Demand in Leisure Markets

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Ethan Cobb
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1 Demand in Leisure Markets An Empirica Anaysis of Time Aocation Shomi Pariat Ph.D Candidate Eitan Bergas Schoo of Economics Te Aviv University

2 Motivation Leisure activities matter 35% of waking time 9.7% of persona consumption ependitures 6.9% of GDP. Ependitures on recreation in U.S. estimated at 702 Biion $ (2004). Previous work either back-boed it or treated one particuar industry. 2

3 10% 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% % Recreation/PCE % Recreation/GDP Price Inde (2000=100) - Recreation Price Inde (2000=100) - A persona consumption

4 Objectives Vauate activities and eisure time as whoe. Wefare impications of activity price and quaity changes. Income and wage effects on time aocation. Trave costs effects. Labor suppy. 4

5 5 Mode ( ) () { } ( ) () : = > = Θ w L trave w trave w ue L X y X T Out p Out Setup I p y w y to subject B y X U Ma w L ε On a given day individuas sove:

6 6 Mode 2 { } ( ) L ue w L L I N data price P rate wage w variabes eogenous of set a B home at are activities a not if Out s definition few A activities eisure non on e ependitur y income unearned y activities eisure non to devoted hours work to devoted hours activity th to devoted hours X = = ~. 1 :..... '... σ ε We take interest in the foowing:

7 Main mode features Binding non-negativity constraints Simutaneous decision on participation (if) and etent of use (how much). Noninear price schedues: Per unit (hour) price is mosty ero. Setup costs eist (e.g. ticket to cinema). Commuting required for certain activities (out of home). Zeros are increasingy important in choice modeing - individua data more avaiabe. Yogurt Soft Drinks Computers (business). 7

8 8 Empirica Specification CES utiity function: is a repackaging parameter. is a transating parameter. Inversey proportiona to the essentiaity of an activity. A taste for variety is embedded. ( ) 0 1; > < < = = y y L y e U ψ ψ θ φ ρ ψ ψ θ φ ρ ρ ρ ρ ε φ θ

9 Estimation Under inear prices we can use Kuhn-Tucker FOC to get a probabiity statement on the tupe * * P { X } L * w U U y p p y If LHS has ony one random component MLE is feasibe (if separabe =>SML). It is more difficut to impement MLE under noninear prices as participation is jointy determined by both unit prices as we as setup costs. 9

10 Method of Simuated Moments Use ero functions defined over S * the soution to utiity ma. probem: E With sampe anaog: ( ( * 0 S obsrved E S ; Θ ) B) = 0 1 n 1 ns n ns o Si i= 1 j= 1 S * i j ε B i = 0 Since S * has no cosed form soution use numerica methods e.g. direct search (nedermead 1965). 10

11 Basic Data ATUS 2004 Weekends Std. Variabe Mean Dev. p_ p_st Out Out () Watching TV Work (w) Socia - Out of Home Read Book Newspaper Socia - at Home Reigious Activities - OUT of HOME Rest Rea Smoke Resturants Active Sports - OUT of Home Computer Use Paying Games - At Home Teephone Cas Cutura Events Museums Shows Concerts Attending Sporting Events Listening to Radio or Music Paying Games - OUT of Home Movies - Out in Cinema Active Sports - at Home Hobbies Gambing

12 Vauating Leisure Base vauation on Compensating Vaue. V ( P y _ ue) Ma U ( ) s. t. (1) (3). CV is impicity defined by: ~ ~ V ( P y _ ue) = V ( P y _ ue CV ) E(CV) is the sum one wi require to be as we off as they were at the base setting. Sove for CV using iterative mapping. 12

13 Vauating Leisure Vaue of a eisure activities 100$/130$. Increasing with unearned income (50-140$) Decreasing with wage (134-10$). Vaue of TV 52$/62$. Decreasing with wage (60-11$). Vaue of Cinema 2.5$/10.3$ (tickets at 6$). Inverse U with income. Decreasing with wage. Vaue of Computer use: 3.3$/10$. 13

14 24 Hours The margina vaue of time if we had 23 hrs/day? 15.3$ average wage at 12.5$. Increases with income 8-21$. Increases sharpy with wage 10-58$. Wake eary? - If we had 25 hrs/day? Leisure gets 60% (36 min.) Work gets 34% (20 min.) Traffic & Congestion if trave time was 1.5h instead of 0.5? Resuts simiar to above - 15$. 14

15 Wage and Income effects Wage increase 10%: Leisure decreases 5%. Other activities decrease 5%. Work increases 14%. Effects are inverse U in wage. Unearned Income increase 10%: Leisure increases 2%. Other activities increase 1.8%. Work decreases 5%. Effects diminish in wage. 15

16 Price and Quaity effects If TV was 50 an hour? TV time woud decrease 17%. Tota eisure decrease 1%. Other activities increase 1.7%. Work increases 3%. If the quaity of TV rose 10%? TV increases 13% tota eisure 2.5%. Work decreases 5%. If a ticket to the movies was 10$? Average time drops 2.6%. Other ependiture drops ~5$. 16

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