Nonlinear Econometric Analysis (ECO 722) Answers to Homework 4 1 Greene and Hensher (1997) report estimates of a model of travel mode choice for travel between Sydney and Melbourne, Australia The dataset contains 210 observations on choice among four travel modes, air, train, bus and car The variables in the dataset travel modedta are: choice - chosen mode mode - Air, Train, Bus, or Car time terminal - terminal waiting time, 0 for car cost invehicle - in vehicle cost time invehicle - in vehicle travel time hhincome - household income partysize - party size in mode chosen id - respondent id a Estimate a conditional logit model for the choice of travel mode as a function of money and total time costs Interpret each slope coefficient use $datapath\travel_modedta, clear gen time_total = time_terminal + time_invehicle clogit choice cost_invehicle time_total, group(id) Iteration 0: log likelihood = -2811013 Iteration 1: log likelihood = -27286067 Iteration 2: log likelihood = -27283036 Iteration 3: log likelihood = -27283036 Conditional (fixed-effects) logistic regression Number of obs = 840 LR chi2(2) = 3658 Log likelihood = -27283036 Pseudo R2 = 00628 cost_invehicle -0162302 0037507-433 0000-0235815 -0088789 time_total -0027022 000473-571 0000-0036293 -0017752 The greater the time or money cost of the travel mode, the less likely an individual is to select it b The ratio of coefficients usually provides economically meaningful information The willingness to pay (wtp) for a minute of lower travel time is the ratio of the time cost coefficient to the monetary cost coefficient What is the estimated wtp from this model? Is it reasonable in magnitude? The wtp for a minute of lower travel time is equal to $0167 (-0027/-0162) or about $10 for every hour saved, which is plausible but seems somewhat low 1
c Add mode-specific constants and household income to the model Estimate and interpret the slope coefficients and wtp clogit choice cost_invehicle time_total imode##chhincome, group(id) note: hhincome omitted because of no within-group variance Iteration 0: log likelihood = -25779602 Iteration 1: log likelihood = -24342298 Iteration 2: log likelihood = -24316224 Iteration 3: log likelihood = -24316195 Iteration 4: log likelihood = -24316195 Conditional (fixed-effects) logistic regression Number of obs = 840 LR chi2(8) = 9592 Log likelihood = -24316195 Pseudo R2 = 01647 cost_invehicle -0097886 0063692-154 0124-022272 0026948 time_total -004343 0007749-560 0000-0058617 -0028243 mode 2 348915 6671618 523 0000 2181537 4796763 3 226944 7294532 311 0002 8397384 3699142 4 1251994 7144778 175 0080-1483571 2652344 hhincome 0 (omitted) mode#chhincome 2-052733 0124335-424 0000-0771022 -0283638 3-0347796 0133286-261 0009-0609031 -008656 4-0034263 0106537-032 0748-0243072 0174545 Now the wtp for minute of lower travel time equals $0444 or $26 per hour, which is bigger than the naive estimate 2 In this exercise, you ll use a dataset from the paper by J A Herriges and C L Kling titled Nonlinear Income Effects in Random Utility Models which was published in Review of Economics and Statistics, 81(1999): 62-72 The dataset fishing modedta consists of information on fishing mode (1 beach, 2 pier, 3 private boat, 4 charter) along with individual (income ) and alternative-specific characteristics (p = price q = catch rate) The data are organized using one line per observation so it is suitable for analysis using mlogit describe, summarize and browse the data for a better understanding of the information in it a Estimate a multinomial logit model of fishing mode on income Interpret the effect of income use $datapath\fishing_modedta, clear mlogit mode income Iteration 0: log likelihood = -14977229 Iteration 1: log likelihood = -14775265 Iteration 2: log likelihood = -14771514 Iteration 3: log likelihood = -14771506 Iteration 4: log likelihood = -14771506 Multinomial logistic regression Number of obs = 1182 LR chi2(3) = 4114 2
Log likelihood = -14771506 Pseudo R2 = 00137 mode Coef Std Err z P> z [95% Conf Interval] beach pier income 0316399 0418463 076 0450-0503774 1136571 _cons -1341291 1945167-690 0000-1722537 -9600457 income -111763 0439795-254 0011-1979612 -0255649 _cons -5271412 1777842-297 0003-8755918 -1786906 private income 1235462 0279106 443 0000 0688425 17825 _cons -6023707 1360964-443 0000-8691147 -3356267 charter (base outcome) Relative to fishing off charter boats, individuals with greater income are more likely to fish from private boats and less likely to fish off piers b Calculate the marginal effects of income Interpret those effects margins, dydx(income) predict(outcome(1)) Expression : Pr(mode==beach), predict(outcome(1)) income 0001647 0037596 004 0965-007204 0075334 margins, dydx(income) predict(outcome(2)) Expression : Pr(mode==pier), predict(outcome(2)) income -020769 0051406-404 0000-0308443 -0106937 margins, dydx(income) predict(outcome(3)) Expression : Pr(mode==private), predict(outcome(3)) income 0317562 0052589 604 0000 021449 0420633 margins, dydx(income) predict(outcome(4)) Expression : Pr(mode==charter), predict(outcome(4)) 3
income -0111519 0059441-188 0061-022802 0004983 c Estimate a conditional logit of fishing mode on price and catch rate Interpret the coefficients gen id = _n gen choice1 = dbeach gen p1 = pbeach gen q1 = qbeach gen choice2 = dpier gen p2 = ppier gen q2 = qpier gen choice3 = dprivate gen p3 = pprivate gen q3 = qprivate gen choice4 = dcharter gen p4 = pcharter gen q4 = qcharter reshape long choice p q, i(id) j(alternative) (note: j = 1 2 3 4) Data wide -> long Number of obs 1182 -> 4728 Number of variables 29 -> 21 j variable (4 values) -> alternative xij variables: choice1 choice2 choice4 -> choice p1 p2 p4 -> p q1 q2 q4 -> q clogit choice p q, group(id) Iteration 0: log likelihood = -13601218 Iteration 1: log likelihood = -13125912 Iteration 2: log likelihood = -1311981 Iteration 3: log likelihood = -13119796 Iteration 4: log likelihood = -13119796 Conditional (fixed-effects) logistic regression Number of obs = 4728 LR chi2(2) = 65324 Log likelihood = -13119796 Pseudo R2 = 01993 p -0204765 0012231-1674 0000-0228737 -0180794 q 9530985 0894134 1066 0000 7778514 1128346 Higher the price of the mode, lower the likelihood of choosing that fishing mode; higher the catch rate, higher the likelihood of choosing that mode d Calculate the marginal effects of price and catch rate Interpret the effects margins, dydx(*) predict(pu0) 4
Average marginal effects Number of obs = 4728 Expression : Pr(choice fixed effect is 0), predict(pu0) dy/dx wrt : p q p -0033346 0001079-3090 0000-0035461 -0031231 q 1552116 0142945 1086 0000 127195 1832282 A $1 increase in price decreases the probability of the fishing mode by 03 percentage points An increase in the catch rate by 100% (1 unit) increases the probability of the fishing mode by 155 percentage points 5