Table 1: Estimated MARS model.

ParameterEstimateT-ratioHansen stability test

Constant8.232071525.898130.044(0.90)
Basis function 10.8313121.829900.053(0.85)
Basis function 2−0.59353−2.997350.016(1.00)
Basis function 30.393185.317710.042(0.92)
Basis function 4−0.30214−5.299110.029(0.98)
Basis function 62.338584.554030.012(1.00)
Basis function 8−6.02882−3.587480.088(0.63)
Basis function 10−0.73692−4.766040.017(1.00)

Hansen variance test0.163(0.34)
Hansen joint test1.015(0.88)

Basis functions

BF1 = max(0, ln(RPDI) − 8.8473)
BF2 = max(0, 8.8473 − ln(RPDI))
BF3 = max(0, ln(DSR) − 2.59525)
BF4 = max(0, 2.59525 − ln(DSR))
BF6 = max(0, 1.46047 − ln(CCNR)) BF4
BF8 = max(0, 1.56752 − ln(CCNR)) BF1
BF10 = max(0, 1.05934 − ln(CCR))

RPDI, DSR, CCNR, and CCR denote real personal disposable income, the debt-service ratio, outstanding nonrevolving consumer credit, and outstanding revolving consumer credit, respectively. Estimation spans 1994 Q4 to 2008 Q3 inclusive allowing a maximum of ten basis functions and two variable interactions. The MARS sum of squared residuals based criterion function was adjusted by a penalty value of two with the dependent variable discretionary personal consumption expenditures. All series were transformed into their natural logarithms. Hansen stability tests refer to the Hansen [11] test (null: no structural change) and the associated probability values (in parentheses) for individual parameter stability, variance stability, and the hypothesis of joint stability. MARS is available at http://www.salford-systems.com/.