A. Discontinuation Shock and Economic Durability

We use the discontinuation of models and brands described in Section IV as a shock to economic durability. Parts availability and servicing expertise for discontinued vehicles are likely to degrade more quickly than for other vehicles. There may also be a loss of prestige that leads to lower current prices. From the perspective of the theoretical framework described in Section II, this suggests that discontinuation may be viewed as a shock that reduces the economic durability of a car.

We begin by using the Black Book data to empirically assess the impact of discontinuation on economic durability. Definition 1a in Section II requires that more durable assets have a higher ratio of residual value to current period price (i.e., lower YOY depreciation), so if discontinuation reduces durability, then it should increase the rate of depreciation. We test this implication by estimating equation (1) and regressing a vehicle’s YOY depreciation on a post-discontinuation indicator, model × vintage year fixed effects, and corporate parent × contract year fixed effects. Our use of model × vintage year fixed effects allows us to contrast vehicles of the exact same model and vintage year before and after discontinuation. Corporate parent × contract year fixed effects remove any impacts that influenced the corporate parent. It is plausible that corporations that discontinue a make or model may differ from those that do not. For example, it could be that corporate parents that discontinue a make or model may have weaker balance sheets and may therefore be less capable of guaranteeing future warranties. The corporate parent-contract year fixed effects control for any impacts of this kind. Taken together, this complement of fixed effects isolates the impact of discontinuation itself on the specific model that will no longer be manufactured.

We find (shown in column 1 of Table 2) that discontinued vehicles depreciate by an additional −1.2% ( $ t $ -stat = −2.60) per year. This is a meaningful effect relative to the average depreciation rate of −15%. This finding of more severe depreciation after discontinuation is consistent with the claim that discontinuation reduces economic durability. In the second column of Table 2, we show that vehicles experience sustained rates of elevated annual depreciation after discontinuation, ranging from −0.8% ( $ t $ -stat = −2.46) in the first year after discontinuation to −3.3% ( $ t $ -stat = −6.17) in the sixth post-discontinuation year. These results are illustrated graphically in Figure 1.

Table 2Vehicle Depreciation and Model Discontinuation

Table 2 Long description

The table is structured with four columns. Columns 1 and 2 measure Y o Y Depreciation percentage, while columns 3 and 4 measure Wholesale value in dollars.

Key findings include:

* Post discontinuation equals 1: Column 1 shows minus 0.012 with a t-stat of minus 2.60. Column 3 shows minus 1,068.22 with a t-stat of minus 2.50.

* Event time analysis (Columns 2 and 4):

- At Event time equals minus 6 to minus 3, coefficients are generally small and statistically insignificant.

- At Event time equals minus 2, depreciation begins to show a significant decrease of minus 0.010.

- Post-event (Event time 1 to 6), there is a sharp and increasing negative impact. By Event time 4, depreciation reaches minus 0.040 (t-stat minus 8.74) and wholesale price drops by minus 2,035.32 (t-stat minus 6.80).

* Fixed Effects: All models include Vehicle model times Vintage F E s and Parent times contract year F E s.

* Summary Statistics: Number of Observations is 48,086 for depreciation models and 53,496 for wholesale models. Adjusted R super 2 ranges from 0.369 to 0.375 for depreciation and 0.887 to 0.888 for wholesale price.

Figure 1YoY Depreciation Against Event Time

Figure 1 presents differences in the year-over-year (YoY) depreciation across vehicles (models and makes) that were discontinued and those that were not. The plot displays the regression coefficients for timing indicators around the year the model was discontinued (discontinuation year = 0). The dependent variable is the percentage change in the average annual wholesale value of the vehicle as reported by Black Book. Included fixed effects are Make/Model $ \times $ Vintage Year and Contract Year $ \times $ Parent Company.

Figure 1 Long description

The X-axis is labeled Event Time, ranging from negative 6 to positive 6 in increments of 1, with 0 representing the discontinuation year. The Y-axis is labeled Y O Y Depreciation, ranging from negative 0.05 to 0.01 in increments of 0.01.

Two reference lines are present: a horizontal dashed black line at Y equals 0 and a vertical dashed red line at X equals 0.

The data is represented by a solid line with diamond markers and a light orange shaded confidence interval.

* From Event Time negative 6 to negative 1, the coefficients fluctuate between negative 0.005 and negative 0.01, showing no clear trend.

* At Event Time 0, the point is fixed at 0.

* Following the discontinuation year (Event Time 1 to 6), there is a sharp downward trend. The coefficient drops to approximately negative 0.008 at year 1, negative 0.016 at years 2 and 3, and reaches a trough of negative 0.04 at year 4.

* Between years 4 and 6, the depreciation remains low, ending at approximately negative 0.033 at year 6.

* The shaded confidence interval is wider before year 0 and narrows slightly as the depreciation increases after the event.

The initial increase in depreciation in the first year after discontinuation likely reflects both the impaired physical durability of discontinued vehicles and the stigma associated with these cars. The fact that the rate of depreciation is greater in subsequent years, however, probably largely arises from a decrease in physical durability, as it seems unlikely that the loss of prestige for discontinued cars would increase over time as a fraction of overall value.

The second key feature of less durable assets, which is highlighted in Definition 1b in Section II, is that they have lower prices. We show in the third column of Table 2 that discontinuation leads to a $1,068.2 drop ( $ t $ -stat = −2.50) in vehicle wholesale values. This is a meaningful decrease compared to the average wholesale value of $12,493. As shown in the fourth column of Table 2, the price effect is substantial in the first year after discontinuation (coefficient = −1055.1 and $ t $ -stat = −3.00) and is larger in subsequent years.Footnote ¹⁸ Table 2 makes clear that discontinued vehicles are less economically durable, exhibiting both increased rates of annual depreciation and lower prices.

Next, we examine the impact of discontinuation on vehicles in our loan data. These data describe sales of individual vehicles, so they can be used to analyze prices, but are not in the form of a panel that allows for the calculation of annual depreciation. We regress the vehicle wholesale value on a post-discontinuation indicator, model × vintage year fixed effects, dealer fixed effects, and corporate parent × contract year fixed effects, which we refer to as the standard set of fixed effects. We find (shown in column 1 of Table 3) that discontinued vehicles experience a change in wholesale value of -$262.6 ( $ t $ -stat = −2.39). The negative sign of this effect is consistent with the results in Table 2. The magnitude of the drop is smaller than for the vehicles in the Black Book sample, which may arise from the fact that the loan data are generated from subprime borrowers sales, whereas the Black Book data describe a broad cross section of vehicles.Footnote ¹⁹

Table 3Vehicle Wholesale Value and Model Discontinuation

Table 3 Long description

The table is divided into two main sections: Wholesale Value in dollars (Models 1, 2, and 3) and Scaled Price in percentage (Models 4, 5, and 6).

Key variables and their coefficients include:

* Post discontinuation (=1): Shows negative coefficients across all models, ranging from minus 246.35 to minus 319.35 for Wholesale Value, and minus 2.85 to minus 3.54 percent for Scaled Price. All are statistically significant.

* Log income: Positive coefficients around 1143 to 1219 for Wholesale Value and 5.48 to 6.09 for Scaled Price.

* Credit score: Small positive coefficients of 1.20 to 1.22 for value and 0.01 for price.

* Chapter 7 Bankruptcy (=1): Positive coefficients (130.06 to 161.74 for value).

* Chapter 13 Bankruptcy (=1): Negative coefficients (minus 130.53 to minus 150.95 for value).

* Homeowner (=1): Negative coefficients (minus 28.31 to minus 44.31 for value).

* Log mileage and Dealer profit (000 dollars): Both show negative coefficients in Models 3 and 6.

Fixed Effects (F E s) for Vehicle model times Vintage, Dealer, and Parent times contract year are included (Yes) for all models. The number of observations ranges from 247,350 to 324,823. Adjusted R-squared values range from 0.676 to 0.816.

Including controls for borrower income and credit score, indicators for prior borrower Chapter 7 or Chapter 13 bankruptcy filings and an indicator for borrower homeowner status leave the qualitative finding unchanged, as shown in the second column of Table 3. Including a control for vehicle mileage and dealer profit yields the result that discontinuation reduces the wholesale value by $246.35 ( $ t $ -stat = −2.33).

We also measure vehicle value using the scaled price, defined as the wholesale value divided by the average wholesale value of the same model and vintage when new. We show in the fourth column of Table 3 that the scaled price is 3.54 percentage points lower ( $ t $ -stat = −4.33) post-discontinuation. The results from the specifications including borrower, vehicle mileage, and dealer profit controls in the scaled price regressions support the conclusion that discontinuation reduces vehicle value, as shown in columns 5 and 6 of Table 3.

As an additional test for whether discontinuation can be viewed as a negative durability shock, we study the recovery percent of a vehicle, which we define to be the value the lender receives from the vehicle’s liquidation after default divided by the vehicle’s wholesale value at origination. We regress the recovery percent on the post-discontinuation dummy and the standard fixed effects. We note here for clarity that we assign the post-discontinuation indicator to a vehicle if it is purchased after discontinuation. As shown in Tables 2 and 3, these vehicles have lower current period prices when purchased. In the present test, we explore whether their future recovery values are lower, as a fraction of their already reduced prices, relative to other vehicles.

We find, as shown in the first column of Table 4, that the recovery percent is 1.49 percentage points lower ( $ t $ -stat = −2.45) for post-discontinuation vehicles. This drop may be compared to the average recovery ratio of 28%. In the second column of Table 4, we show that including borrower, vehicle mileage, and dealer profit controls as well as a control for the time to default yields a coefficient of −2.08 percentage points ( $ t $ -stat = −3.72) on post-discontinuation. Including an additional fixed effect for the model × year of default as well as controlling for the recovery type results in an estimated coefficient of −1.40 percentage points ( $ t $ -stat = −2.20), as shown in the third column of Table 4. These results support the general conclusion that discontinued vehicles have lower residual values, even when viewing these residual values as a fraction of their lower prices at the time of purchase.

Table 4Default Recovery and Model Discontinuation

Table 4 Long description

The table is organized into four columns: Vehicle Recovery percentage, and three numbered models (1, 2, and 3).

* Post discontinuation (=1): Model 1 shows -1.49 with two asterisks and -2.45 in brackets. Model 2 shows -2.08 with three asterisks and -3.72 in brackets. Model 3 shows -1.40 with two asterisks and -2.20 in brackets.

* Vehicle model times Vintage F Es: Yes for all three models.

* Parent times Contract year F Es: Yes for all three models.

* Dealership F Es: Yes for all three models.

* Model times Default year F Es: No for models 1 and 2; Yes for model 3.

* Recovery type F Es: No for models 1 and 2; Yes for model 3.

* Borrower controls: No for model 1; Yes for models 2 and 3.

* Vehicle controls: No for model 1; Yes for models 2 and 3.

* Time to Default control: No for model 1; Yes for models 2 and 3.

* Number of Observations: 73,986 for model 1; 64,634 for model 2; 63,823 for model 3.

* Adjusted R super 2: 0.087 for model 1; 0.272 for model 2; 0.581 for model 3.

Tables 2, 3, and 4 make clear that the discontinuation shock reduces economic durability, as described in Definition 1. Discontinued vehicles have higher depreciation rates, lower prices, and lower residual values, and consequently we view them as less durable assets for the purpose of testing the theoretical predictions outlined in Section II.

B. Durability and Consumer Income

A direct implication from the assumptions of the theoretical framework presented in Section II is that higher-income borrowers will purchase more durable assets. The basic intuition is that more economically durable assets are attractive but expensive. We test this prediction by regressing an indicator for whether a borrower had a bottom-quartile income relative to all borrowers in that year on the post-discontinuation dummy and the standard fixed effects. We find, as shown in the first column of Table 5, that discontinuation increases the probability that the purchaser is in the bottom income quartile by 3.43 percentage points ( $ t $ -stat = 2.81). This represents a large 13.7% increase in the probability that the buyer is lower-income. This finding is consistent with the implication that lower-income borrowers are more likely to buy less durable discontinued vehicles. Including controls yields a similar conclusion, as shown in the second column of Table 5. A regression of the log of borrower income on discontinuation yields a coefficient of −0.014 ( $ t $ -stat = −2.21), as displayed in the third column of Table 5; the negative impact of discontinuation on income is evidently strongest in shifting buyers into the lowest quartile. This result is robust to controlling vehicle mileage and dealer profits and also emerges in specifications using Poisson regressions as suggested by Silva and Tenreyro (Reference Silva and Tenreyro2006) and Cohn, Liu, and Wardlaw (Reference Cohn, Liu and Wardlaw2022), as shown in columns 4–6 of Table 5. Discontinued vehicles are purchased by lower-income borrowers, and the effect is especially pronounced for borrowers in the bottom-income quartile.

Table 5Borrower Income and Model Discontinuation

Table 5 Long description

The table presents regression results for three dependent variables: Low Income (equals 1), Log Income, and Income (Poisson). Each variable is tested across two models (1 through 6).

* Row 1: Post discontinuation (equals 1).

- Model 1: 3.43 (t-stat 2.81) with three asterisks.

- Model 2: 3.31 (t-stat 2.73) with three asterisks.

- Model 3: minus 0.014 (t-stat minus 2.21) with two asterisks.

- Model 4: minus 0.013 (t-stat minus 1.85) with one asterisk.

- Model 5: minus 0.018 (t-stat minus 2.80) with three asterisks.

- Model 6: minus 0.016 (t-stat minus 2.50) with two asterisks.

* Fixed Effects (F E s) and Controls:

- Vehicle model times Vintage F E s: Yes for all models.

- Parent times Contract year F E s: Yes for all models.

- Dealership F E s: Yes for all models.

- Vehicle controls: No for models 1, 3, and 5; Yes for models 2, 4, and 6.

* Summary Statistics:

- Number of Observations: Approximately 284,573 for odd models and 283,928 for even models.

- Adjusted R-squared: Ranges from 0.142 (Model 1) to 0.283 (Model 6).

C. Durability and Down Payments

The results described in Section V.A serve to validate the use of discontinuation as a shock to economic durability, while the results in Section V.B support our assumptions for the relationship between a reduction in durability and borrower income.Footnote ²⁰

The model offers conflicting predictions for the impact of economic durability on the dollar value of the borrower’s down payment (i.e., the cash amount paid by the borrower on the transaction date). When income pledgeability is low, more durable assets require larger down payments (Result 1b); while when income pledgeability is sufficiently high, borrowers purchase less durable assets with larger down payments (Result 1a).

We regress the down payment on the post-discontinuation indicator and the standard fixed effects. We find that discontinuation leads to larger down payments, as shown in the first column of Table 6. Consistent with the implication in the model when income is sufficiently pledgeable, borrowers supply an additional $74.02 ( $ t $ -stat = 3.32) in down payments when purchasing less durable discontinued vehicles. As shown in Figure 2, down payments climb significantly after discontinuation and do not exhibit any apparent pre-trend.

Table 6Down Payment and Model Discontinuation

Table 6 Long description

The table is divided into two main sections: Down Payment in dollars (Models 1 through 3) and Down Payment as a percentage of price (Models 4 through 6).

* Row 1: Post discontinuation (=1). Values for Models 1 to 3 are 74.02, 60.94, and 78.55 respectively. Values for Models 4 to 6 are 0.60, 0.47, and 0.49 respectively. All values are statistically significant.

* Row 2: Standard errors for the post discontinuation row, ranging from 2.05 to 4.85.

* Row 3: Wholesale value in dollars. Only reported for Model 3 (0.07) and Model 6 (0.00), both statistically significant.

* Row 4: Standard errors for wholesale value, 27.57 for Model 3 and 10.09 for Model 6.

* Fixed Effects (F E s) and Controls:

- Vehicle model times Vintage F E s: Yes for all models.

- Dealer F E s: Yes for all models.

- Parent times Transaction year F E s: Yes for all models.

- Borrower controls: No for Models 1 and 4; Yes for Models 2, 3, 5, and 6.

- Vehicle controls: No for Models 1 and 4; Yes for Models 2, 3, 5, and 6.

* Number of Observations: Ranges from 265,708 to 324,567.

* Adjusted R-squared: Ranges from 0.199 to 0.267.

Figure 2Down Payment Against Event Time

Figure 2 presents differences in the down payments across vehicles (models and makes) that were discontinued and those that were not. The plot is the regression coefficients for timing indicators around the year the model was discontinued (discontinuation year = 0). The dependent variable is the down payment for the vehicle. Included fixed effects are Make/Model $ \times $ Vintage Year, Dealership, and Contract Year $ \times $ Parent Company.

Figure 2 Long description

The Y-axis is labeled Down Payment with a scale from minus 50 to 175 in increments of 25. The X-axis is labeled Event Time with a scale from minus 4 to 4. A vertical dashed red line marks the discontinuation year at 0. A horizontal dashed black line marks the zero baseline on the Y-axis.

* From Event Time minus 4 to 0, the data points fluctuate slightly between 0 and 25, showing a relatively flat trend with a light orange shaded confidence interval spanning roughly minus 35 to 75.

* At Event Time 0, the coefficient is exactly 0 with no confidence interval.

* From Event Time 1 to 4, the coefficients show a sharp upward trend. The point at time 1 is approximately 50, time 2 is approximately 30, time 3 peaks at approximately 110, and time 4 is approximately 85.

* The light orange shaded confidence interval widens significantly after time 0, ranging from approximately minus 20 to 170 by time 3.

This down payment result is particularly surprising from the perspective of a model with only asset-based collateral (i.e., if income was not pledgeable). We showed in Table 3 that discontinued vehicles are less expensive. This fact, along with the limited pledgeability of collateral emphasized in asset-backed models of lending, should lead discontinued autos to require lower down payments. Moreover, we demonstrate in Table 5 that these vehicles are purchased by lower-income borrowers who presumably have less cash on hand for a down payment. Despite these two compelling intuitions for a prediction that there will be lower down payments for less durable assets, we find the opposite. This finding in the context of the model shows that IBL is a relatively important feature of auto lending. Given that lower-income consumers have smaller future incomes against which to borrow, lower-income purchasers of less durable assets need to provide larger down payments to close the transactions.Footnote ²¹

The positive impact of discontinuation on down payments continues to hold when controlling for borrower and vehicle characteristics, as detailed in the second column of Table 6. We show in the third column of Table 6 that in the cross section more expensive vehicles with elevated book values generally require higher down payments. There are, however, many unobserved differences between vehicles of different prices. Our result that discontinuation shocks lead to higher down payments on vehicles of specific model × vintage years is somewhat stronger when controlling for this vehicle book value effect, as is displayed in the third column. We also find, as described in columns 4–6 of Table 6, that after discontinuation down payments increase as a fraction of price.

The higher down payments for less durable assets that we find indicate that the empirically relevant regions of Figure B.1 in the Supplementary Material are restricted to region I (light green), region II (orange), or region III (dark pink). Only for the high levels of income pledgeability that hold in those regions will lower-income borrowers make the higher down payments that we observe. The other regions are incompatible with the down payment results in Table 6.

D. Durability and LTV Ratios

In this section, we consider the implications of the model for the LTV ratio. Specifically, in our model, when IBL is relatively unimportant for lower-income borrowers, LTV increases with durability (Result 2b), but when IBL is relatively important for lower-income borrowers, LTV decreases with durability (Result 2a).

We define the LTV as the ratio of the loan balance to the wholesale value of the auto at the time of origination. We regress LTV on the post-discontinuation indicator and the standard fixed effects, and find a positive and significant coefficient of 0.016 ( $ t $ -stat = 3.14), as displayed in the first column of Table 7. This result shows that a discontinuation shock reducing vehicle durability leads to higher LTV ratios, which, as we describe in Section II, arises only in the model when lower-income borrowers are highly dependent on IBL. Figure 3 shows that LTV ratios exhibit no pre-trend before discontinuations and are higher afterward.

Table 7Loan-to-Value (LTV) and Model Discontinuation

Table 7 Long description

The table consists of 4 columns and 9 rows.

Header Row: Loan-to-Value L T V, 1, 2, 3.

Row 1: Post discontinuation equals 1. Column 1 is 0.016 with three asterisks. Column 2 is 0.018 with three asterisks. Column 3 is 0.014 with three asterisks.

Row 2: Standard errors for the previous row. Column 1 is 3.14. Column 2 is 3.53. Column 3 is 6.23.

Row 3: Vehicle model times Vintage F Es. All three columns are Yes.

Row 4: Dealer F Es. All three columns are Yes.

Row 5: Parent times Contract year F Es. All three columns are Yes.

Row 6: Borrower controls. Column 1 is No. Column 2 is Yes. Column 3 is Yes.

Row 7: Vehicle controls. Column 1 is No. Column 2 is No. Column 3 is Yes.

Row 8: Number of Observations. Column 1 is 324,823. Column 2 is 273,365. Column 3 is 272,725.

Row 9: Adjusted R-squared. Column 1 is 0.345. Column 2 is 0.339. Column 3 is 0.709.

Figure 3LTV Against Event Time

Figure 3 presents differences in the loan-to-value (LTV) across vehicles (models and makes) that were discontinued and those that were not. The plot is the regression coefficients for timing indicators around the year the model was discontinued (discontinuation year = 0). The dependent variable is the loan amount divided by the reported vehicle value to the lender for the vehicle. Included fixed effects are Make/Model $ \times $ Vintage Year, Dealership, and Contract Year $ \times $ Parent Company.

Figure 3 Long description

The line graph plots Loan to Value L T V on the Y-axis against Event Time on the X-axis.

* The Y-axis ranges from minus 0.02 to 0.03 with increments of 0.01.

* The X-axis ranges from minus 4 to 4, representing years around the discontinuation event.

* A horizontal dashed black line is fixed at Y equals 0.

* A vertical dashed red line is fixed at X equals 0, marking the discontinuation year.

Data Trend:

* From year minus 4 to minus 1, the regression coefficients remain relatively flat and slightly below the zero line, fluctuating between minus 0.005 and 0.

* At year 0, the data point is exactly at the intersection of the zero lines.

* Immediately following discontinuation at year 1, there is a sharp increase to a peak coefficient of approximately 0.019.

* From year 1 to year 3, the trend shows a steady decline, dropping to approximately 0.004.

* At year 4, there is a slight uptick to approximately 0.005.

* A light orange shaded region surrounds the data line, representing the confidence interval, which is narrowest at year 0 and widest at years 1 and 2.

It is a general and robust feature of models of asset-backed financing that LTV increases with durability (Hart and Moore (Reference Hart and Moore1994)). When the asset constitutes the entire collateral, as in a model without IBL, more durable assets with higher liquidation values support larger loans relative to current values. We also find this implication in our model when IBL is relatively less important for lower-income borrowers (these are regions II, III, IV, and V in Figure B.1 in the Supplementary Material). Our finding to the contrary indicates that in the auto loan market, IBL must play a meaningful role and that it is especially important for lower-income borrowers. Our model describes a setting in which borrowers can rely on their future income to purchase assets. Lower-income borrowers, in particular, use their future income to purchase less durable assets. If the price of the less durable asset is relatively low, then lower-income borrowers will purchase it with a relatively high debt ratio, as the debt is secured by their income, not just by the physical collateral. This mechanism in the model is consistent with the finding that LTV increases after a decline in durability.

Including borrower controls has little impact on the estimated effect of the discontinuation shock on LTV, as shown in the second column of Table 7. In the third column of Table 7, we display the similar results when including the full set of vehicle and borrower controls (coefficient = 0.014 and $ t $ -stat = 6.23). The general conclusion is unchanged: less durable autos are financed with higher LTV ratios, which emerges as a potential outcome in the model only when lower-income borrowers are relatively more dependent on IBL.Footnote ²²

We have thus shown in Tables 6 and 7 that less durable assets have both higher down payments and higher LTVs than more durable assets. The only region in Figure B.1 in the Supplementary Material for which both of these outcomes hold is region I. The data thus indicate that in the U.S. auto loan market income is quite pledgeable and lower-income borrowers rely relatively more heavily on IBL.Footnote ²³

At first glance it may seem surprising that discontinued vehicles have lower prices and higher down payments, yet carry higher LTV ratios. This can occur, however, when dealers charge non-proportional markupsFootnote ²⁴ and LTVs are calculated relative to the book values of the vehicles. For example, suppose that a more durable asset sells for 150, has a book value of 135 and is financed with 145 in debt and a down payment of 5. Suppose the less durable asset sells for 130, has a book value of 115 and is financed with 124 in debt and a down payment of 6. In this case, the less durable asset has a lower price, a higher down payment, and a higher LTV ratio.

We further comment that the mean LTV for our auto borrowers is 129%.Footnote ²⁵ In a model where income pledgeability was low (i.e., little IBL) this high level of debt would be unexpected, as lenders can only seek repayment from the asset value. LTVs of above 100% can be supported, however, when income is sufficiently pledgeable, as the borrower’s future income is also used to meet the required debt payments. This is also consistent with parameters in region I of Figure B.1 in the Supplementary Material.

E. Durability and Payment-to-Income Ratios

Result 3 of the model predicts that the payment-to-income ratio will be lower for less durable assets if lower-income borrowers are more heavily dependent on IBL (as is the case in region I of Figure B.1 in the Supplementary Material). This provides an additional model implication that we explore.

We test this prediction by regressing the log of the borrower’s payment-to-income (PTI) ratio on the post-discontinuation variable and the standard fixed effects. We find a negative and significant effect of discontinuation on the log of PTI (coefficient = −0.017 and $ t $ -stat = −2.12), as displayed in the first column of Table 8. PTI ratios of the purchasers of these vehicles drop by roughly 2% after discontinuation is announced.

Table 8Payment-to-Income (PTI) and Model Discontinuation

Table 8 Long description

The table is divided into two main sections based on the dependent variable: Log P T I (columns 1 to 4) and P T I (columns 5 to 8).

* The primary independent variable is Post discontinuation (=1).

* For Log P T I, the coefficients are -0.017 (model 1), -0.023 (model 2), -0.027 (model 3), and -0.023 (model 4).

* For P T I, the coefficients are -0.163 (model 5), -0.241 (model 6), -0.255 (model 7), and -0.229 (model 8).

* All coefficients are statistically significant at the 1 percent or 5 percent level.

* Fixed Effects (F E s) and Controls:

- Vehicle model times Vintage F E s: Yes for all models.

- Parent times Contract year F E s: Yes for all models.

- Dealership F E s: Yes for all models.

- Income decile F E s: Yes for models 2, 4, 6, and 8; No for others.

- Borrower controls: Yes for models 3, 4, 7, and 8; No for others.

- Vehicle controls: Yes for models 3, 4, 7, and 8; No for others.

* Number of Observations: Ranges from 272,725 to 284,575.

* Adjusted R-squared: Ranges from 0.041 to 0.566 for Log P T I and 0.053 to 0.673 for P T I.

Including fixed effects of the borrower income decile has little impact on the estimated negative coefficient on discontinuation, though it does increase the precision of the estimate, as shown in the second column of Table 8. Introducing borrower and vehicle controls, either with or without fixed effects on borrower income decile, also yields similar estimates, as described in columns 3 and 4 of Table 8. Using the PTI ratio rather than the log as the dependent variable yields similar directional results and significance but lower magnitudes, as displayed in columns 5–8 of Table 8. This is due to a wide distribution in PTI that may skew the results. Figure 4 shows that borrower PTI drops after discontinuation, with no visible pre-trend.

Figure 4PTI Against Event Time

Figure 4 presents differences in the log of the payment-to-income ratio (PTI) across vehicle make-models that were discontinued and those that were not. The plot is the regression coefficients for timing indicators around the year the model was discontinued (discontinuation year = 0). The dependent variable is the log of the borrower’s monthly payment to the borrower’s monthly income. Included fixed effects are Make/Model $ \times $ Vintage Year, Dealership, borrower income decile, and Contract Year $ \times $ Parent Company.

Figure 4 Long description

A line graph with an X-axis labeled Event Time ranging from negative 4 to 4 and a Y-axis labeled Log Payment to Income P T I ranging from negative 0.045 to 0.03. A horizontal dashed black line is at Y equals 0. A vertical dashed red line marks the event at X equals 0.

Data points are represented by small diamonds connected by a solid line, surrounded by a light orange shaded confidence interval.

* From X equals negative 4 to negative 2, the P T I remains slightly above 0, peaking at approximately 0.008 at X equals negative 2.

* At X equals negative 1, the value drops toward 0.

* At X equals 0, the point is exactly on the intersection of the axes at 0.

* Following the event, at X equals 1, there is a sharp decrease to approximately negative 0.018.

* From X equals 2 to 4, the values remain negative, fluctuating between negative 0.02 and negative 0.015.

* The shaded confidence interval is relatively narrow before the event but widens significantly after X equals 1, indicating increased variance in the post-discontinuation period.

The complete set of empirical findings across down payments, LTVs and PTIs offers consistent support for the argument that income is pledgeable and that lower-income borrowers rely more heavily on IBL, as described in region I of Figure B.1 in the Supplementary Material. Moreover, down payments are generally non-negative in our data, so the Model Implications in Section II suggest that there is a constant component to the dealer markup.Footnote ²⁶ In direct tests, in Table F.5 in the Supplementary Material, we show that dealer dollar margins do not vary with vehicle discontinuation status. These results indicate that dealers indeed earn constant margins across more and less durable assets.

F. Durability and Recovery in Default

In the discussion above, we highlight the role of IBL. For IBL to be important, however, it must be that consumers are able to borrow against their future income and need not rely solely on the physical asset to serve as collateral. In this section, we discuss the direct evidence on post-default lender collections. In particular, is it the case that lenders actually recover from the personal resources of borrowers?

We have data on the recovery proceeds from 76,638 defaulted loans where we observe both income and vehicle recoveries. For this sample, we find that the average proceeds from the sales of repossessed vehicles are $3483. The average cash recovery from the borrower is $1171. We thus find that in default, physical assets and personal borrower resources supply 75% and 25%, respectively, of the total recovery proceeds. These summary statistics show that in the auto loan market, a market in which vehicle collateral is generally deemed to serve a central role, borrower personal income pledges do perform a significant function.

G. IBL to Lower-Income Consumers: Default Recoveries

As outlined in the model developed in Section II, the results in Table 6 showing that a reduction in durability leads to larger down payments demonstrate that IBL is important in the auto financing market. The empirical findings on LTV and PTI in Tables 7 and 8 establish that lower-income borrowers are more heavily relying on IBL than higher-income borrowers.

The default recovery data make possible an additional test of these implications. We show in Table 5 that discontinued vehicles tend to be purchased by lower-income consumers. Given the results in Tables 6–8, the model’s implications are that lower-income borrowers rely relatively more on IBL. We should therefore expect to observe lower vehicle recoveries and higher personal income recoveries from the purchasers of discontinued vehicles who default.

In the extension of the model described in Section II, we discuss the idea that different borrowers may experience varying levels of asset depreciation for the same vehicle. The recovery data enable us to examine this hypothesis, as we can contrast the outcomes for borrowers who purchased vehicles that were later discontinued with outcomes for borrowers who purchased vehicles after the discontinuation announcement. Both types of borrowers experience the impact on their vehicles of a discontinuation, but the borrowers themselves differ in that only the first group of borrowers chose to purchase what were at the time non-discontinued cars. Any observed differences across the two borrower types in their recovery rates would therefore constitute evidence in favor of borrower-dependent depreciation. In order to ensure that the vehicles of these two borrower groups are comparable, for cars that are discontinued or eventually discontinued, only autos purchased within 2 years of a discontinuation are included.

We begin by analyzing recovery rates for borrowers who purchased their vehicles after a discontinuation announcement. Consistent with our labeling in the previous tables, we describe these as Post-Discontinuation transactions. We regress the value of the vehicle recovery on the post-discontinuation indicator, the standard fixed effects and additional fixed effects for the corporate parent × default year, and the form of recovery. We find, as shown in the first column of Table 9, that vehicles purchased post-discontinuation are worth $239.03 less ( $ t $ -stat = −3.37) in repossession. These vehicles are less durable and therefore provide diminished physical recovery proceeds, as expected under the model. It may also be the case that the purchasers of the vehicles are less able to maintain them, resulting in even higher rates of depreciation.

Table 9Vehicle Recovery and Purchase Timing

Table 9 Long description

The table presents regression results across six models. Columns 1 through 3 measure Vehicle Recovery in dollars, while columns 4 through 6 measure Vehicle Recovery over Default as a percentage.

Key Data Rows:

* Post discontinuation (=1): Values range from -239.03 to -419.69 in dollars, and -1.54 to -2.88 in percentage. All are significant at the 1 percent level.

* Purchased before, defaulted after (=1): Values range from -175.59 to -205.16 in dollars, and -1.40 to -1.53 in percentage. All are significant at the 5 percent level.

* F-Stat (Post Disc. = Purch. Before, Def. After.): Values range from 7.45 to 8.33 for dollars and 15.87 to 18.75 for percentage.

Fixed Effects (F E s) and Controls:

* Vehicle model times Vintage F E s: Yes for all models.

* Parent times Contract year F E s: Yes for all models.

* Dealership F E s: Yes for all models.

* Parent times Default year F E s: Yes for all models.

* Recovery type F E s: Yes for all models.

* Borrower controls: Yes for models 3 and 6; No for others.

* Vehicle controls: Yes for models 3 and 6; No for others.

* Time to default control: Yes for models 3 and 6; No for others.

Summary Statistics:

* Number of Observations: Approximately 55,700 to 57,500 across models.

* Adjusted R-squared: Ranges from 0.566 to 0.578 for dollar models and 0.502 to 0.508 for percentage models.

As a point of contrast, we examine vehicle recovery proceeds from cars purchased prior to discontinuation that experienced default after discontinuation. We label these transactions as Purchase Before, Default After. Footnote ²⁷ In the second column of Table 9, we show that these vehicles have $205.16 lower ( $ t $ -stat = −2.67) recoveries. The purchasers of these cars did not choose to buy a discontinued auto: discontinuation was an ex post shock that they experienced.Footnote ²⁸ The drop in vehicle recoveries we find for this group therefore constitutes evidence of higher post-discontinuation depreciation that affects the physical asset independent of the borrower type.

The coefficient on Post Discontinuation in this regression is −419.69 ( $ t $ -stat = −4.19). This coefficient is larger in magnitude than the coefficient on Purchase Before, Default After, with the difference statistically significant at the 5% level. The relatively lower recovery for borrowers who purchased their vehicles after discontinuation, compared to those who experienced discontinuation after purchase, is evidence in favor of borrower-dependent depreciation. This regression includes fixed effects for both model × vintage and parent × default year, so we are comparing outcomes for similar vehicles that defaulted at the same time and that had been discontinued at the time of default. The reduced recovery for post-discontinuation buyers suggests that, perhaps due to financial constraints, these consumers were unable to maintain the values of their vehicles in the same manner as those who purchased them before the discontinuation. Including borrower, vehicle mileage, dealer profit, and time to default controls has little impact on the estimated coefficients on Purchase Before, Default After and Post Discontinuation, as detailed in the third column of Table 9; both remain significant and statistically distinct from each other at the 5% level. Figure F.6 in the Supplementary Material provides a graphical depiction of vehicle recoveries for both borrowers who experienced a discontinuation after purchase and for those who purchased after discontinuation.Footnote ²⁹

A decrease in durability reduces not only the dollar amount recovered from the repossessed asset but also the percentage of the loan balance recovered through liquidation. We find, as detailed in the fourth column of Table 9, that the percentage of the loan balance recovered through liquidation of the vehicle is lower for vehicles purchased after discontinuation. In the fifth column of Table 9, we show that the effect of Post Discontinuation (coefficient = −2.88 and $ t $ -stat = −5.62) is greater in magnitude than the impact of Purchase Before, Default After (coefficient = −1.53 and $ t $ -stat = −2.66), and the difference is statistically significant at the 5% level. The results for the specification including the full set of controls outlined in the sixth column of Table 9, are quite similar. These findings buttress the argument that asset depreciation varies by borrower type.

Although it is perhaps unsurprising that vehicle recoveries are lower for discontinued vehicles, it is a novel implication of the model that personal income recoveries as a fraction of the loan balance should be higher for these cars, as they are purchased by lower-income borrowers who rely more heavily on IBL.Footnote ³⁰ We regress the dollar amount of personal post-default payments on the post-discontinuation indicator and the fixed effects described above. We find, as displayed in the first column of Table 10, that the dollar amount weakly increases (coefficient = 104.85 and $ t $ -stat = 1.70) after discontinuation. A similar result holds in the specification with borrower, vehicle, and dealer profit controls, as shown in the second column of Table 10. When including the gross default amount as a control, there is somewhat stronger evidence of an increase in income recovery (coefficient = 139.42 and $ t $ -stat = 2.19), as displayed in the third column of Table 10.

Table 10Income Recovery and Model Discontinuation

Table 10 Long description

The table is organized into five columns representing different regression models. Columns 1, 2, and 3 measure Income Recovery in dollars, while columns 4 and 5 measure Income Recovery as a percentage of default.

* Row 1: Post discontinuation (equals 1). Values are 104.85 star (1), 112.86 star (2), 139.42 double star (3), 1.55 star (4), and 1.78 star (5). Standard errors in parentheses are 1.70, 1.77, 2.19, 1.75, and 2.00 respectively.

* Row 2: Gross default amount in thousands of dollars. Only column 3 has a value of 51.86 triple star with a standard error of 10.54.

* Fixed Effects (F E) and Controls: All models include Vehicle model times Vintage F E, Parent times Contract year F E, Dealership F E, Model times Default year F E, and Recovery type F E. Borrower controls, Vehicle controls, and Time to default control are marked No for models 1 and 4, and Yes for models 2, 3, and 5.

* Row 3: Number of Observations. Values are 70,030 (1), 67,962 (2), 67,961 (3), 70,017 (4), and 67,951 (5).

* Row 4: Adjusted R-squared. Values are 0.102 (1), 0.107 (2), 0.113 (3), 0.111 (4), and 0.114 (5).

The ratio of personal borrower payments to the defaulted loan balance also weakly increases after discontinuation (coefficient = 1.55 and $ t $ -stat = 1.75), as we detail in the fourth column of Table 10. Including controls somewhat strengthens this conclusion (coefficient = 1.78 and $ t $ -stat = 2.00); the results are displayed in the fifth column of the table.

Taken together, the results in Tables 9 and 10 support the contention that lower-income borrowers rely more heavily than higher-income borrowers on their income as a collateral source. It is notable that purchasers of discontinued vehicles make larger personal payments after default. These consumers have lower incomes and buy less expensive vehicles. For both of these reasons, one might have expected them to supply smaller personal recoveries relative to their loan balances in the event of a default, yet we find the opposite. The model supplies the intuition for our finding: purchasers of discontinued less durable vehicles must pledge their own income, rather than the quickly depreciating physical asset, in order to receive a loan. In the event of default, a lender therefore must have recourse to their income, as the physical collateral does not have much value.Footnote ³¹