2.1 PSID summary statistics

Summary statistics for these variables and others of importance are available in Table 1. These values have been adjusted with CPI-U-RS using 2017 as the base year and these values include zeros along with potentially negative values. Medians and averages are displayed for the total sample. These values for overall wealth (Wealth with Home Equity) are in line with that found in Pfeffer et al. (Reference Pfeffer, Schoeni, Kennickell and Andreski2016) that compare the PSID and the 2007 Survey of Consumer Finances. The wealth median is also in line with the more recent Survey of Consumer Finances of 2017 from Bricker et al. (Reference Bricker, Dettling, Henriques, Hsu, Jacobs, Moore, Pack, Sabelhaus, Thompson and Windle2017). However, the average is lower here and generally in the PSID as discussed in Pfeffer et al. (Reference Pfeffer, Schoeni, Kennickell and Andreski2016). Note that the averages for the components of wealth do not add up due to the missing information on IRAs noted above. Finally, the total consumption to wealth ratio aligns with Blundell et al. (Reference Blundell, Pistaferri and Saporta-Eksten2016).Footnote ⁸

Table 1. PSID summary statistics

All the values here have been adjusted to 2017 values. Values for “Displaced” include all the observations before the event in the first column and all the observations after in the next column. See more details on the sample and these variables in Section 2 with a discussion of this table in Section 2.1.

Overall, the sample includes 1751 heads of households who have been displaced at least once along with 3418 heads that have never been displaced. This ratio of displaced workers to those that have never been displaced is similar to that of a recent published paper on displaced workers using the PSID, Krolikowski (Reference Krolikowski2018). The displaced sample has averages for before and after displacement.Footnote ⁹ These averages, whether they be before or after displacement, are lower than the averages in the total sample for every category listed. However, the sample of workers before displacement are younger than the total sample. Therefore, the differences between the total sample and the displaced workers before the event are not as large as the numbers suggest. The workers after displacement have more wealth than they had before since they are now much older. Looking through a few more of the notable variables show what is perhaps a surprise: debt levels for the displaced are lower although this could point to credit constraints. All types of consumption are also smaller although the gap between the total averages and the displaced averages in consumption is not as large as the gaps in wealth. Finally, education levels for heads of displaced households are different compared to the total sample with displaced workers generally having less education.Footnote ¹⁰

These summary statistics also shed light on how households are accumulating wealth. The median household has $118,164 worth of wealth with roughly half of that wealth being home equity. In fact, when calculated separately, the median home equity to wealth ratio is 0.47 with 0.57 as the average value. The median values are zero for most of the wealth components. Therefore, it seems that the households in this sample have their wealth scattered throughout different avenues. This makes it difficult to answer the question of how households end up with less wealth after displacement.

Time since displacement is also an important variable for this article but the new biennial format of the PSID makes estimating some of these years imprecise. Figure 1 provides the positive distribution on time since displacement conditional on being in this article’s samples; the width of each bar represents one year since displacement. The figure indicates that the odd values are much less common than the even values, but this is a much bigger problem for the wealth observations in Figure 1a compared to the income observations in Figure 1b. For example, in Figure 1a, 7% of the displaced wealth observations are from 2 years after displacement and 6% are from 4 years after displacement while 1% are from 1 year after displacement and 2% from 3 years after displacement. Due to the small sample size on the odd years, care must be taken when examining these as is discussed in the next section.

Figure 1. Observations since displacement.

These figures plot the percent density of positive time since displacement for observations from the displaced heads that are part of the wealth sample for this paper. The width of each bar represents one year since displacement. Figure 1a demonstrates the distribution of positive time since displacement for the wealth observations while Figure 1b demonstrates this for the income observations.

3.1 Empirical results from the PSID

Table 2 presents the main findings from this study with the format of this table followed throughout the empirical results. The first row indicates the log transformed dependent variables used in the estimation of equation (1). The first column indicates time since displacement and indicators for multiple displacements. The table reports the values of the coefficients for these displacement indicators without parentheses and the numbers with parentheses are the standard errors clustered for each head of household. Observations can vary due to the log transformation dropping nonpositive values or due to the changing availability of information noted in Section 2. The individual heads of households vary because every estimation requires that each individual have at least two observations.

Table 2. Effects of displacement on income, wealth, and consumption

Significance levels: + : 10% ^* : 5% ^{* *} : 1% ^{* * *} : 0.1%

Note: This table displays the results of equation (1) with m = −4 or −3,..., 4 to 11 and ${D1}_{i,12p}$ controlling for time-varying individual characteristics including composition of household, annual fixed effects, state fixed effects, and individual fixed effects. Income is a control for the wealth and consumption estimations. The wealth estimates control for the holdings of different types of pensions. See Section 3 for more details on this strategy. The first row indicates the dependent variables with the log transformation. The three wealth estimates include wealth with home equity (w/Home), wealth excluding home equity (No Home), and only home equity (Only Home). The values without parentheses are the coefficients for the independent variables listed in the first column which indicate time since displacement and whether the worker has been displaced multiple times. The numbers in parentheses are the standard errors clustered at the individual level.

When workers experience an involuntary displacement, income falls immediately, and their income remains lower than their peers’ income. This is noted in the literature from the introduction and is shown again in Table 2 to put the other results into context. Specifically, the income column of this table shows the results of estimating equation (1) on log annual income. Income is 20% ( $-0.2$ = $e^{-.229}-1$ ) lower for displaced workers compared to their peers upon the first two years of displacement and income is still 10% lower 12 plus years later.Footnote ¹⁴

Table 2 makes clear that when the head of a household experiences an involuntary displacement, wealth is lower than the head’s peers and that fall in wealth displays little to no recovery.Footnote ¹⁵ Specifically, total wealth is 14% lower in the year or in the year after the first displacement and is 15–20% lower than expected in all the following years.Footnote ¹⁶ Housing wealth falls in similar magnitudes although this fall begins before displacement. However, wealth that excludes housing falls by 16% upon displacement with this fall increasing to 23% when the first displacement occurred at least 12 years prior.

The value of wealth should not be driving these results. The estimates in Table 2 include time dummy variables which should capture national changes in several of the assets. While home equity is more local, wealth that excludes this is still much lower for displaced households suggesting that local conditions are also not the primary source for these results.

The literature in the introduction indicated wealth reductions in the 8% to 13% range. Table 2 demonstrates larger magnitudes but given that previous research involved older workers from the HRS, the deviations for this difference are not surprising. Older workers have more wealth and therefore their percentage decreases should be smaller. Additionally, since older workers are closer to retirement, there is less time for the workers to fall further behind their peers.

The results in Table 2 indicate that consumption falls upon displacement but that this fall is small to non-existent. The estimates range from a 2 to 4% decrease for overall consumption but the results are not statistically different from zero. The results on food consumption are similar with the consumption of food falling 3–4% but again these results have relatively large standard errors. The food consumption results are different from the results found in Stephens Jr (Reference Stephens2001) where food consumption falls 9–11% after displacement with much more precision (smaller standard errors). These differences are further explored in the appendix Section C.Footnote ¹⁷

The fact that consumption does not fall much after an involuntary displacement is in line with consumption smoothing theory. The idea that individuals and households attempt to keep their consumption steady (consumption smooth) has a long history as Meghir and Pistaferri (Reference Meghir and Pistaferri2011) discuss in their chapter from the Handbook of Labor. More recent work in this area includes Blundell et al. (Reference Blundell, Pistaferri and Saporta-Eksten2016) who use a flexible life cycle model calibrated to the PSID to show the various avenues used to insure consumption streams within a family. That paper demonstrates the various consumption changes with respect to changes in wages. The two elasticities, which capture these ratios of changes, have different signs indicating that the overall difference in consumption may not be significantly different from zero. Sullivan (Reference Sullivan2008) examines the various impacts of unemployment on consumption for those with assets versus those without assets using the SIPP and the PSID. That paper finds that those with assets do not cut their consumption as much as those without assets. A heavy majority of the sample in Table 2 has assets and therefore, these results do not run counter to those in Sullivan (Reference Sullivan2008).

3.2 Wealth components

Table 3 also emphasizes the main point of this article: when displacement occurs for the household, wealth, no matter the type, falls relative to other similarly educated households. This table presents the results of estimating equation (1) from Section 3 with the dependent variable being the individual components of wealth after a log transformation. Almost all of the estimates in this table indicate a loss in wealth. For example, the last column of this table indicates that the value of a farm or business is 75% ( $-0.75$ = $e^{-1.4}-1$ ) lower than expected for households that have the head displaced.

Table 3. Effects of Displacement on Wealth Components

Significance levels: + : 10% ^* : 5% ^{* *} : 1% ^{* * *} : 0.1%

Note: This table displays the results of equation (1) with m = −4 or −3,..., 4 to 11 and ${D1}_{i,12p}$ controlling for time-varying individual characteristics including all household income, composition of household, annual fixed effects, state fixed effects, and individual fixed effects. See Section 3 for more details. The first row indicates the dependent variables. “Bank Accounts” indicate the sum of checking and savings accounts, “IRA” indicates the value of private annuities and IRAs, “Other Assets” indicate the value of assets such as bonds, life insurance, trusts, estates and collections, “Other Estates” indicates the value of nonprimary real estate; see Section 2 for more details on these components. The values without parentheses are the coefficients for the independent variables listed in the first column which indicate time since displacement and whether the worker has been displaced multiple times. The numbers in parentheses are the standard errors clustered at the individual level.

The interpretation of these results in Table 3 must be done with care since most of these wealth components have a median value of $0 as shown in Table 1. The estimation strategy in this article is to compare workers that have been displaced to workers that have not been displaced and have non-zero values since these results have a natural log transformation.Footnote ¹⁸ The first column of results in Table 3, which is for vehicles, has 27,773 observations or 94% of the total from this paper’s sample but the last column of results for the value of a business or farm indicates 4475 observations or 15% of the total from this paper’s sample. Therefore, when stating that the value of the farm or business is 75% lower than expected, this is based on the individual fixed effect and the non-displaced workers of a similar education who own a farm or business with a positive value.

3.3 Robustness – individual time trends

This section provides a robustness check of Table 2 by examining those results with an individual linear time trend. This time trend goes one step further than the individual fixed effect to examine whether the specific individuals not only have different levels but also different rates of accumulation. This is helpful if displaced workers happen to have different rates of wealth accumulation compared to their counterparts. Specifically, this robustness check is simply estimating equation (1) with an additional term, $\lambda_i t$ . The results are in Table 4 and indicate that the main results still hold; wealth drops upon displacement and this fall in wealth has a lasting impact. This holds whether the wealth includes home equity or not. The results for consumption are also largely unchanged although the point estimates display larger magnitudes. Section D of the appendix contains more robustness results including estimates containing zeros and negative values using the inverse hyperbolic sine transformation along with a note on the results without any transformation.

Table 4. Robustness – Effects of displacement with individual time trends

Significance levels: + : 10% ^* : 5% ^{* *} : 1% ^{* * *} : 0.1%

Note: This table displays the results of equation (1) with m = −4 or −3,..., 4 to 11 and ${D1}_{i,12p}$ controlling for time-varying individual characteristics including composition of household, annual fixed effects, state fixed effects, individual fixed effects, and individual time trends. Income is a control for the wealth and consumption estimations. The wealth estimates control for the holdings of different types of pensions. See Sections 3 and 3.3 for more details. The first row indicates the dependent variables with the log transformation. The three wealth estimates include wealth with home equity (w/Home), wealth excluding home equity (No Home), and only home equity (Only Home). The values without parentheses are the coefficients for the independent variables listed in the first column which indicate time since displacement and whether the worker has been displaced multiple times. The numbers in parentheses are the standard errors clustered at the individual level.

4.1 Model

A general life cycle model is useful because it provides the framework on what should be expected regarding wealth and consumption after displacement. Specifically, it helps to answer whether to expect workers to cut back more on consumption or wealth. This article compares the aforementioned findings from the PSID to the life cycle model available in Carroll (Reference Carroll2012) which is similar to that in Cagetti (Reference Cagetti2003), Carroll et al. (Reference Carroll, Hall and Zeldes1992) and Carroll (Reference Carroll1997). The model is of partial equilibrium where the dynamic problem for the agent is one of choosing consumption and hence savings for wealth. This choice is made to maximize utility for the rest of one’s life based on income that is subject to life cycle growth along with uninsurable shocks. Specifically, the maximization problem for each agent is as follows:

\begin{equation*}\max \left\{ u(C_{t})+E_{t}\left[\sum_{s=t+1}^{T} {\delta}^{s-t}\left( \Pi_{i=t+1}^{s}{\beta}_{i}\pi_{i}\right) u(C_{s}) \right]\right\}\end{equation*}

subject to

\begin{eqnarray*} C_{s}+A_{s} &=&\hat{R}A_{s-1}+P_{s}\Theta_{s} \space \forall s\\ P_{s} &=&G_{s}P_{s-1}N_{s}\end{eqnarray*}

Utility in time period t is derived from consumption ( $C_{t}$ ) along with the expected utility going forward with two discount factors. The time invariant discount factor ( $\delta$ ) makes up the first with the second being a time-variant discount factor ( $\beta_{s}$ ) between ages s and $s-1$ used to reflect changes in spending over an agent’s lifetime. Agents also face the possibility of death later in life with $\pi_{s}$ being the probability of living until age s given living until age $s-1$ . The choice for consumption indicates how much is saved ( $A_{s}$ ) in time s which provides a constant gross interest rate ( $\hat{R}$ ). The right-hand side of the budget constraint also includes permanent income ( $P_{s}$ ) which is exposed to a temporary shock ( $\Theta_{s}$ ) that can take the value of zero with probability p but otherwise follows a log normal distribution. Permanent income grows at a rate $G_{s}$ between age $s-1$ and s while being exposed to another shock ( $N_{s}$ ) with a log normal distribution detailed below:

\begin{eqnarray*} \Theta_s &=& 0 \text{ with probability } p \\ &=& Z_s/(1-p) \text{ with probability }(1-p) \\ \log Z_s &\thicksim& \mathcal{N}(-\sigma _{\Theta }^{2}/2,\sigma_{\Theta}^{2}) \\ \log N_s &\thicksim& \mathcal{N}(-\sigma_{N}^{2}/2,\sigma _{N}^{2})\end{eqnarray*}

Shocks to income create displacements in the model. Displacements for the model depend on the severity ( $\gamma$ ) of the negative shock. Therefore, this article defines a displacement as occurring in the model when either of the following holds:

\begin{eqnarray*} N_{s} &<& 1 - \gamma_N * \sigma_{N} \\ \Theta_s &<& 1 - \gamma_{\Theta} * \sigma_{\Theta}\end{eqnarray*}

Displacements in the model depend on both types of shocks. The model needs displacement from temporary shocks to replicate the fact that several displaced workers recover. If permanent shocks are the only target, there is not enough recovery. If temporary shocks are the only target, the average worker recovers immediately. Thus, the displaced sample needs to be a mix of those that have experienced permanent shocks and those that have experienced temporary shocks. Alternative possibilities of defining displacements for this model are discussed in Section 4.6.

A key reason for using this model is its simplicity with the presence of permanent shocks to income. Its simplicity makes calibrating to new variables easier while previous research demonstrates its use for understanding wealth. The permanent shocks to income are crucial since most involuntary job displacement is accompanied by permanent decreases to income as noted in the introduction and found in Table 2. However, this article does not attempt to explain the nature of these decreases as in Jarosch (Reference Jarosch2015), Krolikowski (Reference Krolikowski2017), or Michaud (Reference Michaud2015). Rather, these shocks are a mechanical part of this framework.

4.2 Simulation

The simulated data on consumption, income, and displacement comes from using the model to generate panel data for the three different types of workers identified in Cagetti (Reference Cagetti2003): those with less than 12 years of education, those with 12–15 years of education, and those with at least 16 years of education. These agents are capable of living up to 90 years old. For purposes of this article, the simulated data is collected on agents aged 25–60 to match the age groups from the empirical work done with the PSID in this paper (Table 2). Therefore, the model is simulated three times to produce a total of 18,000 workers with 648,000 observations where the proportions of the workers roughly reflect those from this paper’s sample. Specifically, the code from Carroll (Reference Carroll2012) solves the model above for one type of worker with variables normalized as a percentage of permanent income ( $P_{s}$ ). Creating permanent income variables that scale the original variables result in the simulated data.

Since this model is closely related to the model in Cagetti (Reference Cagetti2003), a handful of the model’s parameters come from that paper. The values for the probability of staying in the labor force ( $\pi$ ) are equal to one for these 25–60-year-old agents. The real return to saving is set constant at 3% ( $\hat{R}=1.03$ ). The values for the time-varying discount factor ( $\beta$ ) correspond to each type of agent and are summarized in Figure E.1 of the Appendix. The values for the growth rate of income (G) together with each type of worker’s starting permanent income ( $P_{25}$ ) are summarized in Figure E.2 of the Appendix.

The temporary shocks along with the permanent shocks follow a log normal distribution with the shocks having a mean of one and standard deviations calculated from the PSID. The income process for the three different types of workers is estimated using the first differences in log income following Heathcote et al. (Reference Heathcote, Perri and Violante2010) which uses heads of households that have worked more than 260 hours with a calculated hourly rate greater than $2. The results of this approach are much closer to that of Carroll et al. (Reference Carroll, Hall and Zeldes1992) which is used in Carroll (Reference Carroll1997) as opposed to using moments in log income levels. The temporary shock to income ( $\Theta$ ) can result in zero income with probability $p=0.5$ % for all worker types; this number comes from this paper’s PSID sample and is also used in Carroll (Reference Carroll1997). The distribution of these shocks is reported in Table 5.

Table 5. Model parameters

Note: This table summarizes all the parameters used in the model. The first two columns of parameters are found using first differences in log income following Heathcote et al. (Reference Heathcote, Perri and Violante2010). The next two columns are found using simulated method of moments where the targets and the model’s performance are found in Table E.1. The last two columns determine the thresholds for what creates a displacement in the model. These are found using another round of simulated method of moments with the targets and performance in Table E.2. See more details in Section 4.2.

Table 5 provides the rest of the calculated parameters for the model. The functional form for utility is one of constant relative risk aversion ( $u(C_s)= C_{s}^{1-\rho}/(1-\rho)$ ) where the risk parameter ( $\rho$ ) and the time invariant discount factor ( $\delta$ ) for each type of worker is found using the method of simulated moments. This process is used for each type of worker to approximate the median wealth to income ratios for seven age groups (26–30, 31–35, etc.) from the 1992 through the 2007 waves of the Survey of Consumer Finances with each moment having an equal weight following the procedure in Carroll (Reference Carroll2012). As explained in Carroll (Reference Carroll2012), the median wealth to income ratio is the target since this model is not designed for the high concentration levels of the most wealthy. The wealth medians and averages for the PSID sample in this study are also more representative of those outside these high concentration levels as noted in Section 2.1. The targets and the model’s performance are available in Table E.1 of the appendix.

The severity of the shocks denoted with $\gamma_N$ and $\gamma_{\Theta}$ are chosen to target the income distribution for displaced workers using a second round of simulated method of moments after the risk parameter ( $\rho$ ) and the time invariant discount factor ( $\delta$ ) are determined. Specifically, the targets come from the following differences in income found in Table 2: 2–3 years later, 4–11 years later, and 12 plus years later. The targets also include the proportion of each worker type that experiences a displacement and the peak fall in income after displacement. It is important to use the peak fall in income because when displacement occurs in the model, income takes a large fall. The peak fall in income comes 1 year after displacement when income falls by 24%.Footnote ¹⁹ Each of the targets has an equal weight resulting in the values for each $\gamma$ in Table 5. The targets and the model’s performance on these dimensions are listed in Table E.2 of the appendix. However, the calibration strategy is not driving the results; Section 4.6 provides more information on alternative strategies for calibration and their issues.

4.3 Model summary statistics

The data generated by the model is summarized with the model’s summary statistics in Table 6. The model does a decent job with generating displacements correctly although there is one important thing to keep in mind when examining these numbers: displaced agents in the model are older than the displaced workers in the PSID data and the displaced agents are much older than the total sample from the model. This explains why the displaced agents in the model have more wealth than the total sample; they are older. The model also has a smaller percentage of agents being displaced.

Table 6. Summary statistics from the model

All the values here have been adjusted to 2017 values. See Section 4.1 for more details on the model and the calibration. Values for “Displaced” come from all the observations after displacement.

4.4 Estimation using the model

The model, calibrated to generate a permanent decrease in income like that in the data, is now used to examine wealth and consumption after an event like displacement. Equation (1) again considers dependent variables ( $w_{i,t}$ ) to be income, wealth, and consumption. The setup and estimation for the model’s data is nearly the same as the estimation using the PSID. Because the model’s data is more abundant, time since the first displacement is estimated annually. Several controls like state and year fixed effects are unnecessary for this simulation data but for comparison to the empirical results, the individual fixed effect ( $\zeta_i$ ) is included. These individual fixed effects also help correct for the fact that the average values for wealth and consumption differ in the PSID data compared to the generated data from the model.

4.5 Estimation results from the model

Figure 2 demonstrates the drop in income experienced by agents in the model in direct comparison to the heads of households from the PSID. The solid line without markers comes from the $\beta$ coefficients on time since displacement for income based on equation (1) from the model. As shown, these agents experience a slightly larger drop in income with the fall being even worse every year after three years since displacement. When summing the decreases across the first 19 years of displacement, this costs the displaced agents 42% more income relative to the heads from the PSID.

Figure 2. Income differences due to displacement.

The solid line without markers indicates the difference in income which come from $e^{\beta}-1$ where the $\beta$ ’s come from equation (1) for the model and the solid line with square markers identify these values from the PSID data. The thin dashed lines are the 95% confidence intervals for the estimations from the PSID. The model’s extension with habit formation has the identical results as the solid line without markers.

Figure 3 depicts that displaced agents in the model experience a large loss in wealth, but they recover contrary to what is found in the PSID. The line without markers indicates the difference in agents’ wealth that comes from the values for the $\beta$ coefficients from equation (1) when time since displacement is measured annually. In the year of displacement, the agents have 27% less wealth compared to their counterparts from the model that are of equal age and education. However, wealth continues to increase relatively as the agents rebuild their wealth to buffer income shocks. As shown, this is much different than the results from the PSID even though the calibration has a fall in income being worse for those in the model.

Figure 3. Wealth differences due to displacement.

The solid line without markers indicates the difference in wealth which come from $e^{\beta}-1$ where the $\beta$ ’s originate from equation (1) for the model and the solid line with square markers identify these values from the PSID data. The thin dashed lines are the 95% confidence intervals for the estimations from the PSID. The dotted lines provide these values for the model’s extension which include habit formation.

Figure 4 depicts consumption after displacement for agents in the model compared to the PSID, which is an important cause of the different wealth experiences. The agents in the model decrease their consumption by 14% in the year after displacement and this decrease in consumption is still at 9% 20 years after displacement. Comparatively, households in the PSID are not changing their consumption in this fashion although their decreases in consumption are increasing in magnitude over time. In the year of displacement, the fall in consumption for agents in the model appears small due to income as an independent variable for these estimations. In other words, consumption relative to income does not fall much in the year of displacement because income is so low for displaced workers in the model. This also occurs on a smaller scale for the PSID.

Figure 4. Consumption differences due to displacement.

The solid line without markers indicates the difference in consumption which come from $e^{\beta}-1$ where the $\beta$ ’s originate from equation (1) for the model and the solid line with square markers identify these values from the PSID data. The thin dashed lines are the 95% confidence intervals for the estimations from the PSID. The dotted lines provide these values for the model’s extension which include habit formation.

4.6 Alternative calibration strategies

This section considers alternative strategies for defining a displacement in the model. Simply relying on the permanent component of the income process is intuitive since the results in Figure 2 seem to indicate a permanent fall in income. Following a similar method of moments of targeting the income scar along with the displacement ratios leads to permanent falls in income, wealth, and consumption but the magnitudes are much too large, and the model generates too many displacements. Specifically, this strategy leads to 52% of the agents experiencing a displacement, income falling 40% which leads to consumption falling 22%. This performs poorly because there is too little recovery in the model when displacements are only based on permanent shocks. While several workers in the PSID experience a permanent fall in annual income, several others recover which is why both types of shocks are needed.

Another alternative strategy is to only target the initial fall in income and the fall in income 12 years after displacement with the requirement that the lasting fall in income is no more severe than that found in the data. This strategy also requires that the displaced population make up no more than 50% of the population although the results are similar if including the proportion of the population displaced as a target; this 50% threshold gives the parameters their best chance of matching the fall in income. This strategy may be enticing since the current targets lead to an income scar that is worse than that in the data as is clear in Figure 2. However, this strategy leads to wealth recovering even faster. Since wealth recovers faster, the fall in consumption is smaller yet agents in the model still cut consumption by much more than the households in the PSID.

In estimating these displacement parameters ( $\gamma$ ), the estimation strategy either needs to target the proportion of displaced workers or there needs to be a threshold for the percentage of workers displaced. Otherwise, $\gamma$ ’s are found which create too much displacement. The interpretation of the results from estimating equation (1) would then change because the non-displaced population would be small.

4.7 Extending the general model with habits

The general model used thus far follows the literature to show that involuntary job displacement causes a permanent fall in income but the agents drastically change their consumption contrary to the findings from the PSID. Therefore, respondents in the PSID are better at consumption smoothing which may be due to habit formation. In other words, households in the PSID may be accustomed to a certain lifestyle and may be unwilling to change their spending habits unless it is absolutely necessary. For example, previous work uses habit formation mechanisms to study a wide range of issues including the equity premium [Campbell and Cochrane (Reference Campbell and Cochrane1999), among others], income and consumption aggregates [Jawadi and Leoni (Reference Jawadi and Leoni2012), among others], growth and fertility [Schäfer and Valente (Reference Schäfer and Valente2011)], and labor supply with growth dynamics [Gómez (Reference Gómez2015) among others].Footnote ²⁰

Perhaps, the easiest way to add habit formation to the general model above is to simply consider utility to be based on the difference in consumption rather than the consumption itself. Formally, consider the following utility function for time period s:

\begin{equation*}u(C_s)= \frac{(C_{s}-\theta C_{s-1})^{1-\rho}}{(1-\rho)}\end{equation*}

This utility function is one commonly used in the literature on habit formation, but it introduces an unknown variable $\theta$ which indicates the importance of last period’s consumption on utility. This parameter can take a value from zero to one with a value of zero reducing utility to the function used earlier in the paper. A value of one for $\theta$ indicates that utility does not depend on the level of consumption but only on how consumption today compares to consumption in the past.

This article targets the long-lasting scars to consumption and wealth to estimate the value of this $\theta$ parameter by using the same parameterizations and the same agents with the same income and income shocks used in the general model but simply adjusting $\theta$ to essentially minimize the gap between the two solid lines in Figures 3 and 4. Specifically, consider $\beta_{m}$ from equation (1) for the PSID on wealth as $\beta_{w,m}$ and these coefficients on consumption as $\beta_{c,m}$ . For the simulation data, which now vary with different values of $\theta$ , consider the same coefficients denoted as $\hat{\beta}(\theta)_{w,m}$ and $\hat{\beta}(\theta)_{c,m}$ for the estimations with wealth and consumption, respectively. Thus, $\theta=0.73$ is found by solving the following:

\begin{equation*}\min_{\theta} \sum_{m = -4}^{20p}\left(\beta_{w,m} - \hat{\beta}(\theta)_{w,m}\right)^2 + \left(\beta_{c,m} - \hat{\beta}(\theta)_{c,m}\right)^2\end{equation*}

This parameter on the importance of past consumption, $\theta$ , has a wide range of estimated values in the literature. In fact, Deaton (Reference Deaton1986) has nearly the same value on this parameter with it equal to 0.78. A similar value of 0.80 is found in Constantinides (Reference Constantinides1990) who uses the model for understanding the equity premium puzzle. On the higher end, Carroll and Weil (Reference Carroll and Weil1994) find that their value of the parameter must be 0.95 for their model to reproduce high savings with large levels of income growth. On the lower end, Dynan (Reference Dynan2000) has several estimated values for this parameter using food consumption from the 1968 to 1987 waves of the PSID. Most of the values in Dynan (Reference Dynan2000) are less than 0.15 but interestingly, the largest value of 0.66 is found only when using job displacement as the instrument. Additionally, Dynan (Reference Dynan2000) provides a discussion on how this $\theta$ parameter can have such large variation based on different strategies of estimation.

This extension of the model with habits provides an improvement with coefficients closer to those from PSID compared to the general model. However, this improvement comes exclusively from wealth. In fact, the coefficients on wealth are 30% closer to that in the data with the average fall in wealth being 16% in the model’s extension compared to the average 12% fall in wealth for the general model. (Recall that the average fall in wealth for the PSID is 15%.) This difference is visible in Figure 3 where the changes in wealth with habit formation are represented with the dotted line. As is clear in the figure, the model’s extension has a larger fall in wealth upon displacement compared to the general model which is already a larger fall than that in the data and is represented with the markered line.

The reason for the larger fall in wealth is clearer when examining the changes in consumption represented with the dotted lines in Figure 4. First, it appears that consumption increases upon displacement, but this is misleading because consumption actually falls by 17% on average for the agents upon displacement. However, recall from Figure 2 that income falls by nearly 30% for these agents. For this reason, consumption relative to income rises which explains the small jump in the figure at the time of the event.Footnote ²¹ In the year after what has been defined as the model’s displacement, consumption makes an even larger fall than the general model due to the larger fall in wealth. After four periods, the general model and the extension are nearly the same with both lines indicating a long-term fall of about 10% in consumption. This also needs some context because the displaced agents consume more in the model with habits than the agents in the general model; but all agents in the habits model consume more than in the general one used earlier. This explains why wealth does not recover since both models have the exact same incomes. Overall, the model’s extension performs a little worse with the average consumption marker indicating a 9% fall compared to the average 8% fall in consumption from earlier which are both worse than the data’s 3% fall.

4.8 Wealth at death

The results in this article suggest that wealth for displaced workers would be lower upon death if wealth continues its trajectory of non-recovery. Indeed, this lack of recovery persists when broadening the data to include older heads of households from the PSID. When relaxing the requirement that heads of households must be no older than 60 years of age, the figure for changes in wealth has a lasting and statistically significant fall going out to 30 years from the time of displacement. Specifically, the wealth for displaced heads of households from the PSID is 19% lower than their nondisplaced peers when it has been 30–31 years since displacement.

The key result for the extended model with habit formation is that the long run results for wealth are similar to those in the PSID. This is clear in Figure 3. Like the PSID, extending the model to include older agents results in wealth that also does not recover. The wealth for displaced agents when it has been at least 30 periods since the event is 17% lower than their nondisplaced peers.

The extended model provides insight for what we should expect from bequests for displaced workers. Although the PSID collects information on gifts and inheritances, this information is for the recipients rather than for those that provide the bequest. However, wealth held by agents at death provide intuition on what to expect in other datasets. Recall that older agents of age s die at probability $1-\pi_{s}$ as noted in the model’s description above. In the model’s extension, wealth at death is 27% lower for those that have experienced a displacement compared to the agents that have not. Therefore, bequests for displaced workers should be much lower than the bequests for nondisplaced workers and this model provides an idea on the magnitude to expect.