hhfair.gms : Household Optimization Problem by Fair

**Description**

This is a theoretical optimizing model of a typical household. a detailed description can be found in Chapter 3 of Ray Fair's book.

**Reference**

- Fair, R C, Specification, Estimation, and Analysis of Macroeconomic Models. Harvard University Press, Cambridge, Mass, 1984.

**Small Model of Type :** NLP

**Category :** GAMS Model library

**Main file :** hhfair.gms

$Title Household Optimization Model by Fair (HHFAIR,SEQ=69) $Ontext This is a theoretical optimizing model of a typical household. a detailed description can be found in Chapter 3 of Ray Fair's book. Fair, R, Specification, Estimation, and Analysis of Macroeconomic Models. Harvard University Press, Cambridge, Mass, 1984. $Offtext Sets tl long time horizon / 0, 1, 2, 3 / t(tl) optimizing horizon / 1, 2, 3 / tt(t) terminal year / 3 / Scalars p price of goods / 1.0 / r one period interest rate / .07 / tr transfer payment / 0 / th total number of hours in the period / 1004.72366 / w wage rate / 1.0 / d income tax rate / .2 / a1 distribution coefficient in ces function / .5 / a2 elasticity coefficient in ces function / -.5 / am terminal assets target / 1100 / lambda discount rate / .944 / lstar maximum labor available in each time period / 400 / gamma1 coefficient 1 in money holding function / .255905/ gamma2 coefficient 2 in money holding function / 1.0 / Parameter ufact(t) utility function factor ; ufact(t) = power(lambda,ord(t)-1) ; Display ufact; Variables a(tl) assets c(t) consumption l(t) labor supplied m(tl) money holdings n(t) time spent on money holdings obj objective function value s(tl) savings tax(t) net taxes paid u(t) utility y(t) income Equations objective objective function utility(t) utility in each period income(t) before tax income taxes(t) net taxes savings(t) savings budget(tl) budget constraint timemoney(t) time spent taking care of money holdings terminal(t) terminal condition for assets dom1(t) domain constraint on timemoney equation dom2(t) domain constraint on utility equation ; objective.. obj =e= prod(t, u(t)**ufact(t)) ; utility(t).. u(t) =e= (a1*c(t)**(-a2) + (1-a1)*(th-l(t)-n(t))**(-a2))**(-1/a2)/100 ; income(t).. y(t) =e= w*l(t) + r*a(t) ; taxes(t).. tax(t) =e= d*y(t) - tr; savings(t).. s(t) =e= y(t) - tax(t) - p*c(t) ; budget(tl-1).. s(tl) =e= a(tl) - a(tl-1) + m(tl) - m(tl-1) ; timemoney(t).. n(t)*(m(t) - gamma1*p*c(t)) =e= gamma2 ; terminal(tt).. a(tt) + m(tt) =e= am ; dom1(t).. m(t) =g= 1.01*gamma1*p*c(t) ; dom2(t).. l(t) + n(t) =l= .9*th ; Model hh household optimization model / all / ; l.up(t) = lstar; a.fx("0") = 1000; m.fx("0") = 100; c.lo(t) = 100; l.lo(t) = 100; u.lo(t) = .01; a.l(t) = 1000; m.l(t) = 100; l.l(t) = 400; u.l(t) = 1; Solve hh maximizing obj using nlp;