The importance of tax revenue volatility for the design of fiscal policy and automatic stabilizers Estelle Dauchy∗
Nathan Seegert†
July 2013 Keywords: Automatic stabilizers, fiscal policy, personal income tax, tax revenue volatility JEL: Abstract We study the extent of insurance of consumption with respect to income shocks. Specifically, we decompose insurance in two parts, the degree of insurance that is inherent to the tax code, or automatic stabilization (AS), and the degree of insurance that is due to changes in tax policy. Self-insurance appears through both sources, as indirect households’ behavioral reactions to either AS or to activist tax policy changes. We estimate our model with a panel database of U.S. households (the PSID) from 1967 to 2008 and impute consumption using CEX data by estimating a demand function. We find that the degree of insurance from both sources against permanent and transitory income shocks has increase over 30 years by a factor of 5 to 8, except for the ability of changes in tax policy to smooth against permanent shocks, which has decreased by half. Also, the role of active tax policy to smooth consumption against permanent shocks has strongly weakened, leaving this role the the AS effect. Surprisingly, most of the increase in insurance over this period is not directly due to built-in stabilization or active policy. Instead, most of the increase is due to individuals’ behavioral effects to the tax system. ∗ †
[email protected]. New Economic School, Moscow, Russian Federation
[email protected]. Department of Economics, University of Michigan, Ann Arbor,
MI
1
1
Introduction
Recent research has provided strong evidence that consumption inequality has rapidly increased since the 1970s. Blundell and Preston [1998], Cutler and Katz [1992], Souleles, Parker, and Johnson [2006] provide a strong descriptive illustration of these trends for various cohorts and income groups. Blundell, Pistaferri, and Preston [2008] empirically estimate the link between income volatility and consumption volatility, and find partial consumptionsmoothing, or insurance, against permanent shocks and almost full smoothing of transitory shocks for all but the lowest income group. Their purpose however is to empirically estimate the relationship between consumption inequality and income inequality. Therefore, they estimate a single value for the insurance against income shocks, and suggest that it is due to self insurance. In this paper, we demonstrate both theoretically and empirically that the insurance of unexplained consumption variance against income shocks is due to four insurance effects, all of which vary over time and across income groups. The first two are the insurance effects provided from the the changes in the inherent structure of the tax code, also known as “automatic stabilization” or built-in stabilization”, and the last two effects are the insurance that is provided from active tax policy changes over time. We show that each of these changes acts either directly (through the tax code) or indirectly, through individuals’ behavioral reactions to tax policy.
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After building a simple model that decomposes these four parts, and which is an extension of exiting models widely used in the literature [Cutler and Katz, 1992, Meghir and Pistaferri, 2004] we bring the model to the data to evaluate its ability to describe recent evolutions in consumption inequality and consumption insurance against income shocks. We are particularly motivated by the increasing factual evidence that the built-in stabilization of the US tax system may have become less efficient at smoothing consumption over time, as discretionary policy or “active intervention” has been implemented several times, especially since the 2001 recession [Auerbach and Gale, 2009, Feldstein, 2009, Solow, 2005, Souleles, Parker, and Johnson, 2006].1 The goal of this paper is to both explore the ability of these sources of fiscal policy to attenuate the volatility of consumption relative to income volatility, and how they have changed over time and across income groups. Towards this goal we need a panel database of both consumption and income sources. We use panel data from the PSID and impute consumption using the CEX databases. The imputation follows Blundell, Pistaferri, and Preston [2008]’s imputation procedure that maps food consumption into non-durables consumption using the estimates of a demand equation for food, estimated from repeated CEX cross sectional data from 1972 to 2009 and PSID data from 1967 to 2008. The methodology is flexible enough to allow for measurement error in income and consumption (in our case consumption measurement error is automatic from the imputation strategy). 1
See also Auerbach [2009], Dauchy and Balding [2013], Office [2011].
3
This paper is the first to separate the part of insurance against income shocks that is due to automatic insurance inherent to the tax code (i.e., builtin stabilization) and the insurance that is due to active tax policy, and how consumers react to these insurance effects. In the following, we alternatively call the automatic insurance effect the “market” insurance effect because it captures insurance against unpredicted changes in income shocks holding policy constant. We call the second effect the “policy” insurance effect, or active policy effect, because it captures insurance against unpredicted income shocks from changes in active tax policy, holding constant the distribution of income across the population. To separate the market shock from the policy shock, we use a microsimulation approach to simulate income shocks based on NBER’s Taxsim and applied to PSID data, holding either income or policy constant. Then we use a minimum distance methodology to estimate the various insurance parameters.
We find that, probably because of increasing consumption inequality, the insurance from active and built-in policies have both increased over time. However, to assess their efficiency, we separate the direct effects from the behavioral effects. Our results further suggest that the increased insurance effect is due to increased insurance from households reactions to income shocks and their reactions to policy shocks. The direct insurance effect of automatic stabilization is small, and has deteriorated for permanent shocks. 4
The paper is structured as follows. Section 2 provides a detailed description of the theory and the empirical approaches. Section 3 describes the data and the imputation strategy, as well as the microsimulation of income stocks. Section 4 presents the results, and section 5 concludes.
2
Income and Consumption Dynamics
The purpose of the model is to use panel data on individual incomes in order to recover the structure of income shocks, and combine them with consumption data in order to empirically estimate the extent of consumption smoothing due to self-insurance on the one hand, and to government insurance on the other hand. Although this is a purely empirical exercise, it helps to use a simple life-cycle consumption smoothing model in order to understand the relationship between consumption and income shocks. For this we essentially draw from Blundell, Pistaferri, and Preston(2003, 2008).
2.1
Consumption, Income, and Insurance
The unit of analysis is the household, defined as stable prime-age couples with or without children. Because the focus is on market income shocks, we do not model behavioral shocks such as divorce, widowhood, or separation. We also assume that the main source of uncertainty is market income and changes in government insurance (interchangeably called policy stabilizers hereafter), 5
where income includes labor income and cash transfers (such as food stamps and welfare payments). Household i maximizes the present discounted value of its future consumption, as follows
maxEt
∞ X
(1 + δ)−j u(Ci,t+j , Zi,t+j ),
(1)
j=0
subject to an inter-temporal budget constraint and an end of life condition for assets, where individuals have access to a risk-free bond with real return rt+j
Ai,t+j+1 = (1 + rt+j )(Ai,t+j + Yi,t+j − Ci,t+j ), Ai,T = 0.
(2) (3)
Ci,tj is the consumption of household i in period t + j, Zi.t is a set of deterministic factors including both observable and unobservable taste shifts, δ is a subjective discount rate, Ai,t is the real value of assets at the beginning of period t, and Yi,t is household income. The income process, represented in (4), is subject to permanent and transitory shocks and allows the variance of each shock to vary over years.2
0 log(Yi,t ) = Zi,t Γt + Pi,t + νit ,
(4)
2 Carroll [2009] provides simulation of equation (4), and Blundell and Pistaferri [2003] shows that simulations accurately reflect the income process.
6
where Zi,t represents the deterministic component of income, is known in year t, and allowed to shift over time.3 Consistently with previous studies using the PSID, we assume that the permanent component P is a martingale (follows a random walk) and the transitory component νit is a mean-reverting MA(q) process, shown in (5) and (6)
Pi,t = Pi,t−1 + ζi,t , q X νi,t = θj εi,t−j ,
(5) (6)
j=0
where ζi,t is serially uncorrelated.4 Although we determine the order q empirically, as in Blundell, Pistaferri, and Preston [2008], we start with a simple model where εi,t are serially uncorrelated, and assume that θ0 = 1. We estimate the model in two steps, by first, we isolate the unexplained component 0 Γt and then estimate income growth, of income growth yi,t = log(Yi,t ) − Zi,t
represented by
∆yi,t = ζi,t + ∆νi,t ,
(7)
A commonly used utility function in the literature on precautionary savings is a CRRA function (Abowd and Card [1989], Carroll [1994]) which we de3 As shown in our empirical approach, we will use education, labor market experience, ethnicity, and other demographic variables. We also allow for those characteristics to vary across cohorts by including cohorts effects. 4 Many empirical studies show that this is an accurate representation of the income process. See e.g., Abowd and Card [1989], MaCurdy [1982], Meghir and Pistaferri [2004], Moffitt and Gottschalk [2011].
7
0
fine as u(C, Z) = (C 1−γ /1 − γ)eZ ϑ . The Euler equation that results from maximizing (1) under constraints (2) and (3) can be linearized using a Taylor expansion of consumption as follows
5
∆ci,t ∼ = ξi,t + πi,t ζi,t + γt,L πi,t εi,t ,
(8)
0 where ∆ci,t = ∆logCi,t −∆logZi,t ϑ0t −Γi,t is the unexplained (residual) change
in consumption, πi,t is the share of future labor income in current human and financial wealth, and Γi,t is the slope of the consumption path.6 γt,L is a parameter that depends on a common retirement age L and is derived from the approximation of consumption. It can be viewed as an age-increasing annuitization factor. ξi,t is a random term that represents innovations in consumption, is independent from income shocks, and may also capture measurement error in consumption.7 5
See Blundell, Low, and Preston [2013] and appendix B in Blundell, Pistaferri, and Preston [2008] for a detailed derivation of the approximation of consumption and income using a similar utility function. 6 For simplicity, we also assume that the transitory income component is i.i.d (q = 1) and θ0 ≡ 1. Meghir and Pistaferri [2004] show that this equation can be easily extended to MA(q) transitory shock processes of higher order. 7 See Blundell and Preston [1998] for a derivation of γt,L in the case of a CCRA utility function. Carroll [2009] simulates a buffer-stock model that directly explains changes in πi,t . In particular, an increase in the permanent shock may temporarily increase the amount of precautionary savings because it reduces the ratio of assets to permanent income rather than increasing precautionary savings. The term ξi,t has also been characterized as an innovation to higher moments of the income process. For example Caballero [1990] presents a stochastic model in which ξi,t captures revisions to the variance forecast of consumption growth as a response to income shocks, which contrasts with effects that occur to the mean of consumption growth and which are captured by ζi,t and εi,t .
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2.2
Transmission of income shocks to consumption
For individuals many years from retirement age, it is commonly assumed that the present value of financial assets is small relative to the remaining value of labor income, implying πi,t ≈ 1, which means that no part of permanent income shocks is self-insured.8 A tractable version of (8) can be written as
∆ci,t = φi,t ζi,t + ψi,t εi,t + ξi,t
(9)
Equation (9) allows both permanent and transitory shocks to have an impact on consumption with loading factors φi,t and ψi,t , which capture partial insurance. Although we expect the intermediate case where 0 < φi,t < 1 and 0 < ψi,t < 1, this equation allows the two polar cases of no insurance (φi,t = ψi,t = 1) as predicted by the permanent income hypothesis (with only self-insurance through savings) or full insurance (φi,t = ψi,t = 0) as predicted by models of complete markets.9 The lower the loading factors, the larger the degree of insurance. Before delving into details on parameter identification under the simple model presented above, and its generalizations, it is useful to take a step back and 8
Carroll [2009] estimates values of πi,t between 0.85 and 0.95, and Blundell, Low, and Preston [2013] find an average of 0.8 and evidence of smaller values as age increase (from 0.85 at age 30 to 0.78 at age 50) using panel detain Britain. 9 Traditional life-cycle models with forward-looking consumers imply that the marginal propensity to consume out of permanent income shocks should be equal to one. However, extensive macro-economic and micro-economic empirical literature has shown evidence of “excess-smoothness” or excess sensitivity in consumption response to predicted income shocks, implying that the basic intuition from the PIH is not correct. See, among others, Hall [1978], Deaton [1991], Hall and Mishkin [1982].
9
consider more carefully what direct estimations of these parameters should capture. Estimating φi,t < πi,t and ψi,t < γt,L πi,t would provide evidence of “excess-smoothing” over and above self-insurance though asset accumulation, and justify that individuals should insure relatively more against transitory shocks than against permanent (or predicted) income shocks. This “excess-smoothing” of consumption to income shocks has alternatively been explained by the macroeconomic literature as resulting from imperfect markets either due to the existence of private information, or to limited contract enforcements. Under these models, households engage in more precautionary saving (insure more) than with a single, non-contingent bond, but less than with complete markets. In turn, these models allow the relationship between income shocks and consumption to depend on the degree of persistence of income shocks [Alvarez and Jermann, 2000]. Other explanations of the excess-smoothness of consumption in response to perfectly anticipated permanent income shocks has been attributed to the severity of informational problems, such as moral hazard [Attanasio and Pavoni, 2011]. We can now use equations (7) and (9) to derive the covariance restrictions as in Hall and Mishkin [1982] and Blundell, Pistaferri, and Preston [2008]: var(ζt ) + var(∆νt ) cov(∆yt , ∆yt+s ) = −cov(νt , νt+s ) 0
10
if s = 0 if 0 < |s| ≤ q + 1 , if |s| > q + 1
(10)
where cov(., .) and var(.) denote the cross-sectional covariance and variance, respectively, and can be easily computed from data on households belonging to a homogenous group (in which case the index i can be omitted). If q = 0 and ν is serially uncorrelated (νt = εt ) then var(∆νt ) = 2var(∆εt ). In this case, and ignoring issues of measurement error, two years of data are enough to compute the moments of the income process shown in (10).10 The consumption growth restriction from equation (9) is as follows
cov(∆ct , ∆ct+s ) = φ2t var(ζt ) + ψt2 var(εt ) + var(ξt ),
(11)
for s = 0, and zero otherwise (because consumption follows a martingale process). Finally, the covariance between income and consumption at various lags is φt var(ζt ) + ψt var(∆νt ) cov(∆yt+s , ∆ct ) = ψ cov(ε , ∆ν ) t
t
t+s
10
if s = 0
.
(12)
if s > 0
More generally with MA(q), q + 1 years of observations are necessary to estimate the parameters of the income process. As in Blundell, Pistaferri, and Preston [2008] and we allow for the existence of measurement error in our estimation procedure. Although classical measurement error could be captured by the innovations in the MA process, previous work suggests that measurement error in earnings are serially correlated [Bound and Krueger, 1991]. Ludvigson and Paxson [2001] show that the the Taylor expansion traditionally used to linearize inter-temporal changes in consumption and income can also lead to approximation error, which would inflate exiting measurement error in observed values, and discuss the extent to which instrumental variables’ techniques can correct some of the approximation bias.
11
In particular, if ν is serially uncorrelated (νt = εi,t ) then cov(∆yt+s , ∆ct ) = −ψt var(εt ) for s = 1, and 0 if s > 1.11
2.3
Policy and market sources of insurance
Meghir and Pistaferri [2004] show that with an MA(q) process for the transitory shocks, the model summarized by equations (10), (11), and (12) can be fully identified with access to at least 4 + q years of panel data. One important advantage of panel data over cross-sectional data is that one can allow for serial correlation of transitory shocks, measurement error in income and consumption, and directly estimate the loading parameters φt and ψt .12 In this paper, the ability to estimate the level of insurance φt and ψt is critical because our aim is to disentangle insurance effects that are due to tax and benefit policy stabilizers (e.g., built-in flexibility) from changes in insurance due to direct market effects. Moreover, the imputation method to evaluate total consumption in PSID data from CEX data automatically implies measurement error in consumption. Meghir and Pistaferri [2004] show that with serially uncorrelated transitory shocks (i.e., ∆νs = ∆εs ), the five parameters of interest, φ, ψ, var(ξ), var(ζ), and var(ε), can be estimated with just 4 years of panel data. 11 As shown, for instance, in Abowd and Card [1989], and further discussed in the empirical methodology, consumption and income are likely to be contaminated with measurement error. With independent errors, the model above is still fully identifies ψt , while only a lower bound of ψt is identifiable [Blundell, Pistaferri, and Preston, 2008]. 12 By contrast, cross sectional data require the assumption of serially uncorrelated transitory shocks and do not permit full identification of the parameters of interest. For example, Blundell and Preston [1998] assume that φt = 1 and ψt = 0.
12
In the following, we use the simple case of serially uncorrelated transitory shocks to illustrate our claim that insurance to income shocks can occur through two avenues: direct market insurance or self-insurance on the one hand, and changes in automatic stabilizers or policy insurance on the other hand. Equation (12) implies that a simple regression of cov(∆yt+1 , ∆ct ) informs about the size of the transitory income shock (i.e., ψvar(ε).13 In other words, scaling cov(∆yt+1 , ∆ct ) by cov(∆yt , ∆yt+1 ) = var(ε) directly identifies the loading factor ψ. To illustrate the model’s implication that the parameters of interest are derived from the variance-covariance structure of changes in income and consumption, we start with the minimum distance estimator suggested by Blundell, Pistaferri, and Preston [2008], where the LHS variable is the scaled value of cov(∆yt+1 , ∆ct )
Ft = cov(∆yt+1 , ∆ct ) = αt + t ,
(13)
where ∆y and ∆c are unexplained residual income and consumption resulting from preliminary separate regressions of the log of income and the log consumption on household deterministic factors (including demographics and cohort effects). We omit the index i for exposition purposes (empirically, we allow the extent of insurance to vary across households depending on education, age, or income groups). In equation (13), the estimated constant c di13
See and Blundell and Pistaferri [2003] and appendix B in Blundell, Pistaferri, and Preston [2008] for details.
13
rectly identifies the loading factor ψ. Blundell, Pistaferri, and Preston [2008] allow the insurance factor to vary over time by including year dummies. A shortcoming from this expression, however, is that it can only estimate total insurance from transitory income shocks, including market and government insurance. In order to separate the two effects, we use traditional measures of the size of automatic stabilizers capturing the size of changes in tax liability, or disposable income, that follow changes in market income. For example, if Y D denotes disposable income, the stabilization effect due to the tax and benefit system can be written as
St = 1 − ∆YtD /∆Yt ,
(14)
where the second term of the right hand side of (14) captures the extent to which the tax and benefit system dampens changes in disposable income that result from changes in market income. At one extreme, if policy stabilizers completely absorb shocks to market income, this term will be exactly zero and S t = 1. At the other extreme, in the absence of stabilization effect (such as in a system with no taxation), changes in disposable income are equal to changes in market income and St = 0. In the following, we compute St using arithmetic changes in total disposable income from microsimulations based on National Bureau of Economic Research (NBER)’s Taxsim and individual
14
data , where
Si,t
∆Yi,tD ∆Ti,t =1− = , ∆Yi,t ∆Yi,t
(15)
where ∆Ti,t is the change in tax liability that results from an income shock. For example, with no behavioral effect, no change in tax policy (i.e., no change in statutory tax base and tax rates, and no change in personal benefits), and a proportional income tax rate τ , the size of the automatic stabilization effect is exactly τ , meaning that the tax and benefit system insures τ percent of disposable income against income shocks (and Si,t = τ ). Therefore, the definition of automatic stabilizers is close to that of marginal effective tax rates (METR). More generally, the compensatory effect of the tax and benefit system occurs both through automatic changes, due for instance to the progressively of income tax rates, as well as through discretionary tax and benefit policy (e.g., discrete changes in the tax code).14 By separating the built-in stabilization effect from the discretionary effect, this study also evaluates the insurance effect of specific changes in the tax and benefit system. Moreover, the use of a micro-simulation of tax liability at the individual level and based on detailed changes in the tax law permits to estimate a third effect that results from households’ reaction to changes in the tax system and 14
The former compensatory effect is what is generally referred to as “automatic stabilizers,” or “built-in-flexibility”. See for instance Cohen [1959], Musgrave and Miller [1948], Smith [1963].
15
which we sometimes refer to as the behavioral effect of tax policy changes.15 To calculate the stabilization effect of tax policy for each individual, we apply PSID income data to the NBER’s Taxsim software.16 Using a microsimulation approach provides many advantages. First, contrary to aggregate measures of automatic stabilizers, it permits to separate three types of stabilization effects: those that are due to tax policy changes (combining policy changes, automatic stabilizers, and behavioral responses to tax policy), those that are due to general equilibrium effects (or pure market effects), and stabilization that is due to behavioral reactions to income shocks. Second, the microsimulation approach permits to evaluate the extent to which different aspects of the tax and benefit system contribute to automatic stabilization (e.g., definition of the tax base, tax rates, benefits). An important drawback of microsimulation approaches is the lack of individual panel data on consumption, which limits the ability to accurately estimate the effectiveness of tax policy stabilization, defined as the extent to which the tax and benefit system shelters final consumption from income shocks. At best, microsimulations can accurately measure the first step of the stabilization effect of tax policy (i.e., the degree to which taxes and benefits absorb income shocks) as shown in equation (15). The second and important step of the stabi15
In the remaining of this paper, we alternatively refer to the combination of these three effects as the compensatory or stabilizing effect of tax policy. 16 Starting in 1992, the PSID stopped providing estimates of individual income tax liability, but the most important income and demographics variables required an inputs by TaxSim are available in the PSID. For examples of estimation. Butrica and Burkhauser [1997] provide a methodology for calculating tax liability based on Taxsim and PSID data.
16
lization effect relies on the ability of the tax system to shelter consumption from unexpected changes in market income. Papers relying on a microsimulation approach [Auerbach and Feenberg, 2000, Dolls, Fuest, and Peichl, 2012, Pechman, 1973] generally have to make strong assumption about the nature of the transmission from automatic stabilizers to individual consumption, and use arbitrary measures for them.17 . The effectiveness of automatic stabilizers (i.e. the ability of the tax and benefit system to smooth final consumption from income shocks) can be more accurately estimated by the macro-economic literature [Christiano and G. Harrison, 1999, McKay and Reis, 2013] In this paper, we construct panel data on consumption and combine them with PSID data on income using an imputation approach that has been developed by Skinner [1987] and extensively used since then [Blundell, Pistaferri, and Preston, 2004, 2008].18 This enables us to directly estimate the insurance from income shocks that results from tax and benefit policy, and separate it 17
Among the public finance literature, Auerbach and Feenberg [2000] and Pechman [1973] use a micro-simulation approach with cross-sections of individual tax data to calculate the size of automatic stabilizers in the United States. Dolls, Fuest, and Peichl [2012] do a similar exercise and further compare recent changes in automatic stabilizers in the United States and Europe. They assume that automatic stabilizers stabilize consumption of liquidity constrained individuals, and use arbitrary proxies for the proportion of individuals who are liquidity constrained. 18 Skinner [1987] imputes total consumption in the PSID using the estimated coefficients of a regression of total consumption on a series of consumption items (food, utilities, vehicles, etc.) that are present in both the PSID and the CEX. The regression is estimated with CEX data. Ziliak and Kniesner [2005] and Ziliak [1998] impute consumption on the basis of income and the first difference of wealth (defined as the difference between income and savings obtained from the Federal Reserve Board’s Survey of Consumer Finances). As in Blundell, Pistaferri, and Preston [2008], we start from a standard demand function for food based on consumption items that are available in both surveys.
17
from ‘market’ insurance (or direct, private insurance).
2.4
Adjusted model of insurance against income shocks
As in section 2.3, we illustrate our methodology in the simple case of serially uncorrelated transitory shocks, and introduce the policy stabilization effect in the equation that directly estimates insurance from transitory income shocks (in the empirical section, we extend the model to a more general income process and estimate the whole variance-covariance structure). The benchmark methodology extends equation (13) as follows
Fi,t = cov(∆yi,t+1 , ∆ci,t ) = α0 + βSi,t + i,t ,
(16)
where αi,t is a constant that captures direct insurance (or private insurance), Si,t is defined in equation (15), and i,t is a an i.i.d. error term.19 We allow for heterogeneity in behavioral response to market and policy insurance as follows as
Fi,t = α0 +
T X
αt ∗ Dt + β0 Si,t +
T X
t=1
βt ∗ Si,t ∗ Dt + i,t ,
(17)
t=1
where Dt are year dummies. We further separate the total policy effect Si,t in M equation (16) into an automatic stabilization effect Si,t and a discretionary P tax and benefits policy effect Si,t . Allowing for heterogeneity in the behav19
In the empirical part, we allow measurement error in consumption and income as well as heterogeneity in unobserved idiosyncratic factors.
18
ioral response to policy and market shocks, equation (17) becomes
M β0 Si,t +
Fi,t =
T X
M βt ∗ Si,t ∗ Dt
t=1 | {z } Market changes (e.g., Inc. Dist.)
+
T X
P γ0 Si,t +
+
T X
P γt ∗ Si,t ∗ Dt
t=1 | {z } Policy changes (e.g., tax and benefit)
αt ∗ Dt + α0 + i,t ,
(18)
t=1
where the first term in brackets captures changes in insurance due to market changes, for instance changes in the distribution of income, holding policy constant. It includes both a direct effect captured by β0 and an individual’s behavioral effect, which we allow to change over time, captured by βt . The second term in brackets describes changes in insurance that result from changes in tax and benefit policy, holding income (and therefore market effects) constant. It includes both a direct effect captured by γ0 and an individual’s behavioral effect, which we allow to change over time, captured by γt .20 The last term includes year-specific effects and a residual change. Although this model is for illustration purposes only, our empirical model allows for a more general structure of the variance-covariance matrix, and separately estimates the contribution of these various sources of insurance to coverage from transitory and permanent income shocks. We also allow for measurement error in consumption and income. 20
In the empirical part, we allow behavioral changes to change not only over time but also between income groups, education groups, or cohorts.
19
2.5
Measuring policy stabilizers
To estimate equation 18, we separately calculate changes in tax liability that are due to automatic stabilizers and changes that are due to discretionary policy. For this, we apply individual income data obtained from the PSID to the NBER’s Taxsim software from 1972 to 2008.21 . To calculate S P , we simulate a 10% income shock on household’s taxable income by allowing tax policy to change over time, while forcing the income distribution to be fixed to a base year, as follows (we use 1980 as the base year, but also provide regressions using other years to check the sensitivity of our results to the choice of the base year):
P Si,t
f itaxi,x=1980,t − f itaxci,x=1980,t=1980 = c yi,x=1980 − yi,x=1980
(19)
where f itaxi,x=1980,t is household i’s tax liability (as calculated by Taxsim) based on household and income characteristics in the base year, and current tax policy (as of year t), f itaxci,x=1980,t=1980 is household i’s tax liability based on household and income characteristics and tax policy in the base year, and after 10% shock in income (for exposition purposes, we treat positive and negative shocks the same way, but in the empirical part we test whether the 21
Although we have consumption data from the consumer expenditure survey up to 2011, PSID data were available up to 2009 at the time of our study. We have almost continuous PSID data from 1972 to 2008 (PSID data have been collected every year up to 1997 and every other year afterwards). CEX data exist every year starting in 1980. Previous to that year, the CEX has been collected for two years in 1960 and 1961, and two years in 1972-1973. We use 1972-73 CEX data to impute PSID total consumption from 1972 to 1979. More details are provided in the appendix
20
insurance effect depend on the direction of income shocks). The denominator is the size of the income shock (which is 10% for all individuals) and permits to normalize the policy stabilization effect. To calculate S M , we simulate a 10% income shock on household’s taxable income by forcing tax policy to be fixed in a base year, while allowing the income distribution to change over years, as follows
M Si,t
f itaxi,x,t=1980 − f itaxci,x,t=1980 = c yi,x − yi,x
(20)
where f itaxi,x,t=1980 is household i’s tax liability based on current year’s household and income characteristics, and tax policy in the base year, f itaxci,x,t=1980 is household i’s tax liability based on current year’s household and income characteristics and tax policy in the base year, and after a 10% income shock. The denominator is the size of the income shock (i.e.,10% for all individuals). In the empirical part, we allow for the possibility of remaining endogeneity of income by using lagged households’ income and idiosyncratic characteristics as instruments for current income.
3
Data
The goal of our paper is to explore the ability of fiscal policy to attenuate the volatility of consumption relative to income volatility. Towards this goal we use panel data from the PSID imputing consumption data from the re-
21
peated cross sections of the CEX. We follow the imputation presented by Blundell, Pistaferri, and Preston (2008). Their method is similar to previous studies by Jonathan Skinner (1987) and Ziliak (1998) which both combined CEX and PSID data. One advantage of the imputation method by Blundell, Pistaferri, and Preston (2008) is that it allows for demand to change over time, with respect to changes in socioeconomic characteristics, and with respect to relative price changes because it is built upon a standard demand function for food. The demand model allows for food and total expenditures to be jointly endogenous and to be measured with error. Finally, this method produces, with the assumption of normality of food demand, a measure of nondurable consumption in the PSID. One novelty of our paper is that we expand the sample years through 2008 allowing us to compare the imputed values of nondurable consumption produced through this method with data on nondurable consumption collected in the PSID from 1999 to 2008. Furthermore, we present a model explicitly modeling the variation in consumption due to demand shifters (such as socioeconomic characteristics, income variation, and price variation), and fiscal policies with the later being the focus of this paper. Before presenting the model, we briefly describe the data and sample selection. More details are provided in the Data Appendix. We start with an unbalanced panel from the PSID using data from 1967 to 2008. To focus on income risk, rather than variation in consumption due to divorce, widowhood, or other household breaking-up factors, we restrict our sample to households 22
with continuously married couples (excluding 64.2 percent of households, with or without children), headed by a male of age 30 to 65 (excluding 29.7 percent of households).22 An important contribution of our paper is that we allow the effect of fiscal policy to be heterogeneous with respect to income groups, allowing different income groups to have differential access to external smoothing mechanisms in addition to self-insurance, through savings or borrowing and family networks. To this end we use the two available samples of households in the PSID: the representative sample of the US population and the low-income sample (SEO).23 In this sample we create 11 cohorts, each defined as being born in a given half decade starting in 1920 and ending in 1974, eliminating 27.9 percent of the sample. Income outliers, defined as households with income growth above 500 percent, below -80 percent, or with a level of income below $100 in a given year, are eliminated (25.5 percent). To avoid family composition and education changes in the sample we eliminate those younger than 30 (35.8 percent). To avoid changes due to retirement we drop those older than 65 (11.0 percent). We eliminate households with missing report on race (0.6 percent) and region (6.0 percent).24 Starting with 23,107 families and 243,539 22
Families that report changes in head are excluded, further excluding 16.8 percent of the sample. Also, the PSID public files do not report marital status from 1993-1996. To account for this, individual are assigned the marital status they had in 1992 and 1997 if these two years have the same values and dropped otherwise. 23 The PSID’s representative sample of the US population covers 61 percent of the 1967 sample and and the low-income sample (SEO) covers 39 percent of the 1967 sample. 24 The PSID public files do not report state for years 1993-1996. To account for this, individuals are assigned the state where they lived in 1992 and 1997 if those are the same and dropped otherwise (3.8 percent).
23
Table 1: COMPARISON OF MEANS PSID and CEX 1980
Age Family Size No. of Kids White HS graduate College dropout Midwest South West Husband working Wife working Disposable income
PSID(S) 42.3 4.394 1.762 0.335 0.3 0.3 0.139 0.581 0.148 0.905 0.705 16,259
PSID(R) CEX PSID(S) 43.94 43.82 41.88 3.533 3.96 3.724 1.201 1.461 1.35 0.906 0.893 0.443 0.3 0.313 0.343 0.48 0.483 0.387 0.31 0.282 0.127 0.317 0.28 0.618 0.146 0.235 0.124 0.96 0.968 0.888 0.703 0.664 0.758 18,846 25,685 31,106
1988
1996
PSID(R) CEX 44.72 45.81 3.374 3.57 1.108 1.129 0.929 0.882 0.312 0.333 0.526 0.519 0.298 0.258 0.302 0.274 0.164 0.227 0.934 0.912 0.776 0.69 37,848 41,187
PSID(S) 44.92 4.129 1.737 0.0234 0.345 0.374 0.152 0.731 0.0351 NA NA 39,443
PSID(R) CEX 46.22 48.78 3.34 3.457 1.045 1.038 0.924 0.882 0.303 0.286 0.583 0.599 0.314 0.271 0.295 0.327 0.164 0.24 NA 0.878 NA 0.752 52,604 55,357
2004 PSID(S) 45.28 3.649 1.24 0.04 0.369 0.449 0.124 0.756 0.0356 0.893 0.8 58,013
PSID(R) CEX 44.92 53.9 3.284 3.065 1.013 0.617 0.882 0.871 0.297 0.259 0.601 0.648 0.282 0.248 0.299 0.316 0.218 0.272 0.921 0.847 0.806 0.714 68,652 90,234
observations the final sample is composed of 4,139 households (17.9 percent) and 42,582 observations (17.5 percent). This sample selection is followed to the extent possible in the CEX. Table 1 compares the post sample selection PSID and CEX data sets in terms of average demographic and socioeconomic characteristics. The PSID sample includes both the U.S. representative sample (R) and the SEO sample (S). The representative PSID sample has smaller families and fewer children than the CEX, but the PSID SEO has larger families and more children than the CEX. The percentage of families where the wife is working is higher in both samples of the PSID than the CEX. In all other categories the demographics look very similar between the representative subsample of the PSID and the CEX. This is important for the imputation to correctly predict consumption for individuals in the PSID using data from the CEX.
24
3.1
Imputation of Nondurable Expenditures
The imputation method relies on measures of food and nondurable consumption. Food consumption is constructed as the sum of food at home and food away from home, reported in both the PSID and CEX. In the CEX data nondurable consumption is constructed as the sum of food, alcohol, tobacco, services, heating fuel, public and private transport (including gasoline), personal care, clothing, and footwear; as proposed by Attanasio and Guglielmo Weber (1995). The PSID had limited consumption variables until additional questions were added in 1999 and 2005. Consumption variables from 1999 include health care expenses (e.g. hospital, doctor, and prescription expenses), housing expenses (e.g. mortgage payments, rent, property taxes, and home owner’s insurance), utilities, vehicle expenses (e.g. loan payments, down payments, repairs, car insurance, and gasoline costs), transportation expenses (e.g. taxi, bus, and train), education expenses, and adult care expenses. Additional consumption variables added in 2005 include cell phone, internet, and cable expenses, recreation and vacation expenses, furnishing, clothing, home repair, and charitable giving. The additional consumption data in the PSID are compared with the imputed values to provide some external validity to the imputation method. The imputation method uses pooled cross section data from the CEX, 1980 to 2008, and the following demand equation (following Blundell, Pista-
25
ferri, and Preston [2008]’s notation) for food, f , expressed in logs:
0 fi,t = Wi,t µ + p0t θ + β(Di,t )ci,t + ei,t ,
(21)
for each individual i in period t with demographic, W , and relative price, p, demand shifters controlling for nondurable expenditure c expressed in logs, allowing the budget elasticity β to vary with observed household characteristics, D, and allowing for unobserved heterogeneity and measurement error in food expenditures, e. Table 2 reports this specification instrumenting total expenditure to account for its measurement error. We use the average hourly wage of the husband and wife by cohort, year, and education to instrument for total expenditures. These instruments pass the overidentifying restrictions test as the test fails to reject the null hypothesis that the instrumental variables are uncorrelated with the residuals. The price elasticity is -1.63 and the other estimates are generally have the expected sign. The budget elasticity is 0.76 though we reject the null hypothesis that this elasticity has remained constant over this period (p-value less than 0.01 percent). Table 3 provides the same estimates using total consumption as opposed to nondurable consumption expenses as in Table 2. This specification produces similar estimates; budget elasticity 0.81 and price elasticity of -1.76. These estimates allow us to invert the demand function and produce estimates of nondurable consumption for all households in the PSID.
26
Table 2: THE DEMAND FOR FOOD IN THE CEX-NONDURABLES Variable ln c
Estimate 0.762*** (0.199) ln c x HS dropout -0.0478 (0.0673) ln c x HS graduate -0.068 (0.146) ln c x one child -0.0268 (0.0236) ln c x two children -0.0527** (0.0253) ln c x three children + -0.0859*** (0.0253) ln c x 1983 -0.135 (0.109) ln c x 1985 0.0268 (0.0584) ln c x 1986 -0.00586 (0.0943) ln c x 1987 0.0509 (0.09) ln c x 1988 0.0633 (0.0884) ln c x 1989 -0.11 (0.163) ln c x 1990 -0.0682 (0.129) ln c x 1991 -0.0488 (0.128) ln c x 1992 0.000468 (0.118) ln c x 1993 0.058 (0.116) ln c x 1994 -0.0327 (0.173) Number of observations 40,204 Test of overidentifying restrictions Test time consistency of income elasticity
Variable ln c x 1995 ln c x 1996 ln c x 1997 ln c x 1998 ln c x 1999 ln c x 2000 ln c x 2001 ln c x 2002 ln c x 2003 ln c x 2004 ln c x 2005 ln c x 2006 ln c x 2007 ln c x 2009 ln c x 2008 ln c x 2010 ln c x 2011 R-squared
Estimate 0.129 (0.158) 0.137 (0.165) 0.109 (0.175) 0.0329 (0.195) 0.0454 (0.199) 0.132 (0.192) 0.0682 (0.223) 0.0237 (0.232) 0.0413 (0.244) 0.071 (0.249) 0.162 (0.252) 0.193 (0.277) 0.248 (0.297) 0.22 (0.315) -0.0112 (0.395) 0.107 (0.315) 0.365 (0.288) 0.649
Variable Age Age2 pf ood palcohol+tobacco pf uel+utils ptransports HS dropout HS graduate Northeast Midwest South Born 1970-79 Born 1965-69 Born 1960-1964 Born 1955-59 Born 1950-54 Born 1945-49
Estimate 0.0433*** (0.0146) -0.000341*** (0.000123) -1.638 (1.54) 13.88 (10.77) 4.38 (9.966) -27.21 (19.13) 0.482 (0.651) 0.685 (1.428) 0.00505 (0.00517) -0.0191 (0.0153) -0.00316 (0.0185) 0.385** (0.166) 0.324** (0.139) 0.268** (0.122) 0.213** (0.103) 0.176** (0.0875) 0.148** (0.075)
Variable Born 1940-44
Estimate 0.110* (0.0611) Born 1935-40 0.0936* (0.0516) Born 1930-34 0.0725** (0.0346) Born 1925-29 0.036 (0.0264) One Child 0.289 (0.234) Two children 0.567** (0.248) Three children+ 0.888*** (0.252) Family Size 0.0462*** (0.0133) White 0.0879*** (0.0176) Constant -0.724 (1.534) Family Size 0.0462*** (0.0133) White 0.0879*** (0.0176) Constant -0.724 (1.534)
18.73 (d.f. 20; χ2 p-value 54 %) 192.07 (d.f. 31; χ2 p-value 0.0001 %)
Notes: This table reports IV estimates of the demand equation for (the logarithm of) food spending in the CEX. We use cohort-education-year specific average of the log of the husband and wife’s hourly wage as an instrument for the log of total nondurable expenditure (including the interactions with time, education, and kids dummies). Standard errors are in parentheses.
27
Table 3: THE DEMAND FOR FOOD IN THE CEX-TOTAL CONSUMPTION Variable ln c
Estimate 0.816*** (0.214) ln c x HS dropout -0.0335 (0.0787) ln c x HS graduate 0.0158 (0.155) ln c x one child -0.0404* (0.0217) ln c x two children -0.0545** (0.0242) ln c x three children + -0.0948*** (0.0241) ln c x 1980 -0.161 (0.117) ln c x 1982 -0.0228 (0.0535) ln c x 1983 -0.104 (0.0882) ln c x 1984 -0.0313 (0.0788) ln c x 1985 -0.0196 (0.0777) ln c x 1986 -0.300* (0.166) ln c x 1987 -0.220* (0.134) ln c x 1988 -0.194 (0.134) ln c x 1989 -0.124 (0.124) ln c x 1990 -0.0419 (0.122) ln c x 1991 -0.216 (0.186) Test of overidentifying restrictions Test time consistency of income elasticity
Variable ln c x 1992 ln c x 1993 ln c x 1994 ln c x 1995 ln c x 1996 ln c x 1997 ln c x 1998 ln c x 1999 ln c x 2000 ln c x 2001 ln c x 2002 ln c x 2003 ln c x 2004 ln c x 2005 ln c x 2006 ln c x 2007 ln c x 2009
Estimate -0.225 (0.196) -0.168 (0.184) -0.0844 (0.172) 0.0223 (0.17) 0.0265 (0.176) -0.0355 (0.186) -0.151 (0.21) -0.13 (0.215) -0.02 (0.204) -0.172 (0.228) -0.22 (0.245) -0.23 (0.251) -0.2 (0.252) -0.094 (0.244) -0.0839 (0.261) -0.0469 (0.279) -0.0838 (0.293)
Variable ln c x 2008 ln c x 2010 ln c x 2011 Age Age2 pf ood palcohol+tobacco pf uel+utils ptransports HS dropout HS graduate Northeast Midwest South Born 1970-79 Born 1965-69 Born 1960-1964
Estimate -0.47 (0.388) -0.231 (0.303) 0.156 (0.272) 0.0489*** (0.0135) -0.000404*** (0.000111) -1.768 (1.768) 25.29** (12.13) 13.28 (10.12) -47.44** (20.92) 0.344 (0.777) -0.147 (1.565) 0.0122** (0.00571) -0.0443*** (0.0111) -0.0296** (0.0148) 0.348** (0.175) 0.296** (0.148) 0.247* (0.131)
Variable Born 1955-59 Born 1950-54 Born 1945-49 Born 1940-44 Born 1935-40 Born 1930-34 Born 1925-29 One Child Two children Three children+ Family Size White Constant
Estimate 0.194* (0.11) 0.154 (0.0939) 0.126 (0.0803) 0.0878 (0.0656) 0.0769 (0.0552) 0.0616 (0.0377) 0.0272 (0.0288) 0.443** (0.222) 0.622** (0.243) 1.043*** (0.257) 0.0461*** (0.0147) 0.0643** (0.025) -0.772 (1.741)
9.33 (d.f. 26; χ2 p-value 97 %) 339.88 (d.f. 26; χ2 p-value 0.00001 %)
Notes: This table reports IV estimates of the demand equation for (the logarithm of) food spending in the CEX. We use cohort-education-year specific average of the log of the husband and wife’s hourly wage as an instrument for the log of total nondurable expenditure (including the interactions with time, education, and kids dummies). Standard errors are in parentheses.
28
Table 4 compares the imputed values of nondurable consumption with reported nondurable consumption in the PSID for the years in which nondurable consumption was collected in the PSID. In the 2000s the PSID added questions about nondurable consumption providing us the opportunity to produce some external validity to the imputation. The first three rows demonstrate the closeness in fit between food expenditures reported in the PSID and the CEX. For the years 2002, 2004, 2006, and 2008 given in the Table 4 the imputed value is around 1 percent or less different than the PSID value. In addition, the imputed and PSID reported nondurable expenditure exhibit similar trends, which can be seen in Figure 1. These descriptive statistics are supportive of the ability of the imputation method to capture nondurable expenditures, though we only have a few years of data far from enough needed to be conclusive.25 25
Li, Schoeni, Danziger, and Charles [2010] compare the sum of all expenditures reported in the PSID (as opposed to consumption, which would require to include durable goods such as imputed housing and vehicles) with the CEX from 1999 to 2003. Combining all PSID categories, annual spending totals $25,961, 2 percent greater than CEX spending. Estimates for 1999 and 2003 are similar, with PSID total spending 4 percent lower than CEX spending in 1999 and 1 percent higher in 2003. As reported by the CEX in 2001, spending on categories included in the PSID totals $25,340, which accounts for 72 percent of total spending across all CEX categories, including PSID categories or not. This spending gap falls largely into five categories not measured in the 1999, 2001 or 2003 PSID waves: home repairs and maintenance, household furnishing and equipment, clothing and apparel, trips and vacations, and recreation and entertainment. PSID added questions covering these spending items to the 2005 and subsequent waves.
29
9.4
Average Log Nondurable Consumption 9.6 9.8 10
10.2
Figure 1: Nondurable Expenditure Trends
2002
2004
2006
2008
Year PSID Imputed
CEX
Table 4: CONSUMPTION COMPARISON PSID-CEX-IMPUTATION 2002
Food out expenses Food home expenses Food expenses Nondurable consumption
PSID 6.859 (1.026) 7.785 (0.669) 8.206 (0.641) 9.619 (0.983)
CEX 6.735 (1.013) 7.914 (0.416) 8.228 (0.433) 9.953 (0.428)
2004 IMP
PSID 6.930 (1.023) 7.807 (0.714) 8.258 (0.617) 9.623 9.650 (0.575) (0.918)
CEX IMP PSID 6.819 6.978 (1.069) (1.089) 7.921 7.912 (0.409) (0.683) 8.233 8.339 (0.443) (0.678) 9.999 9.525 9.758 (0.459) (0.638) (0.981)
30
2006 CEX IMP 6.811 (1.074) 7.917 (0.416) 8.252 (0.454) 10.10 9.765 (0.444) (0.628)
2008 PSID 7.101 (1.280) 7.839 (0.670) 8.351 (0.812) 9.514 (0.865)
CEX IMP 7.065 (1.006) 7.918 (0.401) 8.317 (0.437) 10.20 9.562 (0.433) (0.657)
3.2
Federal Income Taxes
From 1970 to 1991 the PSID asked respondents their total household federal income tax. Other studies, notably Blundell, Pistaferri, and Preston (2008), supplement this data by simulating federal tax liability using the National Bureau of Economic Research’s Taxsim program with information obtained from the PSID such as wages, other income, marital status, and number of children. Federal tax liability is an integral part of our analysis as we are interested in the role federal taxation has on providing insurance, which helps individuals to smooth consumption relative to income. This investigation is motivated by Blundell, Pistaferri, and Preston [2008] who claim that taxes and transfers have an important role in providing insurance to permanent shocks. We are particularly interested in understanding how insurance from taxation has changed over time. In our study we use the simulated federal tax liability from NBER’s Taxsim program for all years. This choice was made for consistency purposes because NBER’s Taxsim is able to simulate federal tax liability for all years in our sample.26 Figure (2) graphs the average federal tax liability from the PSID and NBER’s Taxsim program. Some of the difference is a 26
NBER’s Taxsim program provides estimates of federal tax liability from 1960 to 2013 and state tax liability from 1977 to 2011. Blundell, Pistaferri, and Preston [2008] use the PSID reported federal tax liability from 1980 to 1991 and use NBER’s Taxsim program to simulate ederal tax liability in 1992 and 1993, the last year covered in their study. Because we extend the data from 1993 to 2008 simply replicating their strategy to measure taxation would imply the use of NBER’s Taxsim program for half of the years covered by our data (1992-2008). Instead of using reported tax payments from the PSID for half of the years and NBER’s Taxsim for the other half, we choose to consistently use NBER’s Taxsim for all years.
31
result of deductions. On the one hand Taxsim assumes all deductions that a household is able to take are taken, regardless what the household actually takes. On the other hand, data covered by the PSID may not cover enough information, in which case Taxsim would not account for all possible deductions that a household could take. To test whether Taxsim systematically under or over simulates federal tax liability for a given characteristic, relative to the PSID, we regress the difference between the PSID and Taxsim on year and state dummies, marital status, number of children, age of husband and wife, labor income of husband and wife, other income, and rent. We find that only husband’s labor income (p-value 4 percent), other income (p-value 0.01 percent), husband’s age (p-value 4 percent), and years 1990, 1991, 1992 were statistically significant. The coefficients suggest that, relative to the PSID, for an additional $100 of husband’s labor income Taxsim under reports federal tax liability by $5, for an additional $100 of other income Taxsim under reports $14 of tax liability, and for an additional year of husband’s age Taxsim under reports $113 of tax liability. Despite these limitations we feel that Taxsim estimates are sufficient to capture the insurance role of taxation we are interested in. As described in equation 18, we decompose changes in insurance from income shocks into three parts: those due to changes in the distribution of income, insurance changes due to changes in tax policy, and insurance changes due to individuals’ behavioral response to policy or market shocks. Tax and benefit policy provides insurance by absorbing part of the shocks, 32
helping individuals smooth consumption relative to income shocks. For example consider an individual with gross income of of $70,000 half of the time and $30,000 the other half of the time. Without taxation this individual’s income can differ by $40,000 year over year. Now assume that there exists a progressive tax schedule such that the average tax rate is 20 percent at $70,000 and 14 percent at $30,000.27 Now the individual’s income net of taxes is $56,000 half of the time and $25,800 half of the time reducing the uncertainty from year to year to $30,200. In this example the government absorbs 24 percent of the uncertainty.28 From the previous example we can identify two mechanical ways in which the insurance from taxation may change over time. First, if tax policy changes such that the average tax rate is now 10 percent at $30,000 and 25 percent at $70,000 then the government absorbs 36.2 percent of the uncertainty. Second, consider the case where the income distribution changes such that now the individual makes $90,000 half of the time and $50,000 the other half of the time. With the same tax code the average tax rates are roughly 21 percent at $90,000 and 17 percent at $50,000. Then in this case the government absorbs 25.6 percent of the shock.29 27
This average tax rate is based on a simple calculation from the United States’ 2009 tax schedule, for a single person. 28 Here we apply simple progressivity of the actual 2009 tax schedules for single individuals, but we disregard exemption amounts. Though the government absorbs 24 percent of the shock they do so at a cost of $9,600, the difference in the average net of taxes income. 29 In this simple example the level of income and shocks was held constant. However, in our analysis we evaluate the shocks based on our summary statistics from our data on income and tax policy, holding either policy constant or market income constant (we also account for inflation when we hold policy and market effects constant).
33
In addition to mechanical changes due to policy or market changes, individuals may react differently to insurance from taxation over time. For example individuals’ views of tax breaks may change over time causing them to have a different propensity to consume given this change in income.30 Therefore the effectiveness of tax policy to smooth consumption relative to income shocks may change based on individual’s changing behavior. We consider all three possibilities in explaining how and why the insurance from permanent and transitory shocks has changed over time. To separate the effects on the insurance parameters due to changes in policy and changes due to the income distribution, we create two variables that capture these changes independently of each other (see section 2.5). Both of these variables determine what percentage of an income shock the tax code absorbs, as the examples given above simply illustrated. Equation 19 captures changes due to policy changes holding an individual’s income in year t constant as of a base year, and after controlling for inflation (e.g., tax brackets are indexed for inflation since 1981). Although our benchmark base year is 1980, we use alternative base years to evaluate the sensitivity of the choice of base years. Then using NBER’s Taxsim we simulate the change in federal tax liability due to a 10 percent shock to individuals’ incomes, in this case 1980 income for all years, allowing the tax policy to change over time. Therefore differences in the part of the income shock that is absorbed by 30
See Agarwal, Liu, and Souleles [2007], Shapiro and Slemrod [1995, 2003], Shapiro, Slemrod, and Sahm [2010], Souleles, Parker, and Johnson [2006] for empirical studies on individual behavioral effects of tax policy changes.
34
taxation is entirely due to differences in the tax code. Equation 20 likewise captures changes due to market changes. To estimate changes due to market income, we use NBER’s Taxsim to simulate the federal tax liability difference due to a 10 percent shock to income, this time holding the tax code fixed to 1980 (or an alternative base year). Therefore, any differences in the percent of the income shock absorbed by taxation is entirely due to market changes, specifically income distribution [Auerbach and Feenberg, 2000]. Table 5 reports summary statistics of the amount of insurance holding the tax code fixed, market insurance, and holding income fixed, policy insurance. These two insurance parameters define the percentage of the shock that the tax code absorbs. The larger the insurance parameter the larger the percent of an income shock the tax schedule absorbs. The first three rows report the average insurance parameter by income groups. At this point, it is important to note that Taxsim captures only the insurance from the tax code (e.g., direct benefits such as food stamps, or state-level welfare, are not included). The tax code provides the most insurance to high income tax payers regardless of whether we hold income distributions fixed or the tax schedule fixed. The rest of the table reports the average insurance parameter through different years, and figure 3 shows the average insurance parameter over time and by income groups. The market insurance parameter converges for the three income groups and increases slightly through time.31 This im31
Some of the convergence of the market insurance parameters across income groups is due to the fact income groups are determined based on 1980 income. Therefore, convergence in income overtime leads to convergence in the insurance parameter over time.
35
plies that income distribution changes has had a slightly increasing pressure on the tax code to provide more insurance on average. The policy insurance parameters have steadily decreased since 1980. This implies that tax policy changes have decreased the average amount of insurance provided by the tax code on average. Figure 3 also demonstrates that policy changes seem to have had a larger impact on the insurance parameter than changes in the income distribution over time. This suggests that total insurance from market and policy shocks has decreased overtime, meaning that individuals are more susceptible to income shocks. If this is true we should find an increasing covariance of changes in income and consumption over time. Of course, behavioral responses to changes in the tax code may also change over this period, which these summary statistics of shocks would not capture. For example, if individuals’ propensity to spend from a tax deduction increased over time, then despite the fact that the tax schedule absorbs a smaller proportion of income shocks, the effectiveness of tax policy changes in terms of consumption smoothing may actually increase. In addition, there may be other changes such as increased credit availability or changes in social norms of family support. We separately estimate the behavioral effects from the policy and market effect in the next section, in which we estimate changes in the consumption-income growth covariance matrix and decompose these changes to determine the changing role of tax policy on consumption smoothing.
36
4000
Federal Tax Liability 6000 7000 5000
8000
Figure 2: Federal Tax Liabilities-NBER and PSID
1978
1980
1982
1984
1986
1988
Year Taxsim
PSID
Table 5: MARKET AND POLICY INSURANCE CHANGES Variable Market Shock Low Income
Variable Policy Shock Low Income
Market Shock
Policy Shock Middle Income
Market Shock Market Shock Market Shock Market Shock Market Shock Market Shock Market Shock Market Shock
Mean (SD) 0.384 (0.121) Middle Income 0.429 (0.093) High Income 0.435 (0.095) 1977 0.34 (0.122) 1982 0.392 (0.119) 1987 0.417 (0.109) 1992 0.438 (0.092) 1998 0.459 (0.062) 2002 0.458 (0.061) 2008 0.451 (0.076)
Policy Shock High Income Policy Shock 1977 Policy Shock 1982 Policy Shock 1987 Policy Shock 1992 Policy Shock 1998 Policy Shock 2002 Policy Shock 2008
37
Mean (SD) 0.172 (0.114) 0.297 (0.119) 0.369 (0.104) 0.423 (0.139) 0.365 (0.112) 0.249 (0.097) 0.2 (0.086) 0.186 (0.099) 0.156 (0.125) 0.146 (0.14)
.5 -.1
0
Changes in Net Income Due To Market Changes .1 .2 .3 .4
.5 Changes in Net Income Due To Policy Changes .2 .4 .1 .3 0 -.1 1980
1990
2000
2010
1980
1990
Year Low Income High Income
2000
2010
Year Middle Income
Low Income High Income
(a) Holding Income Fixed
Middle Income
(b) Holding The Tax Schedule Fixed
Figure 3: Percent Of Income Shock Absorbed By Tax Schedule.
4
Empirical Evidence
This study’s focus is on the insurance parameters φ and ψ against permanent and transitory income shocks which we decompose into parts due to income distribution changes, tax policy changes, behavioral changes, and other market changes. We consider the evolution of these parameters through time and for different income groups. The matrix of variance-covariances of changes in income and consumption automatically produces conditions that generate these parameters. The results from our estimations are reported in tables 6, 7, and 8. We consider the relative size and trends in the variance of permanent and transitory shocks to income and estimate the sources of insurance that buffer consumption from these shocks. Tables 6, 7, and 8 report the unrestricted minimum distance estimates of the variance-covariance matrix of unexplained consumption and income 38
growth. To obtain the unexplained parts of consumption and income, we estimate the model in two steps. First, we remove the deterministic effects Zi,t (see equations 7 and 9). To do this, we separately regress log income and log consumption (imputed) on year dummies, year-of-birth dummies, observable characteristics (education, race, family size, number of children, and region) on log income and log consumption (imputed). The residuals of these regressions, ci,t and yi,t , are the unexplained components of consumption and income, respectively. [INCLUDE FIRST STAGE REGRESSIONS IN APPENDIX IN FUTURE DRAFT]. Then, we estimate these residuals over time and interact them with our market and policy shock measures using the unrestricted minimum distance estimator. Some of the moments in tables 6, 7, and 8 are missing due to missing data (e.g. the PSID did not collect food consumption data in 1987, 1988 or 1993). Table 6 reports the variance and autocovariance of consumption growth. Column 1 reports the variance of (imputed) consumption, which increases from 1969 to 1976, is high in the early 1990s, low in the late 1990s, and high in the 2000s. The magnitude of the variance of consumption is a combination of the effect of the variance in income, slope heterogeneity, and measurement error. The second column reports the first-order autocovariance of consumption growth which is a good estimate of the variance of the imputation error. These values are high and seem to be higher in the 1980s. Finally, second-order consumption growth autocovariances (third column) are small in economic terms and are mostly statistically insignificant. 39
Table 6: CONSUMPTION GROWTH AUTOCOVARIANCE MATRIX
Year 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985
(1) (2) (3) (1) (2) var(∆ct ) cov(∆ct ,∆ct+1 ) cov(∆ct ,∆ct+2 ) Year var(∆ct ) cov(∆ct ,∆ct+1 ) 0.091** -0.047 -0.011 1986 0.219*** -0.254*** (-0.043) (-0.031) (-0.019) (-0.027) (-0.066) 0.095** -0.035 0.005 1987 NA NA (-0.038) (-0.03) (-0.025) 0.096*** -0.056 0.005 1988 NA NA (-0.037) (-0.046) (-0.024) NA NA NA 1989 0.427*** -0.129* (-0.09) (-0.066) 0.134** -0.041 -0.015 1990 0.234*** -0.086*** (-0.065) (-0.045) (-0.023) (-0.035) (-0.026) 0.143*** -0.051* -0.009 1991 0.246*** -0.093*** (-0.038) (-0.026) (-0.014) (-0.031) (-0.024) 0.105*** -0.034 -0.004 1992 0.248*** -0.096*** (-0.035) (-0.025) (-0.013) (-0.03) (-0.029) 0.305*** -0.163*** -0.018 1993 NA NA (-0.034) (-0.024) (-0.012) 0.246*** -0.096*** -0.002 1994 0.238*** -0.097*** (-0.033) (-0.023) (-0.012) (-0.047) (-0.036) 0.153*** -0.057** -0.003 1995 0.194*** -0.055* (-0.032) (-0.022) (-0.011) (-0.034) (-0.029) 0.213*** -0.101*** -0.008 1996 0.192*** -0.060** (-0.031) (-0.021) (-0.011) (-0.037) (-0.027) 0.207*** -0.084*** -0.002 1997 0.168*** -0.050* (-0.025) (-0.017) (-0.009) (-0.038) (-0.028) 0.184*** -0.068*** 0.007 1998 0.185*** NA (-0.024) (-0.017) (-0.009) (-0.038) 0.183*** -0.083*** -0.007 2000 0.261*** NA (-0.024) (-0.016) (-0.009) (-0.037) 0.188*** -0.074*** -0.01 2002 0.356*** NA (-0.023) (-0.016) (-0.008) (-0.037) 0.211*** -0.095*** -0.007 2004 0.344*** NA (-0.023) (-0.016) (-0.01) (-0.036) 0.225*** -0.105*** -0.022 (-0.022) (-0.019) (-0.029)
(3) cov(∆ct ,∆ct+2 ) 0.061* (-0.037) NA NA -0.196*** (-0.038) 0.015 (-0.016) -0.044** (-0.018) -0.023 (-0.019) NA 0.034 (-0.022) -0.021 (-0.016) -0.02 (-0.015) -0.027* (-0.016) -0.092*** (-0.028) -0.107*** (-0.029) -0.196*** (-0.034) -0.049 (-0.146)
Notes: This table reports the variance autocovariance matrix for consumption growth. See the main text for details of how these estimates are used to in later estimates. Standard errors in parentheses.
40
Table 7 reports the variance and autocovariances of income growth. The variance of income, reported in column 1, increases from 1969 through 1976. The blip in 1992 could be due to the fact that the PSID made the questionnaire electronic and made imputations by machine. The variance of income remains high after 1992. The first-order autocovariance of income, reported in column 2, become more negative during the 1969 to 1979 period and then remain fairly stable. Column 3 reports the second-order autocovariance of income which are small and statistically insignificant, which from the model is indicative of serial correlation in transitory income. These estimates suggest that the canonical MA(1) process in growth, as given in the example from section 2, fits the data. Table 8 reports the covariance of consumption and income growth. These estimates are informative about how insurance, whether through the tax system, behavioral changes, or through the market, has changed over time. The contemporaneous covariance of unexplained income and consumption growth, shown in column 1, informs about the combined effect of permanent and transitory income shocks on consumption growth. From 1969 through 1979 these estimates are small and typically statistically insignificant. However, in the 1980s these estimates increase and are statistically significant. The contemporaneous covariance is stable through the 1990s and 2000s. The covariance between current consumption growth and one-period-ahead income growth, shown in column 3, is informative in models with liquidity constraints. These estimates slightly increase in magnitude over time with 41
Table 7: INCOME GROWTH COVARIANCE MATRIX
Year 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985
(1) (2) (3) var(∆yt ) cov(∆yt ,∆yt+1 ) cov(∆yt ,∆yt+2 ) 0.102*** -0.024*** -0.007 (-0.014) (-0.009) (-0.007) 0.079*** -0.020** 0.002 (-0.013) (-0.009) (-0.007) 0.078*** -0.026*** -0.002 (-0.013) (-0.009) (-0.007) 0.089*** -0.041*** -0.005 (-0.013) (-0.008) (-0.007) 0.093*** -0.027*** -0.001 (-0.012) (-0.008) (-0.007) 0.099*** -0.034*** -0.01 (-0.012) (-0.008) (-0.006) 0.110*** -0.042*** -0.016** (-0.012) (-0.008) (-0.006) 0.136*** -0.046*** 0.001 (-0.012) (-0.008) (-0.006) 0.117*** -0.040*** -0.009 (-0.012) (-0.008) (-0.006) 0.104*** -0.039*** -0.001 (-0.011) (-0.008) (-0.006) 0.123*** -0.043*** -0.001 (-0.011) (-0.007) (-0.006) 0.114*** -0.034*** 0.002 (-0.009) (-0.006) (-0.005) 0.100*** -0.044*** -0.007 (-0.009) (-0.006) (-0.004) 0.108*** -0.029*** -0.003 (-0.008) (-0.006) (-0.004) 0.102*** -0.039*** -0.009** (-0.008) (-0.006) (-0.004) 0.108*** -0.035*** -0.004 (-0.008) (-0.005) (-0.004) 0.106*** -0.041*** -0.002 (-0.008) (-0.006) (-0.004)
Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 2000 2002 2004
(1) (2) (3) var(∆yt ) cov(∆yt ,∆yt+1 ) cov(∆yt ,∆yt+2 ) 0.115*** -0.040*** -0.005 (-0.01) (-0.007) (-0.005) 0.109*** -0.046*** 0.001 (-0.01) (-0.007) (-0.005) 0.114*** -0.037*** -0.009* (-0.01) (-0.007) (-0.005) 0.117*** -0.042*** 0.006 (-0.009) (-0.007) (-0.005) 0.112*** -0.043*** -0.003 (-0.011) (-0.007) (-0.006) 0.115*** -0.043*** -0.006 (-0.01) (-0.007) (-0.006) 0.162*** -0.081*** -0.005 (-0.01) (-0.007) (-0.007) 0.184*** -0.054*** -0.003 (-0.015) (-0.01) (-0.008) 0.155*** -0.047*** -0.027*** (-0.012) (-0.009) (-0.007) 0.177*** -0.067*** 0.002 (-0.011) (-0.009) (-0.007) 0.196*** -0.069*** -0.007 (-0.012) (-0.008) (-0.007) 0.146*** -0.036*** -0.008 (-0.013) (-0.009) (-0.008) 0.161*** NA -0.072*** (-0.013) (-0.009) 0.169*** NA -0.073*** (-0.013) (-0.009) 0.152*** NA -0.046*** (-0.013) (-0.011) 0.140*** NA -0.039 (-0.012) (-0.042)
Notes: This table reports the variance autocovariance matrix for income growth. See the main text for details of how these estimates are used to in later estimates. Standard errors in parentheses.
42
three of the four years and become statistically significant in the 1990s. At the bottom of table 8 we report the tests of whether current consumption covaries with future income shocks, to test the presence of advanced knowledge. If future income shocks are known in advanced then current consumption should react to these shocks. However we fail to reject the null that all higher autocovariances of income with respect to current consumption are zero. Finally, the covariances between current income growth and one-period-ahead consumption growth, reported in column 2, is informative about the evolution of insurance with respect to transitory shocks. In theory, a decreasing absolute value of this estimate towards zero means more insurance. These estimates, though small and rarely statistically significant, seem to increase in the early 1990s, implying that insurance of transitory shocks decreased over this period. Table 9 reports the results from the diagonally weighted minimum distance (DWMD) estimates of the variance of the permanent and transitory shocks to income, the variance of unobserved slope heterogeneity, the serial correlation of the transitory shock, and the partial insurance parameters of permanent and transitory shocks. The variance of the permanent shock increases until the late 1980s, remains high into the early 1990s and then decreases. This finding on the permanent shocks is similar to that reported by Moffitt and Gottschalk (1995) using PSID data on male earnings. The variance of the transitory shock begins high in 1979 and 1980, decreases until 1986 and then increases until its peak in 1996 and then a slight decline 43
Table 8: CONSUMPTION-INCOME GROWTH COVARIANCE MATRIX
Year 1969 1970 1971 1972
(1) cov(∆ct ,∆yt ) 0.011 (-0.011) 0.01 (-0.01) 0.007 (-0.01) NA
0.014 (-0.017) 1974 0.014 (-0.01) 1975 0.005 (-0.009) 1976 0.019** (-0.009) 1977 0.021** (-0.009) 1978 0.017* (-0.009) 1979 0.013 (-0.008) 1980 0.012* (-0.007) 1981 0.018*** (-0.006) 1982 0.021*** (-0.006) 1983 0.024*** (-0.006) 1984 0.021*** (-0.006) 1985 0.022*** (-0.006) Test cov(∆yt+1 , ∆ct ) Test cov(∆yt+2 , ∆ct ) Test cov(∆yt+3 , ∆ct ) Test cov(∆yt+4 , ∆ct )
(2) (3) cov(∆ct+1 ,∆yt ) cov(∆ct ,∆yt+1 ) -0.001 -0.004 (-0.01) (-0.01) -0.002 0.008 (-0.01) (-0.009) -0.008 0 (-0.017) (-0.009) NA NA
1973
= = = =
0 0 0 0
0.003 (-0.009) -0.004 (-0.008) -0.006 (-0.009) -0.015* (-0.008) -0.01 (-0.008) 0.005 (-0.008) 0.012 (-0.008) 0.002 (-0.006) -0.004 (-0.006) -0.002 (-0.006) -0.006 (-0.006) -0.009 (-0.006) 0.003 (-0.007) for all t for all t for all t for all t
0.005 (-0.015) -0.009 (-0.009) 0.003 (-0.008) -0.014* (-0.008) -0.002 (-0.008) -0.014* (-0.008) -0.006 (-0.007) 0 (-0.006) -0.008 (-0.006) -0.006 (-0.006) -0.004 (-0.006) 0.003 (-0.005) -0.002 (-0.005)
(1) Year cov(∆ct ,∆yt ) 1986 0.015** (-0.007) 1987 NA
(2) cov(∆ct+1 ,∆yt ) 0.03 (-0.024) NA
(3) cov(∆ct ,∆yt+1 ) -0.005 (-0.006) NA
1988
NA
NA
NA
1989
0.089*** (-0.024) 0.016* (-0.009) 0.022*** (-0.008) 0.020** (-0.008) NA
-0.001 (-0.007) -0.002 (-0.008) -0.019** (-0.008) 0.004 (-0.01) NA
-0.005 (-0.023) -0.01 (-0.009) -0.014* (-0.008) -0.004 (-0.008) NA
0.009 (-0.013) 0.023** (-0.009) 0.022** (-0.01) 0.019* (-0.01) 0.020** (-0.01) 0.021** (-0.01) -0.006 (-0.01) 0.001 (-0.01)
-0.011 (-0.009) -0.014 (-0.01) -0.018* (-0.009) -0.019* (-0.01) NA
-0.021* (-0.012) -0.032*** (-0.01) 0.001 (-0.009) 0 (-0.009) NA
NA
NA
NA
NA
NA
NA
1990 1991 1992 1993 1994 1995 1996 1997 1998 2000 2002 2004
p-value p-value p-value p-value
27% 34% 21% 51%
Notes: This table reports the variance autocovariance matrix for consumption-income growth. See the main text for details of how these estimates are used to in later estimates. Standard errors in parentheses.
44
into the 2000s. This suggests that the increases income inequality were more likely to be due to increased permanent shocks in the 1980s and in the early 1990s, and more likely to be due to transitory shocks in the late 1990s, which corroborates with the results from previous research [?]. Our results also suggest that while the variance or permanent shocks was two to three times as large as that of transitory shocks in the 1980s, the variance of transitory shocks became consistently been two to three times as large as that of permanent shocks in 2000s. Table 10 reports the DWMD estimates of the coefficients on the parameters representing how the tax code insures against market and policy shocks, derived from the simulations discussed previously. These effects are allowed to differ across three time periods; 1979-1985, 1986-1995, and 1996-2006. The estimates suggest that there has been large changes in the insurance parameters, combining behavioral and direct effects of the insurance (against market shocks) that is built in the tax schedule, and the insurance from policy shocks. The former is what we call “market insurance” (columns 1 and 2) and reflects changes that are inherent to the tax code (which we measure as changes in average tax liability due to changes in the income distribution, keeping policy constant). This effect is also known in the literature as built-in stabilization or automatic stabilization. The insurance from policy shocks (columns 3 and 4) reflects active or interventionist tax policy (which we measures as changes in tax by keeping the income distribution constant). The coefficient on the insurance against transitory income shocks (ψ P ) due 45
Table 9: MINIMUM-DISTANCE PARTIAL INSURANCE AND VARIANCE ESTIMATES σζ2 Year (Variance perm. shock) 1979 0.0461 1980 0.0966 1981 0.1515 1982 0.1676 1983 0.1509 1984 0.1619 1985 0.1580 1986 0.1508 1987 0.2175 1988 0.3274 1989 0.2116 1990 0.0903 1991 0.1625 1992 0.2092 1993 0.3265 1994 0.2612 1995 -0.0177 1996 0.0126 1997 0.0364 1998 0.02041 2000 0.0252 2002 0.0268 2004 0.0208 2006 0.0167 σξ2 (Variance unobs. slope heterog.) θ (Serial correl. trans. shock) φ (Partial insurance perm. shock) ψ (Partial insurance trans. shock)
σε2 (Variance trans. shock) 0.0915 0.1154 -0.042 0.0210 0.0228 0.0213 0.1149 -0.018 0.0593 0.0818 0.0563 0.0665 0.0725 0.0613 0.0468 0.0658 0.0451 0.1398 -0.003 0.0528 0.0431 0.0481 0.0490 0.0809 -0.2079 0.1364 0.647 0.054
Notes: This table reports the diagonally weighted minimum distance estimates of the parameters of interest. See the main text for details on the moments used to estimate these parameters. Standard errors (will be) in parentheses.
46
to changes in policy (i.e., changes in the tax schedule) decreased from 0.847 to .108 over three decades meaning that fiscal policy has been increasingly active over time to smooth transitory income shocks. In contrast, the coefficient on the insurance against permanent shocks (φP ) due to changes in policy increased from 0.201 to 0.470, meaning that fiscal policy has been less active at insuring against permanent shocks. In comparison, the coefficient on the insurance against transitory and permanent shocks that is inherent to the tax schedule (ψ M and φM , respectively) both decreased during this time period, meaning that automatic stabilizers (i.e., insurance that is inherent to the tax code) have played an increasing role at smoothing permanent and transitory income shocks, even though the variance in consumption has been rapidly increasing, especially in the last decade. Another striking result is that automatic stabilizers were less prominent in smoothing consumption until the mid-1980s, as compared to tax policy changes. For instance, in 19791985, the coefficient on the role of insurance built in the tax code was almost three times as large as that of changed in policy at smoothing consumption against permanent shocks (0.560 compared to 0.201). By 1996-2006, the coefficient was almost five times smaller than that on the policy effects (0.095 against 0.470), meaning that active tax policy has played a decreasing role at smoothing consumption as compared to built-in effects. This is not the case for transitory shocks, for which the role of built-in effects and policy effects have had about the same weights throughout the period. We can use these estimates of the “market” and “policy” effects to evalu47
Table 10: MINIMUM-DISTANCE PARTIAL INSURANCE AND VARIANCE ESTIMATES - DECOMPOSITION
Partial insurance perm. shock Partial insurance trans. shock
1979-85 1986-95 1996-06 1979-85 1986-95 1996-06
(1)
(2)
Market Insurance φM,1 φM,2 φM,3 ψM,1 ψM,2 ψM,3
DWMD Estimate 0.560 0.512 0.095 0.770 0.158 0.080
(3) Tax Schedule Insurance φP,1 φP,2 φP,3 ψP,1 ψP,2 ψP,3
(4) DWMD Estimate 0.201 0.951 0.470 0.847 0.410 0.108
Notes: This table reports the diagonally weighted minimum distance estimates of the decomposed insurance parameters. See section 2 for details on the moments used to estimate these parameters. Standard errors [REPORT IN FUTURE DRAFT] in parentheses.
ate the effects on insurance of changes in the tax code (tax schedules), income distribution (captured by market insurance), and their associated behavioral responses can be . The change in the insurance parameter over this time period is given by,
∆φ = φM,2 S2M + φP,2 S2P − φM,1 S1M − φP,1 S1P + φM,1 S2M + φP,1 S2P − φM,1 S2M − φP,1 S2P
(22)
= φM,1 (S2M − S1M ) + S2M (φM,2 − φM,1 ) + φP,1 (S2P − S1P ) + S2P (φP,2 − φP,1 ) | {z } | {z } | {z } | {z } ∆ Inc. Dist. ∆ Beh. Inc. ∆ Tax Policy ∆ Beh. Tax where by adding and subtracting off φM,1 S2M + φP,1 S2P we can quantify each of these four pieces separately. This same decomposition can be done 48
for the insurance parameter on the transitory shock. Using the average insurance parameters SiM and SiP and the estimates in table 10 we find that the aggregate amount of the smoothing effect has increased for both the permanent shock and the transitory shock. However, for the permanent income shock the largest effect is the change in behavioral response of individuals who have tended to react to permanent income shocks by smoothing even more their consumption than the amount inherent to the tax code. The numerical quantities are reported in table 11. Interestingly, the automatic stabilization term is now positive (and small, at 0.084), meaning that the tole of automatic stabilizers has in fact be decreasing over time, not increasing. The aggregate increase in insurance to permanent shocks that is due to build-in effect are behavioral reactions to the tax code (-0.21). Fiscal policy has played an increasing role at insuring against permanent shocks (-0.05) and individual’s reaction to active policy has been to insure less against those shocks (0.04) offsetting the direct policy effect. Behavioral effects have implied more insurance against transitory shocks for both the built-in part and the active policy part. the direct stabilization part from built-in stabilization has played a decreasing role at smoothing consumption (+0.12) while the part to to active policy has implied more consumption smoothing against transitory shocks. [TO DO: compare with figure 3]
49
Table 11: MINIMUM-DISTANCE PARTIAL INSURANCE AND VARIANCE ESTIMATES - DECOMPOSITION
∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆
Income distribution Behavioral response Tax policy Behavioral response Income distribution Behavioral response Tax policy Behavioral response
income dist. tax income dist. tax
Algebraic Expression φM,1 (S2M − S1M ) S2M (φM,2 − φM,1 ) φP,1 (S2P − S1P ) S2P (φP,2 − φP,1 ) ψM,1 (S2M − S1M ) S2M (ψM,2 − ψM,1 ) ψP,1 (S2P − S1P ) S2P (ψP,2 − ψP,1 )
Quantity 0.084 -0.21 -0.05 0.04 0.12 -0.31 -0.21 -0.11
Notes:
5
Conclusion
The goal of this paper is to explore the ability of the inherent structure of federal tax system, or built-in stabilization, to smooth consumption against transitory and permanent income shocks. Furthermore, we compare this source of consumption smoothing with active tax policy (e.g., discretionary changes in the tax code), which has been extensively used since 2000. Recent literature has showed that the volatility of income and consumption as rapidly increased in the past 30 years, and that transitory income shocks have become more prominent in the past two decades, while permanent income shocks were much more prominent in the 1970s through the mid-late 1980s. The innovation of this paper is to investigates the degree of policy insurance and self insurance against idiosyncratic income shocks. To do this, we construct a panel consumption for the PSID database using Blundell, Pistaferri, and Preston [2008]’s imputation procedure that maps food con-
50
sumption into non-durables consumption using the estimates of a demand equation for food, estimated from repeated CEX cross sections. We repeat this exercise based on available CEX data from 1972 to 2009 and PSID data from 1967 to 2008. Our results confirm the findings from previous literature that the persistence of income shocks has decreased over time, with the variance of transitory shocks low and the variance of permanent shocks high through the early 1990s, and the reversing trend after that. This paper is the first to separate the part of insurance against income shocks that is due to automatic insurance inherent to the tax code (built-in stabilization or “market effect ”), and the insurance that is due to active tax policy. The former, market effect, acts at insuring unpredicted changes in income shocks even if policy doe not change. The latter, policy effect, insures unpredicted income shocks though changes in active tax policy, even if the distribution of income across the population does not change over time. This paper further decompose each of these two effects into two parts: for each of these effects, the first part is the direct effect of built-in policy or active policy, and the second part represents individual’s behavioral effect to these sources of insurance, the market behavioral effect and the policy behavioral effect. After presenting the model that separates these four insurance effects, we apply a minimum distance estimator to evaluate their contribution to changing consumption smoothing over time and across income groups. Our results show that there has been a significant increase in insurance from both active and automatic policy since the 1970s. In particular from 1979 51
to 2006, the market insurance (or built-in insurance) a has increased by a factor of almost 1 to 6 for permanent income shocks and by a factor or almost 1 to 8 for transitory shocks. Nowadays, the built-in insurance helps more at smoothing consumption against transitory shocks than permanent shocks, while the opposite was true 30 years ago. We also find that over the same period the active policy insurance part has experienced different trends depending on the type of income shocks. The policy insurance against permanent shocks has decreased by more than half its size since the 1980s, but decreased eightfold for transitory shocks. Another important result is that, nowadays, permanent shocks are five times more insured by active fiscal policy than by automatic stabilization, while they were more than twice covered by built-in policy in the early 1980s. The most important result (so far in this draft) is that the behavioral effect from individual changes is the most responsible for increased insurance from built-in and active policies. In fact, the direct automatic stabilization of the tax system (the part that is not due to behavioral effect) has decreased, not increased, insurance over time, regardless of the nature of the income shock. The active policy effect has increased consumption smoothing over time, regardless of the shock, but this effect is small for the permanent shock. In sum, this paper provides strong evidence that combined policy insurance against income shocks has increased over time, probably precisely because consumption inequality has increased in the same period. However, it also suggests that the effectiveness of automatic stabilizers has changed over time, and that their direct 52
consumption-smoothing effect deteriorated in the past 30 years, while the indirect households behavioral responses to built-in stabilization has changed towards more insurance. In future version of this paper, we wish to extend the methodology to allow for measurement error in income and consumption. We also wish to make the empirical model more flexible and tests for longer lags in the income process. One of the main goals of this paper is to compare the insurance effects previously described not only across income groups, but also across education groups and cohorts. We also wish, in future research, to add the effects of direct benefits that are not directly observable from the tax code (e.g., welfare benefits, state benefits). We also wish to compare the contributions of each of the most important parts of the tax and benefit system (e.g., unemployment insurance as compared to the progressively of the tax schedule, food stamps as compared to direct assistance, etc).
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