Nonlinear Econometric Analysis (ECO 722) Answers to Homework 4

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1 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 = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Conditional (fixed-effects) logistic regression Number of obs = 840 LR chi2(2) = 3658 Log likelihood = Pseudo R2 = cost_invehicle time_total 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

2 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 = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Iteration 4: log likelihood = Conditional (fixed-effects) logistic regression Number of obs = 840 LR chi2(8) = 9592 Log likelihood = Pseudo R2 = cost_invehicle time_total mode hhincome 0 (omitted) mode#chhincome 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): 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 = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Iteration 4: log likelihood = Multinomial logistic regression Number of obs = 1182 LR chi2(3) =

3 Log likelihood = Pseudo R2 = mode Coef Std Err z P> z [95% Conf Interval] beach pier income _cons income _cons private income _cons 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 margins, dydx(income) predict(outcome(2)) Expression : Pr(mode==pier), predict(outcome(2)) income margins, dydx(income) predict(outcome(3)) Expression : Pr(mode==private), predict(outcome(3)) income margins, dydx(income) predict(outcome(4)) Expression : Pr(mode==charter), predict(outcome(4)) 3

4 income 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 = ) Data wide -> long Number of obs > 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 = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Iteration 4: log likelihood = Conditional (fixed-effects) logistic regression Number of obs = 4728 LR chi2(2) = Log likelihood = Pseudo R2 = p q 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

5 Average marginal effects Number of obs = 4728 Expression : Pr(choice fixed effect is 0), predict(pu0) dy/dx wrt : p q p q 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