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11.7 Supply and Demand at the Fulton Fish Market Prior to Estimation, W the Fulton Fish Market Has Operated in New York City Foro\Ler 150 Years

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11.7 Supply and Demand at the Fulton Fish Market Prior to Estimation, W the Fulton Fish Market Has Operated in New York City Foro\Ler 150 Years 314 SIMULTANEO US EQUATIONS MODElS It 7 SU I T If bI t 11 . 3 b 2SLS Estimates for Trume Supply .... here QUAN, is the qu \'ote that we are usi ng Variable Coefficient Std. Error I-Statistic ,-, f the time series natu C 20.0328 1.2231 16.3785 o .()() days of the week, will demand, which we ex P 0.3380 0.0249 13.5629 0.00" ' PF - 1.0009 0.0825 - 12.1281 O.()I) ,hifts in demand. The In(Q ha\le statistically significant coefficients and thus ha\le an effect upon the quant! demanded. The coefficient 13 2 is The supply equation results appear in Table Il.3b. As anticipated, increases in the pn.: \ariable indicating StO of trurnes increase the quantity supplied, and increases in the rental rate for trurne-seeki rl" the supply equation t pigs. which is an increase in the cost ofa fac tor of production. reduces supply. Both Oflh o:' ,"u pply of fi sh brough1 \lariables ha\le statistically significam coefficient estimates. 11.7.1 IOENTlflCA 11.7 Supply and Demand at the Fulton Fish Market Prior to estimation, w The Fulton Fish Market has operated in New York City foro\ler 150 years. The prices for fi~ Identified. The necess are detennined daily by the forces of supply and demand. Kathryn Graddl collected dall H = 2 equations, it m data on the price of whiting (a common type of fish). quantities sold, and weather conditiO!" tquation. In the demo during the period December 2, 1991 10 May 8. 1992. These data are in the fil efllllonjish.d,­ .lppear in the supply e Fresh fi sh arri\le at the market about midnight. The wholesalers. or dealers. sell to buyers f( are included in the de retail shops and restaurants. The first interesting feature of this example is to consido:1 .... hile the supply rema whether prices and quant ities are simultaneollsly detennined by supply and demand at all \ariables), thus Iracin We might consider th is a mark et with a fix ed. perfectly inelastic supply. At the stan of the: Similarl y, slomlYco n day, when the market is opened, the supply offish a\lailable for the day is fixed. If suppl) I demand curve. and n fixed, with a \lertical supply curve, then price is demand dClc nnined, wi th higher demand leading to higher prices. but no increase in the quantity supplied. If this is true then tlK feedback between prices lmd quantities is eliminated. Such models arc said to be rccursi\ t 11.7 .2 THE REOl and the demand equation can be estimated by ordinary least squares ralher than the mon:: complicated two-stage least squares procedure. The reduced form I Howe\ler whiting fish can be kept for se\leral days before going bad. and dealers can exogenous \la ri ables decide to se ll less, and add totheir in ventory, or buffer stock. if the pri ce isjudged too low. in hope for better prices the next day. Or. if the price is unusually hi gh on a gi\len day, then sellers can increase the day's catch with addi tional fish from their buffer stock. Thus despite: In(QUAN,) = the perishable nature of the product, and (he daily resupply of fresh fi sh, dail y price i. simultaneously delemlined by supply and demand forces. The key point here is th.u "simultaneity" does nOI require thai events occur at a simultaneous moment in time. In(PRICE,) 0 Let us specify the demand equation for this market as [n (QUAN,) = (11 + (12In (PRICE,) + 0. 3MON, + a 4 TUE, + a s W£D, ( 11.1 3 + 0.6 THU, + e'/ These reduced form' \ ariables are all exo! the Graddy's data (ji. 2 See Kalhryn Graddy (2006) "The Fulton Fish Markct:' inurnlll of ECOlJomic Pt rsptCli,'u, 20(2), 207-21(, 10 Table 11.4. Estim The authors wou td like 10 tllan~ Professor Graddy for remission to use thc dala from IIcr study. ...quares estimation ( J The HUlhors thank Peter Kennedy for Ihis observation. See Kalhryn Gmddy and Peler E. Kcnnt'dy (2006. two-stage least squa' "Whcn are supply and demand detennined recursivcly mtherthan simul1ancotJsly? Anolhcr look at tht Ful10n Fi 'h M Hr~CI dala.·· working paper. See hltp:l/www.eeonomic.~.o~.ac.ukllTlCmbers/l::athryn.gmddy/research . htm. ri ght-hand-side end 11.7 SUPPLYAND DEMAND AT THE FULTON FISH MARKET 315 whereQUANI is the quantity sold, in pounds, andpRICE,the averagedaily price per pound. Note that we are using the subscript "t" to index stic Prob. observationsfor this relationship bicause of the time series nature of the data. The remaining '85 variables are dummy variables for the 0.0m days of the week, with Friday being omitted. The coefficient a2 is the price elasticity of ,29 0.0m demand, which we expect to be negative. The daily dummy variables capture day-to-day )81 0.0m shifts in demand. The supply equation is ln(QUAN,): 9r * B2ln(pNCE,)+ gtSrOnUy,* ei (11.14) t upon the quantiq The coefficient P2 is the price elasticity of supply. The variable sroRMy is a dummy increasesin the pricc variableindicating stormy weatherduring the previous 3 days. This variable is important in rte for truffle-seeking the supply equation becausestormy weather makes fishing more difficult, reducing the supply. Both of ther supply of fish brought to market. ll.7.l IDsNrrrrcATroN Market Prior to estimation, we must determine if the supply and demand equation paramerers are rs.The prices for fisb identified. The necessarycondition for an equation to be identified is that in this systemof .ddy'collected daill M:2equations,itmustbetruethatatleastM - 1: lvariablemustbeomittedfromeach l weatherconditions equation. In the demand equation the weather variable STORMY is omitted, but it does iefilefultonfish.dat. appearin the supply equation. In the supply equation, the four daily dummy variablesthat lrs, sell to buyers for are included in the demand equation are omitted. Thus the demand equation shifts daily, mple is to consider j while the supply remainsfixed (sincethe supply equationdoes not contain the daily dummy and demandat all. variables),thus tracing out the supply curve, making it identified, as shown in Figure 11.4. y. At the start of the Similarly, stormy conditions shift the supply curve relative to a fixed demand, tracing out the is fixed.If supplyis demand curve, and making it identified. vith higher demand his is true then the ;aid to be recursive rther than the morc 17.7.2 Trrr RnoucEo Fonin Equa-rroNs d, and dealers can The reduced form equations specify each endogenous variable as a function of all sjudged too low, in exogenousvariables n a given day, then stock.Thus despite ln(QUAN,): rr1l + rr2lMONsI r3lTUEs * ralWED, * n51THU1 fish, daily price is * ra$TORMYt lvtr point here is that (l l.1s) oment in time. In(PRICE,) : nr2 * r22MON1l r32WE1 I rqzWEDt I rr52TH(11 ,ED, * nezSTORMYt* vtz (1r.16) (11.13) These reduced forrn equations can be estimated by least squaresbecause the right-hand-side variables are all exogenous and uncorrelated with the reduced form errors v'1 and vr2.Using the Graddy's d ata(fultonfish.dat) we estimate these reduced form tives,2OQ),207-220. equations and report them in Table 11.4. Estimation r study. of the reduced form equationsis the first step of two-stage least er E. Kennedy(2006) squaresestimation of the supply and demand equations.It is a requirement for successful lookat theFulton Fish two-stageleast squares estimation that the estimatedcoefficients in the reducedform for the lylresearch.htm. right-hand-side endogenousvariable be statistically significant. We have specified the 11.7 SUPP 316 SIMULTANEOUS EQUATIONS MODELS Table11.5 ZSLSI Tahle 11 .4 a Reduced Form for tn(Quantity) Fish Co Variable Coefficient Std. Error r-Statistic c t C 8.8101 0.1470 s9.9225 0.00il) l^(PRICE) -l STORMY -0.3878 0.1437 -2.6979 0.008t t40N -( MON 0.1010 0.2065 0.4891 0.625t TUE -( TUE -0.4847 0.2011 -2.4097 0.017t WED -( WED -0.5531 0.2058 -2.6876 0.0G. THU ( THU 0.0537 0.2010 0.2671 0.7899 Table 11 .4 & Reduced Form for ln(Price) Fish cstimating the suPPlY Coefficient Std. Error t-Statistic itz : i.SZ: 0, meaninl zero. Then C -0.2717 0.0764 -3.5569 0.006 STORMY 0.3464 0.0747 4.6387 0.00flf MON -0.rt29 0.1073 -r.0525 0.2950 -0.0411 -0.3937 TUE 0.1045 0.6946 lf we replaceln(PNCE WED -0.0118 0.1069 -0.1106 0.9r72 V exact collinearitY bet THU 0.0496 0.1045 0.4753 0.6356 srpply equation, and tw' dummy variables are n' in tht structural equations(11.13) and (11.14) wilhln(QUAM) as the left-hand-sidevariable and s!verecollinearitY bt In(PRICS as the right-hand-side endogenousvariable. Thus the key reduced form equatioo $pply equation can is (11.16) for 1n(PRICE").Inthis equation reduced form estimate significant. Also, the jo . To identify the supply curve, the daily dummy variables must be jointly significant- 0-65, so that we cannor eq This implies that at least one of their coefficients is statistically different from zem, this case the suPPlY meaning that there is at least one significant shift variable in the demand equation for it. However,STORMY which permits us to reliably estimate the supply equation. ' reliably estimated bY . To identify the demand curve, the variable STORMY must be statistically significant, cstimation is that each meaning that supply has a significant shift variable, so that we can reliably estimatc supply equation is nor the demand equation.
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