Women’s Income and Marriage Markets in the United States

Women’s Income and Marriage Markets in the United States: Evidence from the Civil War Pension Abstract Although economic opportunities for women are thought to influence marriage market outcomes today, they receive little attention in accounts of 19th century American marriage patterns. The principle behind this mechanism is simple: women may choose to substitute away from marriage as alternatives become more attractive. However, providing evidence for this behavior is challenging because choices about marriage and career jointly determine one another. In this paper, I demonstrate that women’s income had a causal effect on their behavior in the marriage market during the late 19th century by analyzing the way in which Civil War pension income altered the marital outcomes of Union Army widows. Eligibility for a widow’s pension depended only on her first husband’s military service and the circumstances of his death, so it should be uncorrelated with the widow’s own characteristics; moreover, pensions terminated upon remarriage. Thus, pensions should have affected marital outcomes only insofar as they shifted the balance of costs and benefits women associated with marriage. Using a new database that I compile from widows’ pension files, I estimate that receiving a pension lowered the rate of remarriage by 40 percent, which implies an increase in the median time to remarriage of approximately three years. This indicates that women were willing to substitute away from marriage during this period if the alternatives were favorable enough. By offering evidence for this behavior, the results extend beyond the 19th century to shed light on marriage markets in later periods. 1 1 Introduction Marriage markets in the United States changed substantially over the course of the 19th century. The average female age at first marriage rose from roughly 20 during the colonial period to a peak of 23.6 in 1890 (Haines 1996). While aggregate trends in marriage market outcomes are well documented for this period, a virtual absence of micro-level data following women through marriage makes it difficult to account for these patterns. In particular, the factors affecting women’s decisions about when and whom to marry are not well understood. A number of explanations for the observed patterns have been proposed, including declining land availability, which increased the the cost of establishing new households,1 and falling male-to-female ratios,2 most notably in the aftermath of the Civil War. Much less attention has been paid to the role of women’s economic opportunities in altering the desirability of marriage to women.3 This paper fills this gap in the literature by presenting new evidence exploiting shocks to the income of Union Army widows. Through the compilation of a novel database, this paper also helps to rectify the scarcity of data tracing 19th century women through marriage. The desirability of marriage to women is largely ignored in accounts of 19th century marriage patterns. Economists model marital outcomes as the result of a balancing of costs and benefits; any factor affecting these costs and benefits may influence women’s choices. If outside economic opportunities for women lower the net gains from marriage, we would expect them to substitute away from marriage and toward these alternatives.4 This channel is considered very important for the later decades of the 20th century, which saw a simultaneous drop in marriage rates and explosion of female labor market opportunities. Between 1970 and 1995, the fraction of women ages 20-24 who had ever been marriage dropped from 64 to 34 percent (Blau Kahn and Waldfogel 2000); at the same time, female labor force participation increased from 49 to 72 percent, and the average female-male wage ratio rose from 0.56 to 0.72 (Blau 1998). While the 19th century did not see such a radical increase in opportunities for women, industrialization in the later part of the century facilitated women’s work (Wanamaker 2012), as did the rise of the clerical sector beginning around 1890 (Goldin 1984). In this paper, I offer evidence that women’s income had a causal effect on their choices about marriage during the years immediately following the American Civil War. Using data newly collected for this project, I assess the effect of Civil War pension income on the behavior of Union Army widows in the marriage market. The Civil War pension provides a rare setting for studying this behavior. Under the General Law, passed on July 14, 1862, a woman was eligible to receive a pension if her 1 See for example Easterlin (1971; 1976) and Haines (1996). For example, see Haines (1996) and Hacker (2008). 3 One recent study (Hacker 2008) includes this in a set of possible correlates of first marriage and documents a correlation between the age at first marriage and labor force participation among unmarried women in the 1860 census. However, this paper does not address the potential endogeneity of female labor force participation to norms of marriage or marriage market conditions. 4 See Becker (1973; 1991) for a theoretical development of this argument. 2 2 husband served honorably in the Union Army and died as a consequence of this service; however, she lost her right to the pension if she remarried. As such, a pension increased the value of remaining single, but it was not correlated with individual characteristics that affect marriage market outcomes, nor should it have rendered women more attractive to potential mates. In other words the effect of pension income on marital outcomes should work solely through women’s preferences.5 Such a natural experiment is especially useful because establishing that women’s income has a causal effect marital outcomes is difficult. Simply documenting a correlation between economic opportunities for women and delayed marriage is insufficient because of the interrelatedness of decisions regarding career and family. For example, both of the following explanations for such a correlation are plausible: women marry later because they have better labor market opportunities; or, women invest more in improving their labor market outcomes because norms of marriage have changed.6 Moreover, labor market opportunities for women can affect their behavior through multiple channels: women may prefer market work to home production; at the same time, the increased income these opportunities afford may render them more selective. A social assistance program that carries a marriage penalty directly isolates this latter channel, which is akin to an income effect. Most recent examples of such programs are age-based or means tested.7 During the period of focus of this study, the Civil War pension is neither of these. Providing evidence for any mechanism driving 19th century marriage patterns is challenging because of data limitations. The first Census tabulations of marital status by age and sex were not published until 1890 (Hacker 2008). Moreover, samples that follow women through marriage during this period are all but impossible to construct from census data: a primary tool for creating linked census samples is last names, and all women changed their last names upon marriage. The creation of a novel database following women through marriage is an important contribution of this paper. This database has the potential to provide insight into any number of questions about women’s behavior in marriage markets during this period. This paper seeks to determine the extent to which exogenous income shocks altered the relative costs and benefits associated with marriage. To illustrate how such shocks translate into observable outcomes, I use a theoretical model of search in the marriage market. I show that, by subsidizing the search for mates, pensions allow women to be more selective in their search process. Thus, pensions raise both the average time to remarriage and average match quality, conditional on remarrying at all. I show that the same predictions hold true in a comparison between women with accepted versus pending pension claims; this is due to uncertainty about if and when a pending claim will be approved. To assess the extent to which pensions caused women to delay remarriage, I make use of 5 The argument is somewhat more subtle than this because a soldier’s children could also receive a pension. I explain this in fuller detail in a later section. 6 The latter story is consistent with the work of Goldin and Katz (2002) and Bailey (2006) on the relationship between contraception and marriage and female labor supply. 7 Rosensweig (1999); Baker, Hanna and Kantarevic (2004); Brien, Dickert-Conlin and Weaver (2004). 3 variation in the timing of pension decisions, or pension processing times. Because pension amounts were standardized, I argue that this is the most appropriate source of variation to use. I estimate a proportional hazards model of remarriage in which the rate of remarriage is allowed to shift at the moment a pension is granted. As such, I estimate a treatment effect of transitioning from having a pending claim to having an accepted claim. To evaluate the effect pensions had on match quality, I use links to the 1870 and 1880 censuses, which allow me to observe the characteristics of women’s second husbands. I compare women who remarry with and without pensions along several plausible dimensions of match quality, including the second husband’s occupational status and literacy. One concern this paper addresses is the possible endogeneity of pension processing times to marital outcomes. This is largely due to sample selection, which is generated by the decision to apply for a pension. Women whose pensions take a long time to process tend to be those with ambiguous claims, and those who choose to incur the cost of applying for a pension even though their claims are ambiguous may be systematically different from those who apply with straightforward claims. To address this concern in my analysis of the relationship between pensions and the timing of remarriage, I exploit the fact that my treatment variable is a duration variable, which provides more information than is available in a standard cross-sectional setting. As I explain in a later section, variation in observables and the relationship between the hazard rates of pension receipt and remarriage provide sufficient information to correct for correlated unobserved heterogeneity in these two risks (Abbring and Van den Berg 2003; 2005). As an additional test, I estimate a linear version of this model using two stage least squares. My instrument for pension processing time is a measure of surname spelling homogeneity, calculated as the dispersion of unique spellings within phonetic surname groups in the censuses of 1860, 1870 and 1880. This generates variation in the difficulty of proving a soldier’s identity, which altered the amount of time it took for a claim to be granted. While I do not find conclusive evidence that pensions affected match quality, I do find a significant effect of pensions on the timing of remarriage. Specifically, I find that receiving a pension caused the rate of remarriage to drop by 40 percent, implying an increase in the median time to remarriage of approximately three years. This is especially striking because of the size of the pension. At eight dollars per month, the pension was less than half the monthly income of a typical farm laborer in 1870, so it was hardly enough to comfortably support a family. This finding lends credence to the idea that the incremental changes in female labor market opportunities seen in the 19th century may have contributed to the aggregate changes in marriage patterns that occurred during this period. In addition to offering new information about the way 19th century marriage markets worked, these results shed light on the behavior we observe during the 20th century. In particular, they suggest that the substitution of economic opportunities for marriage is not an entirely new behavior brought about by changing social norms. 4 2 Marriage and Women’s Income in Historical Context While the literature on marriage patterns in the United States before 1890 is small (Hacker 2008), it provides a broad picture of trends since the Colonial period. Haines (1996) shows an increase in the female age at first marriage up to about 1890. Fitch and Ruggles (2000) also find an increase in the female age at first marriage between 1850 and 1880; however, this increase is quite small, and seems to be concentrated in the years following the Civil War. It is well established that, during the last years of the 19th century, the age at first marriage began to fall, for men but more substantially for women, and it continued to decline until the middle of the 20th century.8 Since the 1970s, the age at first marriage for women has been steadily increasing (Blau, Kahn and Waldfogel 2000). Most explanations for 19th century trends in marriage focus on opportunities rather than preferences for marriage. In contrast to Western Europe, where “couples often delayed marriage until the prospective bridegroom inherited the family farm” (Fitch and Ruggles 2000, p. 62), land in the United States was cheap and abundant and did not pose an impediment to early marriage. However, as land became increasingly settled, marriage patterns started to more closely resemble those in Europe. As farmland grew scarcer and more expensive, “men were forced either to postpone marriage, working as farmhands or manual laborers until they had saved up enough money to set up their own farms, or to migrate to the western frontier” (Hacker 2008, p. 312). Easterlin (1976) also links the closing of the frontier to fertility control within marriage.9 As international and internal migration patterns changed over the course of the 19th century, declining male-to-female ratios likely contributed to the rising age at first marriage among women (Haines 1996; Hacker 2008). This would have been especially true in the years immediately following the Civil War.10 A small number of studies link women’s economic opportunities to delayed marriage before the 20th century. Hacker (2008) offers evidence from the 1860 census that women tended to marry later in areas in which economic opportunities for women were greater; this is measured by local unmarried female labor force participation. In a somewhat related study, Wanamaker (2012) links industrialization to declining fertility in the 19th century, with a focus on fertility within marriage. Goldin (1995) indirectly links economic opportunities to delayed marriage by noting a tendency for women’s education and marriage to be mutually exclusive. She describes a “stark set of alternatives between career and family” (p. 1) for women born at the end of the 19th century, noting that approximately half of college-educated women graduating in 1910 were childless. While this references a somewhat later period, women’s colleges in the late 19th century were similarly labeled “spinster factories” (Monahan 1951, p. 242). Some historical writing notes a tendency for women to delay or forgo marriage in the presence of favorable alternatives. Paraphrasing a critical 1871 account 8 See Fitch and Ruggles (2000) and Haines (1996), for example. For further elaborations of this argument, see Haines (1996), Easterlin (1971), Haines and Hacker (2006). 10 See Abramitzky, Delavande and Vasconcelos (2011) for an analysis of the effect of sex ratios on assortative matching in post-WWI France. 9 5 of this behavior, Calhoun (1919) writes that “the opening sphere for women’s talents is rendering marriage less popular for women; they are reluctant to marry a poor man; education inclines toward celibacy rather than marriage with poverty” (p. 205). Overall, the economic literature on 19th century marriage patterns is quite small. Moreover, data limitations severely limit its ability to provide evidence in support of the various drivers of these patterns. Investigations into modern marriage markets place much more stock in the role of women’s income in altering their behavior. There is a well developed theoretical literature about this mechanism. In Becker’s transferable utility model (1973, 1991), marriage generates utility by allowing couples to exploit increasing returns through division of labor, or by allowing both parties to consume collective goods such as children. A marriage will occur if marital output exceeds the sum of the output that both partners produce while single. As the gains from marriage arise from division of labor, married women will tend to specialize in home production as long as their market wages are lower than those of men, which has typically been the case. Thus, “an increase in the wage rate of women relative to men would tend to decrease the incentive to marry” (Becker 1973, p 822). Weiss (1997) notes that if labor market returns are higher for men than for women, high-earning women will experience relatively smaller gains from marriage than low-earning women. Another class of model that generates this relationship between female income and marriage rates comes from search theory. If women’s labor income functions as an alternative to marriage, it should raise the value of being single relative to the value of being matched. If being single increases in value, women will require more valuable matches in order to marry. Under random matching, such an increase in reservation match quality will lower the probability that any given proposal of marriage will be deemed suitable; thus, it will cause women to remain single longer. It will also raise average match qualities conditional on marrying at all.11 Most of the empirical literature on the effect of female income on marriage rates is descriptive, largely demonstrating a negative correlation between opportunities for women and marriage rates.12 This type of exercise is subject to several biases. For one thing, income depends on human capital investment, which may be endogenous to preferences for marriage. A paper that deals explicitly with this causality issue is Blau, Kahn and Waldfogel (2000), who look at the effect of city-wide marriage and labor market conditions on marriage rates. They find that better female labor markets tend to decrease marriage rates, while better male labor markets tend to increase them. Still, it 11 See Rogerson, Shimer and Wright (2005) for a survey of basic search models. See Weiss (1997) for a review of search models applied to marriage markets. Gould and Paserman (2003) and Loughran (2002) use a search framework to investigate the effect of wage inequality on marriage rates. 12 Keeley (1977) finds that women with high wages tend to marry later, although men with high wages tend to marry earlier. Ruggles (1997) argues that increasing female labor market opportunities contributed to the rise in divorce rates during the twentieth century. Weiss and Willis (1997) find that women with high earnings are more likely to divorce, while the opposite is true of men with high earnings. Price-Bonham and Balswick (1980) argue that widows are less likely to remarry than divorced women, as are older and more educated women with fewer children. Bahr (1979) finds that more affluent women are less likely to remarry after divorce. See also Waite and Spitze (1981) for an investigation into determinants of female age at first marriage. 6 is not clear from this analysis that female labor market opportunities cause women’s choices about marriage to change: areas in which these opportunities are greater may have different norms of marriage. A different approach is due to Choo and Siow (2006), who propose a statistic to directly measure the net gain from marriage for a given pair of male and female “types.”13 They attempt to quantify the net benefit from marriage for men and women using data from the 1970 U.S. Census and Vital Statistics. They find that the net benefit of marriage declined between 1970 and 1980 for both men and women, but more so for women. This is suggestive, as opportunities in the labor market for women grew significantly during this decade. Other work takes a similar approach to this paper, looking at the effect of marriage penalties on the behavior of social assistance recipients. Rosensweig (1999) studies the effect of the AFDC program on marriage and out-of-wedlock childbearing for young women, and he finds that AFDC benefits tend to encourage fertility outside marriage. Baker, Hanna and Kantarevic (2004) find a significant negative effect of marriage penalties on remarriage, which they identify through the removal of marriage penalties from the public pension system in Canada during the 1980s. Brien, Dickert-Conlin and Weaver (2004) find that American widows and widowers delayed remarriage until after the age of 60 in response to the marriage penalty built into Social Security before 1979. 3 Institutional Background: Widows and the Civil War Pension Law The original Civil War pension law, called the General Law, was passed on July 14, 1862. This act provided compensation for soldiers and the dependents of soldiers who had fought honorably for the Union and who had been wounded in such a way that they were unable to work. Over time, this pension system expanded into a form of old-age security for Union Army veterans and their families. Pension expenditures grew from $29 million in 1870 to $160 million by 1910, covering almost one million veterans and their dependents (Linares 2001). It is generally considered America’s first large-scale social assistance program (Skocpol 1993; 1995). Eligibility for a widow’s pension under the General Law depended three main criteria. A widow was entitled to a pension if she did not remarry, and if her husband had served honorably in the Union army and died of a disease or injury sustained in the service. The qualifying widow of a private in the Union Army was entitled to eight dollars per month plus two dollars per minor child (under the age of 16) beginning on July 25, 1866.14 To give a sense of the size of this income, a typical daily wage for a common laborer in the north was approximately one dollar in 1860 and two dollars in 1870; a farm worker would typically make 11to 15 dollars per month in 1860 and 18 to 20 13 This statistic is the ratio of the number of matches formed by these types to the geometric mean of the number men and women of these types that remain single. 14 Glasson (1900; 1918); Song (2000). Officers’ widows were entitled to a larger pension than widows, but the UA data contains only privates. 7 dollars per month in 1870, which included room and board (Margo 2000). The pension law was amended at various times. The most significant amendment was the act of June 27, 1890, which changed the eligibility requirements for both veterans and widows. Under this law, a widow could claim a pension if her husband had served honorably for at least 90 days in the Union Army, regardless of how he died. However, she had to demonstrate that she was “dependent upon her daily labor for support” (Linares 2001). Under the act of July 14, 1862, widows permanently lost their right to a pension if they remarried. However, later changes to the General Law altered this somewhat. As of June 7, 1888, a widow who had remarried could apply for a General Law pension in arrears, commencing on the date of her first husband’s death and terminating on the date of her remarriage.15 On March 3, 1901, a widow who was eligible under the General Law but had remarried was allowed to be restored to the pension rolls after her new husband died, provided she had never divorced this second husband, and she was needy. It became progressively easier for remarried widows to be restored to the rolls through the 1920s (Glasson 1900). 3.1 Procedures for Filing for and Collecting Pensions The process of applying for pensions was costly and time consuming. In contrast to soldiers who filed pension claims, widows did not need to be examined by a surgeon; however, they were required to provide a great deal of evidence in support their claims. A widow had to appear before a court of record. If she lived more than 25 miles from a court of record, she could appear before a pension notary stationed in her locality (Oliver 1917). Here, she would make her declaration, which involved filling out a form in the presence of witnesses. The instructions attached to this form outline the information and documents she was required to furnish: She must prove the legality of her marriage, the death of her husband, and that she is still a widow. She must also furnish the names and ages of her children under sixteen years of age, at her husband’s decease, and the place of their residence... The legality of the marriage may be ascertained by the certificate of the clergyman who joined them in wedlock, or by the testimony of respectable persons having knowledge of the fact, in default of Record evidence. (Widow’s Certificate No. 8,336). This evidence was mailed to the pension bureau in Washington, DC, where claims were adjudicated. This adjudication process involved obtaining the soldier’s military record from the war department. If a widow could not prove that she was legally married to the soldier or that his death was a direct result of his military service, her claim would be rejected. In many instances, claimants hired attorneys to prosecute their claims. The quality of the attorney could have a dramatic effect on the speed with which a claim was processed; there are ample instances of claims pending for years because of attorney neglect, a problem well known to 15 ibid 8 the pension board. The 1883 annual report of the pension commissioner condemns the behavior of these pension lawyers: There are certain ignorant, unscrupulous, and useless persons, whose only object seems to be, first, to procure applications from soldiers, regardless of merit, to be filed through them, and then, while acting simply as transmitters of the papers, assiduously dun the claimant until the ten-dollar fee is secured, and thereafter practically abandon the case (United States Pension Bureau 1883, p. 16). Pensions were disbursed from agencies, located in cities and towns across the country. There were 33 such agencies in operation in 1863; by 1872, this had expanded to 57.16 These agencies grew out of an existing infrastructure for distributing military pensions, inherited from the much smaller pension system already in place.17 Payments were initially made semiannually, but this was increased to quarterly in 1870. Vouchers were drawn up and mailed from the pensioner’s local agency. Upon receiving this voucher, the pensioner would fill it out and return it to the agency, which would mail back a check drawn on the U.S. treasury (Oliver 1917, p. 30). 3.2 Minors’ Pensions If a widow remarried, she lost her right to a pension. Entitlement to the pension then passed to the soldier’s minor children, who were allowed to receive it until the youngest turned sixteen.18 I have argued that pensions should only affect marital outcomes through widows’ preferences: because they terminated upon remarriage, pensions should not make widows more desirable in the marriage market. However, if the widow’s children were entitled to the pension when she remarried, she would, in a sense, continue to receive it. This means that she would be bringing an additional income stream into her new marriage, which might change the profile of matches available to her. While the soldier’s children were collectively entitled to the same monthly pension as the widow, there is variation in minors’ pensions that is distinct from widows’ pensions. This means that the effect minors’ pensions had on widows’ outcomes can be controlled for in the empirical analysis. This independent variation is due to several features of the pension law. First of all, minors’ pensions terminated when the youngest child reached the age of sixteen; therefore, the lifetime value of these pensions was significantly lower than that of a widow’s pension. There was an additional cost to obtaining a minor’s pension: the children (or their guardian) needed to file a separate application, which took time to process. They also needed to obtain proof of their ages and legitimacy, as well proof that their mother was no longer eligible for the pension due to remarriage or death. 16 United States Pension Bureau 1864 and 1873. The agencies were generally considered inefficient and expensive (Oliver 1917; United States Pension Bureau 1883), and were reduced in number by the end of the 1870s (United States Pension Bureau 1883). 17 See Glasson 1900 and 1918 for details. These pensions were for veterans (and dependents) of the Revolutionary War, the War of 1812, and the Mexican-American War. 18 One pension could be issued to all the soldier’s children, which they would share. 9 Finally, there were restrictions on the consumption of a minor’s pension. These pensions were intended to be spent only on children’s maintenance and schooling. Funds were paid directly to guardians, not to the children themselves; proof of guardianship had to be provided “under seal of the Court from which their appointment is obtained” (Widow’s Certificate No. 8,336). In some cases, the guardian was the widow or her new husband; in others, it was a third party. Even if the guardian was the widow or her second husband, there were steps taken to ensure that the pension was spent on the children and not on the guardian’s consumption. In particular, the guardian had to account for the expenditure of the children’s property at court. This requirement was laid out explicitly in many guardianship documents and in some cases codified in law. For example, a case from Michigan requires “a true account if the property of said ward in your hands” to be provided to the Probate Office “within one year from this date [December 10, 1867]” (Widow’s Certificate No. 73,022). The law pertaining to guardianship in New York state required such an “inventory and account” annually (Legislature of New York 1837). In order to secure the guardian’s obligations to his wards, he would post a bond with the county probate court. The pension cited above notes that the guardian rendered “a Bond with good and sufficient security to be approved by our said County Judge... in the penal sum of nine hundred” (Widow’s Certificate No. 73,022). Another pension file includes proof of guardianship that describes a bond “in the penalty of fifteen hundred dollars conditional that the said [guardian] should faithfully, in all things, discharge the duties of a guardian” (Widow’s Certificate No. 35,292). Certainly, minors’ pensions would have affected widows’ outcomes, largely by rendering children less of a detriment in the marriage market. Potential husbands may have been more likely to propose to a woman with young children if these children were self-supporting. However, variation in minors’ pensions that is independent of widows’ pensions allows me to control for this effect in the empirical analysis. Specifically, I can control for potential minors’ pensions using information on the number and ages of each widow’s children. 3.3 Fraud An obvious concern with using information about marital status from pension records is accuracy. Widows had a clear incentive to hide remarriages from the pension board, since disclosing this information would result in loss of pension. The incentive to fabricate marriages to veterans also existed. As the 1872 annual report of the pension commissioner remarks, “So long as pensions are to be granted upon evidence which (except record evidence) is purely ex parte, so long frauds will continue to exist” (United States Pension Bureau 1872, p. 13). The pension bureau was especially concerned about widows’ claims: “The evidence to sustain a widow’s or dependent’s case is purely ex parte. As a result of this, a very considerable percentage of those cases are wrongfully established” (United States Pension Bureau 1872, p. 13). If the pension authorities suspected a fraud, they would send a special examiner to the widow’s 10 place of residence to conduct an investigation. If found guilty of fraud, the widow lost her pension. Fraud was usually reported by either the postmaster who oversaw the delivery of pension vouchers and checks, or by members of the pensioner’s community. There are a handful of examples in my sample of both sources reporting frauds19 . However, notwithstanding the pension bureau’s concerns about fraud, there is little evidence that hidden remarriages were a frequent occurrence. Women receiving pensions regularly interacted with the pension board throughout their lives; yet, in only about 15 out of the 500 cases analyzed in this study is there any indication of investigation into pension fraud. Moreover, only a few of these cases resulted in the widow being stripped of her pension. Still, to address concerns about fraud, I check marital status using links to the federal censuses of 1870 and 1880. Unless a large number of women were engaged in an elaborate fraud involving hiding second husbands from census enumerators, hidden remarriages or cohabitation do not appear to pose a significant problem. 4 Theoretical model The aim of this paper is to assess the effect of an independent income source on women’s choices about marriage. In this section, I describe a theoretical model to characterize the way in which such an income source should affect observable outcomes by altering the relative gains women perceived from marriage. A Civil War pension is income that a woman earns while she remains single but loses upon remarriage. As such, it is analogous to unemployment benefits in a search model of the labor market.20 Thus, a simple search model of the marriage market is a natural framework for analyzing this question. I restrict the analysis to the female side of the market, which implicitly assumes that these pensions do not have general equilibrium effects on marriage market conditions. This is justified if the number of pensioners is relatively small.21 19 A letter of instruction to a special examiner in the case of Catherine Matthews describes allegations of remarriage by the postmaster of Malone, New York. The examiner is instructed to ascertain “whether the pensioner, by regular ceremony, by cohabitation, or by any other manner has performed such an act as will constitute marriage (re-marriage) under the laws of New York” (Widow’s Certificate No. 6,916). Another example of fraud is the case of Maria van Buren, whose remarriage to Frank Stoffer is reported to the pension board by a close acquaintance. An excerpt from the examiner’s report reads, “Stoffer had in his possession several letters, written in the same chirography, with the one hereto attached, none having a signature, all about equally dirty, but differing vastly in tone and purpose. The first a threatening message, demanding that she return to him by 7 o’clock and at least bid him farewell ‘like a lady,’ or he would have her in the penitentiary immediately. The next, breathing undying attachment of enormous dimensions, and asking her forgiveness for having ‘told on her’. The third a sarcastic letter to Stoffer, and the fourth a letter of farewell and filled with threats of vengeance for her rejection of his ‘ardent heart.’ Mrs Van Buren acknowledged that she was living wtih Stoffer, and had done so ‘off and on when she felt like it’, but denied that she had married him, denied that he is Van Buren, who is now, she remarked, if not in heaven, certainly not on earth; denied that she intended to run away and professed several times an unusually strong desire to be arrested. I was, of course, satisfied that the case was not one which I was authorized to further investigate without direct instruction” (Widow’s Certificate No. 23,529). She was ultimately removed from the pension rolls because of remarriage, demonstrated by “cohabitation and recognition” (Widow’s Certificate No. 23,529). 20 See Rogerson, Shimer and Wright 2005 for a review. 21 In fact, the number of pensioners was relatively small. There were just over 100,000 widows and other dependents on the pension rolls in 1872 (United States Pension Bureau 1872), and the number of dependents on the General Law pension rolls peaked in the early 1870s (Linares 2001). In 1870, the number of single women over the age of 17 was 11 The model is set up as follows. Unmarried women periodically receive proposals of marriage. A match generates value for the woman, and she must determine whether or not this exceeds the value she derives from remaining single. The value of staying unattached incorporates whatever flow utility she gets, as well as an “option value” of waiting for a potentially better match. If pension income raises the value of remaining single, this will raise the minimum match quality a woman will require in order to accept a proposal of marriage. An increase in this reservation match quality lowers the probability that a given match will be accepted, which will tend to increase the time spent searching. And, it will raise the average quality of a match, conditional on being matched at all. Simply put, if a woman is able to better support herself while single, she will be willing to wait longer for a better match. In this model, I endogenize the frequency of marriage proposals. The effort women spend on search in the marriage market affects their outcomes: the more effort women allocate to search, the more frequently they receive proposals of marriage. However, search is costly. Because pensions raise the value of being single, women with pensions will tend to allocate less effort to the search process. This can be interpreted as an income effect: women “spend” a portion of this additional value on mitigating search costs. Suppose there are two types of single women: those who receive a pension (indexed by P) and those who do not (indexed by N).22 Married women are indexed by M. Assume for simplicity that there is no divorce.23 A marriage generates flow utility θ, which is drawn from a distribution F (θ), and discounting occurs at a rate r. Each state, married or single, is associated with a lifetime expected value, V. For all women, the value of being in a marriage with match quality θ is given by: rV M = θ In words, this is the present discounted value of receiving utility θ forever. The value of being single is different for pensioned and unpensioned women. Suppose remaining single generates a flow utility s, and women with pensions receive additional utility p. Marriage proposals have a poisson arrival rate α, which depends on search effort. Specifically, it costs a widow c(α) in utility to obtain a rate of proposals α. I assume that costs are increasing and convex in α, so c0 (α) > 0 and c00 (α) > 0.24 Then, the value to a pensioned woman of remaining single with proposal rate αP∗ on the order of four million (Ruggles et all 2010), putting the fraction of unmarried women on the pension rolls at no more than two or three percent. 22 For the purposes of the model, I am assuming that women with and without pensions are otherwise identical. 23 Allowing divorce does not qualitatively change the implications of the model. In any case, divorce was relatively uncommon. Preston and McDonald (1979) estimate that around six percent of marriages ended in divorce during the 1870s, compared to more than twenty percent in the 1950s. Work by Cvrcek (2009) demonstrates that this underestimates the true extent of marital separation: he estimates that ten to fifteen percent of marriages contracted during this period were disrupted, which is still a clear minority of marriages. 24 This standard assumption follows Mortenson (1986). It merely means that the marginal cost of search is increasing. 12 can be written rV P = s + p − c(αP∗ ) + αP∗ E[max{V M − V P , 0}] (1) This is composed of two elements: the instantaneous utility a woman receives (s+p−c(αP∗ )) and a term that reflects additional value, over and above the value of remaining single, from anticipated future proposals of marriage. It is a standard result that these unmarried women will have a reservation match quality, θP , which means they will accept any match carrying quality θ ≥ θP . This has the property that V M (θP ) = V P = θP /r. In other words, the reservation match quality is such that the woman is indifferent between remaining single and accepting the match. Substituting this into (1), and re-writing the expectation as an integral, we get the following equation that implicitly defines this reservation match quality: θP = s + p − c(αP∗ ) + αP∗ r Z ∞ (θ − θP )dF (θ) θP Women will choose αP∗ that maximizes the value of being unmarried. The maximizing level αP∗ will solve the following first order condition:25 0 rc (αP∗ ) Z ∞ (θ − θP )dF (θ) = θP Similarly, for women who do not receive pensions, the reservation match quality is θN = s − ∗ c(αN ) α∗ + N r Z ∞ (θ − θN )dF (θ) θN ∗ is defined similarly to α∗ . Notice that α∗ , i ∈ {P, N }, does not depend directly The optimal αN i P on p. Instead, it depends on θi , which in turn depends on p. It is straightforward to show that ∗ . In other words, θP is increasing and αP∗ is decreasing in p;26 therefore, θP > θN and αP∗ < αN women with pensions should be more selective and should spend less effort on search in the marriage market. How are these differences manifested in observable outcomes? First, we can derive the rate of remarriage, which depends on both reservation match qualities and search effort. For a woman of type i ∈ {P, N }, the rate of exit from widowhood into marriage (Hi ), or probability of remarrying at a given point in time conditional on staying single until then, can be written as Hi = αi∗ (1 − F (θi )) This can be interpreted as the probability of both receiving a marriage proposal and accepting it. ∗ , it follows that H < H . This means that the average time Then, because θP > θN and αP∗ < αN P N 25 26 See Mortenson (1986). See Mortenson (1986) or Rogerson Shimer and Wright (2005) 13 spent as a widow will be greater for women with pensions than without. Additionally, we have E[θ|θ ≥ θP ] > E[θ|θ ≥ θN ] Women receiving a pension have higher expected match qualities, conditional on being matched. This is simply because the minimum θ for women with pensions is higher. In the empirical section of this paper, I will find it useful to specify a third group of women: those with a pending pension application. Suppose that, during an interval ∆, the (endogenous) probability of a woman with a pending claim receiving a proposal of marriage is ∆α̃∗ , and the probability of having a claim decided is ∆λ.27 The probability that the decision will be favorable is given by π. Then, the value of being a widow with a pending pension claim can be written:     rṼ = s − c(α̃∗ ) + α̃∗ E[max(V M − Ṽ , 0)] + λ πV P + (1 − π)V N − Ṽ (2) See appendix A for proof. Again, this is composed of three parts: the flow utility while single, additional value from future marriage proposals, and additional value from future pension rulings. Because V M is strictly increasing in θ, the right hand side of this equation is also strictly increasing in θ. This implies that there exists a reservation match quality θ̃ for women with pending pension applications. Then, we have the following equation that implicitly defines this reservation match quality: θ̃ = s − c(α̃∗ ) + α̃∗ r Z ∞ (θ − θ̃)dF (θ) + θ̃  λ πθP + (1 − π)θN − θ̃ r (3) The optimal α̃∗ will resemble that of the other two groups. ∗ > α̃∗ > α∗ . Proposition 1: For π ∈ (0, 1], θN < θ̃ < θP and αN P Proof: See appendix A. The intuition behind this is simple. Women with pending claims should have higher reservation match qualities than women receiving no pension with certainty because of the possibility of future pension income. However, they should have lower reservation match qualities than women whose claims have already been approved because of discounting and the possibility that the pending claim will be rejected. Again, the “income effect” coming from differences in the value of singlehood for these three types will generate differences in optimal search effort. 5 Data 5.1 Pension and Military Records The data used in this paper comes from three main sources, two of which are newly collected from primary sources. The first data source is the Union Army (UA) database created by the Center for 27 This set-up follows Rogerson Shimer and Wright (2005). 14 Population Economics (CPE) at the University of Chicago.28 I have chosen a random sample of 500 women who were married to soldiers in the UA database. Useful for this study, this database provides information about soldiers’ families, including when, where, and to whom they were married, as well as the birth dates and names of their children. I use this information to identify women that meet two important conditions. First, I restrict my attention to women widowed by 1880. This is because I expect such women to be most representative of the unmarried female population; they will be relatively young and thus more plausible marriage candidates.29 I choose 1880 as a cutoff because it facilitates the linking of my observations to the 1880 census.30 The second restriction is that the widow had to apply for a pension within five years of her first husband’s death. This restriction is intended to minimize sample selection bias due to limited data availability. Ideally, one would observe the widows of all soldiers in the UA database. However, because of the nature of this data source, the availability of spousal information depends on actions taken by subjects. For soldiers who died before 1880, all such information comes from dependents’ pension applications, the vast majority of which are widows’ applications. As such, it is extremely rare to know about widows who do not file for a pension at some point in their lives.31 Women who first apply for a pension, say, ten years after widowhood will be those who had not applied earlier and had not remarried during those ten years. This will be a highly selected sample of all widows who did not file for a pension before ten years had elapsed. Given that my sample is necessarily restricted to applicants, there is a certain amount of selection that is unavoidable; however, I expect including late applicants to exacerbate this problem. The majority of the information I use in this paper comes from data that I collected from the Civil War pension files at the National Archives in Washington, DC. The CPE project focuses on 28 These data were collected as part of the project Early Indicators of Later Work Levels, Disease, and Death, sponsored by the National Institutes of Health and the National Science Foundation (Federal grant number P01 AG10120; see Fogel 2000). The data are drawn from three principal sources: the military, pension and medical records are compiled from sources at the National Archives including military service records and Civil War pension records; data from the Surgeons Certificates contain detailed information about veterans health status, which was used to determine pension eligibility; further socioeconomic information is gathered by linking veterans to the Federal Censuses of 1850, 1860, 1900 and 1910. These data have primarily been used to study health and aging in the late 19th and early 20th centuries. See for example Costa 1997, 1995, 1993; Fogel 2004; Eli 2010. They have also been used to analyze group dynamics in military settings (Costa and Kahn 2003, 2008). The data contain information about every soldier who enlisted in 303 randomly sampled companies of white volunteer infantry regiments. The database contains 39,341 observations and 3,230 variables (Fogel et al. 2000). 29 Another consideration has to do with later amendments to the pension law. Under the General Law, the only requirement for pension eligibility was that a woman’s husband served honorably in the Union Army and died from an injury or disease contracted in the service. However, following the act of June 27, 1890, a widow could receive a pension regardless of how her husband died, provided she could prove financial need. I expect financial need to be correlated with marital outcomes, more so than the details of a widow’s first husbands death. So, it is beneficial to restrict the sample to women who could only have applied for a pension under the General Law, at least during the years immediately after widowhood. 30 I cannot link widows to the 1890 census, because these manuscripts were lost in a fire. Linking to the 1900 census is less useful, as most Civil War widows were well past the age at which they could reasonably expect to remarry by 1900. The importance of census links is described later in this section. 31 Soldiers on the pension in 1898 were required to inform the pension bureau of the name of their spouse and children. Before 1898, it is possible to have spousal information about a soldier if his widow never filed a claim but his mother or children did; however, this is quite rare. 15 soldiers’ outcomes, so the UA database does not contain information about widows and children after the soldier died. After drawing my sample, I collect information about widows’ pensions and marriage histories from their pension files. See appendix B for details of the data collection process. Because these data are compiled from historical records and not from surveys designed to avoid selection bias, the source of every piece of information is important. With this in mind, I will explain in detail where my most important variables come from. The pension information is largely straightforward to collect, as any action a widow took with respect to pensions is recorded in her correspondence with the pension bureau. The case files contain all materials in a widow’s pension application, which includes her application form and supporting evidence. If the widow was granted a pension, her file will contain both a pension brief and a pension certificate, indicating the amount of the pension, the effective start date, the date at which the pension was granted, the agency she was to be paid from, and the name of her attorney.32 If the widow did not receive a pension, it is more difficult to determine why. In later years, rejected claims contain a brief indicating the date of and reason for rejection; however, during the years immediately following the Civil War, information about rejection merely consists of a stamp somewhere in the file that reads “rejected.” In such cases, it is impossible to determine the reason for or date of rejection. Similarly, if a widow abandons her claim, we cannot be certain why or when. Information about a widow’s remarriage is slightly more complicated. Figure 1 illustrates the possible pension and marital outcomes for women in my sample. The first thing that occurs is the widow’s pension application. After applying, the widow may remarry or die before her claim is adjudicated. Otherwise, she will receive a decision from the pension board, which may be favorable or not. After receiving this decision, the widow may or may not remarry. The outcome of a pension application is always certain; however, in 20 percent of cases it is impossible to determine whether or not the widow ever remarried.33 Table 1 lists possible sources of information about marital status and their frequency by pension status. A widow’s remarriage is observable if her children file a pension claim or she applies to be restored to the pension rolls under the act of March 3, 1901.34 A widow’s failure to remarry is observable if her death date is known, and there is no indication of remarriage. If she is receiving a pension when she dies, her file will often contain a card indicating that she has been dropped from the pension rolls due to death. If not, this information may come from minors’ pension applications or other correspondence with the pension board. Marital status is not observable if the widow stops communicating with the pension board some time before her death. Notice that the frequency of 32 This information can be independently verified using the index to the pension files, which indicates the number attached to the widow’s application and pension certificate. As these numbers are issued chronologically, the approximate date of application and issuance of the certificate can be inferred from these numbers. 33 After around 1880, the pension bureau started including records of pensioners being dropped from the rolls for any reason. Women whose marital status is unknown are missing these records; thus, if they were on the pension, it is likely that they died, remarried, or stopped collecting their pensions some time before 1880. 34 In some cases, a widow may have filed a claim for a pension she was not entitled to, or there may have been some other correspondence with the pension board indicating that she had remarried. 16 sources of information differs by pension status; this will be important to the sensitivity analysis I do later on. Table 2 presents summary statistics from the pension file data I have collected (498 records in total). All women in this sample applied for a pension within five years of widowhood and had not remarried before doing so. The average age when widowed is 32; however, this ranges from 15 to 73. There are 397 women for whom remarriage status is certain, meaning that I observe them either remarrying or dying while single. There is no evidence that the other 101 women either remarried or died. Of these 397 women, 55 percent remarried at some point in their lives, which implies that the true fraction of women who ever remarried is between 44 and 64 percent. Of the 425 women for whom this information is available, 18 percent remarried before receiving a pension.35 On average, a woman who remarried did so 4.3 years after her first husband’s death. This average is much lower among women who remarried before getting a pension (2.4 years), which is unsurprising. It is, however, suggestive that the average time that elapsed between receiving a pension and remarriage is 3.9 years, which is much greater than 2.4 years. The average amount of time that elapsed between the soldier’s death and his widow filing for a pension was eight months, and the median was less than four months. The probability of ever having a General Law claim accepted was 0.86; however, fewer than 80 percent of women were receiving a General Law pension within five years of applying. The average processing time for a pension was more than two years, although this is highly skewed: the median processing time is slightly less than one year. Most women in my sample were first married during the 1850s and were widowed during the war. These women tended to come from the Mid Atlantic region (30 percent) or the East North Central region (41 percent). Very few come from Southern or Western regions. 5.2 Census Links I use information from the pension file data to link my observations to the federal censuses of 1870 and 1880. These links are important because they provide information about widows’ second marriages. In the pension file data, such information is available in a minority of cases, which makes it difficult to evaluate the effect of pension income on match quality. Another reason for linking widows to the census is that it provides a check on the marriage information available in the pension data. For one thing, these links allow independent verification of widows’ marital status, which alleviates concerns about inaccuracies due to fraud. These links also help mitigate concerns about missing data. As explained above, although marital status is known in most instances, it is unknown for 20 percent of my sample. A concern is that the availability of information about marital status is not random, and this might bias my results. A remarried widow must do one of two things to be 35 Even if I do not know whether or not a widow ever remarried, I may know that she did not remarry with a pending claim if she communicated with the pension board subsequent to her claim being granted. 17 identified in the pension data: she must have young children who apply for a minor’s pension after she remarries; or, she must survive long enough to apply for a pension under the act of March 3, 1901. Women who do not remarry do not need to meet these restrictions in order to be observed. Therefore, my sample of remarried widows may be younger and healthier than my sample of widows who do not remarry, simply by virtue of the way the data are collected. If the effect of the pension on marriage behavior depends on age or health, this sample selection might bias my results. Identifying widows with uncertain marital status through census links is a challenge: if a widow did remarry, her last name would have changed. I use an alternative method for linking these ambiguous cases. The names and ages of children from the widow’s first marriage are available in the pension data, so I can link these children to the census; in principle, a child’s surname would not change if his or her mother remarried.36 If I locate a child who is living with a married mother with a different last name (but whose birth year and first name match the widow in my sample), I assume that I have identified a remarried widow. See appendix B for further details. Data collected this way will still favor women with young children; however, this will apply equally widows who have remarried and those who have not. These data may generate other biases. For example, a remarried woman may be less likely to keep her children living at home, so I might underestimate the fraction of widows who remarry. Still, because the availability of these data does not depend on details of the pension application process, they will be a useful complement to the pension data. Table 3 presents statistics on the success rate of this procedure. The top panel lists the fraction of widows who were linked to the 1870 and 1880 census, overall and by marital status. The linkage rate is quite high overall, close to 60 percent in both years. In 1870, the linkage rate is higher among widows who are known to have remarried (69 percent) than it is among women who are known to have remained unmarried (63 percent); in 1880, the linkage rate is higher among women known not to have remarried (76 versus 68 percent). The fraction of widows with uncertain marital status who were successfully linked through children from their first marriage is much lower (18 to 27 percent); however, this partly reflects the fact that some of these women are childless. Among women who may theoretically be linked this way, 26 to 37 percent were located successfully.37 The vast majority of widows with unknown marital status turned out to be unmarried: only one had remarried by 1880. The bottom panel of table 3 contains the fraction of widows who were theoretically “linkable” through children from their first marriage. This is to get a sense of the effectiveness of my strategy for linking widows with unknown marital status. In fact, a large number of widows, both married 36 The availability of information about children does not impart additional bias, as all widows were required to list minor children in their pension applications; thus, this information is available for every widow who made a pension application. 37 One reason for the linkage rate for these women to fall below the linkage rate for women with known marital status is that, for women with unknown marital status, I have little information on place of residence in 1870 or 1880; these women have largely disappeared from the sample by this time. Note that these linkage rates still compare favorably to other projects that create samples of linked census data. See Ruggles et al (2010) and Ferrie (1996). 18 and unmarried, reside with children who have kept their deceased father’s surname. In 1870, 88 percent of unmarried widows and 52 percent of married widows live with such children. In 1880, these fractions are 80 and 44 percent, respectively. This decline in the fraction of women who are linkable through children is likely caused by the increasing tendency for children to leave home as they age. While at appears that linking widows through their children does underrepresent those who have remarried, a significant fraction of such widows can still be linked. 5.3 Representativeness In order for a widow to appear in my sample, she must satisfy two conditions. First, she must have been married to a Union Army soldier who died before 1880; second, she must have filed an application for a pension. In this section, I investigate the extent of the bias introduced by the decision to apply for a pension, which will be important when considering what these results imply about all women, or even all Civil War widows. A natural starting point is to establish the fraction of women widowed before 1880 who ever made pension applications. Recall that spousal information comes almost exclusively from widows’ pension applications, so I will treat making an application and appearing in the pension data as interchangeable38 . To know for certain the fraction of women widowed by 1880 who made pension applications, we need both a numerator and a denominator. More precisely, we need three pieces of information: (i) the number of women widowed by 1880 who made pension applications; (ii) the number of soldiers who died before 1880; and (iii), how many of these soldiers were married. We know (i) but not (ii) or (iii). In order to establish a lower bound estimate of the application rate among women widowed by 1880, it is necessary to make assumptions about missing data. Table 4 contains some of these estimates. Out of a sample of 39,341, we know for certain that 7,953 soldiers died before 1880. Of these, we know that 3,102 were married because there is spousal information in the UA data; we also know that 714 were not married. If the 7,953 soldiers whose death dates are known to be prior to 1880 constitute a fully representative sample of all soldiers who died before 1880, it would be reasonable to infer the application rate among women widowed by 1880 was at least 45 percent.39 However, these 7,953 soldiers are almost certainly not a representative sample of soldiers who died by 1880, because knowledge of a soldier’s death date is highly correlated with his widow making a pension application. To see this, notice that 95 percent of soldiers with missing death dates also have missing spousal information. This is because information on death dates for soldiers who died prior to 1880 often comes from widows’ pension applications. So, in order to establish a lower bound on the fraction of widows who appear in the data, we must allow for the possibility that some soldiers with missing death dates died before 1880. Depending on the reference group and 38 As described earlier, spousal information before the early 1900s was collected through dependents’ pension applications, so it was very unusual to have this information if no pension application was submitted. 39 This lower bound assumes that every soldier with missing spousal information was married. 19 assumptions about the fraction of soldiers who were married, I derive reasonable lower bounds that range from 17-46 percent.40 Using only soldiers who died during the war as a reference group provides a potentially more reliable lower bound estimate of the true application rate. Information about death dates of soldiers who died in the service can be obtained from sources other than widows’ pension applications, such as military or hospital records. Thus, it is more reasonable to treat these soldiers as a random sample of casualties, with respect to widows’ pension applications. If we assume that the overall Union Army casualty rate of 16 percent (Costa and Kahn 2008) prevailed in this sample, the lower bound ranges from 28-46 percent, depending on assumptions about the marital status of men with missing spousal information. Based on this calculation, a lower bound application rate of about one half is reasonable. While a large fraction of women widowed by 1880 made pension applications, it seems likely that not every widow did so. The next question is: how did women who made pension applications differ from those who did not? Establishing this is complicated by the fact that women who never made pension applications do not appear in the pension file data. However, the UA data contains links to the 1860 federal census.41 Using these links, I infer the soldier’s marital status from the composition of the household in which he resides.42 I compare soldiers who were married in 1860 and whose wives appear in the pension data with those whose wives do not appear. I restrict the sample to men who died during the war, for reasons explained above. Table 5 contains these results. Column (1) contains the mean of each variable among wives who appear in the pension data, and column (2) contains the mean among wives who do not. Column (3) presents the difference in means between these two groups. Column (4) contains an OLS regression of an indicator for appearing in the pension data on all of the variables in the table. These results provide strong evidence for selection on the basis of marriage prospects or affluence. Women who file pension claims tend to be older and to come from less wealthy households. Their husbands are more likely to be illiterate. These husbands are more likely to hold skilled blue collar occupations, such as craftsmen and skilled factory operatives, and are are less likely to be skilled professionals or 40 In calculations using soldiers dead by 1880 as the reference group, I assume that all soldiers with missing death dates died before 1880, which is quite conservative. In the most conservative calculation, I assume that all soldiers with missing marital status were married; in another, I use an imputed marriage rate for these soldiers. This imputation is based on a regression of marital status on age, state, and occupational class dummies using the 1860 one percent IPUMS sample. The imputed marriage rate is the predicted fraction of UA soldiers who would have been married in 1880 (the most conservative death date assumption for individuals with unknown death dates), using the coefficients from the above regression. 41 These data strongly favor men whose wives appear in the pension data, as this information was used to make the links. However, this is the only information I can provide here. 42 I call household occupants “potential wives” if they are female, less than 15 years older or 30 years younger, and have the same last name as the soldier. This is somewhat more conservative than the IPUMS procedure for imputing spousal relationships; this procedure uses 10 and 25 year cutoffs, respectively (Ruggles et al 2010). If the soldier is a household head and the second household member is a potential wife, I assume he is married. If he is not a household head, I infer marital status from the relative position of potential wives and potential children in the household using standard rules for imputing family interrelationships (see Ruggles et al 2010). 20 proprietors. Notice that the regression coefficient on the wife’s age is negative, while the coefficient on the soldier’s age is positive and larger in magnitude. This reflects the high correlation between the ages of husbands and wives, and can be interpreted to mean that women who were married to older men were more likely to apply for a pension.43 These apparent differences between pension applicants and non-applicants have no bearing on the internal validity of this study. However, they are important to keep in mind when extrapolating the results to the general population. I will discuss this further after presenting my empirical findings. 6 Pensions and the Timing of Remarriage 6.1 Empirical Framework In this section, I describe my approach to evaluating the extent to which pension income slowed the rate of remarriage among Civil War widows. This is a challenge because pension amounts are standardized, so there is no variation in pension income among pensioners. Moreover, it is not straightforward to compare women who had pensions to those who did not, as I do not observe women who never make pension applications. The are two possible sources of variation in pension income: the pension board’s decision and the timing of this decision. The pension board’s decision is not an ideal source of variation for a few reasons. First, this variable is only defined for women who complete their claims. Recall from figure 1 that at least twelve percent of my sample remarried while their claims were pending. A simple comparison between women with accepted and rejected claims will discard this potentially valuable information. Another issue is that rejections take significantly longer to process than acceptances. It takes approximately five years longer to reach the “rejected” node in figure 1 than the “accepted” node. Thus, my sample of rejected widows ought to look very different from the universe of potentially rejected widows, as many of these are likely to have remarried before the board’s decision was rendered. A final technical issue has to do with accuracy: it is often unclear when or why a claim was rejected. Because of these issues, I use variation in the timing of the pension board’s decision, rather than the outcome, to estimate the effect of pensions on the timing of remarriage. Specifically, I look for a treatment effect of having a pension claim granted, or of transitioning from having a pending claim to an accepted claim. Recall from section 4 that women with pending claims should behave differently from women who have their pensions in hand, due to discounting and the possibility of rejection. I estimate a proportional hazard model of both pensions and marriage, allowing the rate of remarriage to shift at the moment a pension is granted. Variation in processing times allows me to observe women with and without pensions at every point in time, which allows me to estimate a hazard rate of remarriage that differs by pension status. 43 If husband’s age is omitted from the regression, the coefficient on wife’s age becomes positive and highly significant. 21 Some of this variation is plausibly exogenous. For example, idiosyncrasies in the postal service, clerical errors, or unexpectedly capricious behavior on the part of pension attorneys certainly affected processing times in a random fashion. However, a portion of the variation in processing times is likely endogenous to marital outcomes. For example, women with poor marriage prospects may have been more invested in getting a pension because they knew their alternatives were poor. So, those who got pensions quickly may have tended to remarry slowly because of poor marriage prospects, not because of a causal effect of the pension. Another concern is that processing times are highly correlated with the quality of a pension claim: rejections take significantly longer to process than acceptances. Why is this a threat to identification? If we accept that pension eligibility is random, then the ambiguity of a claim should be similarly exogenous. However, bias may be introduced by the decision to apply. Applying for a pension is costly: a widow will choose to incur this cost if the benefit is great enough. The expected benefit from applying is lower for a widow with an ambiguous claim, as the probability of ever receiving a pension is low. Thus, women who apply with ambiguous claims may be systematically different from women who apply with straightforward claims. In particular, they may have worse alternatives, either financially or in the marriage market. The direction of this bias on the timing of remarriage is unclear: women with poor alternatives might receive fewer proposals per unit of search effort; however, they might also be less selective. To overcome these endogeneity problems, I use a method developed by Abbring and Van den Berg (2003a). This is a novel approach to identifying treatment effects in the presence of an endogenous treatment when both the treatment and outcome are duration variables. The approach involves jointly estimating the hazard rates of pensions and remarriage, allowing for correlation between the unobserved heterogeneity in these two risks. The hazard rate at time t refers to the probability of realizing an outcome (pension or marriage) at t, conditional on not having realized it earlier. The hazard rate of pension income is given by θp (t|X, vp ) = λp (t) exp(Xβp + vp ) (4) and the hazard rate of marriage is given by ( θm (t|X, vm , tp ) = λm (t) exp(Xβm + vm ) if t ≤ tp λm (t) exp(Xβm + δ + vm ) if t > tp (5) For each i ∈ {p, m}, λi is the baseline hazard function, which characterizes duration dependence, and X is a matrix of explanatory variables that may shift the hazard rate. The term tp represents the time at which a pension is granted, and vi reflects unobserved heterogeneity. Allowing for duration dependence (λi (t)) and the effect of covariates (Xβi ) is crucial to the identification of δ. Duration dependence refers to the way in which the hazard rate changes over 22 time; for instance, whether marriage becomes more or less likely as time passes. Failing to account for duration dependence will bias the estimate of δ. For example, suppose there is negative duration dependence in the rate of remarriage, so the probability of remarrying declines with time in the marriage market. Then, women will appear to remarry at a slower rate upon receiving a pension, simply because these women will have been in the marriage market longer. Thus, we will overestimate δ. Failure to account for observables will bias the estimate of δ to the extent that these are correlated with pension status. For example, suppose the hazard rate of pension receipt increases with age, and the hazard rate of marriage declines with age. If we do not control for age when estimating δ, the estimate will be biased away from zero, as women who receive pensions quickly will tend to be older, and these women will tend to remarry slowly. Every concern I have just described applies to a standard proportional hazards model. An additional issue that arises in this particular setting is the possibility that vm and vp are correlated. For example, if vm and vp are negatively correlated, the estimate of δ may be negative even if the true δ is zero. Correlated unobserved heterogeneity generates bias in a similar fashion to omitted observable controls. If women who get pensions quickly tend to have large vp , they will also tend to have small vm , which means they are likely to take longer to remarry. Abbring and Van den Berg (2003a; 2003b) show that this model is identified even if vm and vp are correlated. Moreover, it is identified without exclusion restrictions or assumptions about the functional form of either the baseline hazard or the joint distribution of the unobserved heterogeneity terms. The unobserved heterogeneity directly affects the rate of treatment but not the precise timing of treatment. Put another way, a high vp raises the probability of receiving a pension at time t; however, there remains a stochastic element to which event, pension or no pension, actually occurs at time t. The problem is disentangling this random assignment from the non-random assignment. To understand how this is possible, first notice that, in a simple proportional hazards setting, the distribution of unobserved heterogeneity is identified from variation in observables. To see this, consider the rate of pension receipt. Suppose one woman has a very good pension attorney (high Xβp ), and a second woman has a poor pension attorney (low Xβp ). Now, suppose these two women both take a long time to receive a pension (large tp ). We can infer from this that the probability that the first woman has an ambiguous pension claim (low vp ) is higher than it is for the second woman. In general, the distribution of vp , conditional on t, depends on observables, which allows its distribution to be pinned down. How does this help us identify correlated unobserved heterogeneity in the rates of remarriage and pension receipt? Using the same example, suppose that the quality of pension attorney has no direct effect on the rate of remarriage, so women with good and bad pension attorneys have the same Xβm .44 This means that we should not expect to see systematically different marital outcomes 44 This example is used for clarity and does not imply the necessity of an exclusion restriction for identification. In general, as long as βm 6= βp and there is sufficient variation in the data, there exists some X, X 0 such that Xβm = X 0 βm but Xβp 6= X 0 βp . This is all that is required. Also notice that the values of βm , βp are identified using “early” parts 23 by the quality of pension lawyer. However, recall that, conditional on t, the distribution of vp is not independent of the quality of pension lawyer. So, if vm and vp are correlated, the distribution of vm will similarly be dependent on pension lawyer quality. Say vm and vp are negatively correlated, and recall that, fixing t, E(vp ) is higher for women with bad lawyers than it is for women with good lawyers. This means that, among women who are in the sample at time t, those with good lawyers will tend to remarry fastest, because these women tend to have higher vm . Similarly, if vm and vp are positively correlated, women with bad lawyers will tend to remarry more quickly. In other words, different joint distributions of vm and vp will be observationally distinct. Once the correlation between vm and vp has been corrected for, the remaining difference between the marriage rate before and after a pension is granted can be interpreted as a causal effect of the pension. I estimate this model by maximum likelihood. To explain the estimation process, I define a series of functions that are elements of the likelihood function. The survival function, or the probability of remaining a widow (m) or not having a pension (p) at time t, is denoted Si (t), and it has the following form:45 Z − Si (t) = exp ! t i ∈ {m, p} θi (s)ds , t0 If t is a random variables denoting time an event occurs, its density is given by fi (t) = θi (t)Si (t) So, the likelihood of an event occurring at t depends on both the hazard function and the survival function. For pensions, the survival function is straightforward to define:46 Z Sp (t|X, vp ) = exp ! t − λp (t) exp(Xβp + vp ) t0 The survival function for marriage is somewhat more complicated, because it shifts at a point in time. The survival function before and after receiving a pension are given by the following two equations, respectively: Z Sm,1 (t|X, vm ) = exp ! t − λm (t) exp(Xβm + vm ) t0 Z Sm,2 (t|X, vm , tp ) = Sm,1 (tp |X, vm ) × exp t − ! λm (t) exp(Xβm + δ + vm ) tp of the sample, when vm and vp are independent of observables. This dependency arises “later” in sample, due to selective sample attrition. 45 See Lancaster (1990). 46 This construction follows Abbring and van den Berg (2005), who apply this model to evaluating the effect of unemployment insurance sanctions on the rate of transition to employment. 24 To understand the definition of Sm,2 , consider the meaning of its two parts separately. Suppressing X and vm , the first term reflects P r(tm ≥ tp ), and the second term reflects P r(tm ≥ t|tm ≥ tp ). There are four possible outcomes for women in the sample, which I index by k ∈ {1, 2, 3, 4}. A woman can remarry before she gets her pension (k = 1); she can remarry after her claim is granted (k = 2); she can be censored before her claim is granted, meaning that she dies or disappears from the sample (k = 3); or she can be censored after her claim is granted (k = 4). Each of these events is associated with a different likelihood. Conditional on her unobserved heterogeneity terms, the likelihood contribution of woman i can be written as    θm (t|X, vm , tp )Sm,1 (t|X, vm )Sp (t|X, vp )     θ (t|X, v , t )S (t|X, v , t )θ (t |X, v )S (t|X, v ) m m p m,2 m p p p p p p Li (t) =  Sm,1 (t|X, vm )Sp (t|X, vp )      Sm,2 (t|X, vm , tp )θp (tp |X, vp )Sp (tp |X, vp ) if k=1 if k=2 if k=3 if k = 4 To estimate this model, I make certain parametric assumptions about the baseline hazard rate and the joint distribution of the unobserved heterogeneity terms, vm and vp . I attempt to make the least restrictive parametric assumptions possible. For the baseline hazard, I use a piecewise constant function, where time is divided into discrete “bins,” and λ(t) = λt takes on some unrestricted value for each of these bins. I use bins of one year, with a single bin for the tail of the time distribution, extending from t = 8 until the last observation leaves the sample. Following eight years after widowhood, first marriages and pensions occur with insufficient frequency to identify hazard rates at finer intervals. For the unobserved heterogeneity terms, I assume a discrete distribution in which both vm and low , v high } and v ∈ {v low , v high }. Thus, there are vp have two unrestricted mass points:47 vm ∈ {vm m p p p four possible combinations of vm and vp , each of which is associated with a certain probability. The location of each of these mass points and the probability of each combination of the two are estimated in the model. A discrete distribution is considered the most flexible parametric assumption that can be made about the joint distribution of unobserved heterogeneity terms, as it allows any correlation between the two variables to be achieved; other assumptions, like allowing unobserved heterogeneity terms to take on infinite values that follow a set distribution, restrict these correlations.48 A discrete distribution with more than two mass points is not feasible with the sample size I am working with.49 Intuitively, this particular about the distribution for vm and vp means that women may be one of two “pension types” and one of two “marriage types.” Meaning, a woman can be likely or unlikely to get a pension quickly, and she can be likely or unlikely to remarry quickly. The main threat to identification is that “high” pension types may tend to be “low” marriage types, and vice versa. If 47 This follows an application of this model by Abbring and Van den Berg (2005). Heckman and Singer (1984); Abbring and Van den Berg (2005); Van den Berg (1996). 49 Notice that the number of parameters increases exponentially with each additional mass point in the distribution of vm and vp , as any combination of these two variables must be allowed to occur. 48 25 this is the case, then even if pensions have no true effect on marriage rates, I might estimate such an effect simply because women who remarry quickly also take longer to get their pensions. Estimating a model that accounts for unobserved heterogeneity is complicated because the heterogeneity is unobserved, which means that I cannot calculate the correct likelihood contribution of each observation. To estimate the model, I use the EM algorithm.50 This proce- dure does the following. I start with a vector of parameters, φ0 , which includes δ, αm , αp , βm , βp , low , v high , v low , v high ), and probability weights, π = (π , π , π , π ), associated with each of v = (vm m p 1 2 3 4 p the four unobserved heterogeneity “groups” my observations may fall into. Using these values, I construct a set of weights for each observation: 0 δi,j πi0 L0ij = P4 0 0 k=1 πk Lkj The letter j indexes the individual, and i indexes the unobserved heterogeneity group. Given the data and parameter choices, this reflects the probability that individual j falls into group i. I fix these weights, and then construct an expected log likelihood function, which I maximize over φ to obtain φ1 . Based on φ1 , I construct a new set of weights, δ 1 , and repeat the process to convergence. 6.2 Results Before presenting estimates of the model described above, it is useful to get a sense of what the hazard rates of remarriage and pension receipt look like. Figure 2 plots the empirical hazard rate of both pensions and remarriage, estimated non-parametrically using a kernel method.51 The top panel illustrates the rate of remarriage measured before and after a pension is granted; the bottom panel illustrates the hazard rate of pension decisions. Time is measured in years since widowhood; however, individuals do not enter the sample until they apply for a pension. Notice that, for the first five years, the rate of remarriage for women who have not yet received a pension lies uniformly above that of women who have pensions. After five years, the two lines are very close together. This may indicate that the pension only lowers the rate of remarriage in the short run; however, it may also reflect differences in the characteristics of pensioned and unpensioned women in later years. Women who are still in the sample without pensions, say, ten years after widowhood are those who are still trying, unsuccessfully, to get a pension after ten years. These women may have very different characteristics, either observable or unobservable, than women who are in the sample without pensions only a year or two after widowhood. It is also worth mentioning that the sample of women without pensions becomes very small as time passes. For instance, there are only 27 such 50 This is frequently used procedure, which was developed to deal with missing data. See Heckman and Singer (1984) and Lancaster (1990). 51 This is done using the STS package in STATA. For ease of comparison, I truncate this graph at t = 10. This is because it becomes impossible to estimate the rate of remarriage for women without pensions for later periods, as there are insufficient observations. 26 women in the sample more than five years after widowhood. Table 6 contains parameter estimates for the model described above, with the estimated effect of covariates on the rate of pension receipt listed next to their estimated effect on the rate of remarriage. In column (1), I estimate the model with no covariates or correction for correlated unobserved heterogeneity. In this specification, the estimated effect of the pension is negative, but it is not significantly different from zero. In column (2), I add covariates to the hazard rate of both risks, which significantly increases the magnitude of the estimate, to -0.49 (0.19). This suggests that selection on observables biases this effect toward zero. Recall that this bias could go either way. Women who experience long processing times are likely to have ambiguous claims, and women who apply with ambiguous claims may be different from those who apply with straightforward claims. If these women are less wealthy, for example, it may be more difficult for them to receive marriage propsals; however, they may also be less selective. These results suggest that observable characteristics of women with ambiguous claims tend to slow the rate of remarriage, leading to an underestimate of the effect of the pension when these controls are omitted. In column (3), I introduce the possibility of correlated unobserved heterogeneity in the rates of pension receipt and remarriage. At -0.54 (0.22), the estimated effect of the pension changes little from the previous specification, suggesting that much of the selection problem is captured by the controls for covariates. The estimate from the full model can be interpreted to mean that receiving a pension lowered the hazard rate of remarriage by approximately 40%.52 This estimate implies that, for a woman with median characteristics, immediately granting her a pension would raise her median time to remarriage from 4.7 to 7.8 years, an increase of more than three years.53 This timing increase is consistent with the summary statistics from table 2, although the implied medians are substantially higher than they are in this table, as they should be. These summary statistics are calculated using women who actually remarry. The medians implied by the model estimates incorporate information from women who never remarry, which will tend to raise them substantially. Other variables affect the rate of remarriage in plausible ways. Older women tend to remarry more slowly, as do women with more children. The year of widowhood has a negative effect on the rate of remarriage, which may reflect sample selection, as claims become more ambiguous the farther removed is the soldier’s death from the war. Characteristics of the widow’s first husband have some effect on marriage rates: women who are married to older and shorter men tend to remarry more quickly. This latter finding could reflect women’s reservation match qualities, especially if height is positively correlated with socioeconomic status. The county male to female ratio speeds 52 53 P EN N OP EN This comes from the fact that θP EN /θN OP EN = exp(−0.54) = 0.58, so θ θN−θ OP EN For women with pensions, this calculation is done by solving the following for tmed : = −0.42. 0.5 = P r(t ≥ tmed ) = S2 (tmed |X, vm ) For women without pensions, I do the same calculation, replacing S2 with S1 . For X, I use median characteristics and mean regions; I integrate over vm and vp using estimates from the model. 27 up remarriage quite significantly, which is to be expected. The only variable that significantly affects the hazard rate of pension income is year of widowhood, which presumably reflects the fact that claims become more ambiguous with distance from the war. There are also regional differences: claims from the New England seem to be processed significantly faster than claims from the MidAtlantic, the Midwest or the South. The parameters of λm (t) and λp (t) are also listed in table 6, with λm and λp on the interval [0,1) both normalized to 1. These estimates suggest non-monotonic duration dependence in both risks. In both cases, the hazard rate initially increases and then falls. One can imagine plausible explanations for this pattern in the hazard rate of marriage. The rate of remarriage may rise in the short run if women lower their reservation match qualities as time passes, either due to revised expectations or changing preferences for matching. However, this rate is likely to fall eventually if part of what makes women desirable in the marriage market is fertility. In the case of pensions, this pattern may reflect changes in the composition of claims as time passes. Among very straightforward claims, the probability of receiving a pension is likely to increase with processing time. However, at some point, all straightforward claims will have been processed, leaving only ambiguous ones. The probability of ever getting a pension with an ambiguous claim is low. The unobserved heterogeneity terms are quite imprecisely estimated. Notice that the two estimated values of vp are very close to one another, and the probability weights attached to each unobserved heterogeneity group have very large standard errors. This may indicate that unobserved heterogeneity in the rate of pension receipt is well controlled for by covariates and the duration dependence function, leaving few systematic unobserved differences. 7 Sensitivity Analysis 7.1 Instrumental Variables Analysis The hazard model described in section 6 is the most exact representation of the relationship between the receipt of pensions and the rate of remarriage. However, a concern is that the estimates may be sensitive to some of the parametric assumptions made in estimation. So, as a complement to the analysis in section 6, I include a linear analysis of the relationship between pensions and the timing of remarriage. Using a series of time frames ranging from one to five years (τ ∈ {1, 2, 3, 4, 5}), I create an indicator variable equal to one if a widow had received a pension within the time frame (I(tp ≤ τ )) and an indicator equal to one if she had remarried within the time frame (I(tm ≤ τ )). I estimate the following by OLS: I(tm ≤ τ ) = α + βI(tp ≤ τ ) + Xγ + u The matrix X includes all controls used in section 6. I expect to find β < 0. Here, the endogeneity 28 problem is quite severe: many women who were not receiving pensions within, say, three years of applying had been denied pensions because they had remarried. I use instrumental variables to circumvent this problem. Details of the application and review process provide potentially valid instruments for pension income.54 The instrument that I use is based on the spelling of last names. As described earlier, to receive a pension a widow had to prove that she was married to a soldier, that he served honorably in the military, and that his death was connected to the service. This involved locating military service records, hospital records, and marriage certificates. If there were discrepancies in the spelling of his name in these records, additional steps were required to demonstrate that the records referred to the same individual. In the pension files, there are examples of secondary affidavits explaining name spelling discrepancies. I construct an indicator of name spelling homogeneity from the one percent IPUMS samples from 1860, 1870, and 1880. I compile a list of all household heads in each of these years, and I group last names by codes generated using the NYIIS algorithm (Atack and Batemen 1992). Frequently used to create linked census samples,55 this algorithm collects names into phonetically similar groups. I construct a Herfindahl index of the dispersion of unique name spellings within these phonetic groups. Greater values indicate that there is little variation in name spelling; smaller values indicate that names in this group are spelled in many different ways. I perform two tests of the validity of this measure. First, I check whether or not a low name homogeneity index predicts multiple spellings of the veteran’s last name in the pension data. I find that a one standard deviation increase in this index raises the probability of observing multiple surname spellings in the pension data by 8.5 percentage points; this is highly significant. Second, I check whether or not a name with a high homogeneity index is more likely to exactly match the most common spelling in its phonetic group in the census. Again, I find that a one standard deviation increase in the index raises the probability of such a match by 25 percentage points, which is also highly significant. A concern is that this measure may not be exogenous to marital outcomes. Names that belong 54 This approach is similar in spirit to Maestas, Mullen and Strand (2011) who use spending allowances of the examiners assigned to individual cases as an instrument for disability insurance to identify a causal effect of disability insurance on labor supply. An alternative possibility follows Eli (2010), who uses political variables as instruments for pension income. This approach uses the observation that Union Army pensions were used to secure votes for the Republican party (Eli 2010; and Skocpol 1993), so pension amounts would be inflated in contested congressional districts. It is conceivable that pensions also would have been processed more quickly in politically expedient areas, so political variables may be valid instruments in this case. I do not make use of these variables for several reasons. For one thing, women could not vote, so expediting widows’ pensions would have been less politically beneficial for the Republican party. Still, one could make the argument that generosity with widows’ pensions may have generated good will among male veterans. However, the period during which pensions were widely used as political patronage occurred later, largely in the 1870s and 1880s. The majority of my sample was widowed during the war and applied for a pension before 1870. Thus, political variables ought to explain little of the variation in their pension outcomes. I have experimented with using county-level election variables as instruments in this context, and they are unable to explain a satisfactory amount of variation in pension outcomes. Granted, county-level variables are an approximation: the appropriate unit of analysis is the congressional district. Still, my sample is predominantly rural, so the approximation should be a good one. 55 Ferrie 1996; Abramitzky, Boustan and Eriksson 2010. 29 largely to immigrants may be spelled in multiple ways; immigrant status is likely endogenous to marital outcomes. Names that belong to lower socioeconomic status families may be frequently misspelled if the literacy rate is low among these families. Because there is no information on nativity or literacy in the pension data, I cannot control for these variables without restricting my sample to individuals linked to the census. However, I can control for average literacy, immigrant status and socioeconomic status, measured as the occupational income of the household head,56 by phonetic name group in the IPUMS data. I include these controls to preserve the validity of the instrument. Table 7 contains first stage results. For all possible values of τ , name homogeneity strongly predicts receiving a pension, even conditional on the immigration, occupational income, and literacy controls added from the census. The first stage F statistics are not quite as high as one would like, ranging from 3.18 to 7.16; however, they are substantially higher than the F statistics for any other potential instrument. The relationship between pension status and other explanatory variables is broadly consistent with results on the rate of pension receipt from section 6. Table 8 contains both OLS and 2SLS results. The OLS estimate is negative for all values of τ , but only significant at the five percent level when τ ≥ 3. The 2SLS estimates are also everywhere negative, but they are close to one in magnitude, and the standard errors are quite large. The estimates are only significantly different from zero when τ ≥ 4. Because the first stage F statistics point to the possibility that the instrument is weak, I also present 95 percent Anderson-Rubin confidence intervals for the effect of the pension, which are robust to weak instruments.57 In most cases, these confidence regions do not include zero. Given their imprecision, it is difficult to attach significance to the size of the 2SLS estimates. However, this analysis provides some corroborating evidence that the causal effect of pensions on the timing of remarriage is negative. 7.2 Alternative Sample Restrictions An additional concern is that the results may be sensitive to the source of information on remarriage. Recall that knowledge of a widow’s remarriage is contingent on her communicating in some way with the pension board. Specifically, I observe a widow’s remarriage if her children file a minors’ claim, or if she files a new claim under the act of March 3, 1901. If the source of information is distributed differently among women who remarry before and after obtaining a pension, and if the source of this information is correlated with marital outcomes, this might bias my results. As an example, recall from table 1 that minors’ pension applications are the source of evidence for remarriage in 64 percent of cases that occur before a pension is granted and 84 percent of cases that occur after a pension is granted. This means that my sample of women who remarry before receiving a pension may be disproportionately composed of childless women who lived to 1901. These women may be 56 57 See section 7 for an explanation of this variable. To calculate this confidence region, I use the condivreg command in Stata. 30 younger and healthier by construction, and thus better marriage prospects. I use two alternative sample restrictions to address this concern. First, I restrict the sample to women who have children under the age of 16 when they are widowed, and I stop following these women once their youngest child turns 16. So, the sample is restricted to women whose marital status might be known through a minor’s pension application. Second, I discard any information that comes from a source other than a General Law pension claim, either widow or minor. Thus, any woman whose marital status is known only from a pension application under the law of March 3, 1901 becomes an observation with missing marital status. Panels A and B of figure 3 plot the empirical hazard rate of remarriage by pension status, in similar fashion to figure 2, under these two sample restrictions. While the overall picture looks similar, as time passes the rate of remarriage for women without pensions starts to lie solidly below that of women with pensions. This could reflect the fact that the sample size is substantially reduced by these restrictions. It may also indicate that the effect of the pension on women’s behavior is simply smaller for those with small children, so differences by pension status shrink when the sample is restricted to these women. However, we cannot rule out the possibility that differences in the source of information on remarriage are biasing the estimated effect of the pension away from zero. The model described in section 6 is estimated under these sample restrictions, and the results appear in table 9. The baseline results, with and without a correction for correlated unobserved heterogeneity, are repeated in panel A. Panels B and C contain results from the sample restrictions outlined above. As seen in panel C, the results are not sensitive to the omission of information from pension applications under the act of March 3, 1901. When the sample period is restricted to years in which the widow has a minor child, the estimate remains negative; however, it decreases in magnitude relative to the baseline, and the standard errors increase. In panel B, we can only say with about 80 percent certainty that the coefficient is different from zero. Still, these results broadly support the finding of a negative effect of the pension, even if the estimate becomes noisier under one of the sample restrictions. Panel C of figure 3 and panel D of of table 9 impose a different sample restriction. These use only women who are successfully linked to the census of 1870 and/or 1880. These data provide independent verification of the information on marital status in the pension files. Women have an incentive to lie to the pension board about marital status; however, there should be no such incentive to lie to census enumerators. By including only women whose marital status can be verified in the census, I mitigate accuracy issues that stem from pension fraud. Another benefit of the linked data is that it allows me to observe potentially important demographic variables such as birthplace and literacy. As seen in figure 3 and in table 12, the results are not sensitive to restricting the sample to women linked to the census, or to including controls for immigration and literacy. Panel D of figure 3 and panel G of table 9 restrict the sample to women widowed during the war years. Dying during the war is arguably more random than failing to recover from a non-life-threatening injury or 31 disease contracted during the war, so it is worth verifying that the results are robust to this sample restriction. The restriction has little effect on the estimate. Finally, I estimate OLS and 2SLS models that are similar to those in the previous subsection, restricting the sample to women who are linked to the census of 1870 or 1880 through children from their first marriages. As explained earlier, it is desirable to use an alternative way of identifying remarried widows, as the source of marriage information in the pension data may generate artificial differences between widows who remarry and those who do not. Table 10 contains results from regressions of an indicator for being remarried in the census on an indicator for having received a pension within five years of applying.58 These are similar to the regressions presented in table 8. In column 1, I use links to the 1870 census; in column 2, I use links to the 1880 census; and in column 3, I pool both years and cluster standard errors by widow. Columns 4, 5, and 6 repeat these specifications using two stage least squares, where the instrument is the name homogeneity index used earlier. This instrument explains a reasonable amount of variation in pension status for the sample linked to the 1880 census, but it performs very badly for the sample linked to the 1870 census. This suggests that much of the variation being explained by the instrument is coming from women widowed in the later part of my sample.59 Still, while the number of women linked in this fashion is small, and the estimates are often noisy, these results broadly support the basic findings. The coefficient on pension income is always negative, and the 2SLS estimate is significant at the ten percent level when the 1880 census is used. 8 Pensions and Match Quality 8.1 Empirical Framework If pension income raises the minimum match quality women are willing to accept, it should increase the average quality of the matches they make, conditional on being matched at all. I use links to the federal censuses of 1870 and 1880 to evaluate this empirically. In principle, I would like to measure match-specific quality; however, this is not observable. Instead, I attempt to measure the “quality” of the second husband, controlling for the “quality” of the widow. I use four plausible measures of quality available in the linked census data. The first is the occupational income of the second husband, measured using the 1900 occupational wage distribution, with an imputed wage for farmers, assigned to 1950 occupational codes.60 Another measure is literacy of the second husband. I also use the squared difference between the age of the husband and wife, the idea being that people 58 I also try this with different time frames, and the results are similar. The backlog of claims at the pension office grew over time, so it is possible that variation in processing time stemming from name spelling ambiguity was amplified in later years. See Oliver (1917). In fact, when I re-do the analysis in table 8 using only war dead, the first stage F statistic declines substantially. 60 Occupational wages are taken from Preston and Haines (1991) and the farmer’s wage is imputed from the 1900 census of agriculture using a procedure from Abramitzky Boustan and Eriksson (2010) and Olivetti and Paserman (2012). 59 32 of closer age may be better matched. Finally, I use an indicator equal to one if the second husband is present in the household. Using my sample of remarried widows who have been linked to the census, and I estimate the following by OLS: Qhusb = β0 + β1 P EN + γX + u The variable P EN is an indicator for the marriage having taken place after the widow received a pension, and Qhusb is a measure of match quality. The matrix X contains explanatory variables including the widow’s age, literacy, immigrant status, the woman’s age at widowhood, age at remarriage, characteristics of the woman’s first husband from enlistment records, and county-level and region controls. I also include the number of children from the widow’s first marriage and the potential amount of pension income these children could receive on the date of remarriage; these are both interacted with pension status. I do this to control for the role minors’ pensions may have played in making these women more attractive to potential mates. What remains should capture the effect of the pension on women’s selectivity in choosing a husband.61 I pool all married women linked to 1870 and 1880 in order to maximize the sample size. In some cases, women are linked to both the 1870 and 1880 census, so these individuals appear twice in the sample. With this in mind, I cluster standard errors by widow. 8.2 Results Table 11 contains results from the regression model describe above. These results offer little evidence that marriages that occur after a pension is granted look different from marriages that occur before a pension is granted. With the exception of husband’s literacy, the relationship between pension status and each measure of match quality has the anticipated sign; however, these estimates are very noisy. Because the OLS estimates do not suggest a relationship between pensions and match quality, I do not present additional results that correct for potential endogeneity of pensions to marital outcomes, as I do in the previous section.62 Is this conclusive evidence that pensions had no effect on match quality? Not necessarily. One possibility is that the measures of match quality I am using are very rough approximations, and a much larger sample size would be required to say anything conclusive about the effect of pensions on these measures. It is also possible that the achievable range of variation in match quality was quite small. If marriage markets are segmented by socioeconomic class, it may be difficult for a low 61 Notice that I do not do this in the previous section. This is because I expect the effect of minors’ pensions on the timing of remarriage to go in the opposite direction. If minors’ pensions make women more desirable in the marriage market, they should receive more proposals per unit of search effort, tending to increase the rate of remarriage. Experimenting with interacting the effect of the pension with the number of children or potential minor’s pension suggests that including these does not change the results. For ease of exposition, I do not include these in table 6. 62 Attempting to use an instrumental variables approach, with the instrument described in the next section, yielded similarly noisy results. These are omitted here for the sake of brevity. 33 socioeconomic status woman to marry a high socioeconomic status man, no matter how selective she is. Moreover, my sample is largely rural, which means that marriage markets are quite small. This would also tend to decrease the range of variation in match quality that is possible for individuals. These measures also fail to capture other aspects of match quality that we expect to be important. For example, it matters how much a woman and her potential husband like each other, or how this potential husband relates to her children. In a small number of cases, the case files include descriptions of physical and emotional abuse of the part of second husbands, which is likely underreported. Differences in match quality along dimensions such as these will fail to be included in this analysis. On the other hand, these results may be informative about the precise mechanism behind the results from section 6. I have described two channels through which an increase in the value of being unmarried may affect the rate of remarriage: it is expected to increase a woman’s reservation match quality and to lower her optimal level of search effort. These results might indicate that the latter channel is more important. In fact, this is consistent with recent empirical investigations into the effect of unemployment insurance on post-employment outcomes.63 In any case, the evidence presented in this section is inconclusive, and further investigation is required here. 9 Implications and Discussion This paper’s most robust and important finding is that receiving a pension had a causal effect on the timing of remarriage for Union Army widows who filed for a pension. Having a claim granted lowered the rate of remarriage by 40 percent. This implies that a typical widow who immediately received a pension would tend to remarry three years later than an identical widow with no pension. This is a striking result, for which I provide context and interpretation in this section. The main issue is generalizability. Namely, is it reasonable to infer that allocating this modest amount of income to all single women in the late 19th century U.S. would have raised the median age at first marriage by three years? Perhaps not. Interpreting the results in the context of the model, it seems that pensions did cause women to raise reservations match qualities or lower search effort. However, the size of this shift may very well depend on other parameters of the model: the distribution of match qualities, a woman’s flow utility while single, her discount rate, etc. This effect is estimated using a sample of women who apply for pensions, and I have shown evidence that these women are different from those who do not make pension applications. I also find a significant interaction effect with age at widowhood (not shown): with each additional year of age, the effect of the pension increases in magnitude by 0.07 (0.02). My sample of pension applicants seems to be older on average than non-applicants, and they are certainly older that the average unmarried woman by virtue of the fact that they have been married before. It is possible that the response 63 See Card, Chetty and Weber (2007) and van Ours and Vodopivec (2008). 34 among women in the general population would be more muted. On the other hand, my estimates are generated by a comparison between women who have been granted a pension and women who are still waiting for a pension. The rationale behind this approach is that there is uncertainty about if and when the pension claim will be granted, so discounting and the possibility of rejection should generate differences in behavior. However, if the data allowed a comparison between women with a pension and women with no possibility of a pension, the differences may be starker. Another interesting point to note is that the probability of rejection, at about 14 percent, is quite low. So, the results likely reflect a high discount rate, which suggests liquidity constraints. Again, this may point to different effects in a more representative sample: women in my sample appear to be less wealthy on average, so liquidity constraints may have been more binding. It is probably also important that my sample consists of widows and not never-married women. Preferences for marriage may have been different for these two types of women. Historical literature suggests that widows, if financially viable, may have been less constrained by social norms in their ability to take part in public organizations, such as charities or other benevolent associations.64 If women value this kind of freedom, preferences for marriage may have been lower for widows. However, widows may have been more financially constrained than never-married women, especially if they had small children; this may augment their preferences for marriage. The fact that they had been previously married may also signal greater a preference for marriage. While the composition of my sample makes it difficult to extrapolate the magnitude of this effect to the population of unmarried women, it does offer evidence that women responded to economic alternatives when making decisions about marriage. This is informative about changes in first marriage that occurred over the course of the 19th century, and also across regions. While this pales in comparison to the revolution in female labor market opportunities that occurred more recently, there were increases in women’s work opportunities during this century, largely due to industrialization. There were also regional differences in opportunities for women, which have been shown to be correlated with delayed marriage (Hacker 2008). A major contribution of this paper is to demonstrate that economic opportunities had a causal effect on women’s behavior. This is especially important because of the multitude of potential drivers of the patterns we observe in the 19th century. 10 Conclusion This paper documents the effect of pension income on the marital outcomes of Union Army widows during the late 19th century. While there is little evidence that women receiving pensions married 64 See Reinhart, Tacardon and Hardy (1998) and Boylan (1986) for discussions of the different roles for widows, as opposed to never-married women, in these organizations. 35 systematically “better” husbands, my results suggest that receiving a pension significantly lowered the rate of remarriage. I argue that this effect can be presumed to work through widows’ preferences for mates, suggesting that American women during this period did respond to outside economic opportunities when making decisions about marriage. This gives new insight into the functioning of marriage markets during this period. It also provides an early example of the kind of behavior we observe on a greater scale at the end of the 20th century. The results of this paper demonstrate that women’s economic incentives mattered for marriage market outcomes in the 19th century. As such, my findings suggest that factors affecting the gains from marriage for women are important to understanding differences in behavior over time and in different regions. This paper has focused on the role of economic alternatives in reducing preferences for marriage; however, future work might look into how women responded to events that raised the gains from marriage. Over the course of the 19th century, marriage became a significantly better ‘deal’ for women. Divorce laws were gradually liberalized, allowing women to escape from bad marriages if necessary (Doepke and Tertlit 2008). Laws allowing married women to independently engage in business and to hold property were enacted, with almost all states adopting such laws by 1895 (Doepke and Tertlit 2008; Fernandez 2009). Women’s inheritance laws were also amended to allow widows greater ownership and control of their spouses’ assets (Hirsch 2009). Understanding the way women responded to these and other developments will be key to understanding patterns of marriage in the 19th century. A Proofs Proof of equation (2). Suppose the arrival rate of pension decisions is λ, the arrival rate of marriage proposals if α, and the probability of an acceptance is π. Take ∆ to be an arbitrarily small period of time, and note that, for search effort c(α), the probability of receiving a marriage proposal during this interval is α∆; similarly, the probability of receiving a decision from the pension bureau is λ∆. Call V S the expected value of being single, which will be a weighted average of the value of being single in each 36 potential state of “singlehood”. Then, it must be that  1 − ∆α ∆α  E[max(V M , V S )] + E[V S ] 1 + ∆r 1 + ∆r !   ∆α M P M N M ∆λ πE[max(V , V )] + (1 − π)E[max(V , V )] + (1 − ∆λ)E[max(V , Ṽ )] + = ∆(s − c(α)) + 1 + ∆r !   1 − ∆α + ∆λ πV P + (1 − π)V N + (1 − ∆λ)Ṽ 1 + ∆r Ṽ = ∆(s − c(α)) +   ∆α ∆λ πE[max(V M − V P , 0)] + (1 − π)E[max(V M − V N , 0)] + 1 + ∆r !  1 ∆λ  M + (1 − ∆λ)E[max(V M − Ṽ , 0)] + πV + (1 − π)V N − Ṽ + Ṽ 1 + ∆r 1 + ∆r = ∆(s − c(α)) + Re-arranging, dividing by ∆, and taking the limit as ∆ → 0, we get (2). ∗ > α̃∗ > α∗ . Proposition 1. For π ∈ (0, 1], θN < θ̃ < θP and αN R∞ R∞ P Proof. Throughout, I use the well known result that θi (θ − θi )dF (θ) = θi (1 − F (θ))d(θ) First notice that θ̃ is strictly increasing in π: ∂ θ̃ α̃∗ ∂ θ̃ λ = − (1 − F (θ̃)) + (θP − θN ) ⇒ ∂π r ∂π r ∂ θ̃ λ(θP − θN ) = >0 ∂π r + α̃∗ (1 − F (θ̃)) Now, suppose π = 0. Call θ̃0 the reservation match quality for those with pending claims when π = 0. Then, θ̃ ≥ θ̃0 . So, if θ̃0 ≥ θN , then θ̃ > θN for π > 0. If π = 0, then the reservation match quality for women with pending claims becomes Z α̃∗ λ θ̃ = s − c(α̃∗ ) + (1 − F (θ))d(θ) + (θN − θ̃) r θ̃ r The left hand side of this equation is strictly increasing in θ̃ and the right hand side is strictly ∗ solve both this decreasing in θ̃, so it has a unique solution. I will show that θ̃ = θN and α˜∗ = αN equation and the first order condition: ∗ Z αN λ ∗ θN = θ̃ = s − c(αN ) + (1 − F (θ))d(θ) + (θN − θN ) r θN r Z ∗ α ∗ (1 − F (θ))d(θ) = s − c(αN )+ N r θN = θN R∞ The first order condition defining α̃∗ is rc0 (α̃∗ ) = θ̃ (1 − F (θ))d(θ), which is set up the same way ∗ . Thus, θ̃ = θ ∗ ∗ as the condition defining αN N and α˜ = αN satisfy this condition as well. So, when π = 0, θ̃ = θN . Therefore, for π > 0, θ̃ > θN . 37 Now, define θ̃1 = θ̃ when π = 1. If θP > θ̃1 , then θP > θ̃ for every π ≤ 1. When π = 1: Z λ α̃∗ ∗ (1 − F (θ))d(θ) + (θP − θ̃) θ̃ = s − c(α̃ ) + r θ̃ r Suppose θ̃ ≥ θP . Because the optimal α∗ is decreasing in reservation θi (see below), it follows that αP∗ ≥ α̃∗ . Two inequalities follow from this: First, Z Z 1 1 (1 − F (θ))d(θ) ≤ (1 − F (θ))d(θ) r θ̃ r θP And, from convexity of c(α), we get the following inequality: −c(α̃∗ ) ≤ −c(αP∗ ) + c0 (αP )(αP∗ − α̃∗ ) This implies the following: Z λ α̃∗ (1 − F (θ))d(θ) + (θP − θ̃) θ̃ = s − c(α̃ ) + r θ̃ r ∗ Z λ α̃ ≤ s − c(α̃∗ ) + (1 − F (θ))d(θ) + (θP − θP ) r θ̃ r Z ∗ α̃ (1 − F (θ))d(θ) ≤ s − c(α̃∗ ) + r θP Z α̃∗ ∗ 0 ∗ ∗ ∗ ≤ s − c(αP ) + c (αP )(αP − α̃ ) + (1 − F (θ))d(θ) r θP Z Z 1 ∞ α̃∗ ∗ ∗ ∗ = s − c(αP ) + (1 − F (θ))dθ(αP − α̃ ) + (1 − F (θ))d(θ) r θP r θP Z α∗ = s − c(αP∗ ) + P (1 − F (θ))d(θ) r θP ∗ = θP − p < θP This is a contradiction. So, it must be that, when π = 1, θP > θ̃, which further implies that θP > θ̃ for all π ≤ 1. Therefore, for all π ∈ (0, 1], θN < θ̃ < θP . ∗ follows from the fact that α∗ is decreasing in reservation match The result that αP∗ < α̃∗ < αN quality. Recall that, for reservation match quality θi , α∗ is defined by the following condition: Z ∞ rc0 (α∗ ) = (1 − F (θ))d(θ) θi Then, ∂α∗ /∂θi is given by: ∂α∗ −(1 − F (θi )) = <0 ∂θi rc00 (α∗ ) This follows from the convexity of search costs. 38 B Data B.1 Data Collection In this section, I describe the process by which I collected the data for this project. The most important effort is the collection of pension records from the National Archives in Washington, DC. Using the indices to the Civil War pension files available on ancestry.com and fold3.com, I compile a list of all pension applications made and certificates issued on behalf of soldiers married to the women in my sample. Then, I request these files from the National Archives. In approximately 90 percent of cases, these files are successfully located, and I am able to collect digital images of them. Files that could not be located had either been taken out by another use (37% of cases), or the file number was incorrectly recorded, and the record puller was unable to find it (63% of cases). Where possible, I make use of digital images of widows’ pensions from the website fold3.com. This website is in the process of uploading images of accepted widows’ pensions, which they are doing chronologically. It is not possible to make exclusive use of this resource for several reasons. First, this project is expected to take several years to complete. Second, they do not include rejected pension applications. Third, they do not include minors’ pensions. If a widow remarried and her children applied for the pension, her file would be consolidated with theirs, and the entire file would be classified as a minor’s pension. So, it would be excluded from the fold3.com project. In total, 30 percent of my sample can be collected from this resource. Because of the importance of these variables to the paper, I describe the source of information on pension outcomes and marriages in the body of the text. However, there are other important variables collected from the pension files. Other available information includes the widow’s age and place of residence, as she had to furnish this information in her pension application. If a remarried widow applied to be restored to the pension rolls under the act of March 3, 1901, her file will contain further information about her second husband. For example, she had to provide proof of her husbands death, which usually meant furnishing a death certificate. In some cases, these death certificates contain the age, birthplace, and occupation of the husband. The second source of information consists of links to the census of 1870 and 1880. I perform these links manually using the genealogy website ancestry.com. When marital status is certain, I search for the widow using the appropriate surname. If I am unable to find her, I search for the children from her first marriage. If her marital status is uncertain, I search only for her children. Whenever there is insufficient information to distinguish between two candidate links, I discard the observation. However, because of the detailed information available in the widow’s pension application, including place of residence, this is a rare occurrence. I am able to make very high quality links in most cases. A concern is that being linked to the federal census may not be random. Table B1 contains OLS regressions of an indicator for a widow being linked to the census on explanatory variables 39 from the pension data. For each census year, the sample is comprised of women who are widowed by that year and who are not known to have died. The only significant determinant of linkage to the 1870 census is the number of children from the widow’s first marriage; this is unsurprising, as information about family members is used to create these links. Age and time since widowhood have no significant effect on linkage to the 1870 census. Neither do pension status, measured by an indicator equal to one if the widow had received a pension within five years of applying, or the region in which the widow’s first husband enlisted. The omitted category is the northeast. The number of children from the widow’s first marriage also significantly increases the probability of her being linked to the 1880 census. Women whose husbands died more recently are also more likely to be linked, as are women whose husbands enlisted in the midwest or the south (relative to those who enlisted in the northeast). The former result can likely be explained by the fact that information about women whose husbands died closer to 1880 is more current; women widowed earlier are more likely to have died, which might not have been recorded in the pension data: death records for pensioners were not consistently kept before the 1880s. Linking women from the midwest and the south may be more successful because I am using information about place of residence from the pension file data. Women residing in smaller towns or counties are less likely to have multiple positive matches, so these women may be less likely to go unlinked. This may be more of a problem in 1880 than 1870 because fewer women are residing with linkable children in 1880, so residential information is more important in this census year. Tables B2 and B3 present further descriptive information about the linked data. In table B2, widows linked to the census are compared with nationally representative samples of women from IPUMS by marital status. Mean characteristics from the IPUMS data are presented unadjusted and re-weighted to obey the same distribution of five-year birth cohorts as the analogous sample from the linked widows data. Table B3 conveys information about the household composition in the linked widows data by year and marital status. 40