advertisement

Application to the theory of consumption Lectures in Behavioral economics Spring 2013, Part 3 27.02.2013 G.B. Asheim, ECON4260, #3 1 Relevance of behavioral economics Acc. to Vernon Smith (”Rational choice: The contrast between economics and psychology”, JPE 99, 1991, 877-89) much beh. economic critique stems from the premises that Two-sided auction: buyers announce bids, sellers announce asking prices. 1. ... rationality in the economy … derives from the rationContracts on acceptance. Some information but incomplete information alitytoofeach. theExperiments individual decision makers in theconverges economy. available show that such a market to price and volume represented by theoretical intersection intensive, of supply and demand 2. ... individual rationality is a cognitively calculating curves--competitive equilibrium. "This is some kind of magic!" What it shows process of maximization of the self-interest. is that people are quite good at discovering prices and quantities that clear a 3. ... even economic theory be ptested by testing directly the onlyycan incomplete market information. market if theyy have economic rationality of the individuals isolated from interactive experience in social and economic environments. Instead, V. Smith thinks that beh. economic critique is important if it predicts different economic behavior at an aggregate level. 27.02.2013 G.B. Asheim, ECON4260, #3 2 1 Observed saving behavior Present-biased pref. can explain these phenomena. Illiquid assets combined with credit card debt Illiquid assets are commitments. Credit cards provide consumption smoothing, but facilitate tempting shopping splurges. Co-movement between income and consumption Consequence of self-imposed liquidity constraints. Becomes more binding at the time of retirement. Laibson: A model that explains empirical evidence. 27.02.2013 3 G.B. Asheim, ECON4260, #3 Outline Cons.-saving model w/illiquid asset Laibson (1997). Application of the multi-self approach, where sophisticates use illiquid asset as commitment. Yields explanation of observed saving behavior. A theoretical result in the cons.-saving model Laibson (1998). Empirical test of the cons.-saving model Angeletos et al. (2001). Show that present-biased pref. fit data better. 27.02.2013 G.B. Asheim, ECON4260, #3 4 2 Laibson’s (1997) consumption-saving model Consumer makes decisions in periods 1, , T One liquid asset x One illiquid asset z E Exogenous i i i l asset holdings initial h ldi x0 , z0 0 In period t : earn labor inco me yt earn asset inco me Rt ( xt 1 zt 1 ) choose consumptio n ct and a new asset allocation xt and zt such that The illiquid asset ct xt zt yt Rt ( xt 1 zt 1 ) ct yt Rt xt 1 zt 1 cannot be con - xt , zt 0 sumed at time t . 27.02.2013 5 G.B. Asheim, ECON4260, #3 Laibson’s (1997) consumption-saving model (2) Period - t intertemp oral preference s : U t Et u (ct ) t 1 t u (c ) T 3-period consumption-saving example Budget constraint : c1 y c2 c3 y 2 y1 2 32 W R R R R Instantane ous utility : u (c) ln c Numerical illustrati on : 0.8, 0.9, R 1.1, and W $1000. 27.02.2013 G.B. Asheim, ECON4260, #3 6 3 Optimal period-0 behavior max ln(c1 ) ln(c2 ) 2 ln(c3 ) subject b to c1 c2 c3 y y 2 y1 2 32 W R R R R Solution : W RW (R ) 2 W 0 0 c , c2 , c3 1 2 1 2 1 2 0 1 Numerical illustrati on : c10 $369.00, c20 $365.31, c30 $361.66 27.02.2013 G.B. Asheim, ECON4260, #3 7 Optimal period-1 behavior max ln(c1 ) ln(c2 ) 2 ln(c3 ) subject b to c1 c2 c3 y y 2 y1 2 32 W R R R R Solution : c11 W RW (R ) 2 W 1 1 , c , c 2 3 1 2 1 2 1 2 Numerical illustrati on (optimal period - 1) 0) : c110 $$422 369..30 00,, c1220 $$334 365..46 31, c3130 $$331 361..11 66 27.02.2013 G.B. Asheim, ECON4260, #3 8 4 Naive period-2 behavior max ln(c2 ) ln(c3 ) subject bj to c2 c3 R (1 )W W2N R (W c11 ) R 1 2 Solution : W2N RW2N N c , c3 1 1 N 2 Numerical illustrati on (optimal (naivete) period : - 0) : c110 $$422 369..30 00,, c2N20 $$365 369..31 46,, cc303N$$361 292.66 .61 27.02.2013 G.B. Asheim, ECON4260, #3 9 Sophisticated period-2 behavior max ln(c2 ) ln(c3 ) subject bj to c2 c3 W2 R (W c1 ) R Solution : c 2 (c1 ) W2 R (W c1 ) 1 1 RW2 R 2 (W c1 ) c 3 (c1 ) 1 1 27.02.2013 G.B. Asheim, ECON4260, #3 10 5 Sophisticated period-1 behavior max ln(c1 ) ln(c 2 (c1 )) 2 ln(c 3 (c1 )) R (W c1 ) R 2 (W c1 ) 2 ln max ln l c1 ln l l 1 1 Solution : c1S 1 W 2 , R (1 )W R R (1 )W c2S c 2 (c1 ) 11 , c3S c 3 (c1 ) 1 1 2 1 2 Numerical illustrati on (optimal (sophistic (naivete) period : ation) :- 0) : c110S $$422 369 422..30 00 30,, cc2N202S $$365 369..31 46,, cc303NS $$361 292.66 .61 27.02.2013 G.B. Asheim, ECON4260, #3 11 Sophisticates can implement optimal period-1 behavior by using the illiquid asset If 0.8, 0.9, R 1.1, Y1 1000, and Y2 Y3 0, then In p period 1 : consume $422.30 save $304.05 in the liquid asset (which yields $334.46 in period 2) save $273.64 in the illiquid asset (which yields $331.11 in period 3) Sophisticates strictly prefer the use of illiquid assets. Naifs do not recognize the commitment value of illiquid assets. 27.02.2013 G.B. Asheim, ECON4260, #3 12 6 The illiquid asset is not a perfect commitm. techn. 3-period consumption-saving example 0.5, 1, R 1, and W $1200. You cannot prevent yourself from consuming current income. ● If Optimal period-1 Income Consumption Liquid asset 0.8, 0.9, R 1.1, Y1 500, Y2 550, and Y3 0, then the illiquid asset does not help at all. An illiquid asset does not work as a commitment device if yyou can borrow against g its future payoff. py ● Credit cards (and other liquidity enhancing intruments) may undermine the commitment value of illiquid assets. 27.02.2013 13 G.B. Asheim, ECON4260, #3 A theoretical result in the consum.-saving model Assume no illiquid asset Period - t intertemp oral preference s : (Laibson, 1998) U t Et u (ct ) t 1 t u (c ) T Optimality condition if 1 : Proof of a theoretical result in the cons.-saving model u(ct ) R cash on hand : xt yt R ( xt 1 ct 1 ) dU t 1 choose consumptio n : ct xt dxt 1 dU t 2 dU t 2 u (ct 1 ) u(ct 1 ) R dxt 2 dxt 2 R dc dU t 2 dU t 1 dct 1 u(ct 1 ) R1 t 1 dxt 1 dxt 1 dxt 1 dxt 2 dc dc 1 t 1 1 t 1 u (ct 1 ) dxt 1 dxt 1 dc dc u(ct ) R t 1 1 t 1 u(ct 1 ) dxt 1 dxt 1 u (ct ) Et Ru (ct 1 ) Et R s s u (ct s ) Generalize d opt. condition for sophistica tes with 1 : dc dc u (ct ) Et R t 1 1 t 1 u (ct 1 ) dxt 1 dxt 1 A source of ”under-saving”. 27.02.2013 G.B. Asheim, ECON4260, #3 14 7 Proof of a theoretical result in the cons.-saving model cash on hand : xt yt R ( xt 1 ct 1 ) dU t 1 choose consumptio n : ct xt u (ct ) R dxt 1 dU t 2 dU t 2 u (ct 1 ) u (ct 1 ) R dxt 2 dxt 2 R dct 1 dU t 2 dU t 1 dct 1 u (ct 1 ) R1 dxt 1 dxt 1 dxt 1 dxt 2 dc dc 1 t 1 1 t 1 u (ct 1 ) dxt 1 dxt 1 dc dc u (ct ) R t 1 1 t 1 u (ct 1 ) dxt 1 dxt 1 27.02.2013 G.B. Asheim, ECON4260, #3 15 Empirical test of the consumption-saving model Compare data with simulations Angeletos et al. (2001) under exponential disc. and hyperbolic disc. (sophisticates) Households with liquid assets > 1 month’s income: Exponent. simulation: 73% Hyperbolic simulation: 40% Data: 43% Households with p positive credit-card borrowing: Exponent. simulation: 19% Hyperbolic simulation: 51% Data: 70% 27.02.2013 Mean credit credit-card card borrowing (all households): Exponent. simulation: $900 Hyperbolic simulation: $3400 Data: >$5000 Cons.-income comovement (income coefficent): Exponent. simulation: 0.032 Hyperbolic simulation: 0.166 Data: 0.2 G.B. Asheim, ECON4260, #3 16 8 27.02.2013 G.B. Asheim, ECON4260, #3 17 27.02.2013 G.B. Asheim, ECON4260, #3 18 9 27.02.2013 G.B. Asheim, ECON4260, #3 19 27.02.2013 G.B. Asheim, ECON4260, #3 20 10 Additional references Choi, J., D. Laibson, B. Madrian & A. Metrick (2002), Defined Contribution Pensions: Plan Rules, Participant Decisions, and the Path of Least Resistance, Tax Policy and the Economy 16, 67–114 DellaVigna, S. & U. Malmendier (2006), Paying Not to Go to the Gym, American Economic Review 96, 694–719 Shapiro, J.M. (2005), Is there a daily discount rate? Evidence from the food stamp nutrition cycle, Journal of Public Economics 89, 303–325 27 February 2013 G.B. Asheim, ECON4260, #4 21 11