1. Introduction
Public workers in the United States, including teachers, were not covered by Social Security when it was first introduced in the 1930s. Beginning in the 1950s, groups of public workers were permitted to opt into coverage if desired. In most states, teachers either remained uncovered or opted into coverage together. However, in several states school districts made individual choices, resulting in within-state variation in social security coverage across school districts. We leverage variation in one of these states – Texas – to estimate the incidence of social security taxes on teacher wages and employment.
Our interest in the incidence of social security taxes on teachers is motivated by policy proposals to enroll teachers in social security in states where they are not currently enrolled (Kan and Aldeman, Reference Kan and Aldeman2014; Gale et al., Reference Gale, Holmes and John2015; Koedel and Gassmann, Reference Koedel and Gassmann2018).Footnote 1 Proponents argue this would make teacher retirement compensation more equitable (Kan and Aldeman, Reference Kan and Aldeman2014). It would also diversify the risk in teachers' retirement portfolios, most notably because unlike retirement wealth in most state plans, social security is portable across occupations and states. Thus, expanding social security coverage among teachers would dampen the risks they face of occupational and geographic mobility. Teachers also face risk associated with the poor financial health of most state retirement plans; dual coverage in social security would help teachers diversify away from some of this risk as well (Gale et al., Reference Gale, Holmes and John2015).
In addition, proponents point to the strong association between the financial health of state retirement plans and social security coverage. Although causal inference is difficult, teacher retirement plans in states without dual social security coverage are in much worse financial condition than plans with dual coverage (Backes et al., Reference Backes, Goldhaber, Grout, Koedel, Ni, Podgursky and Brett Xiang2016).Footnote 2 A likely explanation is that in states without social security, the demands of providing for a full retirement exacerbate the influence of actuarial practices that lead to underfunding. Several aspects of actuarial practices are problematic, but the first-order issue is that public pension actuaries consistently understate future liabilities by discounting them at too high of a rate (Novy-Marx and Rauh, Reference Novy-Marx and Rauh2009; Brown et al., Reference Brown, Clark and Rauh2011). Plans in states without dual social security coverage tend to offer more generous pension benefits, amplifying this problem.Footnote 3 Beyond the risk borne by teachers due to the poor funding of state plans, districts and states are also at risk because underfunding can lead to higher long-term costs, reducing the level of resources available to provide government services (Melnicoe et al., Reference Melnicoe, Hahnel, Koedel and Ramanathan2019; Kim et al., Reference Kim, Koedel and Brett Xiang2021).
If states without social security coverage for teachers were to push for coverage, or if the federal government mandated it, tax incidence is an important consideration. We are not aware of any prior research on tax incidence in the teacher labor market specifically (for any tax), though two insights from the general literature suggest the incidence of social security taxes on teachers is likely high. First, tax incidence is higher for the more inelastic side of the market and labor supply is typically more inelastic than labor demand (Fullerton and Metcalf, Reference Fullerton, Metcalf, Auerbach and Feldstein2002). Second, social security taxes are linked to benefits at the individual level, and tax incidence on workers is higher when the tax corresponds to a directly linked benefit (Summers, Reference Summers1989).
However, these insights may not generalize to the teacher labor market, which has unique features and is highly non-competitive. For example, on the supply side, teaching is a licensed occupation and most states have stringent requirements. Occupational licensing restricts labor supply by increasing the cost of entry, which could give teachers more leverage in salary negotiations than typical workers in unlicensed occupations. Alternatively, on the demand side, a somewhat unique feature of the teacher labor market is that school district boundaries are non-overlapping. Noting that the private education sector in the United States is very small, this creates frictions in employment opportunities that may reduce teachers' negotiating power if, as research suggests, they have highly localized geographic employment preferences (Boyd et al., Reference Boyd, Lankford, Loeb and Wyckoff2005; Reininger, Reference Reininger2012). More broadly, the fact that school districts are non-competitive, publicly funded entities could lead to a different incidence outcome than in the private sector. Building on the logic of Glaeser and Ponzetto (Reference Glaeser and Ponzetto2014), one possibility is that if local voters are uninformed about social security costs and benefits, districts with coverage could pass all or part of the costs onto local taxpayers. The combined effect of these and other factors on the incidence of social security taxes in the teacher labor market is theoretically ambiguous, motivating our empirical investigation.
We estimate tax incidence on teacher salaries and staffing levels using an administrative data panel covering all public school teachers in Texas from 1996 to 2020. An analytic challenge we face is that like other covered public employers, most Texas school districts with social security coverage opted into coverage in the mid-20th century, prior to the availability of credible data on teacher wages and employment. Thus, we cannot exploit variation over time in social security coverage for identification and must rely on cross-sectional variation.
Working within this constraint, we begin by estimating the unconditional gap in take-home pay between teachers in covered and uncovered school districts. Teacher pay is about 5 percent lower in covered districts. After controlling for observable teacher and district characteristics, we estimate the conditional pay gap widens, to 9.6 percent. Taken at face value, the conditional gap implies teachers pay 77 percent of the 12.4-percent total social security tax in the form of lower wages. Moreover, the direction of observed sorting suggests this estimate is likely a lower bound. Using modern techniques to adjust for sorting on unobservables (Oster, Reference Oster2019), under reasonable assumptions we cannot rule out that teachers pay 100 percent of the total social security tax in the form of lower wages.
We also conduct a parallel investigation of tax incidence on teacher staffing levels. We find no evidence of incidence along this dimension. This result is consistent with research in other contexts showing that tax incidence on labor supply is primarily on wages, not employment, though there are some exceptions (see discussion below).
Our finding that teachers bear most or all of the cost of social security taxes makes expanding their enrollment in social security appealing from a fiscal perspective, especially if states can leverage social security to bolster the financial stability of their state retirement plans. The effect on teacher well-being is less certain and depends on how much teachers value social security benefits. The best evidence on this question comes from survey experiments conducted by Fuchsman et al. (Reference Fuchsman, McGee and Zamarro2023), who estimate teachers are willing to pay 10.7 percent of their salaries for social security coverage. This estimate is similar to what we estimate for teachers' tax incidence, suggesting the consequences for teacher well-being will be minimal, at least on average.
2. Brief review of previous research on payroll tax incidence
The incidence of payroll taxes in the larger labor market has been widely studied. Gruber (Reference Gruber1997) estimates tax incidence after a reform in Chile that privatized the public social security system, lowering the payroll tax. Wages went up by the same amount as the reduction in taxes, which is the expected result if tax incidence is fully on wages. Similarly, Anderson and Meyer (Reference Anderson and Meyer2000) study a policy in Washington state that changed firms' tax rates for unemployment insurance. They find that tax increases at the industry level were largely passed onto workers through lower earnings. Saez et al. (Reference Saez, Matsaganis and Tsakloglou2012) and Saez et al. (Reference Saez, Schoefer and Seim2019) study payroll tax increases and decreases, in Greece and Sweden respectively, concentrated on young workers. Saez et al. (Reference Saez, Schoefer and Seim2019) show that tax reductions are passed onto workers through higher wages overall – which is consistent with tax incidence falling on workers – but both studies show, somewhat unexpectedly, that the tax wedge between young and old workers does not translate into a gap in wages. Saez et al. (Reference Saez, Schoefer and Seim2019) offer as an explanation that firms are effectively operating under internal wage equity constraints, preventing them from passing on tax incidence differentially to different types of workers.
Bozio et al. (Reference Bozio, Breda and Grenet2019) study a series of tax reforms in France with the goal of isolating the role of linked benefits in driving tax incidence. The reforms in France also led to tax changes for different types of workers, this time based on income levels. For payroll taxes without linked benefits, Bozio et al. (Reference Bozio, Breda and Grenet2019) replicate the findings in Saez et al. (Reference Saez, Matsaganis and Tsakloglou2012, Reference Saez, Schoefer and Seim2019) that firms do not to differentiate tax incidence among workers. However, they find evidence of differential tax incidence when there is a clear tax–benefit linkage. They interpret their results as showing linked benefits are a key determinant of tax incidence at the individual level.Footnote 4
Most studies find workers collectively bear most or all of the incidence of payroll taxes, and do so in the form of lower wages, but there are exceptions. Examples include Bennmarker et al. (Reference Bennmarker, Mellander and Öckert2009) and Benzarti and Harju (Reference Benzarti and Harju2021), who study payroll tax cuts in Sweden and Finland, respectively. Both studies find the majority of the tax incidence is on firms. Of the incidence that does fall on workers, they also find evidence of incidence on employment, which is less common (in Benzarti and Harju (Reference Benzarti and Harju2021), incidence also fluctuates with the business cycle).
Despite some mixed findings, a reasonable prediction based on prior studies is that teachers are likely to bear the bulk of the incidence of US social security taxes, and to do so in the form of lower wages. This prediction is reinforced by evidence from Bozio et al. (Reference Bozio, Breda and Grenet2019) on the importance of linked benefits in determining tax incidence, as linked benefits are a key feature of social security. However, we are not aware of any prior teacher-specific research on tax incidence, or for that matter, any prior research focused on public workers, and the extent to which evidence from the private sector will generalize to the public sector is unclear.Footnote 5
3. Social security and retirement benefits in Texas public schools
Most but not all workers in the United States are covered by social security. Uncovered workers are concentrated primarily in state and local governments, including public schools (Quinby et al., Reference Quinby, Aubry and Munnell2020). Overall, about 40 percent of teachers in US schools lack social security coverage (Morrill and Westall, Reference Morrill and Westall2019; Aldeman, Reference Aldeman2019a). In most states, districts either all offer coverage (33 states) or are all uncovered (12 states). Texas is one of the just five states with mixed social security coverage across districts within a state. Figure 1 documents the national landscape of social security coverage among teachers.
State-level social security coverage in the United States for public school teachers.
Notes: Teachers in 33 states are covered by social security (fully shaded), teachers in 12 states and the District of Columbia do not have social security coverage (Aldeman, Reference Aldeman2019a), and there is mixed coverage of teachers across school districts in five states (partially shaded).
Figure 2 illustrates the variation in social security coverage across school districts in Texas. Teachers in 27 of the 1,059 Texas school districts – accounting for about 4.5 percent of the Texas teaching workforce – are covered. In raw numbers, Texas employs approximately 330,000 full-time equivalent (FTE) teachers, of which about 15,000 are in social security districts. Although districts with social security coverage employ only a small fraction of Texas teachers, owing to the state's large size, they are greater in number than the entire teaching workforce in several states (Snyder et al., Reference Snyder, de Brey and Dillow2019).Footnote 6 Figure 3 shows most districts in Texas that opted into social security did so in the 1950s and 1960s. Since 1996, which is the first year of our administrative data panel, just six districts opted into social security coverage.Footnote 7
District-level social security coverage in Texas for public school teachers.
Notes: Teachers in 27 school districts are covered by social security (shaded).
The Year of social security implementation.
Notes: The initial year of social security coverage is defined as the first school year with social security coverage.
Regardless of social security coverage, all teachers in Texas public schools participate in the same state pension plan: the Teacher Retirement System of Texas (TRS). Teachers in districts covered by social security receive retirement benefits from both social security and TRS, and teachers in uncovered districts receive benefits from TRS only. TRS requires the employer to contribute 8.3 percent and teachers to contribute 7.7 percent of teacher salaries, for a total contribution rate to the retirement plan of 16 percent. For teachers in social security districts, employers and employees additionally (and evenly) split the 12.4 percent total social security tax.Footnote 8
Our ability to observe teachers with the same state pension coverage, but who differ by social security coverage, is an important advantage of our setting. In contrast, cross-state comparisons are difficult because state pension plans have evolved differently in states with and without social security. For example, a typical teacher's replacement rate from their state pension plan is about 10 percentage points higher in states without social security coverage (Clark and Craig, Reference Clark and Craig2011). Plans in uncovered states also have considerably more debt (Backes et al., Reference Backes, Goldhaber, Grout, Koedel, Ni, Podgursky and Brett Xiang2016). The incidence of both of these (i.e., state-plan benefit costs and debt servicing costs) on teachers is unclear and can confound inference about the incidence of social security taxes in cross-state studies. Our analysis within Texas holds these important aspects of pension costs fixed among teachers with and without social security coverage.
4. Data
Our analysis is based on a teacher-level administrative data panel from the Public Education Information Management System (PEIMS) managed by the Texas Education Agency. The PEIMS data cover all teachers in Texas public schools and include information on teacher age, gender, race/ethnicity, school and district of employment, years of experience, highest education level, base pay, and total pay (inclusive of supplemental pay). We merge in district characteristics including district size and urbanicity, student demographics, local revenue, total revenue, pupil–teacher ratios, and benefit costs for instructional employees, from the Common Core of Data published by the US Department of Education.
Table 1 provides summary statistics for our data panel, which spans the years 1996–2020 (we use the spring year to denote the school year – e.g., 1995–96 as 1996). All dollar figures are in 2020 dollars. Net of their direct social security taxes (i.e., the 6.2% of salaries taken out of worker pay), Table 1 shows teachers in social security districts earn $53,664 per year in total salary, on average, over the course of our data panel, which is just over 5 percent lower than the average in non-social security districts. In addition to the salary difference, teachers in covered districts are more likely to have a graduate degree (26.5% versus 23.4%) and more likely to be Hispanic (41% versus 20.7%), which is the predominant minority group in Texas. District characteristics, which are teacher-weighted in the table, also vary considerably by social security coverage. Teaching positions in covered districts are more likely to be in traditional (non-charter) districts in urban areas, with higher enrollments, higher per-pupil revenues, more English Language Learners (ELL), more students enrolled in free and reduced-price lunch programs, and more Hispanic students.
Summary statistics: teacher and district characteristics
Notes: SS = Social Security. Salaries and revenues are expressed in 2020 dollars. Data on ELL rates are unavailable for TX school districts in the Common Core of Data prior to 1999; for the three years prior (1996–98), we impute districts' ELL rates to the first observed value in 1999.
1 All salary values are net of employee social security payments (i.e., 6.2%) when applicable. Total salary is equal to base salary plus supplemental pay.
The differences by coverage status in Table 1 – and other differences they may imply along unobserved dimensions – are potential confounders in our efforts to estimate the incidence of social security taxes. To gain insight into how these differences are likely to affect our analysis, we estimate several versions of the following linear regression:
In the equation, SS idt is an indicator equal to one if teacher i in district d and year t is covered by social security, and zero otherwise. The vectors X idt and Z dt include the teacher and district characteristics listed in Table 1, respectively. For teacher age and experience, we include linear and quadratic terms. λ t is a year fixed effect and η idt is the error term, which we cluster at two levels: by district and by the year of entry into the Texas teaching workforce.Footnote 9 We estimate a version of equation (1) that omits Z dt, then a version that omits X idt, then the full version as shown. The results are provided in Table 2.
Observable differences by Social Security coverage
Notes: We divide all experience variables by 1,000 to illuminate the values of very small coefficients. Standard errors are two-way clustered by district and TRS entry year.
***p < 0.01, **p < 0.05, *p < 0.1.
The first takeaway from Table 2 is that conditional on district characteristics, there is no evidence of observed differences between teachers with and without social security coverage. In column (1), before we condition on district characteristics, teacher experience is the only characteristic that is a significant predictor of social security status. In column (3), after we add district characteristics, none of teacher characteristics are significant. Moreover, the model R 2 is essentially unchanged going from column (2), which includes only district characteristics, to column (3), which includes both district and teacher characteristics (it increases by just 0.0012).
In contrast, district characteristics explain about 9 percent of the total variation in social security coverage across teachers. Many of the district characteristics are highly correlated with each other, making inference from the individual regression coefficients in Table 2 difficult. But reviewing the evidence in Tables 1 and 2 holistically, teaching positions with social security coverage are more likely to be in districts that are larger, urban, have more revenue, and serve more disadvantaged student populations. These observed differences also raise concerns about unobserved differences, which we address below.Footnote 10
5. Empirical strategy
5.1 Main specifications
We begin with the following linear regression of teacher salaries on social security coverage and teacher and district characteristics:
In equation (2), Y idt is the salary for teacher i in district d and year t, net of the 6.2 percent employee social security tax for teachers in covered districts (i.e., we multiply gross salaries for covered teachers by 0.938).Footnote 11 The other terms in equation (2) are as defined in equation (1) (although we remove the i subscript on social security coverage because it does not vary across teachers within district-years). The parameter of interest in equation (2) is β 1, which indicates the incidence of social security taxes on wages.
When we subtract the social security employee tax from the dependent variable prior to estimation, we impose a variant of what Zoutman et al. (Reference Zoutman, Gavrilova and Hopland2018) dub the ‘Ramsey Exclusion Restriction’. This is important so that we do not misattribute the employee tax as take-home pay. Note, however, this does not make any assumption about the incidence of the employee tax – it is merely an accounting tool. For example, our model still allows districts to pay all or part of the employee tax by raising teacher pay, in which case the net-of-tax salaries in social security districts would rise to reflect this, putting positive pressure on β 1.
Equation (2) models tax incidence on wages, where prior research suggests it is most likely concentrated. We also test for incidence on staffing levels using a district-level model of the pupil–teacher ratio. The model is specified similarly to equation (2) but uses the district pupil–teacher ratio as the dependent variable and collapses the data to the district-year level as follows:
In equation (3), R dt is the pupil–teacher ratio for district d in year t, $\bar{X}_{dt}$
includes district-average teacher characteristics, and the other terms are as defined above.
Equations (2) and (3) will allow us to recover unbiased estimates of tax incidence if the differences between teachers with and without social security coverage are along observed dimensions only, and if the provision of other benefits is independent of social security coverage. While possible, this identification condition seems unlikely. Our evaluation setting mitigates what is arguably the biggest threat in terms of correlated benefits because all teachers in our sample share a common state pension plan. This prevents districts from offsetting their social security expenditures by reducing other employer-provided retirement benefits. However, other benefits – most notably health benefits, which combined with retirement benefits constitute the vast majority of benefit costs for teachers (Bruno, Reference Bruno2019; Aldeman, Reference Aldeman2019b) – could be problematic. In addition to the possibility of correlated benefits, a myriad of other unobservables could potentially affect our estimates.
We explore the potential for bias in our estimates in two ways. First, we test directly for correlated benefit costs by estimating a district-level regression specified similarly to equation (3), but where the dependent variable is the district ratio of total benefit costs to gross salaries. If social security coverage is independent of other employer benefit costs, then it should correspond to an increase in total benefit costs of 6.2 percent of gross salaries (i.e., the employer share of the social security tax). A value above 6.2 percent would imply coverage reflects a general proclivity of social security districts to offer benefit-heavy compensation packages, which would bias our estimate of β 1 in equation (2) negatively, and/or γ 1 in equation (3) positively (assuming other benefit costs have at least some incidence on workers). Alternatively, a value below 6.2 percent would imply social security coverage substitutes for other costly employee benefits and cause bias in the other direction.
Second, and more broadly, we follow the approach of Oster (Reference Oster2019) to provide a bounded estimate of tax incidence under assumptions about bias from unobserved differences between districts (and teachers) that differ by social security status. The intuition behind Oster's approach is that differences along observed and unobserved dimensions likely cause bias in the same direction (also see Altonji et al., Reference Altonji, Elder and Taber2005). With knowledge of (1) the direction of bias caused by observed differences and (2) the explanatory power of observables over outcomes, both of which can be estimated, and by making assumptions about (3) the relative magnitudes of observed and unobserved differences and (4) the explanatory power of unobservables over outcomes, one can estimate and adjust for the impact of unobservables. Formally, Oster (Reference Oster2019) proposes that a parameter adjusted for bias from unobservables can be recovered from an ordinary least squares (OLS) estimate that conditions on observables as follows:
In equation (4), β* is the bias-adjusted estimate of the parameter of interest. Four of the parameters on the right-hand side of the equation are directly estimable: $\tilde{\beta }$
is the estimate from an OLS model with full controls for observables, $\dot{\beta }$
is the estimate from a sparse OLS model with no controls (i.e., the model includes just an intercept and the parameter of interest, which in our case is an indicator for social security coverage), and $\tilde{R}$
and $\dot{R}$
are the R 2 values from these models, respectively. δ and R max are unknown and must be parameterized by the researcher. Oster (Reference Oster2019) describes δ as the ‘coefficient of proportionality’ – it is the ratio of the magnitude of unobserved to observed selection. R max is the total explanatory power of observables and unobservables over the outcome. The maximum value of R max is 1.0, but for most outcomes the feasible value is less than 1.0.Footnote 12
For our preferred bounding exercise we set δ = 1.0, or in words, we parameterize the magnitudes of selection on observables and unobservables to be the same. This is a common parameterization in the use of this and related methods in the literature (also see Altonji et al., Reference Altonji, Elder and Taber2005). We set $R_{\max } = \tilde{R} + ( \tilde{R}-\dot{R})$
, or in words, we assume unobservables explain as much of the outcome variation as observables. Given the rich observable information available about teachers and districts in our dataset, this parameterization allows for a substantial role of unobservables in influencing our tax-incidence estimates. We also show results under alternative parameterizations of δ and R max.
6. Results
6.1 Main results
Table 3 shows estimates from several versions of equation (2) where we use total teacher salary as the dependent variable.Footnote 13 In presenting the results, the conventional approach would be to denote statistical significance under the null hypothesis that tax incidence is zero. However, this seems unlikely. Because the expected incidence in our setting is uncertain, we instead simply report our point estimates and 95 percent confidence intervals. We construct the confidence intervals based on our two-way clustered standard errors throughout.
Incidence of Social Security taxes on total salary
Notes: The teacher and district characteristics included in the models are as shown in Table 2. Coefficients for controls are reported in Appendix Table A3. The 95% confidence intervals reported in brackets below the coefficient estimates are calculated using two-way clustered standard errors by district and TRS entry year.
Column (1) of Table 3 shows that unconditionally, teachers covered by social security have salaries that are 5 percent lower than their uncovered counterparts, on average, net of their own social security contributions. This matches the descriptive statistics in Table 1. Column (2) shows this point estimate changes very little if we condition on observable teacher characteristics, which is notable because teacher characteristics (primarily experience) explain about 33 percent of the variation in teacher salaries. The stability of the incidence parameter reflects the lack of selection on observables at the teacher level. Columns (3) and (4) add district characteristics, in isolation in column (3), and in addition to the teacher characteristics in column (4). While district characteristics explain much less of the variation in teacher salaries, their inclusion in the model has a more significant impact on our estimate of the incidence parameter – in total, it increases in magnitude by 94 percent from column (1) to column (4). The point estimate from the full model indicates teachers covered by social security earn 9.6 percent less than uncovered teachers, conditional on observables. Taken at face value, this implies covered teachers pay 77 percent of the total social security tax in the form of lower wages.Footnote 14
In Table 4 we conduct a parallel investigation of tax incidence on staffing levels using equation (3).Footnote 15 The district data are weighted by the teacher sample size to maintain comparability with the teacher-level results in Table 3 (results from unweighted analogs to the weighted regressions are similar and reported in Appendix Table A4). In the full model in column (4), the conditional difference in the pupil–teacher ratio between covered and uncovered districts is just 0.07. This point estimate is very small, corresponding to just 0.5 percent of the sample-average pupil–teacher ratio of 15, and the 95 percent confidence interval comfortably includes zero. This result gives no indication of tax incidence on teacher staffing levels.
Incidence of Social Security taxes on the pupil–teacher ratio
Notes: The district-level models are weighted by number of teachers. The teacher and district characteristics included in the models are as shown in Table 2. The mean value of the pupil–teacher ratio (the dependent variable) is 15.0. We calculate the pupil–teacher ratios using the Common Core of Data based on student enrollment and the number of FTE teachers. These data are available in the Common Core for 99.7% of the district-years represented in the Texas administrative data. The small number of district-years with missing data are dropped from this portion of our analysis. The 95% confidence intervals reported in brackets below the coefficient estimates are calculated using clustered standard errors by district.
6.2 Bias and robustness
In Table 5 we test for potential bias in our estimates due to the presence of correlated benefits. We estimate versions of equation (3) at the district level that use as the dependent variable the ratio of total employer benefit costs to total salaries.Footnote 16 The employer social security tax is 6.2 percent of salary; if other benefits are correlated with social security benefits, we would expect the coefficient on social security coverage to differ from 6.2 percent. Importantly, and unlike in our preceding models, we do not net out the employee social security tax from total salaries in the denominator of the dependent variable for this test. The reason is that we are no longer testing for tax incidence; rather, this supplementary regression is designed to test whether social security coverage is correlated with other employer benefit costs. The 6.2-percent social security tax on employers is levied on gross salaries, so in order for our model to be informative for this test, we must use gross salaries in the denominator of the dependent variable.
Impact of Social Security coverage on the ratio of districts' total benefit costs to total salaries for instructional employees
Notes: The district-level models are weighted by number of teachers. Total benefit costs and instructional salaries are available in the Common Core for 95.9% of the district-years represented in the Texas administrative data. The small number of district-years with missing data are dropped from this portion of our analysis. The teacher and district characteristics included in the models are as shown in Table 2. The 95% confidence intervals reported in brackets below the coefficient estimates are calculated using clustered standard errors by district.
Column (1) of Table 5 shows that unconditionally, benefit costs as a percent of gross salaries are 6.1 percent higher in social security districts. Conditional on observables, this estimate attenuates to 5.1 percent in column (4). Throughout the table, our confidence intervals cannot rule out that social security coverage corresponds to a 6.2 percent of salary increase in total benefit costs. Thus, we cannot reject the null hypothesis that social security coverage is independent of other employer-provided benefits. We interpret this result as ruling out correlated benefits as a source of (meaningful) bias in our estimates of tax incidence.
Noting that this is our preferred interpretation, we can also ignore statistical significance in Table 5 and take the point estimates at face value. Given that they are below 6.2 percent, this would imply social security and other employer-provided benefits are weak substitutes. We believe this interpretation is a stretch given the confidence intervals around our estimates in Table 5, but if true, it would suggest our estimates of tax incidence in Table 3 are biased positively (i.e., toward zero) as long as other benefit costs have at least some incidence on wages. That is, it would imply the true magnitude of the incidence parameters in Table 3 are understated due to correlated benefits.
Next, in Tables 6 and 7 we show incidence estimates for wages and employment, respectively, after we adjust for unobservables following Oster (Reference Oster2019). To reflect the uncertainty inherent to this adjustment, we present a range of adjusted values over different parameterizations of δ and R max. Our preferred parameterizations of δ = 1.0 and $R_{\max } = \tilde{R} + ( \tilde{R}-\dot{R})$
are in bold.
Estimates of Social Security tax incidence on total salaries allowing for sorting into Social Security coverage on unobservables
Notes: The adjustment is following Oster (Reference Oster2019) as described in equation (4). The parameters reported in the first horizontal panel inform the adjustment. The values in the lower table are the adjusted incidence estimates. The symbols in parenthesis identify the parameters used in the adjustment procedure as denoted in equation (4). The bolded entry is for our preferred adjustment.
Estimates of Social Security tax incidence on the pupil–teacher ratio allowing for sorting into Social Security coverage on unobservables
Notes: The adjustment is following Oster (Reference Oster2019) as described in equation (4). The parameters reported in the first horizontal panel inform the adjustment. The values in the lower table are the adjusted incidence estimates. The symbols in parenthesis identify the parameters used in the adjustment procedure as denoted in equation (4). The mean value of the pupil–teacher ratio (the dependent variable) is 15. The bolded entry is for our preferred adjustment.
We begin with our wage estimate in Table 6. The pattern of results in Table 3 indicates the direction of observed sorting into social security with respect to wages is positive and accordingly, the Oster (Reference Oster2019) adjustment for bias from unobservables increases the magnitude of our tax-incidence estimate. Using our preferred parameterization, the adjusted social security coefficient in Table 6 is −0.142, implying wage incidence above 100 percent of the total social security tax. While it is theoretically possible for tax incidence to exceed 100 percent (e.g., if workers value the benefits above the cost), we suspect this high number is more likely the product of our liberal parameterization of δ and R max. Use of smaller values for δ and R max yields smaller incidence estimates. In what we view as a conservative parameterization, where δ and R max are both set to 0.50, we estimate the tax incidence on teacher wages is 10.2 percent.
In Table 7, the adjustments for bias from unobservables have no substantive impact on our estimate of the tax incidence on staffing levels. (Note that in our staffing models, observables explain more than 50 percent of the variation in the outcome. Thus, in Table 7 we present adjusted estimates over a restricted range of R max values.)
Under the assumption that any bias from unobservables is in the same direction as observables, our estimates from the full models in Tables 3 and 4 are lower bounds on the tax incidence of social security. Incorporating our preferred adjustment based on Oster (Reference Oster2019) and focusing on wages – where our analysis suggests the incidence is concentrated – a reasonable range of tax-incidence estimates is between 77 and 100 percent. However, it is also possible that bias from sorting on unobservables is in the opposite direction of observed sorting. While this is an uncommon assumption, it could happen in our context if teachers who select into employment in social security districts value social security coverage more than other teachers, in which case their willingness-to-pay would be higher than in the full population. These teachers would accept lower wages to work in covered districts, causing negative bias in our estimate of the incidence parameter – that is, leading it to be overestimated in our sample relative to a global coverage policy.
While we cannot rule out this possibility with certainty, we believe it is unlikely. One reason is that there is no evidence that social security coverage, or retirement benefits in general, are a first-order concern among teachers when they select where to work (Boyd et al., Reference Boyd, Lankford, Loeb and Wyckoff2005; Horng, Reference Horng2009; Reininger, Reference Reininger2012; Fuchsman et al., Reference Fuchsman, McGee and Zamarro2023). This is especially likely to be true for young teachers, who prior research suggests will place less value on their retirement benefits compared to older teachers, and who are less knowledgeable about retirement (French and Jones, Reference French and Jones2012; Quinby, Reference Quinby2020). In fact, among US teachers with zero to –nine years of experience, Fuchsman et al. (Reference Fuchsman, McGee and Zamarro2024) find that over 20 percent do not correctly answer a basic question about whether they have social security coverage.
If social security is more important to older teachers, we would expect to see older teachers systematically sort into social security districts, but there is no evidence of this type of sorting in our data (per Table 2). It is also possible that districts could respond. One way covered districts could respond is by flattening their salary schedules – that is, raising relative pay for younger teachers and lowering it for older teachers – compared to uncovered districts, reflecting differential teacher preferences for social security. This suggests a testable implication: the wage gap between teachers in covered and uncovered districts will be largest among older and more experienced teachers, and smallest among younger teachers. We test for this possibility in Table 8 by estimating tax incidence separately for teachers with less than five years of experience and more than 15 years of experience. The results in the first two columns of the table give no indication that incidence is lower among inexperienced teachers or higher among experienced teachers.Footnote 17
Robustness: incidence of Social Security taxes on total salary
Notes: The teacher and district characteristics included in the models are as shown in Table 2. The 95% confidence intervals reported in brackets below the coefficient estimates are calculated using two-way clustered standard errors by district and TRS entry year.
We also impose restrictions on the teacher sample to minimize the potential for endogenous sorting during the career. First, in column (3) of Table 8, we restrict the sample to teachers who do not change social security status during our data panel. Next, in column (4), we restrict the sample to teachers who do not change districts during our data panel at all. The restricted mobility of teachers in these samples reduces the potential for endogenous sorting into social security coverage, but our findings are similar regardless of whether we use the full teacher sample or either of the restricted subsamples.Footnote 18
Finally, we explore the potentially confounding effect of a reform to the TRS passed in 2005. Several rules changed after the reform, the most notable of which is that the career length required to be eligible for full TRS retirement benefits increased. There is no clear theoretical expectation for how this reform would affect social security tax incidence, but to test for any potential impact, we estimate models separately for teachers subject to the pre- and post-reform TRS rules (i.e., grandfathered into the old rules, or subject to the new rules). The results, reported in Appendix Table A5, show tax incidence is substantively similar for both groups.
7. Conclusion
We study the incidence of social security taxes on public school teachers in Texas, which is one of the five of states where there is cross-district variation in social security coverage. At what is likely a lower bound, we estimate the incidence of total social security taxes on teacher wages is 77 percent. Under reasonable assumptions about sorting on unobservables, we cannot rule out incidence on wages of 100 percent. We find no evidence of tax incidence on teacher staffing levels using the same methods.Footnote 19
To the best of our knowledge, we are the first to estimate social security tax incidence exclusively for workers in the public sector. Prior studies either exclude public workers, or analyze them in combination with private workers, who are much more common and disproportionately drive the estimates. Our findings for teachers are consistent with most of the literature on tax incidence in the private sector – namely, tax incidence is primarily concentrated on the supply side of the labor market, and on wages specifically. Among other things, this suggests local government agencies (in our case, school districts) are unable to offset the cost of providing social security benefits by raising additional local revenue.
Our findings help to inform policy proposals to enroll teachers in social security in states where they currently lack coverage (Kan and Aldeman, Reference Kan and Aldeman2014; Gale et al., Reference Gale, Holmes and John2015; Koedel and Gassmann, Reference Koedel and Gassmann2018). We find no evidence to suggest the additional social security taxes would lead to changes in teacher staffing levels. Moreover, combining our wage-incidence estimates with evidence from Fuchsman et al. (Reference Fuchsman, McGee and Zamarro2023) – who use survey experiments to estimate that teachers value social security coverage at about 10.7 percent of salary – suggests teachers will be roughly indifferent to social security enrollment. In other words, their tax incidence would be comparable to their valuation of benefits, on average. We conclude that policy proposals to enroll teachers in social security seem promising if states can leverage this to improve the fiscal health of their retirement plans.
Acknowledgments
The authors gratefully acknowledge research support from a Social Sciences Grant from the University of Texas at Dallas. The views expressed here are those of the authors and should not be attributed to their institutions, data providers, or the funders. Any errors are attributable to the authors.
Appendix A
Placebo test: estimated incidence of Social Security taxes on total and base salary when Social Security coverage is falsely coded in school districts adjacent to districts with actual Social Security coverage
Incidence of Social Security taxes on the pupil–teacher ratio, unweighted (analog to Table 4 in the main text)
Heterogeneity: incidence of Social Security taxes on total and base salary
Permutation test: distribution of coefficients with random assignment of Social Security coverage status to school districts.
Notes: This figure shows results from a permutation test where we drop all districts with social security coverage, then in the remaining sample, randomly assign the same number of districts to false social security coverage 1,000 times. At each iteration we estimate the effect of false social security coverage. The histogram shows the distribution of estimates. The dashed vertical line marks the incidence parameter estimated using the real data.
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