The file problem5.xlsx contains data on auctions conducted by the Department of Transportation (DOT) of a particular State. The DOT regularly conducts these auctions to give out contracts to bidders to undertake road construction projects in the state. The winning bid is the bid which is lowest in price for that construction project.

The file has data on 133 such road construction auctions that took place in the recent past. The following variables are given in the file:

FairPr : The overall project cost estimate calculated by DOT engineers, which they call the "fair price"

(in thousands of dollars).

Bidders : The number of contractors that chose to participate in the auction.

Rigged : Dummy that equals 1 if the state attorney general determined that the bidders rigged the

auction (colluded), 0 if not.

Length : The length of the road construction project (in miles).

FxCost : The DOT estimate of the project's fixed costs, i.e., costs (in thousands of dollars) independent

of the length of the project?like the costs of structures.

Days : The DOT estimate of the duration of the construction (in days)

The DOT realizes that bid rigging is a problem that will not go away and you need to come up with a model to help determine the likelihood that bid rigging will occur.

(a) (3 pts) Estimate an appropriate regression model for the likelihood of bid rigging, i.e. with Rigged as your dependent variable and other variables as independent variables.

Report and interpret the estimated coefficient on Length

(b) (3 pts) What effect does the introduction of two additional bidders have on the odds of the auction being rigged?

.

(c) (4 pts) What is the probability that the average project is rigged?

Briefly state your definition of an average project and briefly show your calculations

(d) (4 pts) Consider an "Average project" as a project which has average values across all the explanatory variables observed in the data.

For an "Average project" (as defined above) for what number of bidders would you expect a bidder increase of one additional bidder to most decrease the probability of collusion, all other variables held constant?.

Briefly show your working in support of your answer.

(e) (3 pts) Calculate and fill in the blank in the following statement.

The odds of an auction being rigged which has a Fair Price estimate of 500,000$, Fixed Cost estimate of 200,000$, length of road construction 6.6miles is twice that of an auction with a Fair Price estimate of 450,000$, Fixed Cost estimate of 150,000$ and length of road construction equal to ______ miles, all other variables held constant across the two auctions.

Briefly show your working

(f) (2 pts) Suppose that a variable like Rigged (indicating whether an auction was rigged) did not exist, however the variable Price which is the Price paid by the winning bidder is available. The attorney general asks you to identify projects on which bidders might have colluded so she could focus her inquiry on those projects.

Using the other variables given (other than Rigged) how would you go about detecting likely collusion?

Note that NO calculations are needed for this part. You simply need to briefly outline your approach.

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