Introduction and Literature Review
Demand for loans in general, and for mortgage loans in particular, is the function of the probability of a credit contract agreement and of credit contract terms based on characteristics of the borrower, the goal of crediting, expected loan performance and some macroeconomic variables.
Econometric estimation of parameters of these functions face inconsistency driven by endogeneity and sample selection. Endogeneity is generated by simultaneity in borrower and credit organization decisions on explanatory variables in demand equations. A sample selection arises when the decision-making process of borrowing is made sequentially and some explanatory variables are partially observed in different stages of crediting.
However, these challenges in estimation process have not been addressed by recent papers that studied the crediting process. Mortgage borrowing as a sequence
E. Ozhegov (H)
National Research University Higher School of Economics, Research Group for Applied Markets and Enterprises Studies, Perm, Russia e-mail: tos600@gmail. com
© Springer International Publishing Switzerland 2015
A. K. Bera et al. (eds.), Financial Econometrics and Empirical Market
Microstructure, DOI 10.1007/978-3-319-09946-0_____ 16 of consumer and bank decisions was introduced by Follain (1990). He defines the borrowing process as a choice of how much to borrow (the Loan-To-Value ratio decision), if and when to refinance or default (the termination decision), and the choice of mortgage instrument itself (the contract decision). Rachlis and Yezer (1993) then suggested a system of four simultaneous equations for mortgage lending analysis: (1) borrower’s application, (2) borrower’s selection of mortgage terms, (3) lender’s endorsement, and (4) borrower’s payment according contract or default.
Phillips and Yezer (1996) compared the estimation results of the single-equation approach with those of the bivariate probit model. They showed that discrimination estimation is biased if the lender’s rejection decision is decoupled from the borrower’s self-selection of loan programs, or if the lender’s underwriting decision is decoupled from the borrower’s refusal decision.
Ross (2000) studied the link between loan approval and loan default and found that most of the approval equation parameters have the opposite sign, compared with the same from the default equation after correction for the sample selection.
Previous models that tackled sample selection bias in lending analysis are not appropriate to estimate the loan amount or LTV ratio. The probit model of Ross (2000) and bivariate probit model used by Philips et al. (1994) and Philips and Yezer (1996) are suitable for estimating a binary outcome. The following papers studied the dependence of the decision on loan amount as well as different endogenous variables on the exogenous ones.
Ambrose et al. (2004) constructed a simultaneous equation system of LTV and house value, which is used as a proxy for loan amount to account for endogeneity. Bocian et al. (2008) used three-stage Least Squares for the simultaneous decisions on pricing and credit rating and found empirical evidence that non-white borrowers are more likely to receive higher-priced subprime credit than similar white borrowers. Zhang (2010) investigated the sample selection bias and interaction between pricing and underwriting decisions using the standard Heckman model.
Other literature on mortgage choice has focused on the optimal mortgage contract, given uncertainty about future house prices, household income, risk preferences, and, in some papers, mobility risk. Leece (2001) found the choice between ARM and FRM in the UK market dependent on the expected level of rates. Thus, with sustainable low interest rates, a household intends to lock into a FRM. In order to construct consistent and unbiased estimates, he used a linear additive model with time-dependent explanation variables.
Campbell and Cocco (2003) examine household choice between FRM and ARM in an environment with uncertain inflation, borrowing constraints, and income and mobility risk. They demonstrate that an ARM is generally attractive, but less so for a risk-averse household with a large mortgage, risky income, high default cost, or low probability of moving. Coulibaly and Li (2009), using survey data, also found evidence that borrowers who were more risk-averse, with risky income and low probability of future move prefer fixed rate mortgage contracts.
Forthowski et al. (2011) studied the demand for mortgage loans from the point of choosing an ARM versus FRM as a function of expected mobility. They find that, with all else equal, those who choose ARM estimate their probability of moving in the future as relatively high.
Firestone et al. (2007) analyzed the prepayment behavior of low - and moderate - income (LMI) borrowers. Using the data containing the performance of 1.3 million loans originated from 1993 to 1997 they found that lower-income borrowers prepay more slowly than with higher income and this results are stable over time. Courchane (2007) studied differences in pricing for different ethnicities after controlling for other pricing and underwriting parameters. LaCour-Little (2007) also focused on the question of choosing a credit program among LMI borrowers. Using the loan level data from only one financial organization, he founds that LMI borrowers are more likely to choose Federal Housing Administration-insured mortgage programs and special programs that assumed less down payments and higher scores of expected risks due to high levels of current debt or weaker credit history. He also found that nonprime loans were preferred for those borrowers who are time-limited in providing full documentation.
Some recent papers discussed the theoretical framework of optimal mortgage contraction. For instance, Nichols et al. (2005) showed that rejection rates vary directly with interest rates in the mortgage market and inversely in the personal loan market. Theoretically they demonstrated that the discrete levels of mortgage credit supply and the positive relationship between interest and rejection rates arise from a separating equilibrium in the mortgage market. This separation does rely on the simple observation that processing an application through the underwriting process is costly, and is only partially covered by the application fee. When a subprime lender tries to locate too closely (in credit risk space) to prime lenders, the application costs overwhelm credit losses to the point where it is less costly to lower credit standards and accept a higher proportion of applicants. Equilibrium requires that the subprime lender move a substantial distance from prime lenders, thus leading to a discrete and segmented mortgage market of those borrowers who may apply for prime mortgages and for those who apply for subprime mortgages.
Ghent (2011) discussed the dynamic demand for mortgage loans and steady state equilibrium for borrowers with hyperbolic, compared to exponential, discounting, and the preference of such borrowers on the set of traditional fully amortizing mortgages and no-down-payment mortgages. The main findings of this paper was that young households and retirees are more likely to choose NDP mortgages that arise when those households behave hyperbolically and the age of borrower also explains decision-making process.
Piskorski and Tchistyi (2010, 2011) follow DeMarzo and Sannikov (2006) and pose the theoretical model of choosing the optimal mortgage contract that maximizes both lender’s and borrower’s combined surplus. These papers provide a prediction of higher default rates for adjusted rate mortgages when the interest rate increases but shows that, nevertheless, ARM is an optimal mechanism for mortgage contraction.
Karlan and Zinman (2009) found a different method to solve the endogeneity problem when modeling the loan amount equation. They generated a truly random sample of credit proposals by sending letters to former borrowers. Using a simple
Heckman model, they estimated the elasticities of demand for consumer credits to maturity and interest rates for different risk types of borrowers.
Attanasio et al. (2008) introduced a more progressive approach of managing the sample selection problem when modeling the empirical demand for a loan equation. They studied the existence of credit constraints in different income segments. Using loan-level data of car loans, they found that low-income households have positive elasticity of demand for car loans on the maturity and zero reaction of demand to interest rate change. This means that those households have credit constraints. Attanasio et al. (2008) used a three-stage estimation methodology. At the first stage, they estimated the participance equation. At the second stage, the endogenous variables equations were estimated by semi-parametric regression with correction for self-selection. Then endogenous variables in the demand equation were replaced by fitted values and the parameters were estimated also by semiparametric regression. The only motivation of using semiparametric regression is that the error terms of the loan amount, endogenous variables error terms and error term from the participation equation are correlated in a non-linear way.
The main contribution of this paper is construction of a structural and econometric model that can provide consistent estimates of the demand-for-loan function, using loan-level individual data.