Estimating Firm-Anticipated DEFENSE ACQUISITION COSTS WITH A VALUE-MAXIMIZING FRAMEWORK.
If we assume that the cost of research and development of a contract is predetermined and only known by the contractor, fluctuations during the contract are determined simply by the initial bid. If the initial bid is lower than actual cost, there will be cost overruns. Alternatively, if we assume that contractors have a great amount of control over their costs of development, they should fine-tune their cost performance throughout the project to maximize their value. As we develop our theory, only one of these assumptions must be true.
For cost-plus contracts, the government pays all cost overruns and the contractor is virtually unaffected. The only way that a contractor might be immediately impacted is if there is specific language inserted into the contract detailing a risk-sharing scheme, or if the government decides to cut the number of end-product units ordered in response to overruns. While risk-sharing contracts are difficult to empirically evaluate due to a dearth of available data, changes in quantity ordered are well documented for any Major Defense Acquisition Program (MDAP). This reduction in quantity ordered will hurt the firm as most contracts have a research phase, resulting in a predetermined, negotiated rate for the cost of each manufactured unit. Production revenue can often be a significant portion of a government contractor's cash flow in an MDAP.
Whether we assume that the contractor can adjust its costs or that it bids with a fixed final cost in mind, the market will respond to new projects and fluctuations in value in the same manner. It should also not matter if the diminished contract value is due to an incentive scheme or changes in quantity ordered. This article will estimate the effect that new contracts and later amendments have on a company's value. Once the effects are estimated, government contractors can then use them to determine optimal incentives for cost control and cost predictability.
We developed the model to take into account the market's reaction to the initial award amount, changes in development costs, and changes in the value of quantities ordered after development. Intuition tells us that the stock price will go up with a new contract award and will go down as less quantity is ordered. Our theory states that as development costs go up, the government will cut quantity ordered. Given this relationship, we expect that as development costs increase, firm value will decrease. We will compile evidence that development cost increases in a predominantly "cost-plus" environment will only affect firm value if the government changes quantity ordered in response.
After we estimate our model's coefficients, we will develop a framework for designing optimal contract incentives. Since firms will not purposely lower their own value, we can find the ratio of quantity cuts to development cost overruns that forces the firm to either bid more closely to their estimations of cost or control costs below a certain desired level. We can understand this ratio, [E.sup.1], as an elasticity where we measure the percentage change in quantity ordered for a percentage change in development costs.
Cost overruns in defense acquisition have been a problem for as long as the military has looked to industry to deliver innovative products. Most of the relevant literature views contracting for major, innovative defense projects through an insurance framework with moral hazard.
Cummins (1977) observes that prior to the 1960s, the government's primary focus was on limiting contractor profits. To this end, cost-plus contracts, where the government bore all of the risk of cost overruns, were the primary contract types. As awareness of the risk-sharing problem became better understood, the government shifted to greater use of contracts with incentives built in to share the risk between both parties. This shift of risk to the firm controlled cost overruns, but required a greater fixed fee to firms.
The basic framework of the risk-sharing contract is [pi] = [alpha] - (1-y) C, where n is firm profit, a is a fixed fee, y is the fraction of cost overruns borne by the government, and C is the cost overruns. To ascertain a pareto-optimal contract, Cummins built upon a profit maximizing framework with contingent contracts and positive externalities gained by the firm from contract completion. In this article, we will use a value-maximizing framework. The effective difference is that a firm will likely need some market-designated positive profit to undertake a project in our framework, whereas a firm would accept a contract with zero accounting profit in Cummins' model.
Cummins showed that if we take the government's objective to be lowering total cost vice cost overruns and firm profit, risk-sharing contracts can be ineffective. Hiller and Tollison (1978) provide empirical evidence to support this theory. As we increase the risk sharing in a contract, the firm requires a greater fixed fee. Any savings from increased firm attention to cost may be offset by the increased fixed fee. We could see lower cost overruns, but the same--or even greater-total cost. It is therefore much more important to focus on controlling total cost vice cost overruns. Our model will allow the government to calculate expected total cost prior to the awarding of a contract.
Weitzman (1980) takes the analysis of risk-sharing contracts in another direction. His research presents the risk-sharing contract equation and a utility maximization framework to determine an efficient sharing ratio between the principal (government) and the agent (contractor). Weitzman's chief result is simple: if the sharing rate is high, the firm will bid higher and in turn make bids a more reliable indicator of final cost. We will obtain a similar result, but our "sharing rate" will be between development costs and quantity cuts, vice a contracted agreement on risk sharing. Additionally, we will show our sharing rate to impact total cost, not just cost overruns.
Goel (1995) builds upon Weitzman by including an auction framework. His research develops a model where the principal designates a sharing rate, y, and then allows various agents to bid on the contract. Under the model, the principal is able to coax agents to bid closer to their expectations of cost by increasing the amount of risk borne by the agent. Some differences between Goel and our article are a lack of bidding framework in this article, but the addition of a firm value perspective along with empirical investigation. Because the bidding framework does not affect the underlying result shared between Goel and Weitzman--that a higher sharing rate results in a bid that is more reflective of cost estimations--this article's omission of a bidding framework should not impact its results.
Intuition tells us that markets will generally respond positively to any mention of additional profit flowing to a publicly traded firm. Conversely, any news that suggests the possibility of a loss of profit should result in a negative reaction. Our model defines how markets reward and punish defense contractors for different kinds of news. We will then test our model to see if the market encompasses new information in the manner we predict.
Rational markets should reward firms for securing a new contract. The firm should enjoy a larger increase in value if the contract is larger. Our initial model will look just at time period zero, T0, to determine how much of an effect the award has on stock price. Equation 1 shows this where P0 is the percentage change in stock price and IAt is the initially awarded contract amount divided by the value of the firm.
[P.sub.0] = [[beta].sub.1] * I[A.sub.t] (1)
Next, we need an equation that explains the change in price for all further time periods. Firm value fluctuation during the life of the contract should primarily be affected by changes in the value of the contract. Defense contracts adjust through two main avenues: changes in quantity ordered and changes in development costs. Many MDAPs are of the cost-plus variety, meaning that an overrun in cost will be borne by the government, not the firm. Assuming our model's firm is undertaking a cost-plus contract, its value should only be affected by a change in quantity ordered. Equation 2 shows this where [Q.sub.t] is the percentage change in quantity ordered.
[P.sub.t>0] = [[beta].sub.2] * [Q.sub.t] (2)
We can account for all time periods with Equation 3. In [T.sub.0] of Equation 3, I[A.sub.t] will be equal to the initial amount of the contract whereas [Q.sub.t] will be zero. In all other time periods, IA will be zero whereas [Q.sub.t] will likely be nonzero numbers as long as the contract is still active.
[P.sub.t] = [[beta].sub.1] * I[A.sub.t] + [[beta].sub.2] * [Q.sub.1] (3)
In our model, the government can decide [Q.sub.t] at any given time. If it requires less of the final product, [Q.sub.t] will be negative. If it requires more, [Q.sub.t] will be positive. We suspect that the primary reason that the government will change [Q.sub.t] is a change in [D.sub.t], or the percentage change in development costs. As development costs go up, the government must save costs elsewhere and cut [Q.sub.t]. Equation 4 gives us the relationship between [Q.sub.t] and [D.sub.t], where [E.sub.1] is the amount of [Q.sub.t] that the government will change for a given amount of [D.sub.t]. (Note that [E.sub.1] can be thought of as the elasticity of changes in quantity with respect to development cost fluctuations.) We will use this equation to empirically estimate [E.sub.1] in the Results section of this article.
[Q.sub.t] = [E.sub.1] * [D.sub.t] (4)
So that we can express our change in stock price equation only in terms controllable or estimable by the firm, we substitute Equation 4 into Equation 3 to get Equation 5.
[P.sub.t] = [[beta].sub.1] * I[A.sub.t] + [[beta].sub.2] * [E.sub.t] * [D.sub.t] (5)
The point at which our firm will either not bid on a project given known costs (or will avoid reaching if costs are controllable) is the point where the net change in value of the firm across the project is zero. Condition 1 gives us this mathematically, where i is the number of time periods.
Condition 1: (1 + [P.sub.0]) * [[PI].sup.i-1.sub.t=1] (1 + [P.sub.t]) = 1
If we assume a constant change in development costs over the life of the project, we can sum Equation 5 across all time periods. This allows us to calculate the total value change across the entire project to determine the optimal government reaction to a development cost increase. We use notation P to denote the net percentage change in firm value for the duration of the project. If we take D to be the total development cost growth for the duration of the project and assume constant cost growth, we get each annual cost growth to be D . The variable "i" is the number of years required for project completion.
P = [1 + [[beta].sub.1] * IA] * [1 + [[beta].sub.2] * [[E.sub.1] * [D.sup.1/i]].sup.i] - 1 (6)
By solving Equation 6 for [E.sub.1] where P = 0 (from condition 1), we can estimate the appropriate amount that quantity should be reduced if we know the government's opinion of the acceptable development cost growth of the program.
[E.sub.1] = [D([-.sup.1/i])] * [-1 + [(1/([[beta].sub.1] * IA + 1)).sup.1/i]]/[[beta].sub.2] (7)
If the government sets [E.sub.1] equal to its result from Equation 7, the firm would lose net value from the project if it has greater cost growth than D. Because the firm will avoid losing net value, it will avoid having development cost growth greater than D. It can avoid such cost growth either by implementing cost controls where possible, or by bidding closer to the actual cost if it has a reasonable initial estimate.
Our predicted coefficient for all variables in all equations is displayed in Table 1. We will test Equations 3, 4, 5, and 6 empirically to estimate all relevant coefficients. We will then use those coefficients to develop our methodology for incentive creation and cost estimation from Equation 7.
Table 1 displays all of our empirically evaluated variables and our expected coefficients for each variable in each equation. The only variable that we have not previously discussed is SP. It represents the change in the Standard & Poor's 500 Index (S&P 500) for the given time period. This variable will control for exogenous market variation.
We collected data from Selected Acquisition Reports (SARs) on 20 MDAPs that are published at least annually, sometimes quarterly. The 20 MDAPs were awarded to seven separate contractors between 2000 and 2014. The SARs give top-level summaries of changes in costs categorized by Support, Quantity, Engineering, Estimation, Economic, and Schedule. We categorize Engineering, Estimation, and Schedule cost changes as developmental costs. Quantity changes will help us determine our Q variable, whereas Support and Economic changes will be their own category that we suspect will have little impact on the model.
Hough (1992) discusses the difficulties associated with using SARs to study cost overruns. The most significant problem is that when incentive contracts are used, the costs borne by the contractor are not identified in the SAR. The SAR only identifies costs to the government, though it is intuitive that as the development cost grows in the SAR, a firm engaged in a risk-sharing contract will bear a corresponding cost. It is therefore difficult to dissect the effect that the SAR-measured development cost overruns have on firm value and the effects of the presumed collinearity that the SAR measurement has with firm-borne costs. Since our data do not consist of completely cost-plus contracts, we sanitize our results from this effect by testing for this collinearity in three ways.
Because our data will not exclusively consist of cost-plus contracts, we need to test whether or not [D.sub.t] is impacting the stock price directly or indirectly, as hypothesized. To do this, we can compare the value of [[beta].sub.2] * [E.sub.1], as estimated from Equations 3 and 4, and compare it to our empirical estimation from Equation 5. If the values are close to each other, then our data conform to our theoretical model. If there is a significant difference, then a change in [D.sub.t] is having an effect on firm value independent of its impact on [Q.sub.t].
The second test will be to simply regress both [Q.sub.t] and [D.sub.t] against [P.sub.t]. This will allow us to control for either variable and determine which one is primarily driving [P.sub.t].
For a third way to test whether [D.sub.t] is directly or indirectly changing firm value, we will look to Equation 6. We break [D.sub.t] into [Dq.sub.t] and [Dn.sub.t], where [Dq.sub.t] is [D.sub.t] for all cases where [Q.sub.t] is nonzero and [Dn.sub.t] is [D.sub.t] for all cases where [Q.sub.t] is zero. This way we break up the variable into two categories: one where [D.sub.t] plausibly could have impacted Q and one where it could have no impact.
[P.sub.t] = [[beta].sub.1] * I[A.sub.t] + [[beta].sub.2] * [Dq.sub.t] + [[beta].sub.3] * [Dn.sub.t] (8)
We combined data from the last SAR for each year (usually from December) with the last stock quote of the corresponding company for the same year as reported by Google Finance. While it is unusual to rely on annual stock data for an event study, it is not possible in this instance to use daily, weekly, or monthly data. This is because the information included in a SAR flows to the market at varying times, while the SAR simply summarizes it. It is therefore problematic to decide when to designate the event when using more frequent market return data. This hurts the accuracy of this study, but does not negate its findings. For instance, Holthausen and Leftwich (1986) successfully used 300 days to define their event horizon in another event study. We additionally seek to mitigate this problem by including a larger dataset than is typical for this topic.
The predominant firm awarded each MDAP contract was used as the corresponding company. All cost growths are noted in real dollars with the specified program's start year as the baseline. Hough notes that simply using the real dollar values from the SAR is inadequate since initial cost estimates are based on certain inflation assumptions. To account for this, we discount the cost growth associated with economic factors.
To calculate production cost growth, we normalize to the contemporarily approved quantity, vice normalizing to the baseline-approved quantity. The selected calculation method is as reported in SARs.
In several instances, a contract was ongoing for several years and then was transformed into a new contract. Because the SAR data are very high-level and provide no amplifying information to ascertain estimated changes in quantity and development costs, we treated the change as the final year of the project. This slightly reduces the number of observations, but should not impair the validity of our findings.
Our data include 321 data points at the project level and, when aggregated into firm-level data, 113 data points. We perform our analysis with project-level data.
The following MDAPs appeared in our data:
* AESA--Active Electronically Scanned Array (Radar)
* SM-6--Standard Missile-6 (Rocket Intercept Missile [RIM]-174 Standard Extended Range Active Missile)
* SDBII--Small Diameter Bomb II
* MH-60--Military Helicopter-60 (Seahawk)
* AEHF--Advanced Extremely High Frequency (Satellite)
* ACS--Aegis Combat System (Integrated Command and Control/ Weapons Control System)
* JSF--Joint Strike Fighter (Fighter, Strike, and Ground Attack Aircraft)
* Land Warrior--Integrated Soldier System (Weapon, Helmet, Computer, Digital and Voice Communications, Positional and Navigation System, Protective Clothing, Individual Equipment)
* EFV--Expeditionary Fighting Vehicle
* Stryker--Interim Armored Vehicle
* T-AKE--Auxiliary Cargo (K) and Ammunition (E) Ship, Military Ship Classification (MSC) Manned
* Bradley Upgrade--Infantry Fighting Vehicle
* Comanche--RAH-66 Helicopter
* F/A-18E/F--Ai craft Variants (Based on McDonnell Douglas F/A18 Hornet)
* EA-18G--Boeing Growler (Electronic Attack Aircraft)
* CH-47F--Boeing Chinook (Twin-Engine, Tandem Rotor Heavy-Lift Helicopter)
* P-8A--Boeing Poseidon (Navy Maritime, Patrol, Reconnaissance Aircraft)
* FBCB2--Force XXI Battle Command Brigade and Below (Communications Platform to Track Friendly/Hostile Forces on Battlefield)
* Global Hawk--Unmanned Aircraft System
Summary statistics for our project-level data are summarized in Table 2.
The key variables in our project-level data are summarized in Table 3. Strongly correlated variables are in bold and include Q with D, Q with Dq, and D with Dq. Only Q and D are both used in the same regression, and we should expect them to be negatively correlated as observed.
Validity Test of Data
Since our theory relies on the premise that development cost changes impact firm value, primarily through their impact on order quantities, we must test our data to see that they conform to this assumption. We do this through three regressions, two of which will be discussed in this section, while the third will be discussed in the Results section. For the first test, we will split [D.sub.t] into two variables: one that has value when [Q.sub.t] moves in the same time period, [Dq.sub.t], and one that has value when [Q.sub.t] does not move in the same time period, [Dn.sub.t], as in Equation 8. Table 4 defines and shows the results of this test regression.
[Dq.sub.t] is significant at the 95 percent level in our first model and significant at the 90 percent level in the second. The more interesting result is that [Dn.sub.t] is completely insignificant in both models, suggesting that a change in development costs without a change in quantity ordered has no impact on firm value. In other words, without a corresponding change in quantity ordered, variations in development costs are not associated with a change in firm value.
Our second test for data validity will be to regress both [D.sub.t] and [Q.sub.t] against [P.sub.t] to ascertain whether [D.sub.t] becomes insignificant when controlled for [Q.sub.t]. We will use firm-level data for this regression, as project-level data result in insignificance for both variables. Table 5 shows the results of this regression.
As we can see, [D.sub.t], is completely insignificant when controlled for [Q.sub.t]. This indicates that our data are valid. We will discuss our final test in the Results section as we need to complete our primary analysis prior to completing the discussion on our final test. The test will also indicate that our data conform to our theoretical assumptions.
We tested all regressions herein with OLS (Ordinary Least Squares) and random effects and fixed effects models, with the firm as the panel variable and observed minimal variation from the basic regression. To simplify the reading of these results, we have only included the OLS version of each regression.
Our first OLS model (Table 2) looks at Equation 3, with the addition of the SP variable (percent change in S&P 500 Index) and a constant in one of the models. Data are at the project level, with each year being a data point. Table 6 shows the results of this regression.
We can see that only in the model with a constant is our primary variable of interest, [Q.sub.t], significant at the 95 percent level, though the point estimate is within 20 percent in either model. Its coefficient is positive as predicted, meaning that as the government cuts quantity ordered, the firm's value decreases as well. We can also see that an increase in the S&P 500 and the initial contract award are correlated to an increase in firm value. With our next model, we try to tease out the relationship between a change in development costs and a change in quantity costs. Equation 4 from the model section of this article was [Q.sub.t] = [E.sub.1] * [D.sub.t]. Our model in Table 7 is simply [D.sub.t] regressed against [Q.sub.t] to find [E.sub.1]. With the assumption that the government adjusts [Q.sub.t] as a reaction to [D.sub.t], we understand [E.sub.1] to be the ratio of [Q.sub.t] changes for a given [D.sub.t]. In other words, the elasticity of [Q.sub.t] with respect to [D.sub.t].
Accepting the no constant model as our primary model because the constant is not significant at even the 90 percent level, we can understand the coefficient of [D.sub.t] to mean that for every percent that an MDAP's development costs increase from initial estimates, the government will order about 0.17 percent less quantity. Our 95 percent confidence interval for [E.sub.1] lies between -0.1838 and -0.1562.
We also tested the Pearson correlation between the two variables and found it to be 0.8072, indicating a significant inverse relationship between them.
We can also analyze the relationship between Q and D by viewing them on a scatterplot. As we can see in Figure 1, which contains project-level data, the correlation appears negative.
Shifting our initial model from Table 6 to have [D.sub.t] replace [Q.sub.t], we would expect that the coefficient for [D.sub.t] would simply be [Q.sub.t] coefficient multiplied by [E.sub.1] whereas all other coefficients remain the same. The OLS model for Equation 5 is depicted in Table 8, and the far right column is our theory's prediction of the model.
Whereas the no constant model has a higher [R.sup.2], our constant model has all variables significant at the 95 percent level. For this reason, and because our model from Table 2 used the constant model as its primary one, we will use the constant model. In the far right, we can see our theoretical predictions for the OLS model with a constant and that all values are close to actual estimations (well within the 95 percent confidence interval). Our empirically estimated coefficient for [D.sub.t] is -0.125 with a 95 percent confidence interval of -0.232 to -0.018. This places our theoretical prediction well within the limits of our actual estimations and lends significant credence to the validity of both our data and theory.
All regressions including a constant were tested for heteroscedasticity using the Breusch-Pagan/Cook-Weisberg test. We were not able to reject the null hypothesis of homoscedasticity for any regression. We also observed the residual plot for every regression and found no clear evidence of any specification errors. Figure 2 shows the residual plot for equation 5. The plot is not uniformly distributed, but there is no clearly identifiable pattern suggesting omitted variable bias or another specification error. Various specifications all yield qualitatively similar plots.
Our theory, that even in a cost-plus contract, defense contractors' firm value fluctuates indirectly with development cost changes through the government's quantity cutting response, presents a clear framework for building effective incentives to mitigate potential cost overruns. Our data show that as development costs rise from initial estimates, the quantity ordered by the government decreases. Because our theory and model show that a decrease in quantity ordered leads to a lowered firm value, development cost overruns that lead to less quantity ordered should have a similar effect. The only difference in a dollar of cost overrun and a dollar cut from the final order is the ratio between the two. If the government cuts 25 cents of the final order for every dollar of development cost overruns, the harm to the firm from development cost overruns will not be as strong as a 1:1 ratio. The government is the decider of this elasticity and can therefore determine how great the disincentive is for a firm to allow development costs to climb. It is hard to imagine the government determining at the outset of a contract how much quantity they will cut based on development costs, but by establishing a reputational [E.sub.1], the government can effectively achieve the same objective. [E.sub.1] will simply not be as flexible from contract to contract.
Our models all support the theory as we would expect. Changes in quantity ordered are positively correlated and changes in development costs are negatively correlated with changes in firm value. More convincingly, the magnitudes of these correlations are roughly the same as the ratio that the government chooses. Firm value increases about 0.51 percent per percentage increase in end product purchases. Firm value decreases about 0.12 percent for every percentage increase in development costs. If our theory proved exactly correct, given our estimated ratio of quantity cost changes to development cost changes (~ -.17), firm value should decrease approximately 0.9 percent for every percentage increase in development costs. This value is only 25 percent away from our point estimate and is well within reasonable confidence intervals. Further, when we look at changes in development costs that occurred concurrently to changes in quantity ordered versus those that did not, our theory is further supported. Development costs with no quantity changes have no effect on firm value while those with quantity changes associated do have an effect.
If we take our theory and solve for the ratio of changes in quantity ordered to changes in development costs [E.sub.1] = [D([-.sup.1/i])] * [-1 + (1/[([[beta].sub.1] * IA + 1)).sup.1/i]]/[[beta].sub.2], the government can determine the optimal ratio to incentivize firms as desired. If the government wants the end cost to be below a certain amount and the firm can control costs, it must create incentives such that the firm will lose value on the project if it exceeds that amount. For a $70 billion firm bidding $20 billion on a project that will last 5 years, we might create a graphic as in Figure 3.
If the government does not want total cost to exceed $40 billion, it should set the ratio of quantity ordered cut for a development cost overrun at approximately -0.19. Given our estimated values and the firm's aversion to losing value, the firm will allow development costs to only grow an acceptable amount.
We create Figure 1 by calculating [E.sub.1] for all reasonable values of [D.sub.1]. We can then calculate total cost for each value of [E.sub.1] by adding the development cost effects and quantity-ordered effects to the initial bid. The government could also use Figure 3 to better predict final costs of research and development. All it needs to know is [E.sub.1], and it can then ascertain a firm's incentives to control costs.
If the government alternatively believes that the firm knows its costs, but has no control over them, it can seek to incentivize a realistic bid. The harsher the incentives (lower [E.sub.1]), the more closely the bid will reflect firm expectation of cost. If we assume a $70 billion firm that has known costs of $20 billion for development for a 5-year project, we can build Figure 4.
As we can see, the harsher the incentive, the closer the firm's minimum bid gets to its actual estimate. We can rearrange our chart to give us the desired percentage of the total estimate that the government can reasonably expect all bids to at least reach.
We create Figure 4 by calculating [E.sub.1] for every reasonable [D.sub.1], given the firm's expected development costs. We then infer the bid from [D.sub.1].
This framework has several important implications for policy makers. If the government seeks to control costs or at least obtain an accurate estimation of the firm's expectations of cost, it can use Equation 7 and our estimated coefficients to design an optimal contract. While this article looks at the ratio of quantity cuts to development cost overruns, we could easily calculate the profit lost from the quantity cuts and determine a more straightforward cost-sharing ratio with the same coefficients. A dollar of profit lost from quantity cuts should not impact the firm differently than a dollar of profit lost from a cost-sharing scheme.
The government might be encouraged to cancel projects at a lower threshold than is current policy. It might also be encouraged to establish firmer top-line budgets for projects, from development to production. The firm would then understand that as more funds were used in development, a smaller share of the funds would go toward production. When a higher deterrent to cost overruns is established through a demonstrated willingness to cut quantity ordered, we should see more reasonable bidding, less cost overruns, and lower total cost of future projects.
With an [E.sub.1] established by the government, the firm should bid in a predictable manner, given its own expectations of the final cost of development. The government can then use the bid it receives to estimate the firm's true cost expectations. For instance, if we know that a firm should bid 50 percent of its expected cost for an established [E.sub.1], then the government should budget twice what is called for in the contract bid. This insight could allow the government to more accurately forecast expenses and improve contract stability. This stability could lead to lower costs to the taxpayer.
Cummins, J. M. (1977). Incentive contracting for national defense: A problem of optimal risk sharing. The Bell Journal of Economics, 8(1), 168-185.
Goel, R. K. (1995). Choosing the sharing rate for incentive contracts. The American Economist, 39(2), 68-72.
Hiller, J. R., & Tollison, R. D. Incentive versus cost-plus contracts in defense procurement. The Journal of Industrial Economics, 26(3), 239-248.
Holthausen, R., & Leftwich, R. (1986). The effect of bond rating changes on common stock prices. Journal of Financial Economics, 17(1), 57-89.
Hough, P. G. (1992). Pitfalls in calculating cost growth from Selected Acquisition Reports (Report No. N-3136-AF). Santa Monica, CA: RAND.
Weitzman, M. L. (1980). Efficient incentive contracts. The Quarterly Journal of Economics, 94(4), 719-730.
LTJG Sean Lavelle, USN, is a naval flight officer serving with VP-26 on the P-8A Poseidon in Jacksonville, Florida. He holds a BS in Economics from the U.S. Naval Academy and a Master's in Finance from Johns Hopkins University.
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Caption: FIGURE 1. PROJECT-LEVEL Q VS. D SCATTERPLOT
Caption: FIGURE 2. EQUATION 5 RESIDUAL PLOT
Caption: FIGURE 3. DEVELOPMENT COSTS VS. STRENGTH OF FIRM PENALTIES
Caption: FIGURE 4. BID ACCURACY VS. STRENGTH OF FIRM PENALTIES
TABLE 1. VARIABLE DESCRIPTION TABLE 1: VARIABLE DESCRIPTIONS Variable Symbol Description IA [[beta].sub.1] The Initially Awarded Contract Amount Divided by the Market Cap of the Firm. Only nonzero during time period of initial award. Q [[beta].sub.2] Change in Cost of Quantity Divided by Initial Contract Amount D Eq 4: Change in Cost of [[beta].sub.3] Development Divided by Eq 5: [E.sub. 1] * [[beta].sub.3] Initial Contract Amount Dq [[beta].sub.3] Change in Cost of Development Divided by Initial Contract Amount if Q Changed in Same Time Period Dn [[beta].sub.4] Change in Cost of Development Divided by Initial Contract Amount if Q did not Change in Same Time Period SP [[beta].sub.5] Percentage Change in S&P 500 Variable Expected Coefficient IA Equation 3: Positive Equation 5: Positive Equation 6: Positive Q Equation 3: Positive D Equation 4: Negative Equation 5: Negative Dq Equation 6: Negative Dn Equation 6: Insignificant SP Positive TABLE 2. SUMMARY STATISTICS Project-Level P SP IA Data Mean 0.144073 0.043694 0.013118 Standard Error 0.013847 0.010968 0.004444 Median 0.145455 0.105877 0 Mode 0.535274 -0.10139 0 Standard Deviation 0.240243 0.189972 0.079493 Sample Variance 0.057717 0.036089 0.006319 Kurtosis 0.543315 0.128455 148.0833 Skewness 0.011312 -0.81439 10.99353 Range 1.314126 0.722675 1.175556 Minimum -0.59603 -0.40967 0 Maximum 0.718095 0.313007 1.175556 Project-Level D Q Data Mean 0.017552 -0.00057 Standard Error 0.011839 0.002507 Median 0 0 Mode 0 0 Standard Deviation 0.211774 0.044844 Sample Variance 0.044848 0.002011 Kurtosis 264.9717 161.3609 Skewness 15.69839 -10.383 Range 3.846937 0.912608 Minimum -0.22689 -0.67047 Maximum 3.62005 0.242139 TABLE 3. PROJECT-LEVEL DATA CORRELATIONS Variables IA Q D Dq Dn SP IA 1 Q 0.0015 1 D -0.0147 -0.8073 1 Dq -0.0153 -0.8113 0.9953 1 Dn 0.0057 -0.0005 0.0996 0.0031 1 SP -0.1124 0.038 0.0527 0.056 -0.0232 1 TABLE 4. CATEGORIZED [D.sub.t] REGRESSION [P.sub.t] = [[beta].sub.1] * [IA.sub.t] + With No [[beta].sub.3] * [Dq.sub.t] + [[beta].sub.4] Constant Constant * [Dn.sub.t] +[[beta].sub.5] * [SP.sub.t] + Constant [SP.sub.t] .6584133 .7914403 (.000) (.000) [IA.sub.t] .4269925 .675944 (.004) (.000) [Dq.sub.t] -.1238065 -.0868289 (.024) (.158) [Dn.sub.t] -.26261614 -.3981645 (.641) (.530) Constant .1432938 N/A (.000) [R.sup.2] .2825 .3647 Observations 300 300 Note: Parentheses contain P-Values. TABLE 5. REGRESSION WITH [Q.sub.t] AS CONTROL VARIABLE [P.sub.t] = [[beta].sub.1] * [IA.sub.t] + With No [[beta].sub.2] * [Q.sub.t] + [[beta].sub.3] * Constant Constant [D.sub.t] + [[beta].sub.5] & [SP.sub.t] + Constant [SP.sub.t] .0006096 .0006593 (.000) (.000) [IA.sub.t] .2742662 .4170445 (.010) (.000) [D.sub.t] -.0101116 .0363141 (.918) (.275) [Q.sub.t] .4029882 .4397591 (.003) (.002) Constant .072123 N/A (.000) [R.sup.2] .4487 .4975 Observations 112 112 Note: Parentheses contain P-Values. TABLE 6. EQUATION 3 REGRESSION [P.sub.t] = [[beta].sub.1] * [IA.sub.t] + With No [[beta].sub.2] * [Q.sub.t] + [[beta].sub.5] * Constant Constant [SP.sub.t] + Constant [SP.sub.t] .6468396 .7822163 (.000) (.000) [IA.sub.t] .428198 .6746299 (.004) (.000) [Q.sub.t] .4995067 .4489935 (.052) (.121) Constant .1106027 N/A (.000) [R.sup.2] .2786 .3280 Observations 300 300 Note: Parentheses contain P-Values. TABLE 7. EQUATION 4 REGRESSION [Q.sub.t] = [E.sub.1] & With Constant No Constant [D.sub.t] + Constant [D.sub.t] -.1709295 -.1699817 (.000) (.000) Constant .0024306 N/A (.103) [R.sup.2] .6516 .6487 Observations 320 320 Note: Parentheses contain P-Values. TABLE 8. EQUATION 5 REGRESSION [P.sub.t] = [[beta].sub.1] * With No Predicted [IA.sub.t] + [[beta].sub.2] * Constant Constant [E.sub.1] * [D.sub.1] + [[beta].sub.5] * [SP.sub.t] + Constant [SP.sub.t] .6589882 .7930062 .6468396 (.000) (.000) [IA.sub.t] .4268835 .676214 .428198 (.004) (.000) [D.sub.t] -.1251678 -.0898093 -0.08538 (.022) (.142) Constant .1121303 .1430959 (.000) [R.sup.2] .2823 .3275 N/A Observations 300 300 300 Note: Parentheses contain P-Values.
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|Publication:||Defense A R Journal|
|Date:||Jul 1, 2017|
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