An independent trucking company is considering entering the lumber transport market in the Pacific Northwest, in which lumber companies currently have only two choices for how to ship their product: 1. Private Carriage (that is, ship it themselves with their own trucks) 2. Rail Freight The company has hired some consultants to help understand the current shape of the market for lumber shipping services. The first step in predicting the demand for this new trucking service is to estimate lumber companies' sensitivity to different shipping-related variables. A multinomial logit model was specified and then estimated on a dataset that included information on a number of shipping decisions made by shippers in the Pacific Northwest. Table 2.1 includes the specification of the model and the estimation results. TABLE 2.1: Model specification and estimation results BASC_PC BSIZE 1 0 Private Carriage Rail Freight Estimated 0.04 Coefficie nt 0 SIZE 2.5 BVALUE 0 VALUE 7.51 Bcost COST_PC COST_RAIL -14.14 BTIME TIME_PC TIME_RAIL REL RAIL BRELIABILITY BOST SIDING REL PC 0 -6.43 -3.48 DIST SIDING -11.21 Table 2.2: Data on the model's independent variables for one example lumber shipment Observed value for the individual 120,000 pounds $0.50 per pound $4,200 $3,000 Variable SIZE VALUE COST_PC COST_RAIL TIME PC TIME RAIL REL_PC REL RAIL DIST_SIDING 2.5 days 4 days 1 day 2 days 2 miles Definitions of variables: ASC_PC is the alternative-specific constant for Private Carriage. SIZE is the size of the shipment in units of 10,000 pounds. VALUE is the commodity value of the shipment in dollars per pound. COST_PC is the cost of making the given shipment by Private Carriage, in units of $10,000. COST_RAIL is the cost of making the given shipment by Rail Freight, in units of $10,000. TIME_PC is the average transit time in transit of a given shipment by Private Carriage, measured in days. TIME_RAIL is the average transit time of a given shipment by Rail Freight, measured in days. REL PC is the reliability of transit time by Private Carriage, measured in standard deviations of transit time, in days. REL RAIL is the reliability of transit time by Rail Freight, measured in standard deviations of transit time, in days. DIST_SIDING is the distance, in miles, of the shippers' operations from a rail siding. Answer the following questions: a. What are the effects implied by the model of the following variables on an lumber company's shipping decisions: i. ii. b. C. Shipment Size (3 points) Distance from a Siding (3 points) What is the value (in dollars) of one day of transit time implied by the model? What about a day of potential variability in transit time? Does the difference between these two values make sense? Explain. (8 points) Table 2.2 contains data on the model's independent variables for one lumber shipment. From the data in Table 2.2 and the estimation results in Table 2.1, calculate the probability that the shipment will be made by each of the two alternatives. (9 points) Table 2.2: Data on the model's independent variables for one example lumber shipment Observed value for the individual 120,000 pounds $0.50 per pound $4,200 $3,000 Variable SIZE VALUE COST PC COST_RAIL TIME_PC TIME_RAIL REL PC REL RAIL DIST_SIDING 2.5 days 4 days 1 day 2 days 2 miles d. e. The consultants generated a sample of 1,000 lumber shipments that they believed was representative of the entire lumber shipping market in the Pacific Northwest. For each shipment in that sample, there were data on each of the two currently available alternatives (similar to the information shown in Table 2.2). How would you use these data to estimate the proportion of all shipments in the Pacific Northwest that are made by Private Carriage? (4 points) After the trucking service is introduced, a new model for mode choice has to be specified and estimated with three alternatives (Private Carriage, Rail Freight, Truck Freight). How would you structure such a new model? Please explain your thinking. (Hint: Think of the similarities among some of the three alternatives. Your answer can be in the form of a sketch.) (7 points)