Public Economics Lectures Taxes and Behavior: Savingscholz/Teaching_742/Behavior...Public Economics Lectures Taxes and Behavior: Saving John Karl Scholz University of Wisconsin ŒMadison

Public Economics LecturesTaxes and Behavior: Saving

John Karl Scholz

University of Wisconsin —MadisonFall 2011

JK Scholz ()Tax Incentives and Saving 1 / 32



Saving

Policymakers and others are concerned about saving.

Saving is thought to be virtuous: prudence, thrift and apple pie.Some like to use movements in this NIPA measure to make inferencesabout the quality of household balance sheets. But this is problematicbecause of asset revaluations.There is some evidence on a link between domestic saving andinvestment, despite the mobility of capital across borders.

IRAs have been a favorite policy response.

IRAs, Roth IRAs, education saving accounts, health saving accounts,IRA-like accounts have been suggested for UI

How would IRAs work? Intermediate micro (the 2-period "FisherianConsumption diagram" after Irving Fisher).


Measuring Saving

Two approaches: S = I − C or S = Wt −Wt−1 What’s thedifference?

Asset revaluations. I suspect (strongly) that much of the movement inthe NIPA saving measures are not driven by changes in the inherentthriftiness of Americans, but rather by changes in the value of housingor stock market portfolios.

With panel data on wealth components (which are available in someSCF years; the PSID, and the HRS), you can compute an "incomeminus consumption" measure of contributions in the following way(following G&S ’94).

Bal86 − Bal83(1+ r)3 = Con83(1+ r)2 + Con84(1+ r) + Con85

which implies Con = Bal86−Bal83(1+r )3(1+r )2+2+r


Why Read G&S ’94?

In its day, the paper received a good deal of attention. Venti andWise (1986, RES) suggested that IRAs were strikingly successful inpromoting household saving. IRAs were very popular. We felt theV&W approach was problematic, so we developed a project toexamine the effects of expanding IRA limits on household saving.

The specific details of the estimates are much less important 16 yearslater. But the paper remains (in my mind) a nice example of the valueof developing an economic model (in this case, a very simple one) toplace discipline on the analysis you are conducting.Hence, we will focus on the modelling of the problem and devote onlycursory attention to the actual estimation results.


Modelling IRAs

There are three essential characteristics of IRAs.

They offer a higher rate of return than other investments.There are contribution limits.There are early withdrawal penalties.

We need a model that captures the essential features of the issuebeing studied. There is no (or little) reason for additional detail thatclutters things up.

So... we need at least two assets (IRAs and other saving), uncertainty(otherwise early withdrawal penalties wouldn’t matter), and we can befully general with 3 periods.

Utility comes from the discounted value of consumption;R(I ) > R(O) > 1; IRA ≤ L; Y1,Y2,Y3 is labor income, Y3 = 0 anduncertainty is resolved prior to period 2.


The IRA problem

Optimization problem: (2)

max{S jI ,S j

O }Vj (Wj ) = U(Cj ) +

11+ρEj

{Vj+1(Wj+1)

}subject to borrowing constraints (3): S 1O ≥ 0, S

1I ≥ 0, S

2O ≥ S

1O R0,

S 2I ≥ −S1I

per-period budget constrains (4a): Yj = Cj + SjO + S

jI (1− t) if

S jI ≥ 0(4b): Yj = Cj + S

jO + S

jI if S jI < 0

evolution of resources available for C (5a): W1 = Y1(5b) W2 = Y2 + S

1O R0 + S

1I ; (5c)

W3 = S1O (R0)

2 + S 2O R0 + S1I (RI )

2 + S 2I RI if S2I ≥ 0

(5d) W3 = S1O (R0)

2 + S 2O R0 + S1I (RI )

2 + S 2I (RI )2 if S 2I < 0; (5e)

W4 = 0


The Model Captures the Essential Features of IRAs

IRAs in the model...

Offer a higher rate of return than other investments:R(I ) > R(O) > 1.There are contribution limits: IRA ≤ LThere are early withdrawal penalties (see above).

For early withdrawal penalties to matter, we need uncertainty. Threeperiod is enough to model the problem.


A further simplification.

To get an analytic (closed form) solution to the problem, we assumequadratic utility: U(Cj ) = −(k − Cj )2.

This is a simple dynamic programming problem. Starting in the lastperiod, the decision rule is simple: eat everything.In period 2, use the following portfolio rules (recall, uncertainty isresolved). The first $L of income or non-IRA saving should be placedin an IRA, with the remainder going in other saving. If low Y2 forcesdissaving, it should come out of other assets first.With these saving rules worked out, period 2 wealth can be calculatedin each of 3 scenarios: increase other saving, draw down other saving,or draw down other saving and first period IRA saving. We calculateoptimal consumption in each scenario and choose the C2 thatgenerates the highest overall utility.


Period 1

Period 1 is trickier.

Individuals like IRAs since they offer a higher return, but are worriedabout paying the early withdrawal penalty. We can write the period 1optimization problem as(B7): V1(W1) = −[k −W1 + S

1O + S

1I ]2−

11+ρE1

{[(1− q h1 )k − q

h2

{S 1O R0 +

S 1I R2I

Rh+ Y2 +Dh

}]2+ ∆

}where ∆ =11+ρ

[(1− q h1Rh)k − (Rh(1− q

h2 )

{S 1O R0 +

S 1I R2I

Rh+ Y2 +Dh

}]2The q and Rh terms are defined in the appendix to G&S.We’re choosing three things here: consumption, IRA saving and othersaving. We use the budget constraint to substitute out for C .


Period 1, continued

Maximizing (B7) with respect to IRA saving and other saving andmanipulating like crazy, we get.

(6): SO = α1k + α2W1 + α3 − α4SI andSI = β1k + β2W1 + β3 − β4SOwhere the α and βs are complicated functions of the underlying modelparameters (and expectations). Solving for S1O and S

1I gives

(7): SO = δ4k + δ5W1 + δ6 and SI = δ1k + δ2W1 + δ3 where δ′sdepend on the α′s and β′s


Incorporate IRA limits

Let desired IRA saving be S∗I = δ1k + δ2W1 + δ3

If no IRA contribution, SO comes from (6) and we have(8): SO = α1k + α2W1 + α3 and SI = 0 if S∗I ≤ 0(9): SO = δ4k + δ5W1 + δ6 and SI = S∗I = δ1k + δ2W1 + δ3 if0 < S∗I ≤ L(10): SO = α1k + α2W1 + α3 − α4L and SI = L if S∗I ≥ L

Equations (8)-(10) determine IRA and other saving, incorporatingcontribution limits, early withdrawal penalties and the tax preferencefor IRAs. We can manipulate further to rewrite equation (10).


Manipulate equation 10 (when households are at the IRAcontribution limit)

(10) SI = L and SO = α1k + α2W1 + α3 − α4L andL = δ1k + δ2W1 + δ3

This implies SO = α1k + α2W1 + α3 − α4 [δ1k + δ2W1 + δ3 ] but by(9) SO = δ4k + δ5W1 + δ6Use this to write all the α′s as δ′s and find(10) SO = δ4k + δ5W1 + δ6 + α4(δ1k + δ2W1 + δ3 − L)This implies (11): SO = δ4k + δ5W1 + δ6 + α4(S∗I − L) and SI = L


The model then is

(8): SO = α1k + α2W1 + α3 and SI = 0 if S∗I ≤ 0(9): SO = δ4k + δ5W1 + δ6 and SI = S∗I = δ1k + δ2W1 + δ3 if0 < S∗I ≤ L(11): SO = δ4k + δ5W1 + δ6 + α4(S∗I − L) and SI = L if S∗I ≥ L

α4 measures the effect of limit changes on non-IRA saving,dSOdL = −α4

α4 also measures the substitutability of IRA and non-IRA saving. α4close to 1 indicates a high degree of substitutability.

We can test whether heterogeneity matters by setting the coeffi cientsin (8) (for SO ) equal to the coeffi cients in (9) and (11)


An Empirical Version of the model

(8): SO = α1k + α2W1 + α3 and SI = 0 if S∗I ≤ 0(9): SO = δ4k + δ5W1 + δ6 and SI = S∗I = δ1k + δ2W1 + δ3 if0 < S∗I ≤ L(11): SO = δ4k + δ5W1 + δ6 + α4(S∗I − L) and SI = L if S∗I ≥ L


Our empirical work

We assume the errors are bivariate normal and estimate the model bymaximum likelihood.

The model takes a "random coeffi cients" form, as we make β, γ1 andγ2 a function of individual characteristics.

There are three branches to the likelihood function, corresponding toS∗I ≤ 0 and SO ; SI and SO as observed (this just uses the bivariatenormal density), and S∗I ≥ L and SO .

The two censored portions of the likelihood function are like a Tobitlikelihood, but in a bivariate normal setting.

We find a high degree of substitutability between IRA and non-IRAsaving — η is around (or above) 1.

Our estimates imply that increases in the IRA contribution limitsduring the "golden age" of IRAs (when there was universal eligibility)would have yielded no net national saving, once the tax losses to thegovernment were taken into account.


The changing landscape of tax incentives for saving

Since the "golden age" of IRAs ended (the period of universaleligibility), IRAs mainly serve as the "rollover" vehicle for other typesof pension plans.

Instead, 401(k)s (and their cousins, 403(b)s and 457 plans) are by farthe most important saving vehicle for most American households.

401(k)s are offered by the employer. They have much highercontribution limits than the IRA ($16,500 and an additional $5,500 ifyou are over 50).

Employers often match contributions (presumably to meetanti-discrimination rules). Match rates can be 100 percent or more.Employers will offer a menu of investment options and the employeemakes decisions about the investment allocation.401(k) plans are portable, meaning that after "vesting," the employeeowns the account and can roll it over into another account if theychange jobs.


Pensions are evolving

Traditional pensions were "defined benefit" (DB) plans.The WI state and federal governments have DB plans, as do manylarge companies (particularly those that are unionized).DB plans would pay benefits based on years of service, and somefunction of average or 3 highest years of salary.Employers bore the investment risk of DB plans, since they made a DBpension promise based on earned benefits.The PBGC would step in if companies were unable to meet theirpension obligations.There is an interesting literature on the incentive effects of DB pensionentitlements and labor contracts: were DB benefits backloaded in away that bound workers to specific firms?

401(k)s are the primary example of a "defined contribution" (DC)pension.

They are more portable than DB plans, which is a virtue for workerswho change jobs.Workers, not employers, bear the investment risk and workers mustmake investment decisions.


Issues in pension economics

We will briefly discuss two issues:

Individuals are responsible for their participation and management of401(k)s. Needless to say, "behavioral" issues arise.Bill Gale’s paper provides a nice discussion of issues that arise inthinking about DB pensions and household saving.

Surprisingly, however, there is no good model-based paper on theeffects of 401(k)s on household saving that, for example, mirrors theVenti-Wise, Gale-Scholz debates.

There are various reduced form and/or "natural experiment" papers on401(k)s and saving.But more formal (or model-based) work does not exist on the topic.It’s hard, but the omission is puzzling.


Madrian and Shea 2001: Defaults and Savings Behavior




Defaults matter on 401(k) contributions

Defaults affect participation:Participation rates in 401(k) plans are higher when the default is thatthe employee participates unless they opt out, compared to thetraditional case where employees are out, unless they opt in.

Defaults affect contribution rates conditional on participation.Households are much more likely to contribution at the default fractionof salary (and choose the default investment option) than they are tochoose other contribution levels and investment options.

Madrian and coauthors have an interesting recent paper that shows (Imay be slightly off in the details — I only heard the paper described...)

If defaults are really whacky, people will undo them. They have datafrom a company in the U.K. that matches contributions in excess of 12percent of salary (up to 18 percent).They default employees to 12 percent of salary in their 401(k). That’sa fairly high fraction of salary and people get no employer match.People fairly aggressively altered the default behavior (though not alldid). This suggests that people aren’t completely passive.


Work continues that emphasizes "behavioral" issues thatarise with pensions

What’s important to keep in mind in this literature, however, is thatparticipation in a 401(k) does not necessarily mean people are savingmore.

This summer I discussed a paper by Breshears, Choi, Laibson andMadrian.

The paper was about public sector workers: Are DC plansundesirable?

The authors note that people procrastinate, defaults matter, they chasepast returns, and under appreciate costs.But, they are portable, an individuals can exert control, and, becausethey shift risk, employers may be more likely than they otherwise wouldbe to offer pension arrangements.


Suboptimality and behavioral biases

It is not clear what aspect of "sub-optimality” that behavioral biaseslead to.

Do people behave precisely as we model them when we write down DPmodels? Surely not, but this is not a very interesting definition ofsub-optimality. The bigger question is whether people make mistakesthat have substantial consequences for lifetime wellbeing.We can’t focus on one margin. Dennis Rodman was a horrible offensiveplayer, yet he could end up in the basketball Hall of Fame. We havecolleagues who couldn’t teach a dog to roll over, but write amazingpapers. Puzzling pension choices can be offset by career choices,spouses, intergenerational transfers, or other consumption decisions.

I will have a lot of say about saving optimality later in the course!


This line of work

I am convinced that defaults matter, at least in the short run. Thalerand Sunstein ("Nudge") —paternalistic defaults are sensible, in myview.

It is less clear how much they matter.

Other issues when thinking about public pensions.

Governance issues strike me as being fundamental when thinking aboutpublic sector pension generosity. Legislators can promise benefits butdon’t bear the burden of financing them.“Anti-spiking”gets mentioned in the paper. I think it’s a really bigdeal:????There is a long-standing, interesting question about the relativecompensation of public and otherwise identical private sectoremployees.


Gale (1998) on pensions and saving

The issue about the effects of pensions on household wealth isinteresting. Pensions can be a substantial component of householdwealth. Any intertemporal optimization problem would suggest thatincreases in pension wealth should reduce accumulation innon-pension sources. But by how much?

Pensions are illiquid. Credit-constrained households would not offsetpension wealth.Pensions provide insurance against longevity — this should reducesaving by more than dollar-for-dollar, since they mitigate one reasonwhy households might engage in precautionary saving.Pensions may hasten earlier retirement. With longer periods out of thepaid labor market for longer periods, saving likely is higher than itotherwise would be.Lastly, many think that households are innumerate or live in a cognitivefog, so they perhaps might not recognize their pension entitlementsand hence they may have little effect on behavior.


A simple lifecycle problem

Gale writes a simple life-cycle problem (with no uncertainty)

(1) maxCtV =∫ T

0C 1−ρt1−ρ e

−δtdt + λ(∫ R0 Ete

−rtdt −∫ T0 Cte−rtdt +

∫ TR Bte−rtdt

)Work this problem out and you get(6) WA =∫ A0 Ete

−r (A−t)dt −Q[∫ R0 Ete

−r (A−t)dt]−Q

[∫ TR Bte−r (A−t)dt

]where Q = exS−1

exT−1 if x 6= 0 and q = S/T if x = 0

Here, think of S as age, T is lifespan, and x = r−δρ − r

The three terms in (6) are present value of earnings to date; the pdvof lifetime cash earnings, adjusted by "Q"; and the pdv of futurepension benefits, adjusted by "Q".


What’s going on here?

Equation (6) resembles the typical expressions that are estimated inthe (old) literature on pensions and wealth.

The first term is some measure of lifetime earnings to date and somemeasure of future pension benefits. Since Q is less than one, pensionbenefits offset wealth by less than dollar for dollar.Let me give a very simple example:

max{C0,C1,C2}

Vj (Wj ) = U(Cj ) + β{Vj+1(Wj+1)

}, s.t.

Yj = Cj + Sj ; W0 = Y0; W1 = Y1 + RS0; W2 = P + R2S0 + RS1;W3 = 0; and RS0 + S1 ≥ 0.If we assume β = R = 1 thenC0 = C1 = C2 =

Y0+Y1+P3


The simple example and equation six

The simple example then implies the following:

S0 = Y0 − C0 = 23Y0 −

13Y1 −

13P

Here in this simple case, divide pension wealth by 3 (meaning thatunder the given assumptions, households should increase period 0consumption by one-third the value of the period 2 pension).After adjusting pension wealth by the appropriate scaling factor, theoffset coeffi cient will again equal -1.0 in the certainty life-cycle model.


The empirical work

Gale implements these insights using a cross-sectional dataset onwealth, the 1983 Survey of Consumer Finances.

The data have a very nice "pension provider supplement," whichpermits unusually good measures of pension entitlements.The data have a lousy measure of lifetime earnings to date — this is acritical covariate in lifecycle models of optimal wealth accumulation.Many factors influence wealth accumulation and the wealth distributionis highly skewed (rightward). So Gale estimates median (least absolutedeviation) regression and a Stata-supplied "robust" regression.Quantile regression is common in the empirical literature on wealthaccumulation.He finds significantly larger estimates of pension offsets than did priorauthors. It is nevertheless heroic to try to infer the effects of pensionson wealth in a cross-sectional dataset.


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Public Economics Lectures Taxes and Behavior: Savingscholz/Teaching_742/Behavior...Public Economics Lectures Taxes and Behavior: Saving John Karl Scholz University of Wisconsin ŒMadison