VOL 99 NO. I ADAMS ETAL.: SUBPRIME LENDING lot is 30 percent higher in the month of February than in other months. There are also positive but less pronounced demand effects for January and March. Consistent with the liquidity story, we also find that the seasonal pattern reported above is mainly driven by cash transactions, while purchases that involve trade-ins, which are less likely to be affected by tax rebates, do not exhibit noticeable seasonal variation Our estimates of loan demand, discussed in Section IV, are also consistent with the hypoth esis that tax rebates represent a substantial liquidity shock that significantly affects behavior In particular, down payments are substantially higher in tax season even after factoring in the higher minimum requirements. About 65 percent of February purchasers make a down payment above the required(higher) minimum compared to 54 percent in the rest of the year. Moreover, we estimate that after controlling for transaction characteristics, the desired down payment of a February buyer is about $300 higher than that of the average buyer. This is a nontrivial effect given that the average down payment is under $1, 000. 4 B. Estimating Purchasing demand Empirical Strategy.Additional evidence on the role of short-term liquidity in purchasin comes from looking at the demand sensitivity to current and deferred payment requirements. To study this, we consider a probit model for the purchase decision, estimated at the level of the dividual applicant. Let qi denote a dummy variable equal to one if applicant i purchases a car. We assume that qi q=xa+E1≥0 where x; =(xi, x, x is a vector of transaction characteristics and e; is an i.i.d normally distributed error term Here, x denotes the offer characteristics: car price, interest rate, loan term, and minimum down payment. 5 The vector xf denotes car characteristics including the cost of acquiring and reconditioning the car, the mileage, car age, and, as a useful proxy for any unobserved quality, the time the car has spent on the lot. Finally, x; denotes applicant characteristics, including the applicant's credit category and monthly income, as well as city, month, and year dummies. We estimate the model on individual applicant data. Using the individual applicant data offers substantial advantages but requires us to address a missing data problem. We observe nonpur- haser's individual characteristics, but not the car and car price they considered. Our solution is imputation. We assign each applicant to one of three credit categories and one of three income categories. Then for each nonpurchaser, we randomly select a purchaser in the same credit and income category, and in the same city and week, and assume the nonpurchaser faced the same car and price. As we discuss below, our conclusions are quite robust to the imputation specifics, and also to estimation where we avoid explicit imputation by using aggregated data. on 14 Defaults on existing loans are also lower in tax season than in other months of the year, providing furtherevidence The realized interest rate can depend on the size of the down payment, so we instead use as a covariate the interes rate the applicant would have paid making the minimum down payment. As an empirical matter, the differences are relatively small, and using the realized interest rate has no effect on the other coefficients Ib The income categories correspond to household annual income of less than $24, 000 dollars, $,000-30,000 and more than $30,000 imputation is identifying the effect of price changes. Because prices are individu- ally negotiated, it seems plausible that nonpurchasers might have faced somewhat higher prices. Even if the difference in offers arises for random exogenous reasons, a straight demand regression would underestimate the effect of price
VOL. 99 NO. 1 Adams Et al.: Subprime Lending 59 lot is 30 percent higher in the month of February than in other months. There are also positive but less pronounced demand effects for January and March. Consistent with the liquidity story, we also find that the seasonal pattern reported above is mainly driven by cash transactions, while purchases that involve trade-ins, which are less likely to be affected by tax rebates, do not exhibit noticeable seasonal variation. Our estimates of loan demand, discussed in Section IV, are also consistent with the hypothesis that tax rebates represent a substantial liquidity shock that significantly affects behavior. In particular, down payments are substantially higher in tax season even after factoring in the higher minimum requirements. About 65 percent of February purchasers make a down payment above the required (higher) minimum compared to 54 percent in the rest of the year. Moreover, we estimate that after controlling for transaction characteristics, the desired down payment of a February buyer is about $300 higher than that of the average buyer. This is a nontrivial effect given that the average down payment is under $1,000.14 B. Estimating Purchasing Demand Empirical Strategy.—Additional evidence on the role of short-term liquidity in purchasing comes from looking at the demand sensitivity to current and deferred payment requirements. To study this, we consider a probit model for the purchase decision, estimated at the level of the individual applicant. Let qi denote a dummy variable equal to one if applicant i purchases a car. We assume that (1) qi 5 1 3 qi * 5 xi 9a 1 ei $ 0, where xi 5 1xi o , xi c ,xi a 2 is a vector of transaction characteristics and ei is an i.i.d normally distributed error term. Here, xi o denotes the offer characteristics: car price, interest rate, loan term, and minimum down payment.15 The vector xi c denotes car characteristics including the cost of acquiring and reconditioning the car, the mileage, car age, and, as a useful proxy for any unobserved quality, the time the car has spent on the lot. Finally, xi a denotes applicant characteristics, including the applicant’s credit category and monthly income, as well as city, month, and year dummies. We estimate the model on individual applicant data. Using the individual applicant data offers substantial advantages but requires us to address a missing data problem. We observe nonpurchaser’s individual characteristics, but not the car and car price they considered. Our solution is imputation. We assign each applicant to one of three credit categories and one of three income categories.16 Then for each nonpurchaser, we randomly select a purchaser in the same credit and income category, and in the same city and week, and assume the nonpurchaser faced the same car and price.17 As we discuss below, our conclusions are quite robust to the imputation specifics, and also to estimation where we avoid explicit imputation by using aggregated data. 14 Defaults on existing loans are also lower in tax season than in other months of the year, providing further evidence of a liquidity effect. 15 The realized interest rate can depend on the size of the down payment, so we instead use as a covariate the interest rate the applicant would have paid making the minimum down payment. As an empirical matter, the differences are relatively small, and using the realized interest rate has no effect on the other coefficients. 16 The income categories correspond to household annual income of less than $24,000 dollars, $24,000–30,000, and more than $30,000. 17 An obvious concern with this imputation is identifying the effect of price changes. Because prices are individually negotiated, it seems plausible that nonpurchasers might have faced somewhat higher prices. Even if the difference in offers arises for random exogenous reasons, a straight demand regression would underestimate the effect of price
THE AMERICAN ECONOMIC REVIEW MARCH 2009 Our demand model views purchasing as a binary decision made once an applicant arrives ne lot. That is, we neglect any effect of pricing on applications. This seems reasonable in light of the fact that financing terms are not publicly posted and, in the case of price, are negotiated at the individual level. We also downplay an applicants choice among cars by focusing on the yes-or-no decision of whether to purchase. Incorporating car choice might improve the efficiency of our estimates. In our particular setting, however, car choice is much less of ue than at the car dealerships with which most professional economists are familiar. Indeed, the match between applicants and cars is driven substantially by company policy. We return to this point later, and also provide some evidence that price changes do not appear to induce much cross-car substitution ldentification.--To look at the effect of current and deferred payments on consumer deci- sions, we focus on car prices and required down payments. To identify their effect on demand, we need to understand how they are set and why they vary in the data. The typical concern here is endogeneity-the firms pricing choices may reflect information about demand that is not available in the data. In our case, however, we observe the same information as company headquarters. So we feel comfortable assuming that, with sufficient controls, decisions made at the company level are exogenous to individual applicants, i.e., uncorrelated with unobservable ndividual characteristics(the es) Minimum down payments are indeed set at the company level. There are separate require ments for each credit category, with some regional adjustment, and these requirements are adjusted periodically. Moreover, because minimum payment requirements are set for groups, two identical (or near-identical) applicants can face different down payment requirements due to variation in the characteristics of other applicants in their pool. Our data, therefore, contain three sources of identifying variation in minimum down payments: variation over time, varia- tion across credit categories, and regional variation In our baseline specification, we include city and category dummies, meaning that we focus on changes over time and on differential changes across categories and cities. We have also run a wide range of alternative specifications, sum marized later, where we separately isolate each source of variation in the data Identifying the demand response to changes in car prices is more subtle because the actual transaction price is negotiated individually. Individual salespeople start with a"list"price for each car that is set centrally, but may incorporate further information into the negotiation. This additional information creates a possible endogeneity problem. Our solution is to use the cen- trally set list price as an instrument for the negotiated pric To do this, we specify an additional equation for the negotiated price: Pi=liA+xjA+vi where L, is the company list price, x, includes all of the relevant car, buyer, and offer character istics apart from price, and vi is a normally distributed error, potentially correlated with ai(thus accounting for the possible endogeneity of price in the demand equation). Our instrumental vari- le estimates are based on joint maximum likelihood estimation of equations (I)and (2). The f-statistic on A, is over 100, indicating that a significant portion of list price changes are passed nto negotiated prices. In the instrumental variable specification, variation in list price identifies the price coefficient in the demand equation. The list price itself derives from a mechanical formula used to mark hanges. We address this problem, as well as the concern that negotiated prices may incorporate information not avail- able to us as analysts, with the instrumental variables strategy described below
60 THE AMERICAN ECONOMIC REVIEW March 2009 Our demand model views purchasing as a binary decision made once an applicant arrives on the lot. That is, we neglect any effect of pricing on applications. This seems reasonable in light of the fact that financing terms are not publicly posted and, in the case of price, are negotiated at the individual level. We also downplay an applicant’s choice among cars by focusing on the yes-or-no decision of whether to purchase. Incorporating car choice might improve the efficiency of our estimates. In our particular setting, however, car choice is much less of an issue than at the car dealerships with which most professional economists are familiar. Indeed, the match between applicants and cars is driven substantially by company policy. We return to this point later, and also provide some evidence that price changes do not appear to induce much cross-car substitution. Identification.—To look at the effect of current and deferred payments on consumer decisions, we focus on car prices and required down payments. To identify their effect on demand, we need to understand how they are set and why they vary in the data. The typical concern here is endogeneity—the firm’s pricing choices may reflect information about demand that is not available in the data. In our case, however, we observe the same information as company headquarters. So we feel comfortable assuming that, with sufficient controls, decisions made at the company level are exogenous to individual applicants, i.e., uncorrelated with unobservable individual characteristics (the ei’s). Minimum down payments are indeed set at the company level. There are separate requirements for each credit category, with some regional adjustment, and these requirements are adjusted periodically. Moreover, because minimum payment requirements are set for groups, two identical (or near-identical) applicants can face different down payment requirements due to variation in the characteristics of other applicants in their pool. Our data, therefore, contain three sources of identifying variation in minimum down payments: variation over time, variation across credit categories, and regional variation. In our baseline specification, we include city and category dummies, meaning that we focus on changes over time and on differential changes across categories and cities. We have also run a wide range of alternative specifications, summarized later, where we separately isolate each source of variation in the data. Identifying the demand response to changes in car prices is more subtle because the actual transaction price is negotiated individually. Individual salespeople start with a “list” price for each car that is set centrally, but may incorporate further information into the negotiation. This additional information creates a possible endogeneity problem. Our solution is to use the centrally set list price as an instrument for the negotiated price. To do this, we specify an additional equation for the negotiated price: (2) pi 5 lill 1 xi 9lx 1 ni, where li is the company list price, xi includes all of the relevant car, buyer, and offer characteristics apart from price, and ni is a normally distributed error, potentially correlated with ei (thus accounting for the possible endogeneity of price in the demand equation). Our instrumental variable estimates are based on joint maximum likelihood estimation of equations (1) and (2). The t-statistic on ll is over 100, indicating that a significant portion of list price changes are passed into negotiated prices. In the instrumental variable specification, variation in list price identifies the price coefficient in the demand equation. The list price itself derives from a mechanical formula used to mark changes. We address this problem, as well as the concern that negotiated prices may incorporate information not available to us as analysts, with the instrumental variables strategy described below