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Given the strength of the first stage, and the indication that the instrument may be valid, I now turn to estimating the impact of Medigap coverage on annuitization. I focus on three outcomes. First I study total income from employer pensions and annuities. This covers all permanent retirement income other than Social Security payments and therefore provides a useful summary measure of annuity income. Annuity income is highly skewed and, as Table 12 shows, many people have no annuity income at all. As a second outcome, I therefore focus on the probability of having any annuity or pension income. Finally, while the annuity variable usefully captures the total response of retirement income to Medigap coverage, it may be too broad. It includes pensions and annuities with limited payout horizons, for example, and these are not true life annuities. As a final outcome, I take advantage of the HRS’s detailed annuity questions to determine whether an individual reports having any income from a “true” annuity, defined as an annuity that pays out until death and stops then. As Table 1 shows, these annuities are more rare; about three percent of the population has such income.

All these measures exclude income from Social Security. People can effectively buy an annuity by delaying Social Security claiming, which increases their future Social Security payments. In results not reported, I found some evidence that people do indeed earn more

Social Security income and claim later when they face lower Medigap prices, but these results were imprecise and not robust across specifications, so I omit them.

Table 15 shows the impact of Medigap coverage on total income from employer pensions

or annuities. Panel A provides the reduced form result, where the coefficient on lnprice

is obtained by regressing annuity income on lnprice and the indicated controls. The co-

efficient on lnprice is a statistically significant -8.46 indicating that increasing the price

of Medigap coverage by 10 percent would reduce annuity income by about $850. At the mean level of annuity income, this works out to a cross price elasticity of -1.31. Figure 11 Panel A, constructed analogously to Figure 10, illustrates the reduced form relationship be- tween annuitization coverage and prices: it shows the nonparametric fit between (residual) annuitization probability and (residual) prices (net of controls). There is a clear negative relationship, although it is not as precise as the first stage relationship. This figure shows the exact variation underlying the reduced form results.

Panel B of Table 15 presents the instrumental variables estimate ofα, the impact of Medigap

coverage on annuitization, estimated via two stage least squares with lnpriceas the excluded

instrument. The coefficient is 19.6. To interpret this number, it is helpful to calculate the elasticity of (aggregate) total annuity income it implies. With mean Medigap coverage of 0.30 and mean annuity income of $6,510, the elasticity of total annuity income with respect to Medigap coverage is about 0.9.

Columns (2), (3), and (4) include successively more controls. The basic results changes very little with the inclusion of these extra controls. The point estimates fall slightly when controlling for permanent income, and it falls more when controlling for the health variables. Controlling for preferences, however, raises the point estimate almost back to the original. Medigap coverage appears to have a large and robust positive impact on annuitization. These results reflect the total impact of Medigap on annuity income. Many people have zero annuity income, however, and much of the annuity puzzle is that many households do

not annuitize at all, not that households have relatively low annuity income conditional on having any annuity income. In Table 16, I investigate the extensive margin response, looking at the impact of Medigap on the probability of having any annuity income, estimated using

linear probability models.9

The reduced form results in Panel A of Table 16 indicate a strong and negative relationship between Medigap prices and the extensive margin of annuity demand, with a cross price extensive margin elasticity of about 0.78. Figure 11, Panel B shows the visual reduced form. Increasing Medigap prices by 10 percent decreases reduces the probability of having any

annuity income by about 2.8 percentage points. The instrumental variables estimate ofγ in

panel B gives the impact of Medigap coverage on the extensive margin of annuity demand. The point estimate of 0.65 implies an aggregate elasticity of about 0.53. Comparing this to the extensive margin elasticity implies that about two-thirds of the impact of Medigap coverage on annuitization comes from the extensive margin, and the remainder from the extensive margin. Adding successive controls in columns (2), (3), and (4) changes the point estimate only very slightly.

These results therefore show an important intensive and extensive margin response of overall annuity income to Medigap coverage. This response reflects the overall change in retirement income to health insurance coverage. To home in on the response from “true”, voluntarily purchased annuities, I examine a final outcome in Table 17: whether respondents report having income from an annuity that lasts until death and stops payment then, which I refer

to as true annuity income. Panel A of Table 17 shows the reduced form impact of lnprice

on true annuity income. Figure 11, Panel C shows the visual reduced form. The point estimate of -0.04 is large relative to the main of 0.03, but it is imprecisely estimated. The cost of focussing on such a narrow measure of annuity income is that it likely introduces considerable measurement error, as people may miscategorize their retirement income while nonetheless recording the total amount correctly. While the point estimates remain roughly

9_{The reduced form estimate of}∂P r(1{Has annuity income})

∂lnprice btained from the linear probability models is very

constant once I control for permanent income in column (2), it is no longer statistically significant at traditional levels. Adding additional controls for health in column (3) and preferences in column (4) has little effect on the point estimate, and raises the reduced form coefficient to statistical significance. Across all specifications, the extensive margin elasticity of true annuity income with respect to Medigap coverage is about 0.87.

The results show a clear impact of Medigap coverage on both the extensive and intensive margin of annuity demand. While the instrument is uncorrelated with observed deter- minants of annuity demand, it might nonetheless be correlated with unobserved factors, including the price of annuities. To test for this possibility, Table 18 presents evidence from

a placebo test. This table shows the reduced form estimate of lnprice on annuity demand,

but the sample is modified: it contains only retirees with employer provided health insur-

ance. If the isntrument is valid, then for this sample, lnprice should have no effect on

medical expenditure risk, and hence the reduced form coefficient should be zero. If lnprice

is correlated with annuity prices or other unobserved determinants of annuity demand, how- ever, then even retirees with employer provided health insurance will appear to respond to

it. As the table shows, the coefficient on lnprice is statistically insignificant, much smaller

in magnitude than in the analysis sample, and, for two outcomes, wrong signed. Unfortu- nately the results are not precise enough for me to reject the hypothesis that the placebo point estimates are significantly different from the main point estimates. Nonetheless the

results suggest that if lnprice is correlated with unobserved determinants of annuity de-

mand, the correlation is not strong enough to generate the observed relationship between Medigap coverage and annuity demand.