Optimal Government Procurement

What contracts are best?

There are two basic models of procurement contracts in the government. One, cost-plus, has the contractor tell the government how much doing the job cost. The other, fixed-price, has the contractor put in a bid to do a job for a given amount, and to eat the loss should they exceed it. Fixed price is often itemized into specific tasks and prices for each task, but it is still paying for the job, not the method. The difference between the two is who holds the risk. Cost-plus puts the risk of an overrun on the government, while a fixed-price contract puts the risk on the contractor. 

What is strange about this is that a sensible analysis should come down heavily against cost-plus contracts and for fixed price contracts. In any instance where there are possible innovations in the productive process, and it is not possible to perfectly reward the contributor of the innovation, the allocation of property rights should reflect who is best able to provide that innovation. We can see this in the context of land, as I covered before on my blog, where the decision to rent land, hire employees, or sharecrop is a function of who is most likely to innovate. The government does not plausibly know what can be done to make road construction more efficient, or how to better launch rockets into space. The government doesn’t need to worry about the contractor not providing the thing that they want if they don’t dictate every step of the production process — so long as they can ascertain payoffs, a la Maskin-Tirole 1999, they can control what is made. 

What argument could there be for cost-plus? What explains its persistence? While allowing for the possibility that “the government is stupid and inefficient”, I will focus on the best arguments I can find. They center around it being insurance, which we might reasonably think the private sector could not provide — there is too much moral hazard if an entirely uninvolved firm is bearing the risk of any cost over run.

First, some minor arguments. Cost-plus contracts, to some degree, mitigate the government’s temptation to seize by changing the parameters of the design after the fact. The government could rebid after every substantial change, and to some degree we would expect the price of fixed bid contracts to reflect expected changes. Still, I don’t believe this. The government cannot be bound by contract. Either it means to stick by them, or nothing can stop it. Cost-plus contracts could also be justified if payoffs are hard to ascertain, but the making of the project is easy. This doesn’t make sense though. The government doesn’t have to observe the project only once it is done — no matter what contractual structure there is, they can always watch the project as it goes on.

A better counter-argument for cost-plus contracts is that it solves a winner’s curse problem for bidding companies. The “winner’s curse” arises when companies are bidding for an object whose value will be the same for all parties, they simply differ in how much they assess it to be. Yes, some firms are more productive than others, but much of the reason for a valuation is common to all companies. A road will need asphalt, and that asphalt will cost all companies about the same. The company which wins the auction is the one which is most confident about its prospects, but if we think that (since all of the companies are trying just as hard) the average is the most accurate measure, then whoever wins will lose money. Therefore, companies “shade” their bid away from what they earnestly think. If firms are indifferent to missing high or low, then revenue equivalence holds, and they end up having the same expected revenue no matter the format. If firms are risk averse, though, the price is distorted when firms bear the risk.

In order to come to a solid answer, we must estimate how risk firms are. This is surprisingly tricky – as Rabin showed, if your conception of risk-aversion is based on a declining marginal utility of income, then plausible levels of risk aversion imply ludicrously unrealistic levels of risk aversion as sums get larger. To give a very simple example, many of us would not take a 50/50 chance of losing $100 to gain $200, and yet if we had the option of taking 100 gambles of that kind in a row, we surely would. It should be possible, nevertheless, to estimate firm's risk aversion, and compare its size to an estimate of possible improvements in the process.

So how risk-averse are firms? I cannot find a general answer, but there is reason to think that it is not insubstantial. We might expect companies to be much more risk neutral than individual, but we mustn’t forget that companies are run by managers whose particular areas are much smaller than the company as a whole. Lovallo, Kohler, Uhlaner, and Kahneman (2020) argue that companies are actually quite risk averse due to this, and that substantial gains for businesses are possible if they take into account the whole size of their business. (This challenges, btw, the beliefs expressed earlier by me regarding the self-insurance function of conglomerates). These companies are often not all that big either, especially in infrastructure bidding. Bolotnyy and Vasserman (2023) document bidding consistent with risk aversion, where prices are skewed on items for which there is more uncertainty.

My empirical strategy will be to find instances where government procurement auctions for a homogeneous good abruptly changed format. The difference in price, after controlling for any simultaneous changes in the price of materials, can be taken as solely being the value which firms place on insurance. Ideally, we could calculate how it varies by size of firm, and then estimate different industries by extending that coefficient. If there is a change with size, that suggests that there will be more bidders with cost-plus than with fixed price. This would have an impact on firm markups, as the market power of some contractors would increase, which would need to be considered in any estimates of the losses from a fixed price contract. 

This essay suggests a simple rubric of when contracting should be cost-plus, and when it should be for fixed price contracts. When the thing being made is unlikely to be improved, and firms are risk-averse, cost-plus contracting is optimal. When firms are more risk neutral, and we expect there to be many possible innovations, a fixed price contract becomes optimal. This suggests that Sen. Nelson was right when he called cost-plus contracts a “plague” upon NASA, but at the same time, cost-plus contracts might be optimal for paving half a mile of road. Rocketry has lots of possible improvements; asphalt, probably not. Either way, the optimal method is not necessarily clear, and we should experiment more. Government policy is insufficiently varied for us to think we’re at an optimum.