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SUICIDE AND THE SOCIAL SECURITY EARLY RETIREMENT AGE.

I. INTRODUCTION

This paper is motivated by the observation that over the years 1990-2014, the age trend in U.S. suicide rates experienced a discontinuous drop at age 62. Figure 1 graphs the U.S. average suicide rate by year of age during this period for ages 39 through 84. (1) Although there is some natural variation around it, the suicide rate shows a distinct age trend with a discrete break at age 62, representing a nearly 8% decline from the age 61 rate. (2)

In light of this discovery, the paper has two goals. First, the empirical work employs a regression discontinuity (RD) design to thoroughly quantify the decrease in suicides at age 62. Econometrically, I find that this reduction is statistically significant, with the aforementioned raw magnitude also being an accurate estimate of the causal effect of turning 62 years old on suicide, or the amount by which the age 62 rate is lower than what would be predicted based on the prevailing trends at surrounding ages. RD results further establish that this drop in suicides is concentrated among men, has increased considerably starting in the mid-2000s, is robust to various ways of specifying the underlying estimation procedure, and is evident neither for other ages in a wide radius around age 62 nor for other variables, namely homicide and population, that should not be affected by Social Security policy. (3)

Second, I rely on the research of others concerning various facets of retirement, Social Security claiming behavior, and suicide to argue that the age 62 suicide decline is much more likely to reflect the impact of the Social Security early retirement age than that of retirement per se. Throughout the period, individuals who worked sufficiently could start receiving Social Security retirement benefits at age 62. (4) While the average retirement age over the period was in fact younger than age 62 (Rutledge, Gillis, and Webb 2015), nearly half of recipients claim Social Security retirement benefits within a few months after turning 62 years old (Henriques 2012). Additionally, men and women have similar age patterns of retirement (Rutledge, Gillis, and Webb 2015), but differ in the Social Security benefit level turning age 62 triggers (Henriques 2012) and potentially the responsiveness of their suicide behavior to income (Daly, Wilson, and Johnson 2013; Denney et al. 2009), while several of the same socioeconomic characteristics predict both early benefit claims (Haaga and Johnson, 2012) and higher rates of suicide (Daly, Wilson, and Johnson 2013; Denney etal. 2009; Ross, Masters, and Hummer 2012). Furthermore, the magnitude of the age 62 suicide decline became more pronounced beginning in the mid-2000s, coinciding with an increase in family incomes of individuals age 62 and slightly older relative to those slightly younger.

The fall in suicides at age 62 seems to have gone undetected by previous research, making this the first investigation of a potentially important unintended consequence of Social Security policy. More generally, this study contributes to, and specifically may clarify, the literature on mental health consequences of Social Security income and retirement. As discussed subsequently in greater detail, several studies have found no or adverse mental health impacts of retirement, each using only within-person variation in retirement status to identify effects. In contrast, a number of other analyses have estimated mental health improvements in response to either larger Social Security benefits, or to retirement when instead identified using exogenous aspects of program benefit structures. Viewed in this light, my results suggest that a unified interpretation of the literature might be simply that retirement income is beneficial to mental health, whereas retirement on its own is not necessarily.

Moreover, suicide is arguably a both more concrete measure and severe form of mental distress, but has not been evaluated as an outcome influenced by retirement or associated benefits. In fact, little economics research has examined suicides among the older middle-aged and younger elderly, specifically those in their mid-50s through late 60s who are most relevant for my analysis, in any context beyond describing temporal changes in age distributions. Case and Deaton (2015) thoroughly documented the suicide age profiles that prevailed during my sample period and their differences by gender, along with a fall in elderly suicide rates starting in the 1990s that is consistent with rates among the previous elderly cohort, those born in the 1910s, being unusually high. Phillips etal. (2010), Sullivan etal. (2013), and Case and Deaton (2015) each observed that suicide rates rose substantially among the middle-aged since the late 1990s. Phillips et al. (2010) noted that the timing coincided with the complete entry of the baby boom cohort into this age group and, as had earlier been reported by Mcintosh (1994), that baby boomers have had historically high suicide rates since their adolescent years. As will become apparent, elements of these changes are relevant for this analysis. (5)

II. DATA

The dataset consists of annual age-specific suicide rates from 1990 through 2014, along with homicide rates that are used to check robustness. All are from the Centers for Disease Control and Prevention's (CDC) Fatal Injury Reports (www.cdc.gov/injury/wisqars/fatal_injury_ reports.html), which provide data on suicides and homicides from the National Center for Health Statistics and population estimates from the Census Bureau. I restrict the sample to ages 39-84. The upper limit is the oldest single year of age for which the CDC reports fatal injuries, and the lower limit is imposed in response to maintain symmetry around the threshold age of 62 at which the suicide rate is observed to drop.

Figure 1 shows how the average suicide rate in the United States changed with age over the sample period. Suicides per 1,000 residents rose from 0.153 at age 39 to 0.168 at age 48, then fell steadily to 0.131 by age 65 before rising to 0.205 at ages 83-84. The RD analysis does not attempt to explain this overall age path. Rather, it estimates the magnitude of the decline in the suicide rate upon turning 62 years old as the difference between the rates implied by extending the age profiles for both younger and older ages to age 62.

III. EMPIRICAL SPECIFICATION

I estimate the size of the drop in the suicide rate at age 62 using a RD framework. The general form of the corresponding regression equation is

[mathematical expression not reproducible]

where a = 39, ..., 84 and t = 1990, ..., 2014 represent sample ages and years, respectively. The suicide rate S is modeled as a function of D, an indicator for ages 62 and above, continuous functions of age profiles among those at least (f) and younger than (g) age 62, and an unobserved error term u. The RD estimator of the discontinuous change in the suicide rate upon turning 62 years old is [beta].

Conceptually, RD takes the limit of the functions f(a) and g(a) as each approaches age 62. Effectively, RD obtains predictions for the age 62 suicide rate as those projected by slightly extending each profile f (a) and g(a) in that direction, and estimates the size of the age 62 discontinuity, [beta], as the difference between these predicted rates. In this sense, as opposed to the observed difference in average suicide rates between ages 61 and 62, p is the difference in expected suicide rates on the 62nd birthday, based on trends prevailing at younger and older ages.

Computationally, I estimate the RD model in Stata using the "rdrobust" command, which implements the methodology developed by Calonico, Cattaneo, and Titiunik (2014). This estimates the discontinuity nonparametrically using local polynomial regression, which generates smoothed suicide rate age profiles. For each age [a.sup.0], a weighted least squares regression of the suicide rate on a polynomial function of (age-a (0)) for ages close to a (0) is estimated. The smoothed profiles are simply the set of estimated intercepts from these regressions. A specified bandwidth determines the age range used in each regression, which is weighted by a kernel function. (6) The baseline specification uses local linear regression, the bandwidth selection algorithm proposed by Imbens and Kalyanaraman (2012), and a triangular kernel, although robustness to each of these three choices is tested. Standard errors (SEs) are constructed from the conventional Huber-Eicker-White estimator (analogous to specifying the "robust" option in Stata), and are thus robust to heteroskedasticity of unknown form.

As mentioned, this study is unique in using information only on age in years, rather than months or days. (7) I operationalize this within the RD framework by specifying a threshold age of exactly 62, and coding ages as (year of age +0.5). This places the discontinuity exactly halfway between the age profiles on either side. Substantively, this reflects the premise that the distribution of exact ages at any given age in years will be roughly uniform, implying that the average exact age will be close to that age in years plus 6 months. (8)

The baseline model uses the log suicide rate, which allows the RD estimate to be interpreted in percentage terms, and the full sample age range. Included among the aforementioned robustness checks, though, is substituting unlogged rates and substantially narrower age ranges, as well as several other specification variants.

IV. RESULTS

This section presents the main RD estimates, both graphically and quantitatively, along with the results of numerous robustness and falsification tests.

A. RD Plots

Figure 2A depicts the discontinuity at age 62 for log suicide rates among all residents, while Figures 2B and 2C do the same for each gender. The scatterplots represent log rates at each year of age, while the overlaid curves are predicted log rates from fourth-order polynomial regressions for the scatterplot profiles on either side of age 62. To focus on the discontinuity, only ages 47-76 are included, although the RD estimates are ultimately invariant to considerably narrowing or widening this age range.

The discontinuity in the age profile represented by the decrease in suicides at age 62 is apparent in Figure 2A, which replicates Figure 1 over the corresponding age range but for the log suicide rate, for both genders combined and in Figure 2C for males. Interpreting the change in log rates as a percentage, the magnitude of the suicide rate reduction in Figure 2A is similar to the 7%-8% decrease in Figure 1, and in Figure 2C appears slightly larger. In contrast, the decline at age 62 represents a minimal, if any, break in the age profile for females in Figure 2B. The age profiles themselves also vary substantially by gender, as the decline in suicide rates at younger ages is steeper for females and continues into their mid-70s, whereas male rates increase sharply after age 65. (9) These differences across genders suggest formally estimating the discontinuity not only for the combined sample but also separately for females and males, which the rest of the analysis does. (10)

B. Baseline RD Estimates

Table 1 displays RD estimates of the decline in suicide rates upon turning 62 years old. The top row, a., contains results for the baseline model, with columns 1 -3 quantifying the graphical evidence observed in Figures 2A-2C, respectively. At age 62, suicide rates are estimated to have fallen by 7.9% overall and 9.1 % among men, both of which are significant at 1 % (as the /-statistics in parentheses reveal), but by a much smaller and insignificant 3.5% among women. The formal RD findings thus match those suggested by the plots: the age 62 suicide rate drop is large and occurs particularly for men.

The bracketed numbers in Table 1 are band-widths, representing the number of age years on each side of 62 that are included in the sample used by the local linear regressions to estimate the discontinuity. Only one optimal bandwidth is calculated for each regression, meaning that the number of ages used is the same on either side of age 62. Given the earlier-outlined coding of ages as (age +0.5), a bandwidth within [b - 0.5, b + 0.5) includes b years on each side of age 62. Consequently, the bandwidths in row a. imply that ages 55-61 and 62-68 were used to estimate the discontinuity for the combined and male samples, while ages 54 and 69 were also incorporated in estimating the discontinuity among females. Bandwidths estimated for each regression are insightful for comparing RD estimates across specifications over the remainder of Table 1.

C. Robustness Checks

Subsequent rows of Table 1 assess the robustness of the baseline RD estimates. In particular, rows b.-m. show that the results are highly insensitive to numerous model specification variants. Both sizes and significance levels of effects remain similar to baseline values. For the combined and male samples, significance is often 1% and always at least 5%. Among females, t-statistics are rarely above 1.0 and always below 1.5.

Row b. shows the age 62 discontinuity in the unlogged suicide rate, as originally observed in Figure 1. When not rounded, the coefficients, as a percentage of the age 61 suicide rates listed in the Table 1 footnote, imply decreases of 7.8% overall, 4.2% for women, and 8.7% for men. These, along with their significance levels and band-widths, are similar to the corresponding values using logged rates in row a.

Row c. corresponds to the simplest-possible ordinary least squares (OLS) RD model: the log suicide rate is regressed on a polynomial in age along with an indicator of age 62 and above, with the coefficient of the latter serving as the RD estimate. (11) The similarity of the results with those of the baseline model suggests that the local linear regression strategy is reliable. Moreover, an expanded version of the OLS polynomial model provides evidence that using age in years does not produce rounding bias, perhaps the most problematic possible consequence of not having more precise age information. As Dong (2015) shows, rounding bias exists only when interactions between age terms and the age 62 indicator are significant when added to the above specification. However, in the three models of row c. (as well as the six OLS polynomial models of Table 2 to follow), these interactions are always individually and jointly very highly insignificant, implying that the treatment effect is "locally constant" at age 62 (Dong 2015, 430) and therefore rounding bias is zero. (12)

Row d. gives estimates using local quadratic rather than linear regression. The additional data required to estimate the quadratic term substantially increases the optimal bandwidths. Estimated discontinuities are smaller, but only slightly, and conclusions are unaltered.

As the choice of bandwidth is particularly influential in the RD framework, rows e. and f. provide estimates obtained using two alternative bandwidth selection algorithms. The procedure proposed by Calonico, Cattaneo, and Titiunik (2014), that is, CCT, in row e. produces bandwidths that are quite similar to the baseline method and thus results that are nearly identical. The procedure proposed by Ludwig and Miller (2007), that is, LM, in row f. generates wider bandwidths and correspondingly larger discontinuities, although the estimate for women remains insignificant.

The baseline kernel function is triangular, which linearly decreases the weight given to each observed age from one at age 62 (or generally the age at which the response function is being smoothed), to zero at the boundary of the bandwidth. As alternatives, the rectangular kernel in row g. equally weights every age within the bandwidth, while the Epanechnikov kernel in row h., for which the weight on each age decreases nonlinearly and initially more slowly from 0.75 to zero moving away from the discontinuity, minimizes the local linear regression mean squared error. While the rectangular kernel is associated with somewhat smaller bandwidths, the choice of kernel appears to have little impact on the estimates.

A drawback to the Huber-Eicker-White standard error estimator is its reliance on an additional bandwidth choice for implementation. The obvious candidate, and the one employed here, is the same bandwidth used to estimate the discontinuity, but the resulting variance estimator does not necessarily have good finite sample properties. As an alternative, Calonico, Cattaneo, and Titiunik (2014) suggest a variance estimator constructed using nearest-neighbor matching to estimate the residuals that is both consistent and unbiased. Row i. displays baseline coefficients along with t-statistics that use nearest-neighbor standard errors with three matches, which are only minimally different from the conventional t-statistics.

Extending the analysis over a 45-year age range establishes the uniqueness of the suicide rate decline at age 62 relative to its profile over a substantial majority of the adult lifespan. Nonetheless, this approach raises the question of whether the decline would represent as much of a discontinuity in the context of more restricted age ranges. Rows j.-m., however, show that utilizing substantially narrower age spans produces little change in the results. The reason is that the value of the optimal bandwidth varies only slightly with changes in the age composition of the sample. Even the broader samples use the same, or only a small additional number of, ages compared with the most constrained sample, which encompasses just ages 55-68.

D. Temporal Variation

The 25-year sample time span is a strength of the research design in terms of generalizability, but leaves open the possibility of heterogeneous age 62 suicide declines within the period. To investigate this, I estimate the discontinuity separately for the five non-overlapping 5-year sub-periods within the broader 1990-2014 period. Beyond mathematical convenience, this timing coincides with that of increases in the age at which full Social Security benefits are available. Statutorily normal retirement age was 65 years old for those born in 1937 or earlier, increased by 2 months each year for those born between 1938 and 1942, and was 66 years old for those born in 1943 or later. (13) For age 62 beneficiaries, normal retirement age was thus 65 through 1999, or the first two 5-year subperiods, rose from 65 and 2 months to 65 and 10 months for the middle 2000-2004 subperiod, and was 66 for the latter two subperiods starting in 2005.

Column 1 of rows n.-r. indicate that within 5-year subperiods, the age 62 suicide rate decrease, while never much smaller than that estimated for the full sample period and always significant at close to 5% or more, in fact increased after the normal retirement age rose to 66, from 7.2% over 1995-2004 to 9.9% in 2005-2009 and 13.4% during 2010-2014. In concordance with the literature on suicides among middle-aged and elderly adults reviewed in the introduction, this trend appears to be attributable particularly to an increase in suicide rates among those younger than 62, as opposed to a decrease among 62-year-olds. For instance, the average suicide rate rose from 0.126 per 1,000 in 2000-2004 to 0.145 in 2005-2009 and 0.170 in 2010-2014for61-year-olds, but from 0.121 only to 0.131 and then 0.147 over the same intervals for 62-year-olds.

The other notable finding revealed by temporal disaggregation is that the above result is driven in large part by an increase in the discontinuity among women. Columns 2 and 3 reveal that in sharp contrast to the first 15 years of the sample and especially 1995-2004, female suicide rates also declined significantly at age 62 over the last sample decade. An increase in the age 62 suicide rate drop also occurred for men, but not until the final 5-year subperiod. Potential explanations for the changes in estimates over the last 10 sample years are discussed in the following section.

E. Regional Variation

While there is no particular underlying theory predicting spatial variation in the age 62 suicide rate decline, I also estimate it separately, for both genders combined, in each of the four Census regions. Rows s.-v. show that compared to baseline, the discontinuity is smaller and less significant in the Northeast and Midwest, but larger and similarly significant in the South and West.

The reasons for these regional differences are not entirely clear. Higher suicide rates, and thus greater variation, might explain why the effect is slightly smaller yet more significant in the Midwest than Northeast. Union membership, educational attainment, and household income are all particularly low in the South, implying lower incomes for a relatively larger less-educated population, and as the next section documents suicide rates are higher among those with less income and education. High school graduation rates are also lower in the West compared with the Northeast and Midwest. In addition, unemployment rates have been higher and more variable in the West, and household income is below that of the Northeast. For both the South and West, these factors suggest higher suicide rates among mid-to-late career workers and thus a larger decrease upon reaching early retirement age, given that Social Security benefits are progressive with respect to, and thus less variable across workers than, pre-retirement earnings.

F Falsification #1: Homicides and Population

As another type of robustness check, I estimate the RD model using outcomes that should not be affected by Social Security policy or otherwise expected to vary non-smoothly by age, specifically homicide death rates and population totals. A significant age 62 discontinuity for these measures would presumably be spurious, and thus suggest that the findings for suicides might be as well. However, Table 2 verifies that unlike for suicide rates, changes in homicide rates and population upon turning 62 years old do not deviate from their trends at surrounding ages. This is true for both genders combined and separately, and in each of the specifications from rows a.-m. of Table 1, which are repeated for homicides (columns 1-3) and population (columns 4-6) using the same row headings in Table 2.

In the combined homicide and each population sample, the change at age 62 is never greater than 2% and the associated t-statistic is never larger than 0.5. For males, homicides fall at age 62, but never by more than 4%, with t-statistics that are always below 1.0. Among females, homicides increase at age 62 by a slightly larger amount, but by more than 5% rarely and 6% only for the narrowest age group, and always with t-statistics below 1.2. In sum, using specifications in which the age 62 effect on suicides is significant at 5% always and at 1% often, the same effect on homicides and population is never significant even at 20%.

G. Falsification #2: Ages other than 62

While Figures 1 and 2A-2C provide convincing evidence that the largest deviation in the suicide rate from its overall age profile occurs at age 62, they also show some, albeit lesser, variation around the trends at other ages. A second falsification exercise, therefore, tests whether suicide rate changes at ages other than 62 deviate significantly from their surrounding age profiles. Specifically, using the baseline model from row a. of Table 1, I use the RD framework to estimate discontinuities at each age from 45 to 79 for the combined (columns 1 -2) and male (columns 3-4) samples in Table 3. (14) Columns 1 and 3 use all ages, whereas columns 2 and 4 impose symmetry around the discontinuity by using the same number of age-years on either side, starting from age 39 below or from age 84 above depending on whether the discontinuity is at an age younger or older than 62, respectively.

As in Table 2, all estimated discontinuities in Table 3 are insignificant, largely because magnitudes are small rather than merely being imprecisely estimated. RD-estimated changes at age 62 are typically smaller than 3%, rarely above 4%, and never above 5%, and associated r-statistics are often below 1.0 and never above 1.5. Overall, then, the age 62 suicide rate decline is not only large and significant, but stands in contrast to the complete absence of analogous discontinuous changes at all other ages within nearly two decades in either direction.

V. DISCUSSION

As mentioned previously, the fact that the sudden drop in suicides occurs at age 62 suggests that Social Security retirement benefits, for which those with at least a minimal amount of work history become eligible upon turning 62 years old, are a potential factor. This section begins by arguing that based on evidence compiled from numerous recent studies, the suicide rate discontinuity is indeed likely attributable to Social Security early retirement eligibility, rather than the act of retiring itself, and in particular to a positive impact of benefit receipt on mental health. Subsequently, I make the case that this explanation is consistent with the observed differences in effects across genders and time.

A. Social Security versus Retirement

Four pieces of evidence point toward the Social Security early retirement age, rather than actual retirement from the labor force, as the factor triggering the reduction in suicides at age 62. First, a large subset of individuals claims Social Security benefits at age 62, many not long after becoming eligible. Second, age 62 is comparatively a much smaller focal point for retirement, the prevalence of which is high at younger ages. Third, rates of both age 62 Social Security benefit claiming and suicide are simultaneously high among several relatively sizable demographic subgroups. Fourth, while evidence on how retirement affects mental health is mixed, every study finding that retirement improves mental health uses financial incentives of Social Security or other pension programs, including eligibility, to identify the retirement effect.

Empirical work on retirement behavior relies predominantly on two datasets, the Health and Retirement Study (HRS) and the Survey of Income and Program Participation (SIPP). Both indicate that across several decades, a substantial proportion of each birth cohort claims Social Security benefits shortly after turning 62 years old. Gustman and Steinmeier (2015, Figure 3) shows that among married male HRS respondents who were ages 51-61 in 1992, nearly 50% claimed Social Security benefits at age 62. A potential mental health boost from Social Security receipt, thus adding intrinsic value to a given benefit payment amount, is consistent with their finding that simulations severely underpredict age 62 claims. This result, attributable largely to pre-age 62 retirees for whom delaying receipt would be actuarially advantageous, "reflect(s) the common feeling of many who have examined this issue: that claiming is higher than would be expected, given the actuarial benefits of delaying claiming" (57).

Observing these same HRS cohorts through 2012, Sanzenbacher, Wu, and Rutledge (2015) constructed two groups of respondents prospectively eligible for an income assistance program, one for Unemployment Insurance and the other for Medicaid and the Supplemental Nutrition Assistance Program. Although access to an alternative income source provides an incentive to delay Social Security benefit claiming, their Figures 1 and 2 demonstrate that nearly 50% of each group still claimed benefits at age 62.

In Haaga and Johnson (2012), which examined the 1920-1944 SIPP birth cohorts, Figures 3 and 4 likewise reveal that among those who were age 62 by 2006, the percentage claiming Social Security benefits at age 62 was always close to or above 50% for both men and women. Moreover, their Figure 6 shows that during 1990-2009, the percentage of respondents claiming Social Security benefits within 3 months of turning 62 was always above 30%, did not fall below 40% before 2004, and was above 50% at its peak in the mid-1990s. Similarly, Figure 4 of Henriques (2012), using SIPP birth cohorts 1922-1940, shows that nearly 45% of married respondents, and 50% of unmarried, claimed Social Security benefits within 2 months after reaching age 62.

Compared with entry into Social Security beneficiary status, entry into retirement at exactly age 62 is far less prevalent. Figures 1 and 2 in Gustman and Steinmeier (2015) indicate that while retirement spikes at age 62, the rate peaks at only around 15% for at least partial retirement, relative to 6%-9% at other ages from 60-65, and 12% for full retirement, compared with 6% at ages 60-61 and 7% at ages 64-65. In addition, retirement rates decline substantially at age 63 while national suicide rates continue falling, and both begin to rise at age 64, a post-age 62 pattern which is also inconsistent with retirement reducing suicide. More generally, Rutledge, Gillis, and Webb (2015) reports that among the 1931-1953 HRS birth cohorts, the timing of retirement was widely dispersed across the age spectrum. In accordance with an average retirement age of 61.8, over half of respondents had retired before reaching their 62nd birthdays; 20% had retired by age 57, while 20% had not retired by age 65.

Furthermore, Tables 1-3 of Haaga and Johnson (2012) provide evidence that the demographic groups that are most likely to claim Social Security benefits at age 62 are precisely those for which suicide rates are highest among young and middle-aged adults. In particular, for the birth cohorts potentially overlapping with my data, the age 62 claim percentage was between 53% and 63% for respondents with no more than a high school education, 46% and 68% for those with income below the top quartile (and at least 53% for pre-1940 birth cohorts), and 60% and 62% for those who reported health status of fair or poor (compared with good or better). Corresponding with these results, research has found that suicide is more likely among adults with no more than a high school education (Denney et al. 2009; Ross, Masters, and Hummer 2012), lower income (Daly, Wilson, and Johnson 2013; Denney et al. 2009), worse self-rated health (Denney et al. 2009), more physical pain (Case and Deaton 2015), and worse physical health (Bell and Blanchflower 2007). Thus, several population components most at risk of suicide are the ones for which age 62 Social Security benefit claiming behavior has the greatest scope for altering outcomes. In contrast, Rutledge, Gillis, and Webb (2015) shows that having a high school or less education, lower earnings, and worse self-reported health each raises the likelihood of already being retired by age 62.

A conclusion that retirement per se, as opposed to Social Security eligibility, reduces suicide would be inconsistent with some prior evidence on how retirement affects mental health. For instance, Dave, Rashad, and Spasojevic (2008) estimated among HRS respondents that retirement adversely impacted not only mental health but also illnesses and difficulties with mobility and daily activities, which as just discussed would be expected to increase the likelihood of suicide. Latif (2013) found in Canadian data that retirement did not affect depression, including in samples stratified by gender or education. Similarly, in Dutch data, Lindeboom, Portrait, and Berg (2002) established the absence of a relationship between early retirement and depression.

Other research has estimated a positive effect of retirement on mental health, well-being, and life satisfaction in the United States (Charles 2004; Gorry, Gorry, and Slavov 2015), England (Johnston and Lee 2009), and Germany (Eibich 2015). Besides the results, an important difference between the two groups of studies is in their sources of variation for identifying retirement effects: the studies from the previous paragraph all relied on within-person changes in status using individual fixed effects in longitudinal data, while the studies finding beneficial impacts each used benefit eligibility and other retirement program financial incentives that induce discontinuous changes in retirement probabilities at specific ages. The results of these latter analyses are taken to imply that retirement directly improves mental health, but are also consistent with the possibility that mental health responds positively to eligibility or other sharp increases in retirement benefits. In addition, using variation generated by the Social Security "Notch" created by 1970s amendments to the Social Security Act, Ayyagari (2015) and Golberstein (2015) each found a positive direct impact of Social Security retirement income on mental health. (15)

B. Pathways from Social Security Eligibility to Reduced Suicide

The preceding discussion implicitly assumed that the primary mechanism through which becoming eligible for Social Security reduces suicides is a positive effect of benefit income on mental health. While income will fall for many claimants who simultaneously retire, because benefits typically do not fully replace earnings, the preceding subsection showed that reaching age 62 is much more likely to trigger Social Security benefit claiming than retirement. For instance, recall that Gustman and Steinmeier (2015) report that almost 50% of 62-year-olds begin Social Security receipt, compared to 12% who retire full-time. The share of 62-year-olds experiencing an increase in income upon claiming Social Security is therefore much larger than the share for which income declines. Furthermore, the previous subsection also outlined evidence that three groups likely to have high replacement rates, those with low income, education, and health status, are also those that have both elevated suicide risk and particularly high likelihoods of both retirement prior to age 62 and Social Security benefit claiming at age 62.

The argument above also implies that for many 62-year-olds, income relative to others in the physical or social community, for whom on average there is no reason to expect concurrent positive income shocks, will rise. Based on evidence from Daly, Wilson, and Johnson (2013) that an improvement in relative status lowers suicide risk, this is another avenue through which the additional Social Security income available at age 62 can produce an abrupt decline in suicides.

Even for age 62 retirees who experience a reduction in income despite claiming Social Security, the additional income provided by Social Security benefits might be the margin by which expected well-being from retirement exceeds that in the alternative state of continuing to work. Results of the previously described studies, which imply that retirement has beneficial mental health consequences when triggered by financial incentives but might otherwise be psychologically neutral or deleterious, support this conjecture.

It is also possible that Social Security eligibility could lower suicide by reducing income uncertainty. By definition, this effect is relevant only for those who have yet to retire upon attaining eligibility, potentially including those not claiming Social Security at age 62 given that they can henceforth choose to start receiving benefits at any time. The fact that those with lower income, less education, and worse health are most likely to commit suicide, face income uncertainty, and retire before age 62, however, suggests that this avenue has limited relevance.

In theory, Social Security eligibility could also enable job mobility, as beneficiaries no longer need depend on wage earnings for income. But Figures 2-4 of Fairlie, Kapur, and Gates (2016) indicate that rates of job mobility, defined as changing jobs from the previous month, are only around 1.5% and trend smoothly in the vicinity of age 62.

Consequently, Social Security benefit income would appear to be the most likely explanation for the drop in suicides at age 62, and the remainder of the narrative assumes that this is the case.

C. Gender Differences

An important feature of the results that any explanation must account for is the large effect among men relative to women, for whom there is no significant age 62 suicide rate discontinuity overall and during 1990-2004. As illustrated in Figures 3A and 3B, which plot the age profiles in suicide rates on either side of age 62 separately by gender, and mentioned previously, suicide rates are substantially higher for men than women, by a factor of around three at age 50, four at age 62, and 10 at the oldest ages. The exact mechanism through which this difference would induce differential suicide rate declines by gender is unclear. However, perhaps it implies, and the contrasting slopes of the profiles to the right of age 62 embody, that at the margin, external factors such as the ability to collect retirement benefits have more scope to affect suicide behavior at retirement age for men than women.

One possibility is that Social Security benefit receipt simply matters more to men than women. For instance, Denney et al. (2009) reports that suicides fall when income rises among men, but not women, which is relevant particularly for pre-age 62 retirees. In contrast, Daly, Wilson, and Johnson (2013) found that income gains reduce suicide for both genders, with a larger gradient for women than men. Even if so, the fact that Social Security benefit levels of men exceed those of women on average, because of both higher wages and more years of work, would contribute to the gender difference in discontinuities. This applies even for married women, for whom Social Security benefits would be expected to contribute less to family income upon reaching age 62 than would be true for their husbands upon turning 62.

Extending this logic, the most important gender distinction regarding Social Security benefits is conceivably that reaching age 62 is a considerably larger focal point for men than women. Henriques (2012) points out that over 50% of female beneficiaries receive benefits exclusively as a spouse (20%) or survivor (over 30%). Eligibility for spousal benefits also begins at age 62, but these are at most one-half the amount of primary beneficiary benefits. Meanwhile, survivors can receive benefits starting at age 60, or earlier if they have dependent children. For all these reasons, to the extent that the ability to claim Social Security retirement benefits reduces suicide, reaching age 62 is likely to have a stronger dampening effect on suicide for men than women.

Consistent with this, Ayyagari (2015) found that higher Social Security benefits received by Notch cohorts decreased functional limitations. This would be expected to lower suicide through the health status link; functional impairment is explicitly listed as a critical suicide risk factor for older adults by Salvatore (2016). Moreover, increased benefits reduced depressive symptoms, which would also presumably lower suicide rates, and this was concentrated in households for which the primary beneficiary had less than a high school education. (16)

On the other hand, gender differences in the suicide rate decline are inconsistent with the cause being retirement itself. Perhaps surprisingly in light of traditional labor force participation patterns, Rutledge, Gillis, and Webb (2015, Figure 3) shows that the timing of retirement among HRS respondents is quite similar for men and women. In addition, none of the studies reviewed earlier report gender differences in the mental health effects of retirement.

D. Time Differences

As described earlier, from the perspective of 62-year-olds, the Social Security normal retirement age rose by 2 months each year, from age 65 to 66, from 1999 to 2005. This change increased the percentage by which benefits received at age 62 were discounted, relative to levels provided at normal retirement age, and thereby provided incentive to delay benefit claiming. Consistent with this, Haaga and Johnson (2012) and Song and Manchester (2007) each show that the proportion of 62-year-olds claiming Social Security benefits fell considerably during this time. The strengthening of the suicide effect over the latter part of the sample period would thus seem to present a puzzle. Since this appears to have not begun until after the normal retirement age reached 66, other factors must be at work.

One prospective candidate is differences in how incomes of the relevant age groups changed over time. Data from the Current Population Survey Annual Social and Economic Supplement (Flood et al. 2015) show that, for instance, average family income of 61-year-olds was steadily 6%-7% higher than that of 62-year-olds during each 5-year period over 1990-2004, but this premium fell abruptly to just over 2% during the two 5-year periods over 2005-2014. More broadly, family incomes of ages 55-61 exceeded those of ages 62-68 by 28% in 1990-1994 and 33%-34% during 1995-2004, but by only 26% over 2005-2009 and 17% in 2010-2014. Combined with the reported inverse relationship between income and suicide, these changes imply exactly the pattern of changes in the size of the age 62 suicide rate discontinuity that is apparent from column 1 of rows m.-q. in Table 1.

Columns 2 and 3 of these rows make clear that the growth in magnitude of the overall suicide rate discontinuity is, in turn, largely attributable to its emergence for females, particularly in 2005-2009. Figure 4 plots female suicide age profiles on either side of age 62 for (a) 1990-2004 and (b) 2005-2014 in samples restricted to the narrowest age range, 55-68, to focus on behavior at ages immediately surrounding the discontinuity. These diagrams reveal that the appearance of the discontinuity in the later sample is largely attributable to a substantial increase in suicide rates among younger women, as suggested by the observations of Case and Deaton (2015) alluded to in the introduction. In particular, suicide rates increased from Figures 4A to 4B by 0.006 in 1,000 for 62-year-olds, but 0.016 for 61-year-olds, with smaller shifts at older ages but larger shifts at younger ages.

These changes in suicide rates are consistent with those in the relative incomes of the corresponding age groups, especially given three pieces of evidence from Daly, Wilson, and Johnson (2013). First, a decrease in family income raises suicide more for women than men. Second, a reduction in relative income, that is, an increase in others' income holding own income constant, has a strong positive effect on suicide risk. Third, this impact is particularly large for women: the point estimate (from their Table 4) implies a relative shift in suicides similar in size to that observed in Figures 4A and 4B, given the corresponding shift in relative incomes reported above.

Moreover, Haaga and Johnson (2012, Figure 6) shows that the percentage of SIPP respondents claiming Social Security at age 62 was similar for women and men in 1995-2004 when the gender discrepancy in the age 62 suicide discontinuity was widest, and larger for women than men in other sample years by up to 10 percentage points when the gender suicide discontinuity difference was considerably narrower. Falling gender wage and labor force participation gaps over time would also imply that the gender difference in Social Security benefit levels has also shrunk. (17)

VI. CONCLUSION

Using a RD framework, this study has documented a significant, sudden drop in suicide rates upon turning 62 years old over the period 1990-2014 that has not received much previous attention. This decline is large, particularly among males, has emerged for females and widened for males in recent years, is not contingent on particular model specification details, and is not apparent at other ages or for outcomes that should not vary discretely at that age. Much evidence suggests that this discontinuity is attributable to the Social Security early retirement age, more so than the act of retiring itself.

The analysis uses RD with only year of age observed. A potential issue with having fewer separate age-year levels, compared with the alternative of measuring age in months or days, is reduced statistical power to identify effects. This is offset somewhat by the ability to include a large number of years, and thus observations per age level. (18) Moreover, Tables 2 and 3 indicate that using a less precise measure of the running variable does not systematically bias RD toward false positive results. In contrast, an advantage of using RD with a more aggregated age measure is that virtually any publically available dataset reports age in years, whereas few contain a more exact measure of age. Furthermore, my framework allows a more generalizable conclusion: whereas most analogous RD studies use only 2 or 3 years of data on each side of the discontinuity, the falsification tests here fail to uncover other discontinuities within a 35-year age range centered at 62 years old.

Given that Social Security is now the largest line item in the federal budget, with spending approaching 25% of gross domestic product (http://taxfoundation.org/blog/where-do-your-tax-dollars-go), evidence that Social Security policy has a presumably unintended effect on an important outcome such as suicide should not necessarily be surprising. While some commentators trivialize the importance of the Social Security program because of its low replacement rates for high earners, benefit levels are still apparently sufficient to significantly raise the well-being of recipients, even in the reduced amounts available when claimed early.

These results heighten the already substantial concern regarding the future solvency of the Social Security Trust Fund. They also identify a potential drawback of the impending additional increase in the normal retirement age, further discounting early retirement benefit amounts, which begins to affect 62-year-olds in 2017. Similarly, the findings here serve as an argument against proposals to raise either the normal retirement age beyond 67, which is currently legislated for cohorts born in 1960 or later, or the early retirement age beyond 62.

Finally, in necessarily focusing on the suicide rate discontinuity at age 62, my analysis has mostly ignored the broader suicide rate age profiles. Results from Case and Deaton (2015) suggest that the change in profiles over time, displayed for women in Figures 4A and 4B, might be partially attributable to physical pain, which they report is both strongly predictive of suicide and increasing recently particularly among the middle-aged. Findings from Denney et al. (2009) that being unmarried, particularly widowed, increase suicide for men but not women is a potential factor contributing to the divergence in suicide rates across genders in older individuals observed in Figures 3A and 3B. Understanding these relationships, and the factors shaping the overall age profiles in Figures 1 and 2A-2C, seemingly would necessitate further research.

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JEFFREY DESIMONE (*)

(*) I thank the Editor. Maureen Pirog, and three anonymous referees for encouragement and helpful comments. I declare that I have no relevant or material financial interests that relate to the research described in this paper. DeSimone: Associate Professor, Department of Marketing, Industrial Distribution and Economics, University of Alabama at Birmingham, Birmingham, AL 35205. Phone 205-934-8840, Fax 205-934-0058, E-mail desimone@uab.edu

(1.) Throughout the analysis, ages are coded as (age + 0.5) to reflect that the average 55-year-old, for instance, is in fact about halfway between his or her 55th and 56th birthdays.

(2.) Observing this discontinuity literally motivated the paper: I noticed it from a graph similar to Figure I produced while examining an analogous jump in suicides at age 21, presumably attributable to that being the minimum legal drinking age (Carpenter and Dobkin 2009; DeSimone 2016).

(3.) In contrast to this finding for mortality specifically from suicide, ongoing work by Fitzpatrick and Moore, using RD with individual-level administrative data and more precise information on date of birth, suggests that overall mortality increases upon reaching age 62 (abstract available at http://crr.bc.edu/about-us/grants/how-does-early-retirement-affect-mortality/).

(4.) During this time, the full retirement age increased from 65 to 66. This raised the discount rate applied to benefits claimed before reaching age 66, but did not alter the ability to claim benefits starting at age 62.

(5.) Case and Deaton (2015) link the recent upsurge in middle-aged suicides to an emerging "epidemic" of physical and mental pain, further manifested by concurrent increases in accidental deaths attributable to poisoning from alcohol, illegal drugs, and prescription opioids. Salvatore (2016) independently highlights these same risk factors, and suggests that greater social isolation stemming from particularly high divorce rates in this group also contributed.

(6.) While this model provides the underlying framework to generate the entire age profile on either side of the discontinuity, in actuality regressions are estimated only for [a.sub.0] = 62, separately using younger and older ages within the bandwidth. The RD estimate is the difference between the two corresponding intercept estimates.

(7.) While this approach is dictated by data availability, the mechanics of Social Security retirement benefit eligibility and payment timing imply variance of over a month in the threshold age for payment receipt. Specifically, an individual must be age 62 for the entire month to receive benefits, and benefits are paid on either the second, third or fourth Wednesday of the month depending on birthdate. A beneficiary could therefore be eligible for initial benefit payment as early as 7 days after the 62nd birthday (if on the 1st and this falls on a Wednesday) or as late as a month and 13 days after (if on the 2nd and this falls on a Thursday). Consequently, even if a more precise measure of age was observed, a gap would exist between ages at which potential beneficiaries were known with certainty to be either ineligible or eligible.

(8.) Because of deaths, the true average age is slightly less than (age + 0.5), and the implied upward bias increases with age. However, based on CDC mortality data (http://wonder.cdc.gov/cmf-icdlO.html), any such bias should be small, particularly near the discontinuity. For instance, over 1999-2014, the average mortality rate was about 0.9% for ages 55-64 and 5.1% for ages 75-84. Assuming a uniform within-group death rate for simplicity, even for ages 75-84, this would imply adjusting the additive factor only from 0.5 to about 0.493.

(9.) Moreover, while this is not directly apparent from Figures 2B and 2C, suicide rates are several times higher for men than women. For example, at age 61 (just before the abrupt drop at age 62) the average suicide rate is 0.238 per 1,000 among men but 0.060 among women.

(10.) The change in age profile slope that accompanies the discontinuity at age 62 in Figures 2A and 2C suggests the possibility of identifying the relevant effect using a kink along with the jump captured by RD, an approach introduced by Dong (2016).

(11.) A quintic in age is chosen because for each of the three gender-defined samples, coefficients of all five age terms are significant, whereas adding the sixth power renders all of the age terms insignificant without changing the RD estimate. Analogous logic leads to using quartic models in Table 2. For all OLS polynomial models in both tables, heteroskedasticityrobus t (-Statistics are reported.

(12.) As Dong (2015) describes, the test is implemented using age terms that are centered at age 62 and recorded as integers (e.g., age 61 rather than 61.5), although in the OLS polynomial model these changes have no bearing on the estimated RD effect.

(13.) The normal retirement age will once again increase by 2 months per year starting with individuals born in 1955, reaching age 67 for those born in 1960 or later, but this is not relevant for 62-year-olds until 2017.

(14.) I do not examine the female sample since the age 62 discontinuity is never significant using all years, or the youngest and oldest sample ages so that a minimum of six age-years on either side of the discontinuity is preserved.

(15.) In contrast to my results, Golberstein (2015) finds significant effects only for women, although he compares outcomes for retirees with different benefit levels, as opposed to individuals on either side of the eligibility threshold. The Social Security Notch increased benefits for the 1911-1916 birth cohorts, which reached age 62 well before the beginning of my sample period.

(16.) If having less education exacerbates the effect of reaching age 62 on suicides, it might also be relevant that the education gradient in suicide likelihood found by Denney et al. (2009) is significant for men but not women.

(17.) Meanwhile, the divergence of unemployment by gender over 2009-2012, during which male unemployment rates exceeded those of females by as much as two percentage points, might have contributed to the increase in the suicide decline at age 62 for males relative to females at the end of the sample period. Both Daly. Wilson, and Johnson (2013) and Denney et al. (2009) show that unemployment has a strong positive relationship with suicide.

(18.) Table 1 shows that in the baseline model with the combined or male sample, standard errors are sufficiently small to identify an effect of 5% at the 10% significance level, although power also depends on the variance of the outcome: for females, among whom suicide is far less prevalent, an effect size of 7% would be required to achieve significance at 10%.
ABBREVIATION
CCT: Calonico, Cattaneo, and Titiunik
CDC: Centers for Disease Control and Prevention
HRS: Health and Retirement Study
LM: Ludwig and Miller
OLS: Ordinary Least Squares
RD: Regression Discontinuity
SE: Standard Error
SIPP: Survey of Income and Program Participation


doi.10.1111/coep.12215
TABLE 1
RD Estimates of the Suicide Rate Decline at Age 62

                             Both Genders           Females
                                (1)                   (2)

a)  Baseline             -0.079 (2.61) [6.8]   -0.035 (0.83) [8.1]
b)  Unlogged rate        -0.011 (2.63)[6.91    -0.003 (1.05) [8.7]
c)  OLS quintic          -0.098 (3.98) [N/A]   -0.028 (0.75) [N/A]
d)  Local quadratic      -0.070 (2.33) [14.8]  -0.016 (0.35) [15.4]
e)  CCT bandwidth        -0.079 (2.62) [6.8]   -0.035 (0.77) [6.9]
f)  LM bandwidth         -0.103 (4.25) [11.0]  -0.051 (1.43) [11.0]
g)  Rectangular kernel   -0.079 (2.40) [5.3]   -0.046 (1.03) [6.4]
b)  Epanechnikov kernel  -0.079 (2.57) [6.3]   -0.037 (0.86) [7.5]
i)  Nearest-neighbor SE  -0.079 (2.56) [6.8]   -0.035 (0.79) [8.1]
j)  Ages 43-80           -0.079 (2.65) [6.9]   -0.035 (0.80) [7.7]
k)  Ages 47-76           -0.080 (2.67) [6.9]   -0.035 (0.84) [8.3]
l)  Ages 51-72           -0.073 (2.23) [5.8]   -0.035 (0.74) [6.6]
m)  Ages 55-68           -0.074 (2.29) [5.9]   -0.026 (0.48) [4.9]
n)  Years 1990-1994      -0.082 (2.37) [11.3]  -0.047 (0.90) [13.4]
o)  Years 1995-1999      -0.072 (1.94)[10.1]    0.036 (0.51) [9.6]
P)  Years 2000-2004      -0.072 (2.20) [8.3]    0.013 (0.20) [9.0]
q)  Years 2005-2009      -0.099 (3.05) [7.3]   -0.085 (1.81) [8.6]
r)  Years 2010-2014      -0.134 (3.30) [6.8]   -0.111 (2.57) [9.0]
s)  Northeast region     -0.060 (1.36) [7.8]   (Age 61 mean suicide
                                                rate = 0.107)
t)  Midwest region       -0.056 (1.72) [6.8]   (Age 61 mean suicide
                                                rate = 0.158)
u)  South region         -0.114 (3.20) [9.5]   (Age 61 mean suicide
                                                rate = 0.126)
v)  West region          -0.103 (2.61) [6.8]   (Age 61 mean suicide
                                                rate = 0.180)

           Males
           (3)

a)  -0.091 (3.05) [6.7]
b)  -0.021 (2.91) [6.5]
c)  -0.118 (4.82) [N/A]
d)  -0.088 (3.01) [15.4]
e)  -0.090 (2.94) [6.5]
f)  -0.119 (5.02) [11.0]
g)  -0.094 (2.94) [5.2]
b)  -0.092 (3.04) [6.2]
i)  -0.091 (3.05) [6.7]
j)  -0.092 (3.06) [6.7]
k)  -0.089 (2.93) [6.5]
l)  -0.086 (2.71) [5.8]
m)  -0.081 (2.40) [5.1]
n)  -0.089 (2.62) [10.5]
o)  -0.110(2.89) [11.5]
P)  -0.104 (2.78) [8.8]
q)  -0.099 (2.59) [7.6]
r)  -0.136 (3.02) [6.3]
s)
t)
u)
v)

Notes: Data are national averages of suicides per 1,000 populationover
1990-2014 for each year of age among 39- to 84-year-olds, with
exceptions as indicated in rows j.-v. Columns 1-3 contain estimates
using the sample listed in the column heading. These are from local
linear regressions of log suicide rates (so can be interpreted as
percentage changes) using the bandwidth selector from Imbens and
Kalyanaraman (2012) and a triangular kernel, with exceptions as
indicated in rows b.-h. Parentheses contain absolute t-statistics and
brackets contain bandwidths. Only estimates for both genders combined
were obtained for Census regions in rows s.-v. The sample size is the
number of years multiplied by the number of distinct years of age
included, which equals 1,150 in rows a.-i. and s.-v., 230 in n.-r.,
950 in j., 750 in k., 550 in 1, and 350 in m. Average suicide rates
among 61-year-olds are 0.145 overall, 0.060 for females, and 0.238 for
males in rows a.-m., given in the text for n.-r. and listed next to
the estimates for s.-v.

TABLE 2
Falsification: RD Estimates of Homicide & Population Discontinuities
at Age 62

                          Log Homicide Rate
                          Both Genders  Females       Males
                          (1)           (2)           (3)

a)  Baseline             -0.014 (0.30)  0.047 (0.91)  -0.038 (0.77)
b)  Unlogged rate         0.000 (0.10)  0.001 (1.16)  -0.001 (0.46)
c)  OLS quartic          -0.021 (0.53)  0.043 (0.99)  -0.039 (0.85)
d)  Local quadratic       0.005 (0.10)  0.053 (1.00)  -0.022 (0.34)
e)  CCT bandwidth        -0.007 (0.14)  0.049 (0.89)  -0.030 (0.52)
f)  LM bandwidth         -0.020 (0.46)  0.034 (0.73)  -0.042 (0.93)
g)  Rectangular kernel   -0.013 (0.28)  0.037 (0.68)  -0.041 (0.84)
h)  Epanechnikov kernel  -0.015 (0.32)  0.045 (0.87)  -0.038 (0.78)
i)  Nearest-neighbor SE  -0.014 (0.30)  0.047 (0.90)  -0.038 (0.76)
j)  Ages 43-80           -0.015 (0.33)  0.028 (0.64)  -0.036 (0.68)
k)  Ages 47-76           -0.008 (0.15)  0.047 (0.92)  -0.032 (0.55)
1)  Ages 51-72           -0.001 (0.02)  0.061 (0.97)  -0.029 (0.46)
m)  Ages 55-68            0.010 (0.13)  0.096 (1.16)  -0.016(0.21)

      Log Population
      Both Genders       Females           Females
      (4)                (5)               (5)
a)         0.013 (0.37)      0.007 (0.22)      0.007 (0.22)
b)    12,177 (0.12)      2,756 (0.05)      2,756 (0.05)
c)        -0.003 (0.08)     -0.003 (0.10)     -0.003 (0.10)
d)         0.011 (0.24)      0.011 (0.24)      0.011 (0.24)
e)         0.010 (0.21)      0.008( 0.17)      0.008 (0.17)
f)         0.012 (0.29)      0.009 (0.24)      0.009 (0.24)
g)         0.016 (0.47)      0.007 (0.24)      0.007 (0.24)
h)         0.014 (0.40)      0.007 (0.23)      0.007 (0.23)
i)         0.013 (0.37)      0.007 (0.22)      0.007 (0.22)
j)         0.013 (0.42)      0.006 (0.21)      0.006 (0.21)
k)         0.012 (0.29)      0.009 (0.24)      0.009 (0.24)
1)         0.011 (0.25)      0.009 (0.20)      0.009 (0.20)
m)         0.006 (0.11)      0.004 (0.06)      0.004 (0.06)


      Males
      (6)
a)        0.017 (0.43)
b)    9,120 (0.18)
c)       -0.004 (0.13)
d)        0.010 (0.21)
e)        0.012 (0.25)
f)        0.014 (0.33)
g)        0.016 (0.40)
h)        0.017 (0.43)
i)        0.017 (0.42)
j)        0.019 (0.52)
k)        0.015 (0.35)
1)        0.014 (0.31)
m)        0.009 (0.17)

Notes: Data are national averages of suicides per 1,000 population over
1990-2014 for each year of age among 39- to 84-year-olds, except for
the narrower age ranges in rows j.-m. The sample size is the number of
years multiplied by the number of distinct years of age included, which
is 1,150 in rows a.-i., 950 in j., 750 in k., 550 in 1., and 350 in m.
Columns 1 -3 contain estimates of the decrease in the log homicide rate
at age 62 using the sample listed in the column heading, while columns
4-6 do the same for total population. These are from local linear
regressions of the log homicide rate and population using the bandwidth
selector from Imbens and Kalyanaraman (2012) and a triangular kernel,
with exceptions as indicated in rows b.- Parentheses contain absolute
r-statistics.

TABLE 3
Falsification: RD Estimates of Suicide Rate Discontinuities at Ages
other than 62

Gender:      Both                          Males
Age Range:   All Ages (1)   Symmetric (2)  All Ages (3)   Symmetric (4)

Age 45       0.015 (0.79)  -0.021 (0.61)   0.000 (0.02)  -0.019 (0.56)
Age 46       0.011 (0.47)   0.006 (0.19)   0.017 (0.79)   0.001 (0.03)
Age 47       0.017 (0.78)   0.016 (0.67)   0.020 (0.84)   0.021 (0.81)
Age 48       0.009 (0.37)   0.006 (0.21)   0.008 (0.36)   0.007 (0.25)
Age 49      -0.012 (0.43)  -0.020 (0.57)  -0.021 (0.77)  -0.032 (0.92)
Age 50      -0.009 (0.32)  -0.008 (0.30)  -0.016 (0.56)  -0.015 (0.57)
Age 51       0.006 (0.22)   0.012 (0.35)   0.005 (0.18)   0.021 (0.54)
Age 52      -0.003 (0.10)  -0.003 (0.08)  -0.001 (0.04)   0.001 (0.04)
Age 53      -0.008 (0.25)  -0.003 (0.11)  -0.009 (0.27)   0.000 (0.01)
Age 54       0.006 (0.18)   0.006 (0.19)   0.003 (0.11)   0.005 (0.15)
Age 55       0.003 (0.08)   0.003 (0.08)   0.005 (0.15)   0.004 (0.13)
Age 56      -0.006 (0.18)  -0.010 (0.28)   0.002 (0.06)  -0.005 (0.14)
Age 57       0.004 (0.12)   0.004 (0.12)   0.010 (0.28)   0.009 (0.26)
Age 58       0.035 (0.94)   0.034 (0.94)   0.047 (1.33)   0.047 (1.31)
Age 59       0.011 (0.30)   0.011 (0.30)   0.001 (0.04)   0.001 (0.04)
Age 60       0.003 (0.09)   0.007 (0.18)   0.009 (0.25)   0.012 (0.31)
Age 61      -0.034 (0.96)  -0.033 (0.93)  -0.033 (0.96)  -0.031 (0.91)
Age 63      -0.031 (1.07)  -0.030 (1.05)  -0.040 (1.35)  -0.037 (1.25)
Age 64       0.007 (0.25)   0.008 (0.29)   0.016 (0.54)   0.016 (0.56)
Age 65       0.005 (0.20)   0.004 (0.17)   0.011 (0.38)   0.011 (0.40)
Age 66       0.028 (1.06)   0.028 (1.12)   0.033 (1.25)   0.034 (1.30)
Age 67       0.028 (1.10)   0.033 (1.44)   0.026 (1.01)   0.032 (1.37)
Age 68       0.027 (0.98)   0.026 (0.94)   0.039 (1.50)   0.039 (1.48)
Age 69      -0.001 (0.04)  -0.013 (0.38)  -0.000 (0.01)  -0.009 (0.28)
Age 70       0.004 (0.14)   0.002 (0.07)  -0.004 (0.14)  -0.007 (0.21)
Age 71       0.013 (0.48)   0.002 (0.08)   0.006 (0.21)  -0.012 (0.33)
Age 72       0.013 (0.49)   0.001 (0.02)   0.035 (1.35)   0.008 (0.21)
Age 73       0.019 (0.60)   0.019 (0.63)   0.035 (1.07)   0.034 (1.05)
Age 74      -0.025 (0.77)  -0.043 (1.18)  -0.015 (0.44)  -0.038 (1.00)
Age 75       0.039 (1.34)   0.044 (1.39)   0.028 (0.89)   0.029 (0.89)
Age 76       0.010 (0.31)   0.010 (0.30)   0.009 (0.25)   0.010 (0.24)
Age 77      -0.014 (0.39)  -0.013 (0.30)  -0.009 (0.23)  -0.008 (0.17)
Age 78      -0.035 (0.90)  -0.040 (0.84)  -0.038 (0.88)  -0.046 (0.86)
Age 79      -0.007 (0.17)  -0.004 (0.09)  -0.013 (0.30)  -0.010 (0.18)

Notes: Data are national averages of suicides per 1,000 population over
1990-2014 for each year of age, among 39- to 84-year-olds in columns 1
and 3, and a symmetric age range from age 39 below (for discontinuities
at ages below 62), or from age 84 above (for discontinuities at ages
above 62), around the row heading discontinuity in columns 2 and 4. The
sample size, which is the number of years multiplied by the number of
distinct years of age included, is 1,150 in columns 1 and 3, and in
columns 2 and 4 increases from 300 (age 45) to 1,100 (age 61 and 63)
and then decreases back to 300 (age 79) in increments of 50. Estimates
are from local linear regressions of log suicide rates using the
bandwidth selector from Imbens and Kalyanaraman (2012) and a triangular
kernel. Parentheses contain absolute f-statistics.

TABLE 1
RD Estimates of the Suicide Rate Decline at Age 62

                         Both Genders
                         (1)

a)  Baseline             -0.079 (2.61) [6.8]
b)  Unlogged rate        -0.011 (2.63) [6.9]
c)  OLS quintic          -0.098 (3.98) [N/A]
d)  Local quadratic      -0.070 (2.33) [14.8]
e)  CCT bandwidth        -0.079 (2.62) [6.8]
f)  LM bandwidth         -0.103 (4.25) [11.0]
g)  Rectangular kernel   -0.079 (2.40) [5.3]
b)  Epanechnikov kernel  -0.079 (2.57) [6.3]
i)  Nearest-neighbor SE  -0.079 (2.56) [6.8]
j)  Ages 43-80           -0.079 (2.65) [6.9]
k)  Ages 47-76           -0.080 (2.67) [6.9]
l)  Ages 51-72           -0.073 (2.23) [5.8]
m)  Ages 55-68           -0.074 (2.29) [5.9]
n)  Years 1990-1994      -0.082 (2.37) [11.3]
o)  Years 1995-1999      -0.072 (1.94) [10.1]
P)  Years 2000-2004      -0.072 (2.20) [8.3]
q)  Years 2005-2009      -0.099 (3.05) [7.3]
r)  Years 2010-2014      -0.134 (3.30) [6.8]
s)  Northeast region     -0.060 (1.36) [7.8]
t)  Midwest region       -0.056 (1.72) [6.8]
u)  South region         -0.114 (3.20) [9.5]
v)  West region          -0.103 (2.61) [6.8]

    Females                             Males
    (2)                                 (3)

a)  -0.035 (0.83) [8.1]                 -0.091 (3.05) [6.7]
b)  -0.003 (1.05) [8.7]                 -0.021 (2.91) [6.5]
c)  -0.028 (0.75) [N/A]                 -0.118 (4.82) [N/A]
d)  -0.016 (0.35) [15.4]                -0.088 (3.01) [15.4]
e)  -0.035 (0.77) [6.9]                 -0.090 (2.94) [6.5]
f)  -0.051 (1.43) [11.0]                -0.119 (5.02) [11.0]
g)  -0.046 (1.03) [6.4]                 -0.094 (2.94) [5.2]
b)  -0.037 (0.86) [7.5]                 -0.092 (3.04) [6.2]
i)  -0.035 (0.79) [8.1]                 -0.091 (3.05) [6.7]
j)  -0.035 (0.80) [7.7]                 -0.092 (3.06) [6.7]
k)  -0.035 (0.84) [8.3]                 -0.089 (2.93) [6.5]
l)  -0.035 (0.74) [6.6]                 -0.086 (2.71) [5.8]
m)  -0.026 (0.48) [4.9]                 -0.081 (2.40) [5.1]
n)  -0.047 (0.90) [13.4]                -0.089 (2.62) [10.5]
o)   0.036 (0.51) [9.6]                 -0.110 (2.89) [11.5]
P)   0.013 (0.20) [9.0]                 -0.104 (2.78) [8.8]
q)  -0.085 (1.81) [8.6]                 -0.099 (2.59) [7.6]
r)  -0.111 (2.57) [9.0]                 -0.136 (3.02) [6.3]
s)  (Age 61 mean suicide rate = 0.107)
t)  (Age 61 mean suicide rate = 0.158)
u)  (Age 61 mean suicide rate = 0.126)
v)  (Age 61 mean suicide rate = 0.180)

Notes: Data are national averages of suicides per 1,000 population over
1990-2014 for each year of age among 39- to 84-year-olds, with
exceptions as indicated in rows j.-v. Columns 1-3 contain estimates
using the sample listed in the column heading. These are from local
linear regressions of log suicide rates (so can be interpreted as
percentage changes) using the bandwidth selector from Imbens and
Kalyanaraman (2012) and a triangular kernel, with exceptions as
indicated in rows b.-h. Parentheses contain absolute t-statistics and
brackets contain bandwidths. Only estimates for both genders combined
were obtained for Census regions in rows s.-v. The sample size is the
number of years multiplied by the number of distinct years of age
included, which equals 1,150 in rows a.-i. and s.-v., 230 in n.-r., 950
in j., 750 in k., 550 in 1, and 350 in m. Average suicide rates among
61-year-olds are 0.145 overall, 0.060 for females, and 0.238 for males
in rows a.-m., given in the text for n.-r. and listed next to the
estimates for s.-v.

TABLE 2
Falsification: RD Estimates of Homicide & Population Discontinuities
at Age 62

                          Log Homicide Rate
                          Both Genders   Females       Males
                          (1)            (2)           (3)

a)  Baseline             -0.014 (0.30)   0.047 (0.91)  -0.038 (0.77)
b)  Unlogged rate         0.000 (0.10)   0.001 (1.16)  -0.001 (0.46)
c)  OLS quartic          -0.021 (0.53)   0.043 (0.99)  -0.039 (0.85)
d)  Local quadratic       0.005 (0.10)   0.053 (1.00)  -0.022 (0.34)
e)  CCT bandwidth        -0.007 (0.14)   0.049 (0.89)  -0.030 (0.52)
f)  LM bandwidth         -0.020 (0.46)   0.034 (0.73)  -0.042 (0.93)
g)  Rectangular kernel   -0.013 (0.28)   0.037 (0.68)  -0.041 (0.84)
h)  Epanechnikov kernel  -0.015 (0.32)   0.045 (0.87)  -0.038 (0.78)
i)  Nearest-neighbor SE  -0.014 (0.30)   0.047 (0.90)  -0.038 (0.76)
j)  Ages 43-80           -0.015 (0.33)   0.028 (0.64)  -0.036 (0.68)
k)  Ages 47-76           -0.008 (0.15)   0.047 (0.92)  -0.032 (0.55)
l)  Ages 51-72           -0.001 (0.02)   0.061 (0.97)  -0.029 (0.46)
m)  Ages 55-68            0.010 (0.13)   0.096 (1.16)  -0.016 (0.21)

          Log Population
          Both Genders       Females           Males
          (4)                (5)               (6)

a)        0.013 (0.37)       0.007 (0.22)      0.017 (0.43)
b)   12,177 (0.12)       2,756 (0.05)      9,120 (0.18)
c)       -0.003 (0.08)      -0.003 (0.10)     -0.004 (0.13)
d)        0.011 (0.24)       0.011 (0.24)      0.010 (0.21)
e)        0.010 (0.21)       0.008 (0.17)      0.012 (0.25)
f)        0.012 (0.29)       0.009 (0.24)      0.014 (0.33)
g)        0.016 (0.47)       0.007 (0.24)      0.016 (0.40)
h)        0.014 (0.40)       0.007 (0.23)      0.017 (0.43)
i)        0.013 (0.37)       0.007 (0.22)      0.017 (0.42)
j)        0.013 (0.42)       0.006 (0.21)      0.019 (0.52)
k)        0.012 (0.29)       0.009 (0.24)      0.015 (0.35)
l)        0.011 (0.25)       0.009 (0.20)      0.014 (0.31)
m)        0.006 (0.11)       0.004 (0.06)      0.009 (0.17

Notes: Data are national averages of suicides per 1,000 population over
1990-2014 for each year of age among 39- to 84-year-olds, except for
the narrower age ranges in rows j.-m. The sample size is the number of
years multiplied by the number of distinct years of age included, which
is 1,150 in rows a.-i., 950 in j., 750 in k., 550 in 1., and 350 in m.
Columns 1 -3 contain estimates of the decrease in the log homicide rate
at age 62 using the sample listed in the column heading, while columns
4-6 do the same for total population. These are from local linear
regressions of the log homicide rate and population using the bandwidth
selector from Imbens and Kalyanaraman (2012) and a triangular kernel,
with exceptions as indicated in rows b.-h. Parentheses contain absolute
r-statistics.

TABLE 3
Falsification: RD Estimates of Suicide Rate Discontinuities at Ages
other than 62

Gender:     Both                          Males
Age Range:  All Ages (1)   Symmetric (2)  All Ages (3)   Symmetric (4)

Age 45       0.015 (0.79)  -0.021 (0.61)   0.000 (0.02)  -0.019 (0.56)
Age 46       0.011 (0.47)   0.006 (0.19)   0.017 (0.79)   0.001 (0.03)
Age 47       0.017 (0.78)   0.016 (0.67)   0.020 (0.84)   0.021 (0.81)
Age 48       0.009 (0.37)   0.006 (0.21)   0.008 (0.36)   0.007 (0.25)
Age 49      -0.012 (0.43)  -0.020 (0.57)  -0.021 (0.77)  -0.032 (0.92)
Age 50      -0.009 (0.32)  -0.008 (0.30)  -0.016 (0.56)  -0.015 (0.57)
Age 51       0.006 (0.22)   0.012 (0.35)   0.005 (0.18)   0.021 (0.54)
Age 52      -0.003 (0.10)  -0.003 (0.08)  -0.001 (0.04)   0.001 (0.04)
Age 53      -0.008 (0.25)  -0.003 (0.11)  -0.009 (0.27)   0.000 (0.01)
Age 54       0.006 (0.18)   0.006 (0.19)   0.003 (0.11)   0.005 (0.15)
Age 55       0.003 (0.08)   0.003 (0.08)   0.005 (0.15)   0.004 (0.13)
Age 56      -0.006 (0.18)  -0.010 (0.28)   0.002 (0.06)  -0.005 (0.14)
Age 57       0.004 (0.12)   0.004 (0.12)   0.010 (0.28)   0.009 (0.26)
Age 58       0.035 (0.94)   0.034 (0.94)   0.047 (1.33)   0.047 (1.31)
Age 59       0.011 (0.30)   0.011 (0.30)   0.001 (0.04)   0.001 (0.04)
Age 60       0.003 (0.09)   0.007 (0.18)   0.009 (0.25)   0.012 (0.31)
Age 61      -0.034 (0.96)  -0.033 (0.93)  -0.033 (0.96)  -0.031 (0.91)
Age 63      -0.031 (1.07)  -0.030 (1.05)  -0.040 (1.35)  -0.037 (1.25)
Age 64       0.007 (0.25)   0.008 (0.29)   0.016 (0.54)   0.016 (0.56)
Age 65       0.005 (0.20)   0.004 (0.17)   0.011 (0.38)   0.011 (0.40)
Age 66       0.028 (1.06)   0.028 (1.12)   0.033 (1.25)   0.034 (1.30)
Age 67       0.028 (1.10)   0.033 (1.44)   0.026 (1.01)   0.032 (1.37)
Age 68       0.027 (0.98)   0.026 (0.94)   0.039 (1.50)   0.039 (1.48)
Age 69      -0.001 (0.04)  -0.013 (0.38)  -0.000 (0.01)  -0.009 (0.28)
Age 70       0.004 (0.14)   0.002 (0.07)  -0.004 (0.14)  -0.007 (0.21)
Age 71       0.013 (0.48)   0.002 (0.08)   0.006 (0.21)  -0.012 (0.33)
Age 72       0.013 (0.49)   0.001 (0.02)   0.035 (1.35)   0.008 (0.21)
Age 73       0.019 (0.60)   0.019 (0.63)   0.035 (1.07)   0.034 (1.05)
Age 74      -0.025 (0.77)  -0.043 (1.18)  -0.015 (0.44)  -0.038 (1.00)
Age 75       0.039 (1.34)   0.044 (1.39)   0.028 (0.89)   0.029 (0.89)
Age 76       0.010 (0.31)   0.010 (0.30)   0.009 (0.25)   0.010 (0.24)
Age 77      -0.014 (0.39)  -0.013 (0.30)  -0.009 (0.23)  -0.008 (0.17)
Age 78      -0.035 (0.90)  -0.040 (0.84)  -0.038 (0.88)  -0.046 (0.86)
Age 79      -0.007 (0.17)  -0.004 (0.09)  -0.013 (0.30)  -0.010 (0.18)

Notes: Data are national averages of suicides per 1,000 population over
1990-2014 for each year of age, among 39- to 84-year-olds in columns 1
and 3, and a symmetric age range from age 39 below (for discontinuities
at ages below 62), or from age 84 above (for discontinuities at ages
above 62), around the row heading discontinuity in columns 2 and 4. The
sample size, which is the number of years multiplied by the number of
distinct years of age included, is 1,150 in columns 1 and 3, and in
columns 2 and 4 increases from 300 (age 45) to 1,100 (age 61 and 63)
and then decreases back to 300 (age 79) in increments of 50. Estimates
are from local linear regressions of log suicide rates using the
bandwidth selector from Imbens and Kalyanaraman (2012) and a triangular
kernel. Parentheses contain absolute f-statistics.
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Author:Desimone, Jeffrey
Publication:Contemporary Economic Policy
Article Type:Report
Geographic Code:1USA
Date:Jul 1, 2018
Words:13547
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