Household consumption of luxury goods has attracted increasing attention in various areas of finance and economics research. For example, Aït-Sahalia, Parker, and Yogo (2004) show that the equity premium is less of a puzzle when fluctuations of luxury goods consumption are taken into account. Charles, Hurst, and Roussanov (2009) and Bricker, Ramcharan, and Krimmel (2014) argue that some people consume luxury goods to signal social status. This note presents novel evidence on the ephemeral nature of household luxury car ownership, adding new support to these two strands of literature. Specifically, we show that about 40 percent of the households that own a luxury car in a given year no longer own luxury vehicles four years later. The transition out of luxury car ownership is in stark contrast to non-luxury car owners, for which 90 percent will continue to own a non-luxury car four years later. Moreover, we find that lower-income households are most likely to drive a luxury vehicle for a relatively short time period. The results are consistent with the notion that the consumption of luxury goods is less of a habit and, as a result, tends to be more volatile. Furthermore, our findings imply status-signaling consumption tends to be less lasting than a standard model's habit-persistent consumption would imply.

1. Data Description and Vehicle Ownership Statistics
We use data from the Panel Study of Income Dynamics (PSID), a nationwide representative household longitudinal survey.² Starting in 1999, the PSID collects biennially detailed information on light vehicle stocks, including make, model/year, and year acquired. To the best of our knowledge, the PSID presents the longest panel data on U.S. household vehicle ownership. In addition, the PSID has extensive data on household socioeconomic and demographic characteristics and labor market activities. Our sample covers the seven most recent waves of the survey, which occurred every other year from 1999 to 2011.

Following the industry practice, we define Acura, Audi, BMW, Cadillac, Infinity, Jaguar, Lexus, Lincoln, Mercedes-Benz, Porsche, Saab, and Volvo as luxury brands.³ In addition, we restrict a vehicle to be younger than 10 years to qualify a luxury vehicle. Table 1 presents the summary statistics of vehicle ownership in the PSID for households whose heads were ages between 20 and 65 and with family incomes between $3,000 and $300,000. For simplicity, we focus on light vehicles--autos and light trucks--purchased by households.⁴ As shown in the table, among the 47,763 light vehicles in our sample, 6.3 percent were of luxury brands. Our seven-wave pooling sample has 47,227 households, of which 6.2 percent owned luxury and non-luxury vehicles simultaneously and 2.1 percent owned only luxury vehicles. Notably, among the households who participated in at least five out of the seven waves of the survey, about one quarter owned a luxury vehicle at some point in time. The substantial gap between luxury vehicle ownership in a given year and over a decade underscores the transitory nature of such ownership among many households.

Table 1: Light Vehicle Ownership in the PSID

	Percent of vehicles	Total number of vehicles
Luxury vehicles	6.3	47,763
	Percent of households	Total number of households x waves
Do not own any vehicles	9.8	47,227
Non-luxury vehicles only	81.9
Luxury and non-luxury	6.2
Luxury vehicles only	2.1
	Percent of households (participating five or more waves)	Number of households satisfying the criterion
Households ever owned any luxury vehicles	23.3	5,040

Table 2 contains information on the transition between the number of luxury and non-luxury light vehicles a household owns. Of note, the table provides evidence that the four-year transition matrix of luxury vehicle ownership is markedly different from that of non-luxury vehicle ownership. Specifically, nearly 40 percent of the households who owned one luxury vehicle in a given year no longer owned a luxury vehicle four years later.⁵

Table 2: Light Vehicle Ownership Transitions

at year t	Number of luxury vehicles at year t+4				Number of non-luxury vehicles at year t+4
	0	1	2 +	Share of sample	0	1	2 +	Share of sample
0	94.5%	5.3%	0.3%	92.3%	59.4%	30.8%	9.8%	10.5%
1	39.1%	52.7%	8.2%	6.9%	10.2%	63.9%	26.0%	34.4%
2 +	12.8%	37.7%	49.5%	0.9%	2.2%	15.7%	82.1%	55.1%

Moreover, not shown in the table, over 90 percent of the households who gave up owning their current luxury vehicles replaced them with non-luxury ones. Putting the share in perspective, only 10 percent of the households owning one non-luxury vehicle in a given year are found not owning any vehicle four years later, and fewer than 5 percent of such households acquired a luxury vehicle as a replacement. In addition, among the households who owned two or more luxury vehicles, half of them decreased the number of luxury vehicles they owned within the next four years.

Furthermore, similar contrasts of ownership transitions of luxury versus non-luxury vehicles can be found for shorter and longer time intervals. For example, 25 percent of the households who owned one luxury vehicle in a given year owned no luxury vehicles two year later; the share rises to 50 percent when compared to six years later (relative to 9 and 12 percent, respectively, for non-luxury vehicles owners).

The higher rates of transitioning out of luxury vehicle ownership do not appear to be attributable to shorter durations of households owning such vehicles. As shown in table 3 below, the distribution of the ownership duration of luxury vehicles is very similar to that of non-luxury vehicles. Our analysis therefore suggests that many households who ever owned a luxury vehicle tended to own it only once and replace it with a non-luxury vehicle at a schedule similar to the turnover of non-luxury vehicles.

Table 3: Distribution of Years of Ownership of Light Vehicles

Percentile:	10th	25th	median	75th	90th
Luxury	0	1	3	5	9
Non-luxury	0	1	3	6	9

2. Econometric Analysis

We now explore factors that influence households' decision on purchasing and disposing luxury vehicles. Specifically, we consider the following specification of a logistic model

AD_t,t+τ = α + βAge_t + γZ + θV_t + φΔV_t,t+τ + δE_t,t+τ + ρYear_t + ε_{t,t+τ ,}

where AD_t,t+τ is a dummy indicating whether the household acquired or disposed a luxury vehicle between year t and t+τ. In our baseline analysis, τ = 4. We estimate the model of acquisition using the subsample of households who did not own any luxury vehicle in year t and the model of disposition of the subsample who owned at least one luxury vehicle in year t. Age is a third-order polynomial of age of the household head, capturing lifecycle variations in vehicle choices; Z is a vector of time-invariant household characteristics that include the race of head of household and educational attainment; V_t is a vector of time-dependent household characteristics that include family size, number of children, and household income as of year t; ΔV_t,t+τ is a vector of changes of these variables between year t and t+τ. E_t,t+τ represents a vector of important events occurred between year t and t+τ that include home purchases, becoming married, divorced, and unemployed; and finally a vector of year dummies capture the yearly fixed effects.

The results regarding luxury vehicle acquisitions are presented in table 4, with column 1 showing the estimated coefficients, column 2 standard errors in parentheses, and column 3 implied odds ratios in brackets. Our analysis suggests that, while income appears to be the most prominent factor influencing luxury vehicle acquisitions, other socioeconomic and demographic characteristics and important lifecycle events also play a role. Specifically, the estimated odds ratios indicate that, relative to households in the lowest quartile of family income distribution, those in upper three quartiles are 36 percent, 90 percent, and 250 percent more likely to enter luxury vehicle ownership within a four-year time period. Moreover, holding income in year t constant, a one-standard-deviation increase in income growth between t and t+4 boosts chances of buying a luxury vehicle by 40 percent. In addition, households headed by college graduates and newly wedded households are about 50 percent more likely to buy luxury vehicles, respectively, within such a time period. By contrast, holding other factors constant, households with a white head of household are more than 50 percent less likely to enter into luxury vehicle ownership within a time period of four years. Having a larger number of children relative to other households and introducing a newborn into the household also imply a lower chance of purchasing luxury vehicles--each by about 10 to 15 percent. Finally, divorced households are on average more than 30 percent less likely to buy a luxury vehicle. Other factors, such as family size and purchasing a home, do not appear to significantly affect the likelihood of buying a luxury vehicle. In addition, becoming unemployed does not have a significant effect after controlling for the level of income and income growth.

Table 4: Logistic Analysis of Luxury Vehicle Acquisition and Disposition

	Luxury vehicle acquisition				Luxury vehicle dispositions
White	-0.720	***	(0.061)	[0.487]	0.083		(0.09)	[1.086]
College	0.397	***	(0.062)	[1.487]	-0.407	***	(0.09)	[0.665]
Fam. size	0.017		(0.053)	[1.017]	0.156	**	(0.077)	[1.168]
Num. Children	-0.111	*	(0.063)	[0.895]	0.015		(0.097)	[1.015]
Income quartile
Lower inner	0.310	***	(0.112)	[1.364]	-0.278		(0.196)	[0.757]
Higher inner	0.644	***	(0.117)	[1.904]	-0.567	***	(0.191)	[0.567]
Top	1.256	***	(0.125)	[3.512]	-0.973	***	(0.198)	[0.378]
∆Fam. size	0.052		(0.05)	[1.053]	0.011		(0.077)	[1.011]
∆Num. children	-0.159	***	(0.058)	[0.853]	0.022		(0.093)	[1.022]
∆log(income)	0.452	***	(0.055)	[1.406]	-0.07		(0.061)	[0.951]
Stay married	-0.059		(0.089)	[0.942]	-0.14		(0.134)	[0.870]
Recently Married	0.390	***	(0.14)	[1.478]	0.608	**	(0.26)	[1.837]
Recently divorced	-0.393	*	(0.23)	[0.675]	1.081	***	(0.3)	[2.947]
Became unemp.	0.133		(0.138)	[1.142]	0.08		(0.231)	[1.083]
New homeowner	-0.033		(0.093)	[0.968]	0.387	***	(0.173)	[1.474]
Control for
Age polynomial	Yes				Yes
Yearly fixed effects	Yes				Yes
Num obs.	20,289				2,711

Now focusing on the results of luxury vehicle dispositions, presented in column 4 to 6, we find that income remains the most potent factor. Relative to the lowest-quartile households, those in the two upper quartiles are much less likely to transition out of luxury vehicle ownership within four years (44 percent and 62 percent lower, respectively). Of note, recalculating the transition matrix analysis in table 2 for households in the top decile of family income distribution, we find that about 75 percent of such households retained or expanded their luxury car ownership, compared with about 60 percent (52.7 percent plus 8.2 percent) among all luxury vehicle owners across the entire income distribution. Moreover, college graduates are more than 30 percent more likely to retain their luxury vehicle ownership. By contrast, larger family size, getting married or divorced, and purchasing a home all appear to increase the chance by a substantial margin of giving up one's luxury vehicles.

3. Discussion
Our results indicate that many households, particularly those with lower income, tend to own a luxury vehicle for a relatively short period of time before switching back to non-luxury brands. The findings are consistent with the notion that, relative to necessities, exposures to luxury goods leave a less pronounced imprint on household consumption habits (à la Constantinides 1990). Indeed, most households revert to non-luxury vehicle ownership after a limited stint of luxury-car ownership. We hypothesize that two factors may account for household's willingness to try luxury goods over a relatively short period of time. First, such consumption allows them to calculate the marginal utility of luxury brands. Many discover the realized utility incompatible with their budget conditions and return to non-luxury vehicles. Second, households buy luxury vehicles due to social status signaling motivations that might retreat after a certain image is established and no longer supports conspicuous consumption.

References:
Ait-Sahalia, Yacine, Jonathan Parker, and Motohiro Yogo, "Luxury Goods and the Equity Premium," Journal of Finance, 59(6), 2004, 2959-3004.

Bricker, Jesse, Rodney Ramcharan, and Jacob Krimmel, "Signaling Status: The Impact of Relative Income on Household Consumption and Financial Decisions," Finance and Economics Discussion Series 2014-76.

Constantinides, George, "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy 98(3), 1990, 519-543.

Charles, Kerwin, Erik Hurst, and Nikolai Roussanov, "Conspicuous Consumption and Race," Quarterly Journal of Economics, 124(2), 2009, 42-67.

---