Financial Econometrics and Empirical Market Microstructure
Structural and Econometric Model
Demand-for-mortgage function can be represented by the following equation:
ln L = PlD C ylC C SlF C VlP + д-lM C el (1)
where L is usually the loan amount (or LTV ratio), D are socio-demographic characteristics of borrower, C are the contract terms, F are specific variables that describe property, P are contract performance characteristics, and M are macroeconomic and financial variables. All of them can be divided as endogenous and exogenous ones, as described in Table 1.
The borrowing process can be represented by the following sequence of decisions:
1. Application of borrower. Potential borrower realizes the necessity of borrowing, chooses the credit organization and credit program that match her preferences, and fills out an application form with demographic characteristics.
2. Approval of borrower. Considering the application form and recent credit history, the credit organization endorses the application or not, inquires about the form data and set the limit of loan amount when endorsed.
3. Choice of credit terms. The approved borrower makes a choice on contract agreement and, when agreed, on property to buy and credit terms from a feasible
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Table 1 Explanatory variables in demand equation
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Variables
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Endogenous for borrower
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Endogenous for credit organization
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Exogenous
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Contract terms
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Down payment; maturity; annual payment; date of contract agreement; program choice (ARM/FRM, prime/nonprime, conventional/spe - cial/FHA programs); self-selection for participation in mortgage
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Loan limit; program parameters (minimum down payment, maximum maturity)
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Program parameters (interest rate, insurance, Government Subsidied
Enterprises); cost of application
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Socio-demographic
characteristics
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Number of co-borrowers; aggregated income of co-borrowers; aggregated expenses of co-borrowers; income of borrower; providing of full documentation
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Probability of creditworthness (FICO score of riskiness); flag of endorsement
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Expenses of borrower; age; number of children; marriage status; level of education; parameters of job; nationality/race; expected mobility; recent credit history
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Desired property
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Value
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Specification the property
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Loan performance
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Month of first delinquency; date of first delinquency; flag of delinquency; default, refinancing, prepayment
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Loss given default
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Macro - and financial variables
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Yield on treasury notes; refinancing rate; volatility of interest rate; unemployment rate; volume of new construction
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set: approved loan amount, down payment, annual payment, rate and maturity determined by the credit program.
4. Loan performance. Borrower chooses the strategy of loan payment: to pay in respect to contract terms or to default, prepay or refinance the loan.
Econometric model repeats the steps of structural one:
1. Using instrumental variables for endogenous demographic characteristics:
Den — ZdPd C (2)
where Den is a vector of endogenous socio-demographic characteristics, ZD are instrumental variables for demographics.
2. Modeling the probability of application:
( 1, if DPD c MfM c ei — “1 ( 0; if dPD + MfM C ei <“l,
where y1 — 1 is an application decision, D — yDex, DenJ is a vector of exogenous demographics and fitted endogenous demographics, M —macrovariables.
3. Modeling the probability of approval for all applied:
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1; if WD C MfM C e2 — “2
0, if DfiD C MP2M C Є2 < “2
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where y2 — 1 is an approval decision.
4. Choice of loan amount limit for all endorsed:
where D is a decision on loan limit.
5. Modeling the probability of contract agreement:
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( 1; if DfD c MfM c C e3 — “э I 0, if DfD c MfM c DfL C e3 < “э
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where y3 — 1 is an agreement decision; D is a fitted value of loan amount limit.
6. Choice of credit terms and property:
(Cl |уэ — 1 ,c e c) — D^D1 C MfcM C C_1^C11 C FfC1 C eci (Скуэ — 1, c ec) — DfC* C MfMk C C-kfCkk C FfC* C ec*
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where y4 = j is a fact of j-th credit event, C are fitted values of credit terms, Uj is a loss given j-th event.
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Conclusion and Discussion
The proposed modelcan take care of endogeneity problem caused by simultaneity by instrumenting and fitting endogenous explanatory variables using a multistage estimation procedure.
Inconsistency of estimates due the sample selection will be released by introduction and estimation of the bias terms in outcome equations. Effectiveness of this correction depends on accuracy of assumptions about distribution of error terms in selection equations. Thus, it is appropriate to use inverse Mills ratio in outcome equations when selection equation terms are normally distributed. More general assumptions about the error term distributions can be achieved through the use of semi-parametric methods for correction for sample selection bias. But these estimates will be less effective in terms of standard errors.
Questions could be raised about the rationality of borrower and credit organizations’ decisions. Sequential estimation procedures like the multivariate probit or multistage Heckman procedure, make no assumptions about rationality of agents. We use partially observed data in selection equations to consider lack of borrower’s ability to predict decisions made by her and the credit organization. Full rationality of agents assumes that a borrower in every stage of the decision-making process can predict outcomes of next stages, and this prediction affects her present choice. A model of the fully rational borrowing process should contain fitted predictions on future outcomes as explanatory variables in all Eqs. (2)-(8) which should be estimated as a system of simultaneous equations. This strategy is very complex for estimation purposes because of the discrete and continuous variable equations compounded by the sample selection problems.
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Acknowledgements This study (research grant no. 14-01-0104) was supported by The National Research University-Higher School of Economics’ Academic Fund Program in 2014-2015.
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