Statistical Analysis and Representation Models of Working-Days Liquidated Damages

Contractors tend to challenge the enforceability of liquidated damages (LDs), claiming they are unreasonable, excessive, penalty statements, or concurrently caused. States customarily assert that the LD rates are a genuine reflection of the expenses expected to be suffered when a project gets delayed due to noncompletion. While there are common practices among the states for articulating LD specifications, which generally follow the Federal Code of Regulations, there are no published studies that assist states in comparing their LD rates to those of other states so that the LD rates might be defended. Further, there are no studies that offer models that would uncover the relationship between the LD rates and the contract sizes so that the LD rates might be justified. This work addresses such gaps in the body of knowledge (BOK) in LDs. With emphasis on the working-days (WD) LD rate schedules, the objectives of this work are to characterize the LD rate schedules across the states and to model a formula(s) that would represent the relationship between the WD LD rates and the contract amounts. The data set for the work represents the LD schedules in the standard specifications of all departments of transportation in the United States. Descriptive and cluster statistical analyses were used for the LD rate characterization. For model development, several linear and nonlinear regression models were employed. The results highlighted considerable LDs variability in the smaller contract sizes and exceptional LD rates stability in the larger sizes. Despite the economic differences among the states, it is found that the LD rate is, on average, 0.02 ¢/$ for projects $20 million or above. Below that, the rate increases between 0.03 ¢/$ and 0.18 ¢/$ until the contracts reach $750,000. LD rates tend to decrease sharply with the increase in contract sizes, forming an L or reverse J shape. This pattern proved complex, and only nonlinear regression with transformed variables successfully modeled it. Credible models were obtained after satisfying the least-squares regression assumptions. The work contributes to the BOK by adding a new statistical dimension to understanding LDs and developing regression model(s) that explain the relationships between the LD rates and the contract sizes. The work should help SHAs create, evaluate, and justify their LD rates.