 | 0 | 0 |
169 | 127 | 0 | 0 |
170 | 128 | 0 | 0 |
171 | 128 | 0 | 0 |
172 | 129 | 0 | 0 |
173 | 130 | 0 | 0 |
174 | 131 | 0 | 0 |
175 | 131 | 0 | 0 |
176 | 132 | 0 | 0 |
177 | 133 | 0 | 0 |
178 | 134 | 0 | 0 |
179 | 134 | 0 | 0 |
180 | 135 | 0 | 0 |
181 | 136 | 0 | 0 |
182 | 137 | 0 | 0 |
183 | 137 | 0 | 0 |
184 | 138 | 0 | 0 |
185 | 139 | 0 | 0 |
186 | 140 | 0 | 0 |
187 | 140 | 0 | 0 |
188 | 141 | 0 | 0 |
189 | 142 | 0 | 0 |
190 | 143 | 0 | 0 |
191 | 143 | 0 | 0 |
192 | 144 | 0 | 0 |
193 | 145 | 0 | 0 |
194 | 146 | 0 | 0 |
195 | 146 | 0 | 0 |
196 | 147 | 0 | 0 |
197 | 148 | 0 | 0 |
198 | 149 | 0 | 0 |
199 | 149 | 0 | 0 |
200 | 150 | 0 | 0 |
201 | 151 | 0 | 0 |
202 | 152 | 0 | 0 |
203 | 152 | 0 | 0 |
204 | 153 | 0 | 0 |
205 | 154 | 0 | 0 |
206 | 155 | 0 | 0 |
207 | 155 | 0 | 0 |
208 | 156 | 0 | 0 |
209 | 157 | 0 | 0 |
210 | 158 | 0 | 0 |
211 | 158 | 0 | 0 |
212 | 159 | 0 | 0 |
213 | 160 | 0 | 0 |
214 | 161 | 0 | 0 |
215 | 161 | 0 | 0 |
216 | 162 | 0 | 0 |
217 | 163 | 0 | 0 |
218 | 164 | 0 | 0 |
219 | 164 | 0 | 0 |
220 | 165 | 0 | 0 |
221 | 166 | 0 | 0 |
222 | 167 | 0 | 0 |
223 | 167 | 0 | 0 |
224 | 168 | 0 | 0 |
225 | 169 | 0 | 0 |
226 | 170 | 0 | 0 |
227 | 170 | 0 | 0 |
228 | 171 | 0 | 0 |
229 | 172 | 0 | 0 |
230 | 173 | 0 | 0 |
231 | 173 | 0 | 0 |
232 | 174 | 0 | 0 |
233 | 175 | 0 | 0 |
234 | 176 | 0 | 0 |
235 | 176 | 0 | 0 |
236 | 177 | 0 | 0 |
237 | 178 | 0 | 0 |
238 | 179 | 0 | 0 |
239 | 179 | 0 | 0 |
240 | 180 | 0 | 0 |
241 | 181 | 0 | 0 |
242 | 182 | 0 | 0 |
243 | 182 | 0 | 0 |
244 | 183 | 0 | 0 |
245 | 184 | 0 | 0 |
246 | 185 | 0 | 0 |
247 | 185 | 0 | 0 |
248 | 186 | 0 | 0 |
249 | 187 | 0 | 0 |
250 | 188 | 0 | 0 |
251 | 188 | 0 | 0 |
252 | 189 | 0 | 0 |
253 | 190 | 0 | 0 |
254 | 191 | 0 | 0 |
255 | 191 | 0 | 0 |
256 | 192 | 0 | 0 |
257 | 193 | 0 | 0 |
258 | 194 | 0 | 0 |
259 | 194 | 0 | 0 |
260 | 195 | 0 | 0 |
261 | 196 | 0 | 0 |
262 | 197 | 0 | 0 |
263 | 197 | 0 | 0 |
264 | 198 | 0 | 0 |
265 | 199 | 0 | 0 |
266 | 200 | 0 | 0 |
267 | 200 | 0 | 0 |
268 | 201 | 0 | 0 |
269 | 202 | 0 | 0 |
270 | 203 | 0 | 0 |
271 | 203 | 0 | 0 |
272 | 204 | 0 | 0 |
273 | 205 | 0 | 0 |
274 | 206 | 0 | 0 |
275 | 206 | 0 | 0 |
276 | 207 | 0 | 0 |
277 | 208 | 0 | 0 |
278 | 209 | 0 | 0 |
279 | 209 | 0 | 0 |
280 | 210 | 0 | 0 |
281 | 211 | 0 | 0 |
282 | 212 | 0 | 0 |
283 | 212 | 0 | 0 |
284 | 213 | 0 | 0 |
285 | 214 | 0 | 0 |
286 | 215 | 0 | 0 |
287 | 215 | 0 | 0 |
288 | 216 | 0 | 0 |
289 | 217 | 0 | 0 |
290 | 218 | 0 | 0 |
291 | 218 | 0 | 0 |
292 | 219 | 0 | 0 |
293 | 220 | 0 | 0 |
294 | 221 | 0 | 0 |
295 | 221 | 0 | 0 |
296 | 222 | 0 | 0 |
297 | 223 | 0 | 0 |
298 | 224 | 0 | 0 |
299 | 224 | 0 | 0 |
300 | 225 | 0 | 0 |
301 | 226 | 0 | 0 |
302 | 227 | 0 | 0 |
303 | 227 | 0 | 0 |
304 | 228 | 0 | 0 |
305 | 229 | 0 | 0 |
306 | 230 | 0 | 0 |
307 | 230 | 0 | 0 |
308 | 231 | 0 | 0 |
309 | 232 | 0 | 0 |
310 | 233 | 0 | 0 |
311 | 233 | 0 | 0 |
312 | 234 | 0 | 0 |
313 | 235 | 0 | 0 |
314 | 236 | 0 | 0 |
315 | 236 | 0 | 0 |
316 | 237 | 0 | 0 |
317 | 238 | 0 | 0 |
318 | 239 | 0 | 0 |
319 | 239 | 0 | 0 |
320 | 240 | 0 | 0 |
321 | 241 | 0 | 0 |
322 | 242 | 0 | 0 |
323 | 242 | 0 | 0 |
324 | 243 | 0 | 0 |
325 | 244 | 0 | 0 |
326 | 245 | 0 | 0 |
327 | 245 | 0 | 0 |
328 | 246 | 0 | 0 |
329 | 247 | 0 | 0 |
330 | 248 | 0 | 0 |
331 | 248 | 0 | 0 |
332 | 249 | 0 | 0 |
333 | 250 | 0 | 0 |
334 | 251 | 0 | 0 |
335 | 251 | 0 | 0 |
336 | 252 | 0 | 0 |
337 | 253 | 0 | 0 |
338 | 254 | 0 | 0 |
339 | 254 | 0 | 0 |
340 | 255 | 0 | 0 |
341 | 256 | 0 | 0 |
342 | 257 | 0 | 0 |
343 | 257 | 0 | 0 |
344 | 258 | 0 | 0 |
345 | 259 | 0 | 0 |
346 | 260 | 0 | 0 |
347 | 260 | 0 | 0 |
348 | 261 | 0 | 0 |
349 | 262 | 0 | 0 |
350 | 263 | 0 | 0 |
351 | 263 | 0 | 0 |
352 | 264 | 0 | 0 |
353 | 265 | 0 | 0 |
354 | 266 | 0 | 0 |
355 | 266 | 0 | 0 |
356 | 267 | 0 | 0 |
357 | 268 | 0 | 0 |
358 | 269 | 0 | 0 |
359 | 269 | 0 | 0 |
360 | 270 | 0 | 0 |
361 | 271 | 0 | 0 |
362 | 272 | 0 | 0 |
363 | 272 | 0 | 0 |
364 | 273 | 0 | 0 |
365 | 274 | 0 | 0 |
366 | 275 | 0 | 0 |
367 | 275 | 0 | 0 |
368 | 276 | 0 | 0 |
369 | 277 | 0 | 0 |
370 | 278 | 0 | 0 |
371 | 278 | 0 | 0 |
372 | 279 | 0 | 0 |
373 | 280 | 0 | 0 |
374 | 281 | 0 | 0 |
375 | 281 | 0 | 0 |
376 | 282 | 0 | 0 |
377 | 283 | 0 | 0 |
378 | 284 | 0 | 0 |
379 | 284 | 0 | 0 |
380 | 285 | 0 | 0 |
381 | 286 | 0 | 0 |
382 | 287 | 0 | 0 |
383 | 287 | 0 | 0 |
384 | 288 | 0 | 0 |
385 | 289 | 0 | 0 |
386 | 290 | 0 | 0 |
387 | 290 | 0 | 0 |
388 | 291 | 0 | 0 |
389 | 292 | 0 | 0 |
390 | 293 | 0 | 0 |
391 | 293 | 0 | 0 |
392 | 294 | 0 | 0 |
393 | 295 | 0 | 0 |
394 | 296 | 0 | 0 |
395 | 296 | 0 | 0 |
396 | 297 | 0 | 0 |
397 | 298 | 0 | 0 |
398 | 299 | 0 | 0 |
399 | 299 | 0 | 0 |
400 | 300 | 0 | 0 |
401 | 301 | 0 | 0 |
402 | 302 | 0 | 0 |
403 | 302 | 0 | 0 |
404 | 303 | 0 | 0 |
405 | 304 | 0 | 0 |
406 | 305 | 0 | 0 |
407 | 305 | 0 | 0 |
408 | 306 | 0 | 0 |
409 | 307 | 0 | 0 |
410 | 308 | 0 | 0 |
411 | 308 | 0 | 0 |
412 | 309 | 0 | 0 |
413 | 310 | 0 | 0 |
414 | 311 | 0 | 0 |
415 | 311 | 0 | 0 |
416 | 312 | 0 | 0 |
417 | 313 | 0 | 0 |
418 | 314 | 0 | 0 |
419 | 314 | 0 | 0 |
420 | 315 | 0 | 0 |
421 | 316 | 0 | 0 |
422 | 317 | 0 | 0 |
423 | 317 | 0 | 0 |
424 | 318 | 0 | 0 |
425 | 319 | 0 | 0 |
426 | 320 | 0 | 0 |
427 | 320 | 0 | 0 |
428 | 321 | 0 | 0 |
429 | 322 | 0 | 0 |
430 | 323 | 0 | 0 |
431 | 323 | 0 | 0 |
432 | 324 | 0 | 0 |
433 | 325 | 0 | 0 |
434 | 326 | 0 | 0 |
435 | 326 | 0 | 0 |
436 | 327 | 0 | 0 |
437 | 328 | 0 | 0 |
438 | 329 | 0 | 0 |
439 | 329 | 0 | 0 |
440 | 330 | 0 | 0 |
441 | 331 | 0 | 0 |
442 | 332 | 0 | 0 |
443 | 332 | 0 | 0 |
444 | 333 | 0 | 0 |
445 | 334 | 0 | 0 |
446 | 335 | 0 | 0 |
447 | 335 | 0 | 0 |
448 | 336 | 0 | 0 |
449 | 337 | 0 | 0 |
450 | 338 | 0 | 0 |
451 | 338 | 0 | 0 |
452 | 339 | 0 | 0 |
453 | 340 | 0 | 0 |
454 | 341 | 0 | 0 |
455 | 341 | 0 | 0 |
456 | 342 | 0 | 0 |
457 | 343 | 0 | 0 |
458 | 344 | 0 | 0 |
459 | 344 | 0 | 0 |
460 | 345 | 0 | 0 |
461 | 346 | 0 | 0 |
462 | 347 | 0 | 0 |
463 | 347 | 0 | 0 |
464 | 348 | 0 | 0 |
465 | 349 | 0 | 0 |
466 | 350 | 0 | 0 |
467 | 350 | 0 | 0 |
468 | 351 | 0 | 0 |
469 | 352 | 0 | 0 |
470 | 353 | 0 | 0 |
471 | 353 | 0 | 0 |
472 | 354 | 0 | 0 |
473 | 355 | 0 | 0 |
474 | 356 | 0 | 0 |
475 | 356 | 0 | 0 |
476 | 357 | 0 | 0 |
477 | 358 | 0 | 0 |
478 | 359 | 0 | 0 |
479 | 359 | 0 | 0 |
480 | 360 | 0 | 0 |
481 | 361 | 0 | 0 |
482 | 362 | 0 | 0 |
483 | 362 | 0 | 0 |
484 | 363 | 0 | 0 |
485 | 364 | 0 | 0 |
486 | 365 | 0 | 0 |
487 | 365 | 0 | 0 |
488 | 366 | 0 | 0 |
489 | 367 | 0 | 0 |
490 | 368 | 0 | 0 |
491 | 368 | 0 | 0 |
492 | 369 | 0 | 0 |
493 | 370 | 0 | 0 |
494 | 371 | 0 | 0 |
495 | 371 | 0 | 0 |
496 | 372 | 0 | 0 |
497 | 373 | 0 | 0 |
498 | 374 | 0 | 0 |
499 | 374 | 0 | 0 |
500 | 375 | 0 | 0 |
501 | 376 | 0 | 0 |
502 | 377 | 0 | 0 |
503 | 377 | 0 | 0 |
504 | 378 | 0 | 0 |
505 | 379 | 0 | 0 |
506 | 380 | 0 | 0 |
507 | 380 | 0 | 0 |
508 | 381 | 0 | 0 |
509 | 382 | 0 | 0 |
510 | 383 | 0 | 0 |
511 | 383 | 0 | 0 |
512 | 384 | 0 | 0 |
513 | 385 | 0 | 0 |
514 | 386 | 0 | 0 |
515 | 386 | 0 | 0 |
516 | 387 | 0 | 0 |
517 | 388 | 0 | 0 |
518 | 389 | 0 | 0 |
519 | 389 | 0 | 0 |
520 | 390 | 0 | 0 |
521 | 391 | 0 | 0 |
522 | 392 | 0 | 0 |
523 | 392 | 0 | 0 |
524 | 393 | 0 | 0 |
525 | 394 | 0 | 0 |
526 | 395 | 0 | 0 |
527 | 395 | 0 | 0 |
528 | 396 | 0 | 0 |
529 | 397 | 0 | 0 |
530 | 398 | 0 | 0 |
531 | 398 | 0 | 0 |
532 | 399 | 0 | 0 |
533 | 400 | 0 | 0 |
534 | 401 | 0 | 0 |
535 | 401 | 0 | 0 |
536 | 402 | 0 | 0 |
537 | 403 | 0 | 0 |
538 | 404 | 0 | 0 |
539 | 404 | 0 | 0 |
540 | 405 | 0 | 0 |
541 | 406 | 0 | 0 |
542 | 407 | 0 | 0 |
543 | 407 | 0 | 0 |
544 | 408 | 0 | 0 |
545 | 409 | 0 | 0 |
546 | 410 | 0 | 0 |
547 | 410 | 0 | 0 |
548 | 411 | 0 | 0 |
549 | 412 | 0 | 0 |
550 | 413 | 0 | 0 |
551 | 413 | 0 | 0 |
552 | 414 | 0 | 0 |
553 | 415 | 0 | 0 |
554 | 416 | 0 | 0 |
555 | 416 | 0 | 0 |
556 | 417 | 0 | 0 |
557 | 418 | 0 | 0 |
558 | 419 | 0 | 0 |
559 | 419 | 0 | 0 |
560 | 420 | 0 | 0 |
561 | 421 | 0 | 0 |
562 | 422 | 0 | 0 |
563 | 422 | 0 | 0 |
564 | 423 | 0 | 0 |
565 | 424 | 0 | 0 |
566 | 425 | 0 | 0 |
567 | 425 | 0 | 0 |
568 | 426 | 0 | 0 |
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1,858 | 1,394 | 464 | 0 |
1,859 | 1,394 | 464 | 0 |
1,860 | 1,395 | 464 | 0 |
1,861 | 1,396 | 464 | 0 |
1,862 | 1,397 | 465 | 0 |
1,863 | 1,397 | 465 | 0 |
1,864 | 1,398 | 465 | 0 |
1,865 | 1,399 | 465 | 0 |
1,866 | 1,400 | 466 | 0 |
1,867 | 1,400 | 466 | 0 |
1,868 | 1,401 | 466 | 0 |
1,869 | 1,402 | 466 | 0 |
1,870 | 1,403 | 467 | 0 |
1,871 | 1,403 | 467 | 0 |
1,872 | 1,404 | 467 | 0 |
1,873 | 1,405 | 467 | 0 |
1,874 | 1,406 | 468 | 0 |
1,875 | 1,406 | 468 | 0 |
1,876 | 1,407 | 468 | 0 |
1,877 | 1,408 | 468 | 0 |
1,878 | 1,409 | 469 | 0 |
1,879 | 1,409 | 469 | 0 |
1,880 | 1,410 | 469 | 0 |
1,881 | 1,411 | 469 | 0 |
1,882 | 1,412 | 470 | 0 |
1,883 | 1,412 | 470 | 0 |
1,884 | 1,413 | 470 | 0 |
1,885 | 1,414 | 470 | 0 |
1,886 | 1,415 | 471 | 0 |
1,887 | 1,415 | 471 | 0 |
1,888 | 1,416 | 471 | 0 |
1,889 | 1,417 | 471 | 0 |
1,890 | 1,418 | 472 | 0 |
1,891 | 1,418 | 472 | 0 |
1,892 | 1,419 | 472 | 0 |
1,893 | 1,420 | 472 | 0 |
1,894 | 1,421 | 473 | 0 |
1,895 | 1,421 | 473 | 0 |
1,896 | 1,422 | 473 | 0 |
1,897 | 1,423 | 473 | 0 |
1,898 | 1,424 | 474 | 0 |
1,899 | 1,424 | 474 | 0 |
1,900 | 1,425 | 474 | 0 |
1,901 | 1,426 | 474 | 0 |
1,902 | 1,427 | 475 | 0 |
1,903 | 1,427 | 475 | 0 |
1,904 | 1,428 | 475 | 0 |
1,905 | 1,429 | 475 | 0 |
1,906 | 1,430 | 476 | 0 |
1,907 | 1,430 | 476 | 0 |
1,908 | 1,431 | 476 | 0 |
1,909 | 1,432 | 476 | 0 |
1,910 | 1,433 | 477 | 0 |
1,911 | 1,433 | 477 | 0 |
1,912 | 1,434 | 477 | 0 |
1,913 | 1,435 | 477 | 0 |
1,914 | 1,436 | 478 | 0 |
1,915 | 1,436 | 478 | 0 |
1,916 | 1,437 | 478 | 0 |
1,917 | 1,438 | 478 | 0 |
1,918 | 1,439 | 479 | 0 |
1,919 | 1,439 | 479 | 0 |
1,920 | 1,440 | 479 | 0 |
1,921 | 1,441 | 479 | 0 |
1,922 | 1,442 | 480 | 0 |
1,923 | 1,442 | 480 | 0 |
1,924 | 1,443 | 480 | 0 |
1,925 | 1,444 | 480 | 0 |
1,926 | 1,445 | 481 | 0 |
1,927 | 1,445 | 481 | 0 |
1,928 | 1,446 | 481 | 0 |
1,929 | 1,447 | 481 | 0 |
1,930 | 1,448 | 482 | 0 |
1,931 | 1,448 | 482 | 0 |
1,932 | 1,449 | 482 | 0 |
1,933 | 1,450 | 482 | 0 |
1,934 | 1,451 | 483 | 0 |
1,935 | 1,451 | 483 | 0 |
1,936 | 1,452 | 483 | 0 |
1,937 | 1,453 | 483 | 0 |
1,938 | 1,454 | 484 | 0 |
1,939 | 1,454 | 484 | 0 |
1,940 | 1,455 | 484 | 0 |
1,941 | 1,456 | 484 | 0 |
1,942 | 1,457 | 485 | 0 |
1,943 | 1,457 | 485 | 0 |
1,944 | 1,458 | 485 | 0 |
1,945 | 1,459 | 485 | 0 |
1,946 | 1,460 | 486 | 0 |
1,947 | 1,460 | 486 | 0 |
1,948 | 1,461 | 486 | 0 |
1,949 | 1,462 | 486 | 0 |
1,950 | 1,463 | 487 | 0 |
1,951 | 1,463 | 487 | 0 |
1,952 | 1,464 | 487 | 0 |
1,953 | 1,465 | 487 | 0 |
1,954 | 1,466 | 488 | 0 |
1,955 | 1,466 | 488 | 0 |
1,956 | 1,467 | 488 | 0 |
1,957 | 1,468 | 488 | 0 |
1,958 | 1,469 | 489 | 0 |
1,959 | 1,469 | 489 | 0 |
1,960 | 1,470 | 489 | 0 |
1,961 | 1,471 | 489 | 0 |
1,962 | 1,472 | 490 | 0 |
1,963 | 1,472 | 490 | 0 |
1,964 | 1,473 | 490 | 0 |
1,965 | 1,474 | 490 | 0 |
1,966 | 1,475 | 491 | 0 |
1,967 | 1,475 | 491 | 0 |
1,968 | 1,476 | 491 | 0 |
1,969 | 1,477 | 491 | 0 |
1,970 | 1,478 | 492 | 0 |
1,971 | 1,478 | 492 | 0 |
1,972 | 1,479 | 492 | 0 |
1,973 | 1,480 | 492 | 0 |
1,974 | 1,481 | 493 | 0 |
1,975 | 1,481 | 493 | 0 |
1,976 | 1,482 | 493 | 0 |
1,977 | 1,483 | 493 | 0 |
1,978 | 1,484 | 494 | 0 |
1,979 | 1,484 | 494 | 0 |
1,980 | 1,485 | 494 | 0 |
1,981 | 1,486 | 494 | 0 |
1,982 | 1,487 | 495 | 0 |
1,983 | 1,487 | 495 | 0 |
1,984 | 1,488 | 495 | 0 |
1,985 | 1,489 | 495 | 0 |
1,986 | 1,490 | 496 | 0 |
1,987 | 1,490 | 496 | 0 |
1,988 | 1,491 | 496 | 0 |
1,989 | 1,492 | 496 | 0 |
1,990 | 1,493 | 497 | 0 |
1,991 | 1,493 | 497 | 0 |
1,992 | 1,494 | 497 | 0 |
1,993 | 1,495 | 497 | 0 |
1,994 | 1,496 | 498 | 0 |
1,995 | 1,496 | 498 | 0 |
1,996 | 1,497 | 498 | 0 |
1,997 | 1,498 | 498 | 0 |
1,998 | 1,499 | 499 | 0 |
1,999 | 1,499 | 499 | 0 |
2,000 | 1,500 | 499 | 0 |
As noted above, the earnings test of Social Security also affects the marriage penalty a widow(er) faces. In 2001 the earnings test requires that, for each two dollars of annual earnings above $10,680, a widow(er) loses one dollar of his or her Social Security benefit (the $10,680 figure is referred to as the exempt amount and is adjusted annually by the Social Security Administration (SSA) based on wage growth in the economy). To see how the earnings test affects marriage penalties, consider a specific example: a family composed of a widow(er) and two children for whom the PIA is $1,034 and the family maximum is $1,938. If the widow(er) had no earnings, each family member would receive 62.5 percent of the PIA, which is the family maximum divided by three, or $646. Now suppose the widow(er) earns $18,432 in 2001.12 This is $7,752 above the exempt amount of $10,680 and the widow(er)'s Social Security must be reduced by $3,876 (that is, 7,752 * 0.5). This is equal to exactly 6 months of Social Security benefits, so SSA would not pay the widow(er) his or her $646 benefit for the first 6 months of the year. Because the widow(er) does not receive a benefit, the family maximum does not bind and the children, in those 6 months, would get their full 75 percent of PIA. So, for the first 6 months, the family receives 150 percent of the PIA ($1,551 a month). Starting with the 7th month, each family member—including the widow(er)—receives $646 (for a total of $1,938). If the widow(er) had remarried, the family would receive $1,551 for all months, implying that the marriage penalty is zero in the first 6 months and $387 ($1,938 − $1,551) in the final 6 months. Note that, in this example, if the widow(er) had earnings greater than $26,184, the earnings test would have prevented payment of widow(er) benefits for all months in 2001 and no marriage penalty would exist for that year.
In sum, the monthly marriage penalty faced by a widow(er) depends on the number of children, the PIA, and his or her earnings. The lifetime penalty depends, additionally, on the ages of the children, particularly the age of the youngest child. Child-in-care widow(er) benefits typically terminate when the youngest child reaches age 16. Widow(er)s with very young children who remarry forfeit benefits for a number of years.
Calculating Marriage Penalties in the Child-in-Care Program
To characterize the size of the marriage penalties faced by actual recipients of the child-in-care program and how these penalties vary by recipient characteristics, we use a weighted 10 percent sample of SSA's administrative records.13 As with estimates of marriage penalties in other contexts, we stress that these penalties arise from changes in Social Security benefits simply because of a change in legal marital status and that we are ignoring all other costs and benefits of marriage.
We estimate that, at the start of 2001, there were 239,140 widow(er)s entitled to child-in-care benefits from Social Security. In Table 1, we divide these widow(er)s into three distinct groups: no marriage penalty because of the earnings test, no marriage penalty because of family maximum provisions, and a positive marriage penalty.14 We include summary statistics to relate these groupings to the previous discussion of how marriage penalties arise in the child-in-care program.
Group | Number | Percentage of all entitled |
Average annual earnings (dollars) |
Average number of children |
Average PIA of deceased spouse (dollars) |
---|---|---|---|---|---|
No actual penalty | |||||
Group A. Earnings test prevents payment of widow(er) benefits for all months in 2001 | 34,760 | 14.5 | 37,696 | 1.8 | 870 |
Group B. Family maximum paid regardless of whether widow(er) remarries | 43,230 | 18.1 | 3,951 | 3.0 | 772 |
Positive actual penalty | |||||
Group C. All with positive actual penalty | 161,150 | 67.4 | 5,887 | 1.3 | 986 |
SOURCE: Authors' calculations using data from the Social Security Administration's administrative records, 2001. | |||||
NOTE: PIA = primary insurance amount. |
Note that, for 14.5 percent of widow(er)s (that is, Group A in Table 1), the earnings test prevents the payment of benefits for all months of 2001. For these persons, no widow(er) benefits are paid and there is no actual marriage penalty, and we exclude this group from the remainder of our analysis.15 Some of the widow(er)s in Groups B and C have earnings, but, empirically, the earnings test is of limited importance because the majority (86 percent in Group B and 78 percent in Group C) have earnings below the exempt amount ($10,680).16
For approximately 43,000 widow(er)s (Group B) and their 130,000 children, family benefits will equal the family maximum regardless of remarriage. Recall from the earlier discussion of program rules that these zero-penalty cases occur in all large families (three or more children) and in families with two children and a low PIA. Consistent with this discussion, the average number of children in these families is high (3.0) and the average PIA is low ($772).
Still, the majority of families, 67.4 percent, do face positive marriage penalties. Not surprisingly, in these Group C cases, the average number of children (1.3) is low and the average PIA ($986) is high.
To get a better sense of the distribution of penalties, we use equation 3 to calculate penalties for all widow(er)s in Groups B and C.17 Table 2 shows that 50 percent of widow(er)s face an annual penalty of $4,090 or more. Ten percent of all widow(er)s face an annual marriage penalty in excess of $10,920 per year. Although we do not know whether these penalties are large relative to total income (because Social Security administrative records do not include comprehensive measures of income), over 40 percent of widow(er)s face a penalty equal to 75 percent of the annualized value of their deceased spouses' PIAs. This is presumably a relatively substantial amount given that policymakers believe that 75 percent of PIA is enough to help a widow(er) maintain his or her standard of living following a worker's death.
Decile | Annual dollar amounts |
Annual relative amounts |
---|---|---|
10 | 0 | 0 |
20 | 0 | 0 |
30 | 1,960 | 0.19 |
40 | 3,580 | 0.25 |
50 | 4,090 | 0.35 |
60 | 5,090 | 0.75 |
70 | 6,820 | 0.75 |
80 | 8,650 | 0.75 |
90 | 10,920 | 0.75 |
100 | 16,150 | 0.75 |
Percentage with zero penalty |
21 | 21 |
SOURCE: Authors' calculations using data from the Social Security Administration's administrative records, 2001. | ||
NOTES: The dollar penalty measures the annual change in family benefits if the widow(er) were remarried. The annual relative penalty is the ratio of the widow(er)'s annual penalty to 12 times the amount of the deceased worker's primary insurance amount. Widow(er)s who will have all of their benefits suspended in 2001 because of the earnings test are excluded. |
Summary statistics for several subgroups of the widowed population are presented in Table 3. Recently entitled widow(er)s—those entitled during 2000—have penalties that are somewhat lower than those for the overall widow(er) group. The mean penalty ($4,230) and the median penalty ($3,910) are $560 and $180 less than the mean and median of the overall widow(er) group. One explanation for this difference is that the entire pool of widow(er)s may disproportionately be persons with high penalties who chose not to remarry precisely because of the penalty. Recently entitled widow(er)s have not had much time to remarry and may reflect a less select distribution.
All widow(er)s | Recently entitled (2000) |
Under age 36 |
Men | |
---|---|---|---|---|
Number | 204,380 | 23,580 | 44,230 | 10,850 |
Penalty | ||||
Mean (dollars) | 4,790 | 4,230 | 3,470 | 4,040 |
Median (dollars) | 4,090 | 3,910 | 3,140 | 3,770 |
Percentage with zero penalty | 21 | 26 | 32 | 20 |
Mean PIA (dollars) | 941 | 1,006 | 841 | 783 |
Mean number of children | 1.7 | 1.8 | 2.0 | 1.5 |
SOURCE: Authors' calculations using data from the Social Security Administration's administrative records, 2001. | ||||
NOTES: The penalty measures the annual change in family benefits if the widow(er) were remarried. Widow(er)s who will have all of their benefits suspended in 2001 because of the earnings test are excluded.
PIA = primary insurance amount.
|
Marriage Penalties in the Income Tax Literature
A large literature exists that documents the size of marriage penalties in the U.S. tax code. In addition, several studies within this literature have measured the effect of tax penalties on marriage decisions. In this section, we review the tax literature, compare its findings with results from our work, and discuss its relevance (and limitations) to assessing the effects of Social Security rules on marriage decisions.
The Congressional Budget Office (CBO) and the Office of Tax Analysis in the Department of Treasury conducted two of the more recent studies on the size of marriage penalties in the U.S. tax code. Using its "Basic Measure," CBO found that 42 percent of married couples in 1996 faced a tax penalty, which had an average annual value of $1,380 (Congressional Budget Office 1997). The Department of Treasury study found that 48 percent of couples incurred a marriage penalty, with an average value in 1999 of $1,141 (Bull and others 1999). These are well below the average penalty reported in Table 3 ($4,790) for all 2001 child-in-care widow(er)s.
Alm and Whittington (1996a) examined marriage tax penalties for the period 1967 through 1994. In constant 1994 dollars, the average penalty rose from about $350 in 1967 to a peak of $1,900 in 1981. Alm and Whittington found that the average penalty in 1994 was $1,200, which is similar to results found by Eissa and Hoynes (2000) and Feenberg and Rosen (1995). Again, these values are well below the average reported in Table 3 for child-in-care widow(er)s.
Studies have found that tax laws have small but statistically significant effects on marital decisions. Alm and Whittington (1995), using time series variation in marriage penalties over the 1947 to 1988 period, found that aggregate marriage rates decline as penalties increase. A follow-up study (Alm and Whittington 1999) that used individual longitudinal data also found a negative relationship between penalties and the probability of marriage. At the mean value of the variables, a 10 percent increase in the marriage penalty lowered the probability of marriage by 2.3 percent; much higher elasticities were found at maximum levels of tax penalties. Other economic variables (for example, the potential additional income provided by a spouse) were also found to be important determinants of marriage.
Alm and Whittington (1999) apply their results to one policy discussion, namely, the federal tax changes of 1993. They cite figures indicating that the marriage penalty of a representative low-income person increased by $465. Their empirical results imply such a change would lower the probability of marriage for low-income persons by about 3 percent.
Some research has focused on whether marriage penalties affect the timing of marriage. Sjoquist and Walker (1995), Gelardi (1996), and Alm and Whittington (1996b) found that couples timed their marriages to avoid paying a tax penalty for 1 year.18 Given that researchers find that marriage penalties in the tax code affect marital decisions and we find the penalties in the child-in-care program are higher than those in the tax code, it is plausible that these penalties discourage some marriages or encourage some couples to postpone marriage while the widow(er) is eligible for benefits.19 Of course, a complete analysis of marriage decisions—which is beyond the scope of this paper—would consider factors in addition to Social Security. For example, some widow(er)s who face marriage penalties under Social Security might actually receive marriage "subsidies" from the income tax system. Alternatively, some widow(er)s may face additional "penalties" if remarriage results in the loss of other federal or state benefits. Further, remarriage decisions are probably correlated with a large number of economic, sociological, and demographic characteristics (such as widow(er)'s age, family size, earnings, and education).
Although we do not conduct a complete analysis of marriage decisions for these widow(er)s, we believe it is a topic that researchers should consider in the future. Economic and demographic studies have found that marriage, in general, is associated with improved health, higher income, and better outcomes for children (Waite 1995). Thus, research on remarriage has the potential to inform policy discussions regarding the well-being of widow(er)s and their children.
Conclusions and Future Research
Although the marriage termination provision in Social Security's child-in-care program helps ensure a well-targeted program, it does produce sizable marriage penalties. These marriage penalties are larger than those that have been documented in the U.S. tax code and, because of their size, probably do affect some marriage decisions. For example, 50 percent of widow(er)s face an annual penalty of $4,090 or more, and 10 percent face an annual marriage penalty in excess of $10,920 per year. Because of larger family sizes and lower PIAs, young widow(er)s tend to face relatively smaller penalties. However, among widow(er)s aged 35 or younger, the median penalty is still substantial ($3,140).
The results in this paper raise a number of additional questions and suggest some important avenues for future research. Because of the family maximum, some widow(er)s do not actually face a marriage penalty (that is, their terminated benefits would be redistributed to their children). Whether these widow(er)s perceive a penalty is unknown—some may not understand that benefits will be redistributed. Future research on how individuals perceive penalties may be warranted. Also, given the size of the penalties (and the results from the income tax literature), it is likely that the termination provision affects some marriage decisions. However, we have not measured the magnitude of this effect, nor have we assessed whether the provision is more likely to cause postponement of marriage (as opposed to never remarrying). The welfare implications in the postponement case are serious (that is, postponing marriage while children are in the household may affect the children's well-being) but are of less concern than in the never-remarrying case (which has implications for the children's well-being and for the widow(er)'s well-being later in life). Measuring the effect of the termination provision is difficult because child-in-care widow(er)s are not typically represented in large numbers in federal surveys (which contain extensive information on financial and personal characteristics). However, future research may be able to combine these widow(er)s with other groups (that face marriage subsidies or penalties) in a general model that relates financial and personal characteristics to marriage decisions.
Notes
1. The AFDC program has been replaced by the Temporary Assistance for Needy Families (TANF) program. See Congressional Research Service (2001) for a discussion of TANF provisions relating to marriage.
2. See Moffitt (1998) for a discussion of the AFDC literature and Alm, Dickert-Conlin, and Whittington (1999) for a discussion of the income tax literature. With regard to Social Security, only one other paper has focused on marriage penalties in the Social Security system (Brien, Dickert-Conlin, and Weaver 2001). The authors consider the remarriage penalty facing aged (not child-in-care) widows whose deceased spouses worked in Social Security-covered employment. They find that the 1979 law that reduced the penalty for remarriage over age 60 resulted in more widows aged 60 or older remarrying and that marriage rates among widows drop immediately prior to age 60 and increase at age 60.
3. These statistics are based on weighted samples from administrative records maintained by the Social Security Administration (SSA).
4. The full retirement age of Social Security varies by birth cohort. Two publications by the U.S. Social Security Administration (2001a, 2001b) contain information on this provision and on other program rules.
5. See Leonesio (1993) for a review of the evidence on the incentive effects of the earnings test.
6. As a whole, Social Security probably subsidizes marriage because several types of benefits are based on marriage (U.S. Social Security Administration 2001a).
7. For information on the finances of the overall Social Security system, see Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (2003).
8. Surviving divorced spouses are also eligible for child-in-care benefits. Throughout the paper, the term widow(er) is meant to include surviving divorced spouses. Also, a child-in-care widow(er) benefit terminates upon remarriage, but it can be restored if the marriage ends.
9. The family maximum formula has a somewhat different structure for years prior to 1979.
10. This result is not specific to the 2001 family maximum formula. Because Social Security annually adjusts each bend point by the same factor, it will always be the case that the family maximum ranges from 150 percent of PIA to about 187.5 percent of PIA.
11. The poverty measure is based on a particular definition of the family: individuals related by blood or marriage who reside in the same household. Our definition of family is based on Social Security program features: individuals who receive benefits on the same deceased worker's record. This definition of family has some advantages. For example, it includes dependent children who do not reside with the widow(er), such as a disabled child in an institution. It also has some drawbacks. Although the widow(er) usually is the mother/father or stepmother/stepfather of the children on the deceased worker's account, this will not always be true.
12. A widow(er) would provide an estimate to SSA of his or her earnings for a particular year. If actual earnings ultimately differed from the reported amount, SSA would pay additional benefits or collect for the overpayment of benefits.
13. The 10 percent sample is based on the last two digits of the widow(er)'s Social Security number (SSN). Each person is assigned a weight of 10. The last two digits of the SSN can be used to form a random sample (the two digits are not systematically assigned), and such samples are used for SSA publications, such as the Annual Statistical Supplement to the Social Security Bulletin (U.S. Social Security Administration 2001a). Our data, which are not publicly available due to confidentiality restrictions, include information from SSA's benefit records, earnings records, and SSN application records.
14. We project 2001 earnings on the basis of actual earnings from 1999. Specifically, we assume 2001 earnings will be 11 percent higher than 1999 earnings. Average wages in the United States grew by 11 percent from 1997 to 1999 (U.S. Social Security Administration 2001a, Table 2.A8).
15. A similar group that is excluded is composed of widow(er)s whose earnings were so high that they did not bother to file for benefits (note that this "no filing" group is not listed in Table 1). Such persons do not receive benefits and, consequently, do not face marriage penalties.
16. By definition, no widow(er) in group B or C has all 12 months of benefits suspended because of the earnings test. For the relatively few persons in these groups with earnings above the exempt amount, 1 or more months of benefits (but fewer than 12) will be suspended. For these widow(er)s, we calculate penalties as explained in the discussion of the earnings test.
17. Equation 3 pertains to monthly marriage penalties. Except when the earnings test would prevent payment of benefits for some months of the year, we approximate annual penalties by multiplying the monthly penalty as of January 2001 by 12.
18. For a study that examines how marriage penalties are affected by the interaction between the tax system and government transfer programs, see Dickert-Conlin and Houser (1998).
19. Studies from the income tax literature are not restricted to families with minor or disabled children, so results may not directly apply to child-in-care widow(er)s. However, we also note that the AFDC literature has found marriage effects (Moffitt 1998).
References
Alm, James, and Leslie A. Whittington. 1995. "Income Taxes and the Marriage Decision." Applied Economics 27: 25–31.
———. 1996a. "The Rise and Fall and Rise . . . of the Marriage Tax." National Tax Journal 49(4): 571–589.
———. 1996b. "Income Taxes and the Timing of Marital Decisions." Journal of Public Economics 64(2): 219–240.
———. 1999. "For Love or Money? The Impact of Income Taxes on Marriage." Economica 66(261): 1–24.
Alm, James; Stacy Dickert-Conlin; and Leslie A. Whittington. 1999. "Policy Watch: The Marriage Penalty." Journal of Economic Perspectives 13(3): 193–204.
Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds. 2003. 2003 Annual Report. Washington, D.C.: U.S. Government Printing Office.
Brien, Michael J.; Stacy Dickert-Conlin; and David A. Weaver. 2001. Widows Waiting to Wed? (Re)Marriage and Economic Incentives in Social Security Widow Benefits. Working Paper No. 89, Office of Research, Evaluation, and Statistics, Social Security Administration.
Bull, Nicholas; Janet Holtzblatt; James R. Nunns; and Robert Rebelein. 1999. Defining and Measuring Marriage Penalties and Bonuses. >OTA Paper No. 82 (revised). Washington, D.C.: Office of Tax Analysis, Department of Treasury.
Congressional Budget Office. 1997. For Better or For Worse: Marriage and the Federal Income Tax. Washington, D.C.: U.S. Government Printing Office.
Congressional Research Service. 2001. Welfare Reform: TANF Provisions Related to Marriage and Two-Parent Families. Washington, D.C.: Congressional Research Service.
Dickert-Conlin, Stacy, and Scott Houser. 1998. "Taxes and Transfers: A New Look at the Marriage Penalty." National Tax Journal 51(2): 175–218.
Eissa, Nada, and Hilary Williamson Hoynes. 2000. "Explaining the Fall and Rise in the Tax Cost of Marriage: The Effect of Tax Laws and Demographic Trends, 1984–97." National Tax Journal 53(3, Part 2): 683–711.
Feenberg, Daniel R., and Harvey S. Rosen. 1995. "Recent Developments in the Marriage Tax." National Tax Journal 48(1): 91–101.
Gelardi, A.M.G. 1996. "The Influence of Tax Law Changes on the Timing of Marriage: A Two-Country Analysis." National Tax Journal 49(1): 17–30.
Leonesio, Michael V. 1993. "Social Security and Older Workers." Social Security Bulletin 56(2): 47–57.
Moffitt, Robert. 1998. "The Effect of Welfare on Marriage and Fertility." In Welfare, the Family, and Reproductive Behavior: Research Perspectives, edited by Robert A. Moffitt. Washington, D.C.: National Academy Press.
Sjoquist, David L., and Mary Beth Walker. 1995. "The Marriage Tax and the Rate and Timing of Marriage." National Tax Journal 48(4): 550–564.
U.S. Social Security Administration. 2001a. Annual Statistical Supplement to the Social Security Bulletin, 2001. Washington, D.C.: U.S. Government Printing Office.
———. 2001b. Social Security Handbook. Washington, D.C.: U.S. Government Printing Office.
Waite, Linda J. 1995. "Does Marriage Matter?" Demography 32(4): 483–507.