Welfare Implications of Uncertain Social Security Reform

Abstract

Policy uncertainty is a type of aggregate risk that has important economic and welfare implications. In this article, I develop a simple general equilibrium overlapping generations model in which households are uncertain as to the type and timing of an inevitable Social Security reform. I document how households’ expectations over the path of future policy influences their behavior. I find that the economic and welfare effects of policy uncertainty are highly sensitive to households’ beliefs over the path of future policy.

Keywords

policy uncertainty welfare analysis Social Security reform household beliefs

The Social Security Administration’s Old Age and Survivors Insurance (OASI) trust fund is projected to be depleted by 2032 under current law (Congressional Budget Office 2019). A 2018 study found that while over 90 percent of prime-aged individuals are aware of the projected actuarial shortfall, their expectations over what will happen to the OASI program vary significantly (Luttmer and Samwick 2018).¹ Documenting and understanding the effects of policy uncertainty—and specifically policy uncertainty surrounding pension reform—has been a growing body of literature.² However, until recently, little work has been done on this issue within a general equilibrium overlapping generations (OLG) model framework. This is because policy uncertainty is a type of aggregate risk and as a result adding it to structural general equilibrium models can quickly become computationally costly or intractable.

In this article, I develop a simple three-period general equilibrium OLG model to investigate the economic and welfare implications of policy uncertainty surrounding Social Security reform. Specifically, I examine how those effects are influenced by households’ beliefs over potential policy outcomes. I consider two possible timings of reform (early or late) and two possible reform types (tax increase or benefits cut). These policy options combine to make four distinct reforms: (1) early tax increase, (2) late tax increase, (3) early benefits cut, and (4) late benefits cut. I parameterize the model to the US economy and allow households to have subjective beliefs over the four potential reforms. This approach minimizes the computational cost of adding aggregate risk to an OLG model and allows for the analysis to be done across a large set of household beliefs. I find that the economic and welfare effects of policy uncertainty are highly sensitive to households’ beliefs in both the type and timing dimensions of the reform.

A few papers have studied the economic and welfare effects of policy uncertainty through empirical exercises and partial equilibrium life cycle models. This article extends this literature to a tractable general equilibrium setting. In Luttmer and Samwick’s survey, households were willing to forgo 6 percent of their currently promised Social Security benefits to live in a world absent Social Security benefit uncertainty. Dusek (2007) found that the welfare cost of risk related to the Social Security system in the Czech Republic could amount to 1 percent of lifetime consumption. Bütler (1999) found that uncertainty over the timing of a Social Security reform could significantly affect the macroeconomy. Gomes, Kotlikoff, and Viceira (2012) found that a failure to alleviate uncertainty over future Social Security benefits could yield welfare costs of 0.6 percent of annual consumption. Using a continuous time partial equilibrium model, Caliendo, Gorry, and Slavov (2019) evaluated Social Security reform uncertainty in both the type and timing dimension. They found that the welfare cost of uncertainty is generally less than 0.1 percent of lifetime consumption when households save optimally; however, the effect can be much larger among households who do not save.³

Kitao (2018) is the only paper of which I am aware that quantifies the welfare implications of policy uncertainty surrounding Social Security reform in a large-scale general equilibrium OLG model. Her model is calibrated to the Japanese economy and focuses on three different timings of a reform that consists of both a cut in benefits and an increase in the tax on consumption. This contrasts with the clearly delineated reforms studied in this paper, which allows for a comparison across policy types and a disentangling of their impact on household behavior and welfare. Both Kitao and this paper find that the general equilibrium channel plays an important role in determining the welfare effects of policy uncertainty. However, the papers diverge in how they treat households’ beliefs over potential reforms. In Kitao’s paper, households assume each potential reform is equally likely. Under that assumption, she finds that the welfare implications vary substantially across generations, ranging from −3.4 percent to +3.1 percent of lifetime consumption. In this article, I find that the quantitative—and in some cases qualitative—effects of policy uncertainty on household welfare within a given generation are not robust to changes in households’ subjective beliefs over reforms. For example, the ex post welfare implications of policy uncertainty among the future young generation ranges from −1.2 percent to +1.5 percent of lifetime consumption. This finding suggests that any future research attempting to quantify the effects of policy uncertainty using a structural general equilibrium framework must either empirically pin down or otherwise discipline household beliefs. One potential avenue for future research may be to follow the recent advancements made in Cottle Hunt (2018) whereby households use adaptive learning to update their beliefs about economic aggregates.

Furthermore, I find that the introduction of a positive measure of hand-to-mouth (HtM) households into the model economy partially mitigates the welfare implications of uncertainty among those households that save optimally (non-HtM households). This occurs because the presence of HtM households reduces the sensitivity of market clearing prices to household uncertainty. Consistent with Caliendo, Gorry, and Slavov (2019), I find that the welfare implications for those households that do not save are larger in magnitude relative to non-HtM households. I extend their finding by extending it to a general equilibrium framework and documenting the result’s sensitivity to household beliefs. For example, the welfare cost attributable to a young HtM household’s innate risk aversion ranges from −2.15 percent to 0.01 percent of lifetime consumption. Finally, this is the first paper to document the spillover effect between the presence of HtM households and the welfare implications of policy uncertainty felt by non-HtM households via the general equilibrium channel.

The remainder of the article is organized as follows: the Model section formally introduces the model, defines the competitive equilibrium in a perfect foresight economy, and discusses the model’s parameterization. The Macroeconomic Analysis section discusses how the four reforms studied in this article affect the macroeconomy along the transition path and in the model’s terminal steady states. I also show how the economic effects of the policy options differ once policy uncertainty and HtM households are added to the model. The Perfect Foresight Preferences section outlines how households rank the four reforms in accordance with their preferences along the transition path in a perfect foresight economy. The Welfare Analysis section computes the welfare implications of policy uncertainty using three welfare metrics and over a large set of household beliefs. The Concluding Remarks section contains a final discussion of the results.

Model

The model is a closed economy populated with OLG. Each generation consists of two types of households—HtM and non-HtM—each comprising a fixed proportion of the population, $ϕ$ and $(1 - ϕ)$ , respectively. Each household has a certain lifespan of three periods. Households consume and supply their labor elastically in the first two periods of life and retire exogenously in the third period. Firms are perfectly competitive, and the government’s sole purpose in the model is to operate a Social Security pension system.

Households

Every household in each generation is born with zero capital stock and is endowed with one unit of time in each period to be divided between labor and leisure. Households born in period t have time-separable preferences over consumption and leisure, ${c_{t + j}^{t}, l_{t + j}^{t}}_{j = 0}^{2}$ , and a subjective time discount factor $β$ .

A young non-HtM household born into generation t faces the following problem:⁴

max_{{c_{j}^{t}, l_{j}^{t}, k_{j + 1}^{t}}_{j = t}^{t + 2}} E_{t} [\sum_{j = t}^{t + 2} β^{j - t} u (c_{j}^{t}, l_{j}^{t})],

subject to:

c_{t}^{t} + k_{t + 1}^{t} = w_{t} (1 - τ_{t}) (1 - l_{t}^{t}),

c_{t + 1}^{t} + k_{t + 2}^{t} = w_{t + 1} (1 - τ_{t + 1}) (1 - l_{t + 1}^{t}) + R_{t + 1} k_{t + 1}^{t},

c_{t + 2}^{t} = B_{t + 2} e^{t} + R_{t + 2} k_{t + 2}^{t},

e^{t} = \frac{w_{t} (1 - l_{t}^{t}) + w_{t + 1} (1 - l_{t + 1}^{t})}{2},

k_{t + j}^{t} \geq 0 \forall j \in {0, 1, 2} .

A proportion of the population, $ϕ$ , are HtM and must consume their income in each period of life. HtM households optimize over their labor choice which affects their Social Security benefits in retirement. The HtM households’ problem is:

max_{{{\hat{c}}_{j}^{t}, {\hat{l}}_{j}^{t}}_{j = t}^{t + 2}} E_{t} [\sum_{j = t}^{t + 2} β^{j - t} u ({\hat{c}}_{j}^{t}, {\hat{l}}_{j}^{t})],

subject to:

{\hat{c}}_{t}^{t} = w_{t} (1 - τ_{t}) (1 - {\hat{l}}_{t}^{t}),

{\hat{c}}_{t + 1}^{t} = w_{t + 1} (1 - τ_{t + 1}) (1 - {\hat{l}}_{t + 1}^{t}),

{\hat{c}}_{t + 2}^{t} = B_{t + 2} e^{t},

e^{t} = \frac{w_{t} (1 - {\hat{l}}_{t}^{t}) + w_{t + 1} (1 - {\hat{l}}_{t + 1}^{t})}{2} .

Firms

Firms are perfectly competitive, hire labor from households at rate w_t , rent households’ capital at rate r_t , and have access to a constant returns to scale Cobb–Douglas production technology. The firms’ problem is:

max_{K_{t}, N_{t}} K_{t}^{α} N_{t}^{1 - α} - w_{t} N_{t} - r_{t} K_{t},

where K_t and N_t denote the aggregate capital stock and labor supply respectively at time t.

Government

The government in the model runs a “pseudo” pay-as-you-go Social Security system in which the government levies a tax on the labor earnings of currently working households, $τ_{t}$ , and pays benefits to retired households as a fraction, B_t , of their average lifetime labor earnings, eⁱ . B_t is known as the replacement rate of Social Security. The system can run a surplus, at which point excess revenue in each period is deposited into the Social Security Trust Fund (SSTF), F_t . The SSTF has access to a storage technology. For simplicity, I assume the government does not have access to credit markets and cannot finance its Social Security system through borrowing. As a result, the government must keep the stock value of the SSTF positive in all time periods. Finally, the government does not consume or produce any other goods or services.

Let F_t and A_t denote the stock value and present value of the SSTF at time t, respectively. I assume the Social Security Administration discounts future surpluses and deficits at rate $β$ :

F_{t} = F_{t - 1} + z_{t},

A_{t} = F_{t} + \sum_{j = 1}^{\infty} β^{j} z_{t + j},

where z_t is the period t Social Security surplus or deficit:

z_{t} \equiv τ_{t} w_{t} N_{t} - B_{t} e^{t - 2},

and $e^{t - 2}$ denotes the average lifetime pretax labor earnings of generation $t - 2$ :

e^{t - 2} \equiv \frac{w_{t - 2} n_{t - 2}^{t - 2} + w_{t - 1} n_{t - 1}^{t - 2}}{2} .

Social Security Reforms

In steady state, if $τ < \frac{B}{2}$ , the Social Security program runs a deficit in each period. I parameterize the model such that the program is running a deficit and the SSTF’s initial endowment is positive ( $F_{0} > 0$ ). As a result, absent any government intervention, the SSTF’s stock value will hit zero in period $t = 2$ . As the government is mandated to maintain a weakly positive SSTF, a reform must occur in period $t = 1$ (early) or $t = 2$ (late). In this article, two possible government reform types are considered. The government could increase labor taxes, $τ$ , or cut benefits, B. All told, there are four possible reforms: (1) early tax increase where $τ_{t} = τ_{e} \forall t \geq 1$ , (2) late tax increase where $τ_{t} = τ_{L} \forall t \geq 2$ , (3) early benefits cut where $B_{t} = B_{e} \forall t \geq 1$ , and (4) late benefits cut where $B_{t} = B_{L} \forall t \geq 2$ .

Uncertainty and Beliefs

Policy uncertainty is the only source of uncertainty in the model. Once a reform takes place, all uncertainty is alleviated and the environment becomes a perfect foresight economy. In period $t = 0$ , uncertainty exists in both the timing (early or late) and type (taxes or benefits) dimension. For simplicity, I assume households’ beliefs over the type and timing of reform are independent. This allows for a simple belief updating procedure as information concerning the timing of reform is revealed in period $t = 1$ . When households wake up in period $t = 1$ and an early reform did not occur, their belief over the type of reform to be implemented in period $t = 2$ remains unchanged.

Let $π_{τ}$ denote the subjective probability that households place on the reform being done through a tax increase; furthermore, let $π_{e}$ denote the probability that households place on reform occurring early in period $t = 1$ . Using the independence assumption, we can obtain the subjective probabilities households place on each of the four possible reforms in period $t = 0$ :

π_{e, τ} = π_{e} π_{τ} π_{L, τ} = (1 - π_{e}) π_{τ} π_{e, B} = π_{e} (1 - π_{τ}) π_{L, B} = (1 - π_{e}) (1 - π_{τ}),

where, for example, $π_{L, B}$ denotes the probability weight that households place on the government cutting benefits late in period $t = 2$ . However, if an early reform occurred, then all uncertainty is alleviated in period $t = 1$ . If reform did not occur in period $t = 1$ , then beliefs are updated as follows:

π_{L, τ} = π_{τ} π_{L, B} = (1 - π_{τ}) .

Definition of Equilibrium

In a perfect foresight economy, the competitive equilibrium consists of the Social Security structure ${τ_{t}, B_{t}}_{t = 0}^{\infty}$ , an allocation ${c_{t}^{t}, c_{t + 1}^{t}, c_{t + 2}^{t}, k_{t + 1}^{t}, k_{t + 2}^{t}, l_{t}^{t}, l_{t + 1}^{t}}_{t = 0}^{\infty}$ for non-HtM households, an allocation ${{\hat{c}}_{t}^{t}, {\hat{c}}_{t + 1}^{t}, {\hat{c}}_{t + 2}^{t}, {\hat{l}}_{t}^{t}, {\hat{l}}_{t + 1}^{t}}_{t = 0}^{\infty}$ for HtM households, a measure of the population that is HtM $ϕ$ , and set of prices ${R_{t}, w_{t}}_{t = 0}^{\infty}$ such that:

1. Given the Social Security structure and prices, the households’ allocations solve their optimization problems as described in the Households section.

2. The capital, labor, and goods markets clear in each period:⁵

K_{t} = (1 - ϕ) \times (k_{t}^{t - 1} + k_{t}^{t - 2}),

N_{t} = (1 - ϕ) \times [(1 - l_{t}^{t}) + (1 - l_{t}^{t - 1})] + ϕ \times [(1 - {\hat{l}}_{t}^{t}) + (1 - {\hat{l}}_{t}^{t - 1})],

K_{t}^{α} N_{t}^{1 - α} + (1 - δ) K_{t} - z_{t} = (1 - ϕ) \times (c_{t}^{t} + c_{t}^{t - 1} + c_{t}^{t - 2} + k_{t + 1}^{t} + k_{t + 1}^{t - 1}) + ϕ \times ({\hat{c}}_{t}^{t} + {\hat{c}}_{t}^{t - 1} + {\hat{c}}_{t}^{t - 2}) .

3. Prices are determined competitively in each period:

R_{t} = 1 + α {(\frac{K_{t}}{N_{t}})}^{α - 1} - δ,

w_{t} = (1 - α) {(\frac{K_{t}}{N_{t}})}^{α} .

4. The Social Security structure satisfies the government’s non-negativity constraint on the SSTF in each period:

F_{t} > 0 \forall t .

Parameterization

Households’ period utility function takes the form:

u (c, l) \equiv θ ln c + (1 - θ) ln l,

which when combined with the assumption of a twenty-year model period yields closed form decision rules for non-HtM households in a perfect foresight economy (see Appendix). This saves from having to solve the households’ optimization problem numerically in each period along the transition path under each reform and set of household beliefs. Households’ utility weight on consumption, $θ$ , is set such that under the initial policy parameters, ${τ, B}$ , non-HtM households dedicate 38 percent of their time endowment during their career to the labor market. This is consistent with the share of hours allocated to work over the life cycle in the United States as discussed in Kitao (2014). The households’ time discount factor, $β$ , the capital depreciation rate, $δ$ , and capital’s share of output, $α$ , are similar to Kitao (2014) (see table 1). Kaplan, Violante, and Weidner (2014) documented that approximately 30 percent of the US population is HtM. For this reason, I consider two parameterizations regarding the proportion of households in the model economy that are HtM, $ϕ \in {0.0, 0.3}$ .

The initial Social Security policy parameters, ${τ, B}$ , are chosen to match the 2015 OASI tax rate and the approximate replacement rate for retirees born in 1980 that made, on average, $45,128 per year during their career (Social Security Administration 2014, 2015). The initial SSTF endowment is set such that, in a perfect foresight economy, the fund would hit zero at the beginning of period $t = 2$ if no reform took place. The initial SSTF endowment as a share of steady state output in the model is 9.1 percent, which is consistent with the data from 2000 (also 9.1 percent). The exhaustion of the SSTF in period $t = 2$ is analogous to the year 2040 in the model economy.⁶

The size of the reforms is computed within the model such that the government’s requirement to maintain a positive SSTF is met indefinitely. The early tax reform is exogenously set such that the smallest steady state surplus is zero.⁷ This ensures that the SSTF will never go negative following a reform. In a perfect foresight equilibrium, the reforms are calibrated to yield the same time-zero discounted present value of the infinite sequence of the SSTF’s deficits and surpluses:

A_{0} (a) = \bar{A} = F_{0} + \sum_{t = 1}^{\infty} [β^{t} z_{t} (a)] \forall a \in {τ_{e}, τ_{L}, B_{e}, B_{L}} .

Under each reform, the economy will eventually converge to within a finite tolerance of its terminal steady state by period $\bar{t}$ . Finding the magnitude of the remaining reforms amounts to a one-dimensional root finding problem that solves:

\bar{A} = F_{0} + \sum_{j = 1}^{\bar{t} - 1} [β^{j} z_{j} (a)] + \frac{β^{\bar{t}}}{1 - β} \bar{z} (a) \forall a \in {τ_{e}, τ_{L}, B_{e}, B_{L}} .

As the SSTF experiences an additional period of deficits when the reform occurs late, the late reforms must be larger for equation (26) to hold. Therefore, $τ_{e} < τ_{L}$ and $B_{e} > B_{L}$ . Given the simplicity of the model’s structure, the magnitudes of the reforms considered in this article are larger than those used or estimated in other publications (Kitao 2014; Congressional Budget Office 2019). As a result, the quantitative results discussed in the succeeding sections should be interpreted as a numerical example and not a rigorous quantitative exercise. Finally, I keep the reforms the same across the two parameterizations of the model—the model with and without HtM households—to allow the results to be compared.

Table 1.

Parameterization.

Parameter	Description	Value
$β$	Annual time discount factor	.9815
$θ$	Utility weight on consumption	.3414
$α$	Capital share of output	.4000
$δ$	Annual capital depreciation	.0820
$ϕ$	Share of population that is hand-to-mouth	.0000 or .3000
F ₀	Initial Stock of the Social Security Trust Fund	.0264
$τ$	Initial Social Security tax rate	.1060
$τ_{e}$	Early Social Security tax reform rate	.1844
$τ_{L}$	Late Social Security tax reform rate	.2208
B	Initial Social Security replacement rate	.3640
B_e	Early Social Security replacement rate reform	.2110
B_L	Late Social Security replacement rate reform	.1458

The primary parameters of interest in this article are the probabilities that determine households’ subjective beliefs over the four potential reforms (see the Uncertainty and Beliefs section). I consider the following set of 25 household belief sets:

Π \equiv {π_{e}, π_{τ}} \in {0.0, 0.2, 0.5, 0.8, 1.0} \times {0.0, 0.2, 0.5, 0.8, 1.0} .

Macroeconomic Analysis

In this section, I first discuss the macroeconomic implications of the four reforms in a perfect foresight economy in both the long run—by comparing each reforms’ terminal steady state to the initial steady state—and along the transition path. I then turn to the economic effects of policy uncertainty and the presence of HtM households in the model economy.

Under Perfect Foresight

As there is no source of growth in the model economy, the competitive equilibria converge to a terminal steady state. The main welfare analysis concerning uncertainty in the Welfare Analysis section focuses on the transition path from the initial steady state to each reform’s respective terminal steady state. However, it is a useful exercise to examine how each of the reforms affect household behavior in a perfect foresight economy. Table 2 shows the allocations resulting from the competitive equilibria under the initial Social Security program and under each of the four reforms.

Table 2.

Steady-state Analysis.

	Initial Policy	Early Tax	Late Tax	Early Benefits	Late Benefits
$n_{t}^{t}$	0.446	0.453	0.456	0.442	0.440
$n_{t + 1}^{t}$	0.314	0.299	0.291	0.323	0.327
N_t	0.798	0.752	0.747	0.765	0.767
$k_{t + 1}^{t}$	0.029	0.028	0.027	0.030	0.030
$k_{t + 2}^{t}$	0.039	0.035	0.033	0.044	0.046
K_t	0.091	0.063	0.060	0.074	0.076
$c_{t}^{t}$	0.062	0.054	0.051	0.063	0.063
$c_{t + 1}^{t}$	0.080	0.073	0.070	0.079	0.078
$c_{t + 2}^{t}$	0.104	0.099	0.096	0.098	0.095
Y_t	0.289	0.278	0.273	0.300	0.305
w_t	0.228	0.222	0.219	0.235	0.238
R_t	1.887	1.959	1.995	1.812	1.779

A cut in benefits—holding taxes constant—increases the aggregate capital stock, labor supply, and output in the long run relative to the current system. As non-HtM households save optimally in the model, a reduction in benefits incentivizes these households to save more for retirement in an effort to smooth consumption over their lifetime. Moreover, as resources stored in the SSTF are unproductive and do not enter the capital stock, a cut in benefits leaves more productive resources in the economy. In contrast, increasing the OASI tax magnifies the Social Security program’s distortion on the economy and results in a fall in aggregate capital, labor supply, and output in the long run.

In the beginning of period $t = 0$ , the policy announcement is made followed by households making their work and saving decisions. While an increase in labor taxes reduces the incentive to work, when it is announced in advance households increase their hours worked while their tax rate is still relatively low. For this reason, aggregate hours worked increase in periods $t = 0$ and $t = 1$ when an early or late tax increase in implemented respectively. When a benefit cut is used, households increase their saving in order to smooth consumption over their life cycle. The capital response dominates the labor response and wages rise when a benefit reduction is announced. This increase in the equilibrium wage rate induces households to work more. However, the wage effect is partially offset by the reduction in the return to labor through the Social Security benefit formula (figure 1).

Figure 1.

This figure depicts the transition path of macroeconomic aggregates across each of the four reforms in a perfect foresight economy. Each series is presented as a share of the series’ initial steady-state value. The proportion of the population that is hand-to-mouth, $ϕ$ , is 0 percent.

Under Policy Uncertainty

Figure 2 shows how the realized capital–labor ratio transition path under uncertainty varies across household beliefs relative to a perfect foresight economy. Critically, the qualitative nature of the relative capital–labor ratio isn’t robust to the specification of household beliefs. For example, consider the capital–labor ratio in an economy with policy uncertainty when an early tax increase is used as the benchmark reform. When households place equal weight on each of the four reforms, ${π_{e} = 0.5, π_{τ} = 0.5}$ , the capital–labor ratio is 0.6 percent lower period $t = 1$ in the economy with policy uncertainty relative to the economy with perfect foresight. However, across a broader set of household beliefs, the capital–labor ratio in period $t = 1$ can range from $-$ 3.2 percent to +0.8 percent of its value in a perfect foresight economy.

Figure 2.

The dotted lines show the capital–labor ratio under uncertainty, relative to the perfect foresight economy, across household beliefs (see equation [28]). The solid line shows the relative capital–labor ratio under household beliefs: ${π_{e} = 0.5, π_{τ} = 0.5}$ . The proportion of the population that is hand-to-mouth, $ϕ$ , is 0 percent.

The variation in the relative capital–labor ratio stems from how household beliefs affect households’ saving and labor decisions. Continuing to use an early tax increase as the example benchmark reform, as household beliefs move closer toward expecting a late tax increase, they save less in period $t = 0$ because reform isn’t expected to occur for another period. This yields a capital–labor ratio 3.2 percent lower in period $t = 1$ relative to the benchmark economy. When beliefs move toward early reforms, aggregate savings in period $t = 0$ increase in an attempt to compensate for lower after-tax labor income and/or an expected cut in retirement benefits in period $t = 1$ . As beliefs move closer toward an early benefit cut, the initial middle-aged households save more in period $t = 0$ to better consumption smooth in the face of lower Social Security benefits. The end result is that the capital–labor ratio is 0.8 percent higher in period $t = 1$ when household beliefs are tilted toward an early benefit cut relative to an early tax increase. Ultimately, the realized prices along the transition path are sensitive to the specification of household beliefs.

For HtM households, affecting their Social Security benefits through their labor choices is the only avenue through which they can smooth consumption over their life cycle. As a result, the HtM households choose to work 40 percent of their time endowment in contrast to non-HtM households who choose 36 percent of their time endowment. I find that the addition of HtM households—by setting $ϕ = 0.3$ —results in policy uncertainty having a smaller affect on the capital–labor ratio along the transition path. To illustrate this point, table 3 shows the range of relative capital–labor ratios under each benchmark reform across a large set of household beliefs. While the qualitative results shown in figure 2 are unaffected, the magnitude of the effects is important when computing welfare results.

Table 3.

Range of Relative Capital–Labor Ratios across Reforms and Household Beliefs.

Period	Model without HtM ( $ϕ = 0.0$ )				Model with HtM ( $ϕ = 0.3$ )
Period	$τ_{e}$	$τ_{L}$	B_e	B_L	$τ_{e}$	$τ_{L}$	B_e	B_L
0	(0.0, 1.1)	(−0.8, 0.4)	(−1.1, 0.0)	(−1.0, 0.2)	(0.1, 0.8)	(−0.6, 0.2)	(−0.8, −0.1)	(−0.6, 0.2)
1	(−3.3, 0.9)	(0.0, 5.9)	(−4.1, 0.0)	(−4.0, 1.7)	(−2.7, 0.6)	(0.0, 4.6)	(−3.3, 0.0)	(−3.1, 1.4)
2	(−1.7, 0.0)	(0.0, 2.7)	(−1.4, 0.3)	(−2.5, 0.3)	(−1.5, 0.1)	(0.0, 2.0)	(−1.1, 0.3)	(−1.8, 0.3)
3	(−0.6, 0.1)	(−0.2, 0.6)	(−0.7, 0.1)	(−0.2, 0.6)	(−0.5, 0.1)	(−0.3, 0.5)	(−0.5, 0.1)	(0.0, 0.7)

Note: This table contains the minimum and maximum values—(min, max)—for the relative capital–labor ratio for periods $t \in {0, 1, 2, 3}$ across a large set of household beliefs under each of the four benchmark reforms. The results are shown for two parameterizations of the economy: with and without hand-to-mouth households.

Perfect Foresight Preferences

Understanding how generations along the transition path are affected by the reforms—in a perfect foresight economy—is useful when analyzing how reform uncertainty impacts generations’ welfare. This is especially true when evaluating the welfare effects from a behind-the-veil perspective as done in the Ex Ante Analysis section.

Non-HtM Households’ Preferences

In a perfect foresight economy, every generation of non-HtM households is affected by the four reforms along the transition path in a different way. Table 4 shows how each generation ranks the four reforms based on the total lifetime utility each reform delivers for that generation. In each row, a rank of one signals the reform most preferred by that generation. All generations born after period two have the same preference ordering as generation two. Households born between $t = - 2$ and $t = 2$ have different preference rankings over reforms. The main driver of these differences is that not all generations are directly affected by the reforms themselves and are only affected by the equilibrium prices that differ along the transition path for each reform.

Table 4.

Reform Preferences by Generation.

Generation	Early Tax	Late Tax	Early Benefit	Late Benefit
−2 (initial old)	1	2	4	3
−1 (initial middle-aged)	3	1	4	2
(initial young)	2	1	3	4
(future gen 1)	4	2	1	3
+ (future gen 2+)	3	4	1	2

Note: 1 = best, 4 = worst.

The initial old generation is never affected directly by the Social Security reforms as they die at the end of period $t = 0$ . However, as living generations in period $t = 0$ change their labor supply in anticipation of the impending policy change, the market clearing interest rate is affected. This in turn impacts the initial old’s capital income in retirement. As it turns out, an anticipated early tax increase yields the largest interest rate in period $t = 0$ , making this reform the initial old’s most preferred. An early benefit cut results in the lowest interest rate in period $t = 0$ making it the least preferred reform from the initial old generation’s perspective.

The initial middle-aged are only directly affected by an early benefit cut as they are retired in period $t = 1$ . This makes an early benefit cut the least preferred reform for the initial middle-aged. The remaining three reforms only affect the initial middle-aged through the general equilibrium channel. An early tax increase yields the lowest wage in period $t = 0$ and interest rate in period $t = 1$ , which makes it the second least preferred. A late tax increase is preferred to a late benefit cut as it generates a relatively higher interest rate in period $t = 1$ when the initial middle-aged are retired.

The initial young are directly affected by all the reforms except for a late tax increase, which again makes it this generation’s most preferred reform. Of the remaining three reforms, an early tax increase generates the lowest after-tax wage in period $t = 1$ ; however, it also generates the largest interest rate in period $t = 2$ when the initial young are retired. This boost in retirement capital income makes this reform the second most preferred for the initial young. As the late cut in benefits is larger than an early benefit cut, the initial young prefer an earlier benefit cut to a later one.

The generation born in period $t = 1$ is directly affected by all four reforms. They prefer an early benefit cut the most as it generates higher wages during their career while still offering a relatively large Social Security benefit in retirement. A late tax increase is their second most preferred as the high benefits in retirement and higher wages while young outweigh the low after-tax wages in period $t = 2$ . When comparing an early tax increase to a late benefit cut, there is a trade-off between lower lifetime wages under the tax reform and the large reduction in Social Security benefits in retirement under the benefit cut reform. It turns out that the wage effect dominates their welfare, making an early tax increase this generation’s least preferred reform.

The generations born in periods $t \geq 2$ have identical preference rankings over reforms. Tax style reforms are least preferred as they lower wages and aggregate output. Early benefit cuts are preferred to late benefit cuts as the former returns more resources to the economy through a more generous replacement rate of Social Security.

HtM Households’ Preferences

Table 5 displays HtM households’ preferences over the four reforms in a perfect foresight economy. The initial old HtM households are unaffected by the reforms as they hold zero capital in retirement and are unexposed to the change in the interest rate in period $t = 0$ . The initial middle-aged, initial young, and future young prefer reforms to which they are never directly exposed. However, as Social Security is the only source of income in retirement for HtM households, their preferences must balance lower benefits in retirement with higher wages during their careers.

Table 5.

Reform Preferences by Generation (HtM).

Generation	Early Tax	Late Tax	Early Benefit	Late Benefit
−1 (initial middle-aged)	3	2	4	1
(initial young)	2	1	3	4
(future gen 1)	2	1	3	4
+ (future gen 2+)	1	3	2	4

Note: 1 = best, 4 = worst.

Welfare Analysis

In this section, I document the welfare implications of uncertainty in three ways. As discussed in the Perfect Foresight Preferences section, households may be directly affected by the reforms themselves but also by prices through the general equilibrium channel. Recall that in period $t = 0$ , households become aware of the Social Security budget shortfall and the necessity of reform. Early reforms occur in period $t = 1$ while late reforms occur in period $t = 2$ . Households are uncertain which reform type—taxes or benefits—the government will use and when they plan to implement the change. Once a reform occurs, all uncertainty is alleviated.

In the Ex Post Analysis section, I explore how the general equilibrium channel in an economy with policy uncertainty affects each generation’s realized lifetime well-being at the end of their life. I do this by computing a retrospective ex post consumption equivalent variation (CEV) that measures how much lifetime consumption a household would have required or needed to give up in a perfect foresight economy to have been equally well-off as in an economy with policy uncertainty.

In the Ex Ante Analysis section, I use a behind-the-veil ex ante CEV to measure the welfare implications of reform uncertainty for each benchmark reform. The ex ante CEV captures the amount of lifetime consumption a household would require or need to give up in the perfect foresight economy to be equally well-off as in an economy with policy uncertainty at the being of their life. For those generations not directly exposed to policy uncertainty the ex ante CEV is identical to the ex post CEV used in the Ex Post Analysis section.

In the Effects of Varying Household Beliefs section, I vary households’ subjective beliefs over potential reforms and discuss how they impact the ex post and ex ante welfare implications of policy uncertainty. Then, in Welfare Effects of Adding HtM Households section, I discuss how the welfare results are affected by the addition of HtM households in the model economy. Finally, in the Welfare Effects of Adding HtM Households section, I briefly discuss an alternative CEV metric used to isolate the direct costs of reform uncertainty due to households’ innate risk aversion and compare the results to those found in Caliendo, Gorry, and Slavov (2019).

Ex Post Analysis

Computing the ex post CEV for each generation under the four benchmark reforms offers insight into the interactions between household uncertainty and market clearing prices. Moreover, this allows us to examine how uncertainty affects households’ welfare through the general equilibrium channel. In order to obtain the ex post CEV, I start by computing each generation’s realized lifetime utility under each reform in a perfect foresight economy, $U_{t} (a)$ , and in the economy with uncertainty, ${\tilde{U}}_{t} (a, Π)$ :

U_{t} (a) = \sum_{j = t}^{t + 2} β^{j - t} u (c_{j}^{t} (a), l_{j}^{t} (a)),

{\tilde{U}}_{t} (a, Π) = \sum_{j = t}^{t + 2} β^{j - t} u ({\tilde{c}}_{j}^{t} (a, Π), {\tilde{l}}_{j}^{t} (a, Π)),

where $a \in {τ_{e}, τ_{L}, B_{e}, B_{L}}$ denotes the actual policy implemented by the government and $Π \equiv {π_{e}, π_{τ}}$ is the set of household beliefs in period $t = 0$ . The ex post CEV, $V_{t}^{expost} (a, Π)$ , is defined as:

\sum_{j = t}^{t + 2} β^{j - t} u ((1 + V_{t}^{expost} (a, Π)) c_{j}^{t} (a), l_{j}^{t} (a)) = \sum_{j = t}^{t + 2} β^{j - t} u ({\tilde{c}}_{j}^{t} (a, Π), {\tilde{l}}_{j}^{t} (a, Π)),

which, under the utility specification defined in equation (25), yields the following expression:

V_{t}^{expost} (a, Π) = exp [\frac{{\tilde{U}}_{t} (a, Π) - U_{t} (a)}{θ (1 + β + β^{2})}] - 1.

As each of the four reforms in a perfect foresight economy generates a different transition path for prices, the CEV welfare metrics differ substantially depending on which perfect foresight economy is being used as the benchmark. For this reason, figure 3 shows the ex post CEV for each benchmark economy corresponding to the four reforms. For simplicity, I begin by assuming households’ beliefs in period $t = 0$ place equal weight on the four reforms ( $π_{e} = 0.5$ , $π_{τ} = 0.5$ ). This assumption is relaxed and explored in detail in the Effects of Varying Household Beliefs section. Figure 3 also plots the transition path of the capital–labor ratio under uncertainty relative to the path in a perfect foresight economy. From an ex post perspective, many generations benefit through the general equilibrium channel as uncertainty raises the capital–labor ratio during their careers resulting in higher lifetime wages. While the wage effect tends to be the dominant general equilibrium effect, the interest rate also plays an important role especially for the initial old generation born in period $t = - 2$ . As discussed in the Perfect Foresight Preferences section, the initial old generation is only affected by the interest rate in period $t = 0$ when they are retired. Uncertainty’s affect on prices can make the initial old better off (worse off) if the capital–labor ratio is lower (higher) under uncertainty in period $t = 0$ relative to the prevailing interest rate in the perfect foresight economy.

Figure 3.

Left axis: ex post consumption equivalent variation (CEV) for non-hand-to-mouth (HtM) households across generations under household beliefs: $π_{e} = 0.5$ and $π_{τ} = 0.5$ . An ex post CEV greater than zero indicates a welfare gain. Right axis: capital–labor ratio transition path under uncertainty, relative to the transition path under perfect foresight. The proportion of the population that is HtM, $ϕ$ , is 0 percent.

Ex Ante Analysis

The behind-the-veil ex ante CEV metric captures the welfare implications of policy uncertainty in the same way as in Kitao (2018). The ex ante CEV measures the amount of lifetime consumption a household would require or need to give up in the perfect foresight economy to be made as well off as their expected utility in the world with reform uncertainty. As uncertainty is only present in periods $t = 0$ and $t = 1$ , the only households that face it directly are those born in periods $t \in {- 1, 0, 1}$ . For those generations that do not face uncertainty directly the ex ante and ex post CEV are identical as the only mechanism through which uncertainty impacts their welfare is through the general equilibrium channel. For this reason, this section focuses only on those generations that face uncertainty directly during their lifetime.

As before, $U_{t} (a)$ denotes the realized lifetime utility of generation t under reform $a \in {τ_{e}, τ_{L}, B_{e}, B_{L}}$ in a perfect foresight economy. A household born in period $t \in {- 1, 0, 1}$ has an expected lifetime utility $E_{t} (U_{t} | Π)$ , which depends on household beliefs $Π \equiv {π_{e}, π_{τ}}$ . Generation $t = 1$ faces type uncertainty only when a reform does not occur early. In this case, I compute the household’s expected utility using the two remaining transition paths.

E_{t} (U_{t} | Π) = \sum_{k = 1}^{4} [π_{t} (a_{k}) \sum_{j = t}^{t + 2} β^{j - t} u ({\dot{c}}_{j}^{t} (a_{k}, Π), {\dot{l}}_{j}^{t} (a_{k}, Π))],

where ${{\dot{c}}_{j}^{t} (a, Π), {\dot{l}}_{j}^{t} (a, Π)}_{j = t} = {{\tilde{c}}_{j}^{t} (a, Π), {\tilde{l}}_{j}^{t} (a, Π {)}}_{j = t}$ denotes generation t’s realized allocation when young in an economy with reform uncertainty. However, because of the presence of policy uncertainty, households have to know what their allocations would be in the future for each possible policy realization if they lived in a perfect foresight economy: ${{\dot{c}}_{j}^{t} (a, Π), {\dot{l}}_{j}^{t} (a, Π)}_{j = t + 1}^{t + 2} = {c_{j}^{t} (a), l_{j}^{t} (a {)}}_{j = t + 1}^{t + 2}$ .

The ex ante CEV, $V_{t}^{exante} (a, Π)$ , is defined as:

\sum_{j = t}^{t + 2} β^{j - t} u ((1 + V_{t}^{exante} (a, Π)) c_{j}^{t} (a), l_{j}^{t} (a)) = E_{t} (U_{t} | Π),

which, under the utility specification defined in equation (25), yields the following expression:

V_{t}^{exante} (a, Π) = exp - 1 [\frac{E_{t} (U_{t} | Π) - U_{t} (a)}{θ (1 + β + β^{2})}] .

Similar to figure 3, I plot the ex ante CEV on the left axis and the relative capital–labor ratio on the right axis of figure 4. Once again, I assume that household beliefs in period $t = 0$ are such that equal weight is placed on the four reforms ( $π_{e} = 0.5$ , $π_{τ} = 0.5$ ). If we compare figure 3 to figure 4, it is immediately clear that the ex ante welfare implications differ substantially from the ex post analysis for those households that face uncertainty during their lifetime.

Figure 4.

Left axis: ex ante consumption equivalent variation (CEV) for non-hand-to-mouth (HtM) households across generations under household beliefs: $π_{e} = 0.5$ and $π_{τ} = 0.5$ . An ex ante CEV greater than zero indicates a welfare gain. Right axis: capital–labor ratio transition path under uncertainty, relative to the transition path under perfect foresight. The proportion of the population that is HtM, $ϕ$ , is 0 percent.

The ex ante CEV is positive for some generations. This is not a result of uncertainty loving households but rather a result of two other forces. The first is through the general equilibrium channel. As prices in the economy with uncertainty differ from those in the perfect foresight economy, some generations are made better off in the current period due to higher wages/interest rates. The second channel is due to changes in households’ perceived lifetime wealth. This results from the fact that each reform generates a different income profile for each generation. The ex ante CEV may be positive due to the benchmark economy having a less preferred path for a generation’s income profile than the one expected under uncertainty. The general equilibrium effect and perceived wealth effect can work for or against one another depending on the generation, household beliefs, and benchmark reform being analyzed.

First, consider the initial middle-aged born in period $t = - 1$ . From table 4, we know that in a perfect foresight economy the initial middle-aged ranks the reforms as follows: (1) late tax, (2) late benefits, (3) early tax, and (4) early benefits. When households place a positive probability on an early benefit cut, it decreases their expected old age utility significantly. This lowers their ex ante CEV via the perceived wealth effect when an early tax increase, late tax increase, and a late benefit cut are used as the benchmark. In contrast, the initial middle-aged ex ante CEV is higher when an early benefits cut is used as the benchmark. Households placing a positive weight on the other three reforms increase their expected utility. Furthermore, under uncertainty, the wage rate in period $t = 0$ is lower than it would have been in a perfect foresight economy when benefits are cut early. The relatively lower wage results in the initial middle-aged working fewer hours, consuming more, and saving less for retirement in the presence of uncertainty. The increase in realized utility in $t = 0$ and expected utility in $t = 1$ generates welfare gains for the initial middle-aged relative to a perfectly anticipated early benefit cut. The perceived wealth effect and general equilibrium effect work together to increase the initial middle-aged ex ante CEV when we use an early benefit cut as the benchmark reform.

Second, consider the initial young born in period $t = 0$ . This generation ranks the four reforms in a perfect foresight economy as follows: (1) late tax, (2) early tax, (3) early benefits, and (4) late benefits. The initial young’s expected utility, and ex ante CEV, is decreasing in the probability they place on benefits being cut late. Even though wages in period $t = 0$ are lower under uncertainty relative to a perfectly anticipated late benefit cut, the perceived wealth effect dominates the general equilibrium effect. Similarly, as the probability weights on tax style reforms increases—when using an early benefit cut as the benchmark reform—the initial young’s expected utility increases, which dominates the negative price effect.

Finally, consider the future young born in period $t = 1$ . Recall that households in this generation only face uncertainty in the case of a late reform, leaving them with only reform type uncertainty. In a world where an early reform did not occur, the future young generation prefers a late tax increase to a late benefit cut. Therefore, as households place equal weight on the two reforms, expected utility is smaller than the realized utility level in a prefect foresight economy when taxes are increased late. Under uncertainty, the wage in period $t = 1$ is higher (lower) than it would have been in a perfect foresight economy when taxes were increased late (benefits were cut late). In the end, the perceived wealth effect dominates the general equilibrium channel for the future young when households’ beliefs place equal weight on all reforms.

Effects of Varying Household Beliefs

In this section, I consider a broader set of household beliefs defined by equation (28). I first explore how the relative capital–labor ratio along the transition path affects households’ welfare as measured by the ex post CEV defined in the Ex Post Analysis section. I then discuss how beliefs affect households’ ex ante CEV for those born in periods $t \in {- 1, 0, 1}$ . I find that the quantitative—and in some case qualitative—ex post and ex ante welfare metrics are not robust to varying household beliefs. Qualitative results for a given generation may differ under a specific benchmark reform across household beliefs if that generation has strong preferences over possible policy outcomes. The reforms considered in this article not only differ in magnitude as a function of timing (as in Kitao 2018) but also in their type.

The sensitivity of market clearing prices to beliefs affects households’ ex post CEV. As discussed in the Ex Post Analysis section, households tend to benefit from uncertainty, ex post, when uncertainty generates a higher wage (i.e., a higher capital–labor ratio) during their career relative to the perfect foresight economy. To better understand the interplay between household beliefs and their ex post welfare, I plot households’ ex post CEV in figure 5 for three sets of beliefs:

Figure 5.

The solid line shows the ex post consumption equivalent variation (CEV) for non-hand-to-mouth (HtM) households under household belief set (1): $π_{e} = 0.5$ and $π_{τ} = 0.5$ . The circle line shows the ex post CEV under belief set (2): households place $.8$ probability on the reform used in the benchmark economy. The diamond line shows the ex post CEV under belief set (3): households place $.2$ probability on the reform used in the benchmark economy. The proportion of the population that is HtM, $ϕ$ , is 0 percent.

Π_{1} = {π_{e} = 0.5, π_{τ} = 0.5},

Π_{2} = {\begin{matrix} {π_{e} = 0.8, π_{τ} = 0.8} & if benchmark = early tax increase \\ {π_{e} = 0.2, π_{τ} = 0.8} & if benchmark = late tax increase \\ {π_{e} = 0.8, π_{τ} = 0.2} & if benchmark = early benefit cut \\ {π_{e} = 0.2, π_{τ} = 0.2} & if benchmark = late benefit cut \end{matrix},

Π_{3} = {\begin{matrix} {π_{e} = 0.2, π_{τ} = 0.2} & if benchmark = early tax increase \\ {π_{e} = 0.8, π_{τ} = 0.2} & if benchmark = late tax increase \\ {π_{e} = 0.2, π_{τ} = 0.8} & if benchmark = early benefit cut \\ {π_{e} = 0.8, π_{τ} = 0.8} & if benchmark = late benefit cut \end{matrix} .

The first set is used as a reference whereby households place equal weight on all four reforms. The second set of beliefs is structured such that households place .8 probability on the type and timing of the reform used in the benchmark economy. The third set of beliefs is structured such that households place .2 probability on the type and timing of reform used in the benchmark economy. I will refer to the second and third sets of beliefs as being more “aligned” and “misaligned” than belief set one, respectively. Under belief sets two and three households are equivalently uncertain; however, the belief sets’ degree of misalignment differs. The degree of misalignment matters because beliefs play an important role in determining the transition path of market clearing prices under uncertainty. When households put more (less) weight on the reform ultimately implemented by the government, the welfare implications of uncertainty via the general equilibrium channel are decreased (increased).

The ex post welfare results in figure 5 are only a partial picture of the welfare implications of policy uncertainty. Figure 6 depicts the sensitivity of the ex ante CEV to household beliefs across generations for each benchmark reform. Interpreting how beliefs impact generations born in periods $t \in {- 1, 0, 1}$ follows the analysis conducted in the Ex Ante Analysis section and comes down to how each generation ranks the four reforms in a perfect foresight economy. For example, the initial middle-aged and initial young generations believe themselves to be best off when their beliefs place 100 percent probability on a late tax increase, regardless of which benchmark reform is used. This is because these generations expected lifetime income profile is higher under a certain late tax increase than the other four reforms. This is driven by the fact that they never pay the tax increase because they are either dead or retired by period $t = 2$ . Moreover, they still receive the full amount of their promised Social Security benefits in retirement. Placing weight on other reforms lowers their expected future utility, thereby decreasing their ex ante CEV via the perceived wealth effect.

Figure 6.

The dotted lines show the ex ante consumption equivalent variation (CEV) for non-hand-to-mouth (HtM) households across all beliefs: $Π \in {0.0, 0.2, 0.5, 0.8, 1.0} \times {0.0, 0.2, 0.5, 0.8, 1.0}$ . The solid line shows the ex ante CEV under household beliefs: $π_{e} = 0.5$ and $π_{τ} = 0.5$ . The proportion of the population that is HtM, $ϕ$ , is 0 percent.

When an early tax increase is used as the benchmark reform and when household beliefs place equal weight on each of the four reforms, the initial young generation’s ex ante CEV is −0.5 percent in terms of lifetime consumption. However, as beliefs are varied, the initial young’s ex ante CEV ranges from −1.8 percent to +2.6 percent. The initial young are never directly exposed to a late tax increase making it their most preferred reform. As beliefs move closer toward a late tax increase the initial young’s ex ante CEV increases via the perceived wealth effect. In contrast, the initial young generation’s least preferred reform is a late benefit cut; therefore, as households place a higher likelihood on benefits being cut late, the initial young’s ex ante CEV falls and becomes negative. While the wage rate in period $t = 0$ is higher under uncertainty when household beliefs are heavily tilted toward an early benefit cut, its positive affect on the initial young’s welfare is small relative to the perceived wealth effect.

Welfare Effects of Adding HtM Households

In the previous sections, the measure of HtM households ( $ϕ$ ) was set to 0 percent. This section investigates what happens to the ex ante CEV once the measure of HtM households is increased to 30 percent. As discussed in the Under Policy Uncertainty section, when non-HtM households make up 70 percent of the population, their capital savings have a smaller impact on the relative capital–labor ratio compared to the model economy without HtM households. The introduction of HtM households leaves the qualitative welfare results from the Ex Post Analysis and the Ex Ante Analysis sections unaffected. However, as shown in table 6, the addition of HtM households lowers the magnitude of the ex ante CEV metrics among non-HtM households. This demonstrates a clear spillover effect between the presence of HtM households and the welfare implications of policy uncertainty felt by non-HtM households via the general equilibrium channel.

Table 6.

Range of Ex Ante Consumption Equivalent Variations (CEVs) for Non-hand-to-mouth (HtM) Households across Reforms and Household Beliefs.

Generation	Model without HtM ( $ϕ = 0.0$ )				Model with HtM ( $ϕ = 0.3$ )
Generation	$τ_{e}$	$τ_{L}$	B_e	B_L	$τ_{e}$	$τ_{L}$	B_e	B_L
−2	(−0.1, 0.0)	(−0.1, 0.1)	(0.0, 0.1)	(−0.1, 0.1)	(−0.1, 0.0)	(−0.1, 0.1)	(0.0, 0.1)	(−0.1, 0.1)
−1	(−2.9, 0.5)	(−3.4, 0.0)	(0.0, 3.5)	(−3.0, 0.4)	(−2.3, 0.4)	(−2.7, 0.0)	(0.0, 2.8)	(−2.4, 0.3)
0	(−2.6, 1.8)	(−4.3, 0.0)	(−1.6, 2.9)	(0.0, 4.5)	(−2.1, 1.5)	(−3.5, 0.0)	(−1.1, 2.5)	(0.0, 3.7)
1	(−0.9, 0.3)	(−0.9, 0.9)	(−1.2, 0.0)	(0.0, 1.8)	(−0.7, 0.3)	(−1, 0.7)	(−0.9, 0.0)	(0.0, 1.7)
2	(−0.5, 0.0)	(0.0, 0.8)	(−0.4, 0.1)	(−0.7, 0.1)	(−0.4, 0.0)	(0.0, 0.6)	(−0.3, 0.1)	(−0.6, 0.1)
3	(−0.2, 0.1)	(−0.1, 0.2)	(−0.2, 0.1)	(−0.1, 0.2)	(−0.2, 0.0)	(−0.2, 0.2)	(−0.2, 0.1)	(0.0, 0.2)

Note: This table contains the minimum and maximum values—(min, max)—for the ex ante CEV for non-HtM households for the initial old, initial middle-aged, initial young, and future young generations across a large set of household beliefs under each benchmark reform. The results are shown for two parameterizations of the economy: with and without HtM households.

Figure 7 shows how the ex ante CEV differs for HtM households as we vary their subjective beliefs at time zero. The qualitative results for HtM households are similar to those for non-HtM households; however, the magnitudes are significantly larger. This extends the results found in Caliendo, Gorry, and Slavov (2019) to a general equilibrium framework regarding the welfare implications of policy uncertainty for households that do not save. Moreover, regardless of which reform is used as the benchmark, the ex ante welfare implications of uncertainty for HtM and non-HtM households are highly sensitive to household beliefs.

Figure 7.

The dotted lines show the ex ante consumption equivalent variation (CEV) for hand-to-mouth (HtM) households across all beliefs: $Π \in {0.0, 0.2, 0.5, 0.8, 1.0} \times {0.0, 0.2, 0.5, 0.8, 1.0}$ . The solid line shows the ex ante CEV for HtM households under household beliefs: $π_{e} = 0.5$ and $π_{τ} = 0.5$ . The proportion of the population that is HtM, $ϕ$ , is 30 percent.

An Alternative Welfare Analysis

This section uses an alternative metric to discuss the welfare implications of uncertainty, analogous to the one used in Caliendo, Gorry, and Slavov (2019). This metric captures the welfare costs coming directly from households’ innate risk aversion and accounts for the perceived wealth effects discussed in the previous sections. Specifically, I compare households’ expected utility to the utility they would receive in a perfect foresight economy should they consume the same amount—in terms of consumption and leisure—as they do in expectation in the world with reform uncertainty ( ${\bar{U}}_{t}$ ).

{\bar{U}}_{t} = \sum_{j = t}^{t + 2} β^{j - t} u (\sum_{k = 1}^{4} [π_{t} (a_{k}) {\tilde{c}}_{j}^{t} (a_{k}, Π)], \sum_{k = 1}^{4} [π_{t} (a_{k}) {\tilde{l}}_{j}^{t} (a_{k}, Π)]) = \sum_{j = t}^{t + 2} β^{j - t} u (E_{t} (c_{j}^{t} | Π), E_{t} (l_{j}^{t} | Π)),

where ${{\tilde{c}}_{j}^{t} (a, Π), {\tilde{l}}_{j}^{t} (a, Π)}_{j = t}^{t + 2}$ denotes generation t’s allocations in an economy with reform uncertainty in periods $t \in {0, 1}$ but with reform a being announced at the end of either period $t = 0$ or $t = 1$ . Expected utility is defined by equation (33) and the alternative CEV, $V_{t}^{a l t} (Π)$ , is defined as:

\sum_{j = t}^{t + 2} β^{j - t} u ((1 + V_{t}^{a l t} (Π)) E_{t} (c_{j}^{t} | Π), E_{t} (l_{j}^{t} | Π)) = E_{t} (U_{t} | Π),

which, under the utility specification defined in equation (25), yields the following expression:

V_{t}^{a l t} (Π) = exp [\frac{E_{t} (U_{t} | Π) - {\bar{U}}_{t}}{θ (1 + β + β^{2})}] - 1.

In an economy with a zero-measure of HtM households, young non-HtM households born in period $t = 0$ have an alternative CEV ranging from $- 0.004$ percent to $- 0.027$ percent of lifetime consumption depending on household beliefs. As for HtM households born in period $t = 0$ , their alternative CEV can be much larger and ranges from $- 0.01$ percent to $- 2.15$ percent of lifetime consumption. While the levels should be interpreted with caution as household preferences exhibit a relatively low level of risk aversion (with a constant relative risk aversion of 1.0 compared to 3.0 as used in Caliendo, Gorry, and Slavov [2019]), the relative welfare costs between non-HtM and HtM households are consistent with the results found in Caliendo, Gorry and Slavov (2019). A higher degree of risk aversion in a general equilibrium framework would yield quantitatively larger welfare costs associated with uncertainty relative to the findings in this article or Caliendo, Gorry, and Slavov (2019). Finally, the main result of this article continues to hold as the alternative CEV exhibits sensitivity to household beliefs.

Concluding Remarks

Policy uncertainty is a type of aggregate risk that has practical implications for policy evaluation. While this article specifically looks at policy uncertainty surrounding an inevitable Social Security reform, the approach developed here can be extended to a broad array of policy issues. This is the first article to focus on the importance of households’ subjective beliefs over potential reforms in the determination of the economic and welfare effects of policy uncertainty. I find that the quantitative—and in some case qualitative—economic and welfare effects of policy uncertainty are highly sensitive to household beliefs. This provides a cautionary tale to researchers and policy analysts alike who use structural general equilibrium models to quantify the effects of policy uncertainty.

This article developed a simple three-period general equilibrium OLG model in which households are uncertain as to the type and timing of an inevitable Social Security reform. This approach—along with the assumption of log-utility preferences—greatly minimizes the computational burden of adding aggregate risk to an OLG model. However, due to the relative simplicity of the model’s structure, the results contained in this article should be interpreted as numerical examples and not as a rigorous quantitative exercise. That said, the key mechanisms through which uncertainty affects household behavior and the macroeconomy will be present in any model that shares this basic structure, such as those discussed in Nelson and Phillips (2019).

As households in the model face uncertain future prices and policies, their optimal work and saving decisions deviate from those in the perfect foresight economy. These individual-level decisions aggregate to affect economic output and market clearing prices. The first of three welfare metrics used in this article isolates how realized prices in an economy with policy uncertainty affects households’ well-being in a retrospective (ex post) manner. Generations born after reform has taken place face no uncertainty directly; however, they are still affected by uncertainty through its impact on market clearing prices which propagate for several periods after uncertainty is alleviated. When uncertainty generates a higher market clearing wage—relative to the perfect foresight economy—younger households benefit through higher career earnings while older households are made worse off through the lower rate of return on their savings. Ultimately, the welfare implications of uncertainty stemming from the general equilibrium channel are uneven across generations.

The second welfare metric used in this article takes the common behind-the-veil (ex ante) perspective. While this metric is identical to the ex post CEV for those households that never face policy uncertainty, it differs significantly for those that do. Households’ preferences over potential reforms in conjuncture with their subjective beliefs over which reforms they view as most likely generate a perceived wealth effect. This effect can push households’ ex ante CEV positive or negative depending on their beliefs over relatively desirable or undesirable reforms. At first glance, this is counterintuitive, which is why I also include an alternative welfare metric that negates the perceived wealth effect and computes the welfare cost of uncertainty via households’ innate risk aversion. Regardless of which welfare metric used, the results are highly sensitive to households’ beliefs. Therefore, any attempt to quantify the welfare implications of policy uncertainty depends not only on the reforms themselves but the beliefs held by the public.

Finally, this article extends the literature by investigating how the economic and welfare implications of policy uncertainty are impacted by the presence of HtM households in a general equilibrium setting. The introduction of a positive measure of HtM households into the model economy lowers the sensitivity of prices to policy uncertainty. This in turn lowers the magnitude of the welfare implications of uncertainty for those households with access to a savings technology but leaves the qualitative results unaffected. However, those households precluded from saving experience much larger welfare effects from policy uncertainty.

Footnotes

Appendix

Author's Note

The views expressed in this article are the author's and should not be interpreted as Congressional Budget Office's.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jaeger Nelson

Notes

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