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Finance and Economics Discussion Series: 2012-64 Screen Reader version ^♣

The Effect of Self-Reported Transitory Income Shocks On Household Spending

Samuel Ackerman

John Sabelhaus*

August, 2012

Keywords: Transitory income, household spending

Abstract:

We use repeated cross-sections of the Survey of Consumer Finances (SCF) to study the effect of self-reported transitory income shocks on household food spending. The self-reported shocks in the SCF are derived from survey questions about the gap between actual and "normal" income. This approach stands in contrast to existing income shock measures in the literature, which are generally derived from the residuals of estimated earnings or income equations. Although the self-reported transitory shocks could potentially give very different answers, the overall variance and asymmetry of shocks over the business cycle are similar to those of existing residual-based estimates. Engel Curve analysis shows a significant relationship between self-reported income shocks and household food spending, though the estimated spending responses are only a small part of the substantial slowdown in the growth rate of food consumption observed during the recent economic downturn.

JEL Classification: D12, E21

1. Introduction

One of the continuing legacies of the Great Recession is a dramatic slowdown in the growth rate of aggregate consumer spending. This sharp break in trend growth has led to renewed interest in some very old questions in macroeconomics.¹ Do consumers react to transitory income shocks by reducing spending, or do they smooth consumption over those shocks? If consumers reduce their spending when their income falls, is it because they are liquidity constrained? Do only those consumers actually affected by income shocks reduce their spending, or do unaffected consumers also lower their consumption for precautionary reasons?

In this paper we use repeated cross-sections from the triennial Survey of Consumer Finances (SCF) to study the effect of self-reported income shocks on household food spending.² Food spending includes both food at home and purchased meals and beverages. Together, those account for just over ten percent of total personal consumption expenditures (PCE) in the National Income and Product Accounts (NIPA). Although food spending is more of a necessity than most consumption items, the overall PCE pattern of rapid spending growth between the mid 1990s and 2006 and failure of the growth rate to recover after the Great Recession is evident in the aggregate NIPA food consumption data (Figure 1). Between the two food consumption categories, it is not surprising that purchased meals and beverages show both higher trend growth before the Great Recession and a larger reversal of trend growth after 2006, because purchased meals and beverages are generally more income elastic and discretionary in nature.

The self-reported income shocks analyzed in this paper are derived from survey questions about the gap between actual and "normal" income in the SCF.³ Towards the end of the SCF survey, after detailed income components have been summed to arrive at a total, respondents are asked if that total income is higher than, lower than, or about the same as their income in a "normal" year. Most respondents say their reported total income is in fact about normal-the median gap between actual and normal income is zero in every survey year. However, sizable minorities of respondents indicate that their income is either unusually high or unusually low, and those fractions vary predictably and systematically with business cycle conditions.

The self-reported income deviations in the SCF are intended to capture the principle of a transitory income shock, but the gaps between actual and normal income in the SCF could in practice be very different from the estimated transitory income shocks that are generally used to study consumption behavior. The canonical approach when studying household-level consumption behavior has been to derive transitory income shocks from the residuals of earnings or income equations estimated using panel data. Transitory shocks are solved for as one component of the overall income change: the unexplained change in income that does not appear (to the econometrician) to be permanent.

Although the transitory income shocks in the SCF are estimated using a very different approach, the high-level statistical properties of the self-reported gaps between actual and normal income seem generally consistent with the properties of transitory income shocks derived from the residuals of estimated equations. In particular, the variances of the percentage gap between actual and normal income are of the same general magnitudes as the variances of residual-based annual transitory shocks, and the shape of the distribution of the gaps changes asymmetrically over the course of the business cycle in ways that are consistent with residual-based estimates. Thus, there is reason to believe that the households who self-report experiencing a transitory shock are the same households that the econometrician would identify as having experienced a transitory shock simply by looking at changes in their income over time.

Given these reassuring findings about the statistical properties of the self-reported income shocks in the SCF, the next step involves investigating whether those shocks have explanatory power with respect to household food spending. The SCF has been collecting data on food spending (both food at home and food away from home) since the 2004 survey, and thus there are now three sets of cross-sections to work with (2004, 2007, and 2010). The SCF estimates of food at home match the NIPA values quite well, but the estimated SCF aggregates of food away from home fall short in levels. For our purposes, what matters is that the SCF finds slowly growing inflation-adjusted total food spending over the six year period 2004 through 2010, and a shift from spending on food away from home towards food at home.

Engel Curve analysis shows a clear relationship between self-reported income shocks and household food spending, though the estimated spending responses are not large enough to explain the dramatic slowdown in the growth of food spending observed during the recent economic downturn. The relationship between both types of food spending and normal income is highly non-linear, so we use a linear-spline across vingtiles of normal income as the basic model for analyzing self-reported income shocks. A more parsimonious functional form might dictate the magnitude of income effects at various points in the normal income distribution, and the linear-spline allows us to capture the non-linear relationship between food spending and normal income while preserving flexibility in propensities to consume out of normal income across normal income groups.

Using the linear-spline as our basic model, we evaluate changes in both types of food spending across the surveys using two additional sets of independent variables.⁴ The first set of variables is dummies for 2007 and 2010. The coefficients on these dummies reflect any changes in average food spending after 2004 not captured by the non-linear Engel Curves. If food spending only depends on normal income, and that relationship is stable over time, then the changes in food spending over time should be fully explained by the Engel Curves and the year dummies will be insignificant. For spending on food at home in 2010, that is close to being the case. However, for food away from home, the 2010 dummy is highly significant, and indicates a large drop (about 13 percent) in spending relative to 2004.

One possible reason for the unexplained decline in food away from home is that families self-reporting transitory income shocks cut back on their spending because of liquidity constraints or other reasons. Thus, the second set of regressions includes the gaps between actual and normal income, where positive and negative shocks are introduced separately so they can have different effects. The effects of the two types of shocks are largely the same order of magnitude, and the effects are highly significant for food away from home, but not for food at home. Thus, families self-reporting negative shocks have lower average spending on food away (relative to the Engel Curve prediction) than families not reporting shocks. However, the size of these estimated effects is very small, and they account for only a small fraction of the overall unexplained drop in spending.

These estimates of unexplained residual declines in food spending and the effects of transitory income shocks on food spending both pertain to average spending across all families. In any cross-section analysis, but especially with the SCF where the top end of the wealth distribution is well-represented because of the oversampling strategy, it is useful to investigate differences across households. In the final set of regressions we interact the year dummies and the self-reported income shock terms with dummies for quintile of normal income. It is not surprising that both the unexplained residual decline and the estimated impact of self-reported transitory income shocks are both much smaller at the very top of the normal income distribution. The primary impact in the next highest quintile seems to be a shift towards food at home. Both the unexplained residual and the estimated impact of income shocks are largest for the bottom three quintiles by normal income.

2. Self-Reported Transitory Income Shocks

Macroeconomists who study consumer spending behavior recognize the need to distinguish between transitory and permanent income shocks. Although the concepts of permanent and transitory shocks are clear in principle, and expectations about consumption responses given the two types of shocks (with and without liquidity constraints) are also generally straight-forward, the measurement and analysis of income shocks remains fertile ground for empirical research.⁵ Most of the research on income shocks is based on estimating income or earnings equations using panel data, then manipulating the residuals of those equations in order to separate the unexplained income changes into permanent and transitory components. The SCF measure of transitory income shocks is potentially very different from the typical residual measure, because the SCF measure is based on households' own assessment of how much their actual income deviated from "normal" during the previous year.

Respondents in the SCF are asked to report amounts for individual components of their previous year's income, including income from wages, businesses, capital gains, and transfers; several of these components may have negative amounts. For most income components, the respondent is given the corresponding location on the IRS 1040 form for comparison. The respondent is then asked to confirm whether their previous year's income matches the total of these components. If it is incorrect, the respondent is asked to provide a corrected total. This respondent-approved total income is referred to throughout this paper as "actual" income.

The respondent is then asked, "Is this income unusually high or low compared to what you would expect in a "normal" year, or is it normal?" The three possible answers are unusually high, unusually low, and the same as what they would expect in a normal year. If the respondent reports their income was unusually high or low, they are asked "About what would your total income have been if it had been a normal year?"⁶ Most respondents never hear the second question about the level of normal income, because the majority of respondents in any given SCF indicate their actual income is not in fact different from "normal."

There are, however, sizable minorities of respondents in every SCF survey who indicate that their income in the previous year was either unusually high or low, and the fractions of respondents with gaps between actual and normal income vary predictably and systematically with business cycle conditions. For those respondents, the interpretation of the self-reported gap between actual and normal income is essentially what economists have in mind when they describe a transitory income shock.⁷ Although the self-reported gap is in principle a useful estimate of transitory shocks, there are a number of questions one should ask about the measure in order to understand how it relates to the more typical residual-based estimates.

Transitory income shocks have been estimated using various data sets, different income and earnings concepts, individual and household-level units of observation, and alternative parameterizations of the stochastic process for the shocks themselves. Following Sabelhaus and Song (2010), the simplest specification involves decomposing log earnings or income (y ${}_{it}$ ) into a deterministic component that evolves with observable characteristics (x ${}_{it}$ ), a permanent component that involves slowly over time ( ${\mu}_{it}$ ), and a transitory component ( $\varepsilon$ ${}_{it}$ ). That is,

(1) ${y}_{it} = \beta{x}_{it }+ {\mu}_{it} + {\varepsilon}_{it}$

The permanent component changes when the individual receives a permanent shock ( ${\eta}_{it}$ ),

(2) ${\mu}_{it} = {\mu}_{it-1} + {\eta}_{it}$

Given simplifying iid assumptions on ${\varepsilon}_{it }$ and ${\eta}_{it}$ , it is straight-forward to recover estimates of the variances for the two shocks ( ${\sigma}^{2}_{\varepsilon }$ and ${\sigma}^{2}_{\eta }$ , respectively) using panel data.⁸ ${}^{,}$ ⁹ Although there is a great deal of heterogeneity in underlying income concepts, unit of observation, data sources, and methods, there is a fair amount of uniformity in the literature in estimates for the percentage variance of transitory shocks, with values generally below but near ten percent.¹⁰

The first question one might ask when comparing the SCF normal income measure to estimates from the literature is whether respondents do in fact seem to have a comparable notion of permanent income in mind when they answer the normal income question. Some evidence for a comparable notion is found by comparing various percentiles of actual and normal income across survey years (Table 1). Although it will be shown below that there is significant variation in the distribution of the household-level gaps between actual and normal income, the univariate distributions of the two income measures exhibit a great deal of relative stability over time. In every survey year, actual income is always well below normal income at lower percentile points, while the opposite is true at the very top of the income distributions. However, the relative percentile points in the middle of the distributions are very similar. This relative stability is exactly what one would expect to see when households experience both positive and negative transitory shocks, but on average, their permanent (or normal) income is not systematically different from actual income. The exception that proves the rule occurred in the most recent survey year, 2010, when the ratio of actual to normal income collapsed at every percentile point, indicating widespread negative transitory income shocks associated with the Great Recession.

The second question about self-reported transitory income shocks involves two high-level statistical properties of the gaps between actual and normal income: means and variances. The average gaps tend to be relatively small, though cyclical (Table 2). Variances of the self-reported gaps can be computed in a number of ways, but in order to have measures that are directly comparable to the residual-based estimates in the literature we compute the variance of the percentage gap using var(ln(actual income) - ln(normal income)). Percentage gaps cannot be computed on zero or negative incomes, so we present two sets of estimates: the first has both actual and normal income restricted to be positive, and the second has both restricted to be greater than $5,000.¹¹ Imposing the (modest) $5,000 threshold has a large impact on estimated variances; in 2010, the estimated variance falls from 14.5 percent to 10.9 percent.¹² Although the 2010 value for the self-reported transitory income variance in the SCF is at the high end of the range of estimates found in the literature, 2010 is of course an exceptionally bad year. The variances of the self-reported gaps in other years are very much in line with residual-based estimates.¹³

A third set of questions about self-reported transitory income shocks involve the shape of the shock distribution. Most of the literature on estimating permanent and transitory shocks using panel data has effectively ignored the issue of asymmetry, but Guvenen, Ozkan, and Song (2012) show that in recessions the distribution of transitory shocks (and possibly even permanent shocks) becomes highly asymmetric, in the sense that negative shocks are much more likely than positive shocks. This pattern of increasing asymmetry over the business cycle is also evident in the self-reported transitory shocks in the SCF (Table 3), though to some extent the self-reported shocks in the SCF are somewhat asymmetric in every year.

The fraction of SCF families reporting a negative gap (actual income below normal income) was 25 percent in 2010, up sharply from the 14 percent in 2007 and higher than any other year since the question was first asked in the survey, which was in1995. At the same time, the fraction reporting a positive shock was only 6 percent in 2010, down from 9 percent in 2007, and lower than any other year since 1995. Given that the 2007 survey was focused on 2006 incomes, realized before the on-set of the Great Recession, and the 2010 survey focused on calendar year 2009, when the economy was still struggling, this is good timing from the perspective of confirming previous findings about asymmetric shocks over the business cycle.

In addition, the shift in the fraction of families with positive and negative shocks between 2007 and 2010 was accompanied by relatively stable mean and median shocks, conditional on having shocks in a particular direction. This also confirms findings in Guvenen, Ozkan, and Song (2012), because they find that the best way to describe the stochastic process is in terms of the entire shock distribution shifting to the left during a cyclical downturn. That is, an increasing variance of the transitory shocks may be a part of the story, as it is in the SCF, but the more dominant theme is that the modal tendency of shocks becomes more negative in a recession.

The relatively small fractions of families reporting gaps between actual and normal income, the fact that mean gaps are larger than median gaps conditional on having gaps, and the relative stability of those conditional gaps over time raises a fourth question about self-reported shocks. Are the estimates dominated by shocks experienced by families at particular normal income levels? The answer from the SCF is clearly no-self-reported gaps between actual and normal income occur across all normal income groups, and with a few exceptions, generally to the same relative degree (Table 4). That is, the ratio of average actual income to average normal income and various percentiles of actual income relative to average normal income are largely similar across normal income groups.

In 2010 the ratio of average actual income to average normal income was 94 percent across all families in the SCF. That ratio was higher at the bottom of the normal income distribution-100 percent or more in the bottom two vingtiles of normal income, but to some extent, that may reflect errors in reporting normal income itself. For example, families who under-report normal income, say because they misunderstood the question, are more likely to be sorted into the bottom of the normal income distribution. Setting aside those families with very low normal income, the ratio of average actual income to average normal income is relatively invariant with respect to normal income.

The same stability in reported gaps by normal income holds if we consider various percentiles of the actual to normal income distribution. Table 4 shows the 5 ${}^{th}$ , 10 ${}^{th}$ , 90 ${}^{th}$ , and 95 ${}^{th}$ percentiles of actual income within each normal income vingtile, where each actual percentile is scaled by the average normal income in that normal income vingtile. Thus, for example, for all families in 2010, the 5 ${}^{th}$ percentile of actual income was 12 percent of the overall average for normal income, while the 95 ${}^{th}$ percentile of actual income was 245 percent of the average for normal income, which simply describes the extent of actual income heterogeneity in the data. The more important message of the percentile columns is that the relative distributions of actual income to normal income across normal income groups are very similar, which means the proportional gaps between actual income and self-reported normal income are very similar. The exception in this case occurs for the highest normal income vingtile, where both very low and very high realized incomes are more extreme than in the other normal income groups.

The fifth and final question about self-reported income gaps involves how the gaps compare to actual income changes over (roughly) the same time period, in this case, estimated using the 2009 re-interview of 2007 SCF respondents (Table 5).¹⁴ Movements across income quintiles as measured by the panel re-interview in 2009 will include both permanent and transitory shocks as well as any movements associated with observables like age, and the actual income changes are measured for two years instead of the current-year self-reported gap concept in the SCF cross-sections that we are focused on here. Even so, the matrices of actual quintile-level income movements and self-reported quintile-level actual and normal income positions show remarkable similarities. The differences that do exist appropriately indicate that self-reported one-year income deviations are a subset (meaning there is less mass off the diagonals) of the income movements captured in the 2009 re-interview.

3. Engel Curve Analysis of Household Food Spending

The self-reported gap between actual and normal income in the SCF seems to be a useful indicator of transitory income shocks, and we now turn to the question of how those shocks affect household spending. The direct measures of spending collected in the SCF and considered here are for food at home and food away from home.¹⁵ Ultimately, the questions to be posed to the data involve the extent to which self-reported income shocks affect the two types of food spending. Before turning to those questions, however, we first consider how well the SCF tracks aggregate NIPA food spending over time, and then present an estimation strategy that takes into account the non-linear Engel Curve relationship between food spending and normal income.

The SCF began asking questions about food spending in the 2004 survey. Respondents are asked to report their typical outlays for food purchased for home consumption and for food purchased outside of the home (specifically, spending associated with "eating out"). Respondents are also asked about the share of food at home associated with delivered food, which we reallocate to food away from home. Respondents are asked to report the amounts for a typical week, but the questionnaire is flexible and allows them to answer using any frequency they choose. We multiply by the appropriate frequency to solve for annual spending.

A crucial question to be addressed before proceeding with the analysis is whether or not the food outlays reported in the SCF track the aggregate food spending amounts published in the NIPA. Food consumed at home in the SCF lines up with published aggregate values very well, with about $650 billion spent on food at home in 2010. There may be noise in the micro level estimates, but there does not seem to be any systematic bias associated with asking respondents about food purchased for home consumption.

Food away from home in the SCF is somewhat more problematic, with the SCF reported aggregate of about $250 billion in 2010 that is roughly half the NIPA aggregate. To some extent this is conceptual-the NIPA measure includes all purchased food and beverages, including snacks, lunches, or other items that respondents may not consider a part of "eating out." The nature of the SCF question leads respondents to think about discrete "eating out" events, which means they will generally consider the number of times they engage in those activities per week and the average cost each time they do, and then work out a total spending estimate. Respondents are likely to omit small purchases, and they may not (for example) even consider eating lunch in the work cafeteria as part of "eating out."

For the purposes of studying whether and how income shocks are affecting household spending over time, the growth of food spending in the SCF is what really matters (Table 6). Although the slowdown in NIPA food spending after 2004 is evident in Figure 1, the SCF actually shows even less growth over this period. Aggregate food spending in real terms is basically unchanged in the SCF, while it increased by several percentage points in the NIPA (Figure 1). The growth of overall food spending in the SCF is masking two very different underlying trends, with food at home rising by 4 percent over the 2004 to 2010 period (still below the NIPA growth, but not by much) while food away from home fell by 7 percent. In the NIPA, both food at home and food away from home grew, so the divergence between SCF and NIPA growth rates is primarily in food away from home. The growth in NIPA food away from home may be in the part "missing" in the SCF, or respondents may have believed they cut back on spending for eating out more than they actually did. In either case, the SCF is generally capturing or even overstating the slowdown in food spending.

Analyzing the effects of income shocks on food spending over time requires a framework that acknowledges the highly non-linear relationship between food and normal income. That point is underscored by differential trends in the aggregate, mean, and median values of the various SCF measures we will be working with. The level of aggregate normal income in 2010 is 7 percent above the 2004 value, while the level of actual income is only 1 percent higher. Both income measures have grown much more slowly than in the decade preceding the Great Recession, and the decline in median income indicates very different growth rates across the income distribution. Consistent with expectations about income elasticities for food at home and away from home, the growth in mean and median values for the two types of spending suggest that slower income growth is associated with a shift from food away to food at home.

Formally modeling the relationship between food spending and income requires a functional form for the underlying Engel Curves. Indeed, the original motivation for Engel's analysis was to understand food spending across different income groups. His finding that food spending rises with income but declines as a share of families' budgets as income increases is clearly still the dominant impression one gets from the data (Table 7). Self-reported food at home and food away from home both increase with income, with food at home nearly tripling and food away from home rising by a factor of nearly ten as one moves from the bottom vingtile to the top vingtile of normal income. However, the differential in either type of food spending is nowhere near the differential in normal incomes across those groups, and thus the ratio of food at home to normal income falls from 38 percent to 2 percent across vingtiles, and the ratio of food away from home to normal income falls from 7 percent to 1 percent across vingtiles.

There are a number of ways to parameterize highly non-linear Engel Curves, but the focus here is on studying the effect of income shocks on food spending over time, so we adopt a very simple but flexible linear-spline in normal income to avoid constraining responses at particular income levels.¹⁶ We solve for the maximum values for each of the j=1,...,20 vingtiles of inflation-adjusted normal income in the pooled (2004, 2007, and 2010) sample, and denote those Y ${}_{j}$ ${}^{m}$ ${}^{ax}$ . Denote food spending across the k=1,2 types of food for family i and normal income for family i using food ${}_{i}$ ${}_{k}$ ${}_{ }$ ${}_{ }$ and y ${}_{i}$ ${}^{normal}$ , respectively. We then run separate regressions for the k=1,2 measures of food spending on these normal income splines,

(3) ${food}_{ik} = \alpha _{k} + {\Sigma}_{j=2,20}\beta_{jk} min(max(0, ({y}_{i}^{normal} - {Y}_{j-1}^{max})), ({Y}_{j}^{max} - {Y}_{j-1}^{max})) + \varepsilon_{ik}$

where the first vingtile of income is omitted, and thus the constant term is a lower bound on food spending. The $\beta$ ${}_{jk}$ coefficients can be interpreted as the marginal propensity to consume on food type k out of a dollar of normal income in the jth normal income vingtile.

This linear-spline Engel Curve formulation will be used in the next section as the basic framework for analyzing the effect of income shocks on food spending, and it is useful to have a visual impression of the estimated splines as we consider how income shocks might have affected spending (Figure 2). Predicted food at home and food away from home based on equation (1) are plotted at income levels from $1,000 through $250,000, and the predicted pattern of increasing spending at a decreasing rate is clear for both types of food spending. There is also a clear differential between the two in the rate of increase at various income levels, and as expected, food away from home accounts for an increasing share of total food spending as normal income increases.

4. Can Self-Reported Income Shocks Explain the Recent Decline in Food Spending?

The motivation for this paper is to address some long-standing questions about the effect of income shocks on consumer spending behavior. The dramatic slowdown in household spending on food during and subsequent to the Great Recession can in principle be explained by a number of different theoretical mechanisms that connect current spending to either current income or expected future income. One mechanism in particular to be explored is the effect of self-reported transitory shocks. We use the Engel Curve framework described in the last section to investigate whether the drop in food spending relative to normal income can be attributed to those families who experienced transitory income shocks, versus the alternative that the declines in spending between 2004 and 2010 were more widespread.

The strategy used to identify the effects of transitory income shocks on food spending takes into account the highly non-linear relationship between food spending and normal income, but is otherwise extremely naïve. The identifying assumption is that the Engel Curves for food at home and for food away from home with respect to normal income are both stable across the three survey years, 2004, 2007, and 2010. Given that assumption, dummy variables for the years 2007 and 2010 capture any residual differences in average food spending not explained by the Engel Curves.

Self-reported transitory income shocks are entered into the food spending equations in order to isolate the component of the spending relative to normal income shift that can be explained by income shortfalls or income windfalls. Positive and negative shocks are entered separately in order to allow the effect of transitory income fluctuations to be asymmetric, and the estimated coefficients are generally of the correct sign and statistically significant. Including both the self-reported income gaps and the year dummies refines the interpretation of the dummies described above. Positive and negative transitory income shocks occur in every year, so the year dummies in an equation that also has the income shock terms is interpreted as the residual change in average food spending not explained by either shifts in normal income or a change in the distribution of transitory income shocks.

The simple linear-spline Engel Curve described in the previous section is the starting point for the analysis of changes in food spending over time. Food spending is modeled in total and separately for food away from home and for food at home (Table 8). Models for each type of food spending are estimated using three variants: the first regression is a fitted linear-spline Engel Curve with just year dummies, the second regression includes additional demographic controls, and the third includes both the positive and negative income shock terms and the additional demographic controls.¹⁷

The first set of observations from the estimated Engel Curves involves the year dummies. SCF food spending data indicate anemic growth or even a decrease in food spending after 2004, depending on which measure of food one looks at and for which survey year.¹⁸ Simply looking at aggregate normal income growth (Table 6) might lead one to conjecture that food consumption fell relative to normal income, because total food spending was basically flat while normal income increased between 2004 and 2010 by 7 percent in total. However, this is where the non-linearity of the Engel Curves becomes potentially important: median normal income in the SCF fell more than average income between 2004 and 2010, and lower-income households have a higher propensity to spend on food out of normal income.

The estimated year dummies for 2010 indicate that the non-linearity of the Engel Curves does not capture the entire shift in spending behavior over time, however. For total food, the 2010 dummies across the three specifications center around $325 and are highly significant.¹⁹ The estimated value for the 2010 dummies corresponds to roughly 5 percent of total food spending in a given year. Thus, even after controlling for changes in the distribution of normal income over time, there is an overall unexplained drop in total food spending of about 5 percent between 2004 and 2010.

The separate regressions for food away from home and food at home make it possible to further sort out the changes in behavior underlying the unexplained drop in food spending. The 2010 dummies for food away from home are all highly significant and in the vicinity of $250, while the 2010 dummies for food at home are generally in the neighborhood around $75 and are either insignificant or only marginally significant. The difference in estimated 2010 residuals is underscored by the fact that average food spending away from home is less than a third of total food spending. That is, the $250 residuals in 2010 represent about 13 percent of average food away from home, while the $75 residuals for food at home represent something less than 2 percent of food at home. Thus, another conclusion from the Engel Curve analysis is that the unexplained drop in food spending is concentrated in food away from home.²⁰

How much of this residual drop in food spending relative to normal income can be explained by transitory income shocks? The fact that the estimated year dummies for 2010 do not change much when the positive and negative income shock terms are included when moving from the Model 2 to the Model 3 regressions is one clue that the answer will be small. Starting with total food, it is clear that self-reported transitory income shocks have an effect on food spending, and that effect is both statistically significant and in the correct direction. Not unexpectedly, negative income shocks have a larger absolute effect than positive shocks. However, the effects are very small in magnitude. For example, the average negative income shock in 2010 was about -$9,000 (25 percent of families had negative shocks, and the average shock conditional on having experienced a negative shocks is -$35,995; Table 3). The coefficient on negative transitory shocks is -.0014, which implies the overall average effect of negative shocks on total food spending was only about -$13 in 2010. However, there were also negative shocks in 2004, so the net effect in 2010 is even less than -$13. Again, this "small but statistically significant" finding on transitory income shocks is consistent with the lack of substantial change in estimated year dummies when the income shocks are added.

There is a substantial difference in the estimated effect of transitory income shocks across the two components of total food spending, and those differences are also consistent with the results on year dummies discussed above. Focusing just on negative shocks, the entire average effect of shocks on food spending is concentrated in food away from home, as the coefficient on negative shocks in the food at home equation is effectively zero. Even though the effect of negative transitory income shocks is highly significant for food away from home, the self-reported shocks in 2010 only explain a small part of the overall decline in that category of spending. That is, the estimated average net effect of something like $5 (the difference between the 2010 and 2004 gross effects of negative shocks) may all be concentrated in food away from home, but that is still only a fraction of the $250 unexplained residual decline.

The finding that transitory income shocks have a small but statistically significant effect on total food spending (through the food away from home component) can be interpreted as evidence against the proposition that transitory income fluctuations have a quantitatively significant impact on spending. That is, families self-reporting having experienced a transitory income shock spent only marginally less on food, given their level of reported normal income. Although food is a relatively small component of household spending, this result does raise some doubts about models in which declines in household spending are driven by liquidity constraints.

One possible explanation for the failure to estimate significant effects of income shocks on spending is that responses differ across income groups. A simple extension of Model 3 in the basic regressions suggests that there are in fact differential responses across normal income groups. To test for this, we interact both the year dummy and self-reported transitory income shock terms with dummies for quintile of normal income, and we find that the unexplained residual decline in total food spending is concentrated in the lowest three normal income quintiles (Table 9). We also find that the magnitudes of the coefficients on both positive and negative income shocks generally decline with normal income, but as with the overall average, none of the coefficients are large enough to account for a substantial share of the unexplained decline in food spending within any normal income quintile. Lastly, we find evidence of substitution towards food at home within the second-highest normal income quintile, as food at home went up by roughly the same amount by which food away from home declined.

Thus, there is a statistically and economically significant decline in spending on food between 2004 and 2010 that remains unexplained by changes in normal income, demographics, or self-reported transitory income shocks. The decline holds for food generally, but is most pronounced for food away from home. Assuming that the families who self-reported income shocks are the ones who actually experienced those shocks, plausible explanations for the decline in aggregate food spending will have to account for the much more widespread decline in food spending and the shift towards food at home. One possibility is that a combination of housing price shocks and high debt levels continues to depress spending (Mian, Rao, and Sufi, 2011). Another possibility is that lower to middle income families generally cut back on food away from home after 2004 because of either precautionary reasons or because their expectations about future permanent income growth became more pessimistic.

5. Conclusions

There are a few key takeaways from this analysis of how income shocks affect food spending. First, the self-reported transitory income shocks collected in the SCF since 1995 appear to have very desirable statistical properties when compared to the more traditional estimates of shocks based on income equation residuals, which suggests that the self-reported measure is a useful independent variable for analyzing household behavior. Second, the measures of food spending collected in the SCF since 2004 show the same basic trends as NIPA aggregates during and subsequent to the Great Recession. The third key takeaway builds on the first two, because in a very simple Engel Curve model relating food spending to normal income, self-reported transitory income shocks have a statistically significant effect on food spending away from home, but the effects on food at home are mixed. However, the magnitude of the transitory income effect falls far short of explaining the decline in spending on food away from home between 2004 and 2010.

This vetting and application of the SCF self-reported income shock measure for analyzing household spending behavior sends an important message about opportunities for studying other aspects of household behavior using the SCF. The SCF is a unique data set because of the high-wealth oversample and the combination of extensive and high quality data collected for each family. Knowing that there is a useful indicator of transitory income shocks on the data set makes it possible to take advantage of the SCF for studying how income shocks affect behavior. Researchers can analyze spending and other household behavior without having to rely on data sets where earnings shocks are inferred from residuals of estimated income equations. The SCF has extensive and high-quality data on household financial outcomes along with a key independent variable many researchers want to use to study those outcomes.

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Figure 1: Inflation-Adjusted Aggregate Consumer Spending on Food

Figure 1 Data

Figure 2: Fitted Engel Curves for Food Expenditures by Normal Income