Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies (2020)

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15 Cost Indexing Alternatives 3.1 Introduction This chapter discusses cost indexing alternatives available to state transportation agencies (STAs) to support cost forecasting procedures. In order from the least- to the most-effective cost indexing method for construction cost forecasting, these alternatives are as follows: 1. Macroeconomic indexes, 2. Traditional external and in-house construction cost indexes (CCIs), and 3. The innovative multilevel construction cost index (MCCI) system. The benefits and drawbacks associated with each alternative are addressed. It should be noted that two different CCIs would most likely always yield different inflation rates (Rueda-Benavides 2016), even if they had been developed for the same purpose and with the same inputs. Output differences depend on several factors, including, but not limited to, data sources, data processing and cleaning procedures, index composition, and index calcula- tion approach. This poses a challenge for STAs when an inflation rate needs to be determined. How can an STA know which cost index is offering the best inflation rates? To help with that challenge, the last part of this chapter describes a protocol for the comparative analysis of cost indexing alternatives that is designed to identify the best cost indexing approach among a set of available alternatives. 3.2 Use of Macroeconomic Indexes A number of agencies that use cost indexes for forecasting purposes use the Consumer Price Index (CPI) or the Personal Consumption Expenditures (PCE) Price Index. Those are macroeconomic indexes published by the Bureau of Labor Statistics (BLS) and the Bureau of Economic Analysis (BEA), respectively. The CPI is calculated from monthly price fluctuations of about 80,000 items in a market basket of goods and services purchased by urban consumers (BLS 2018a). Input items considered for the calculation of this index include, but are not limited to, milk, shampoo, rent, housekeeping supplies, apparel, gasoline, medical care, recre- ation services, college tuition and fees, and funeral services (BLS 2018b). The PCE price index is calculated for a slightly different market basket and uses other quantitative methods under different assumptions than those applied to the CPI, but it is still based on a broad set of goods and services regularly consumed by the general public. Although the CPI and PCE are not calculated with construction-related inputs, they seem to be a popular option for supporting cost estimation among STAs. Macroeconomic trends could align with construction market trends during some periods, but macroeconomic indexes such as the CPI and the PCE would not effectively perceive the C H A P T E R 3

16 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies impact that a drastic change in asphalt prices would have on the construction industry. Likewise, some STAs have found that “construction inflation generally outpaces consumer inflation” (Duncan et al. 2017), implying that the use of the CPI or PCE could lead to an underestimation of future construction costs. 3.3 External Traditional Construction Cost Indexes FHWA has made it clear that its recommendation of a 4% inflation rate (see Section 1.4) is a suggestion to be considered only in the absence of better information or methods. FHWA considers that the use of cost indexes to produce inflation rates would be more appropriate than blindly relying on recommended standard inflation rates, even if the available cost index is an external CCI. An external CCI is a cost index developed with construction-related input but not developed by the agency or exclusively for the agency. Some external CCIs are published by the Engineering News-Record (ENR), RSMeans, and FHWA itself, which publishes the National Highway Construction Cost Index (NHCCI) on a quarterly basis (Pakalapati 2018). NCHRP 10-101 found that external CCIs are widely used by STAs for contract price adjustments or to support other cost estimating tasks but are less commonly used in cost forecasting as a means of developing inflation rates for midterm, intermediate, or long-range forecasting (Rueda-Benavides et al. 2020). Table 3-1 outlines some examples of external CCIs. 3.4 In-House Traditional Construction Cost Indexes NCHRP 10-101 also found that a large number of STAs currently maintain in-house CCIs, but, again, that only a few of them use these for cost forecasting purposes (Rueda-Benavides et al. 2020). Even though FHWA is in charge of maintaining and publishing the NHCCI, it is aware that its cost index is more suitable for application at the national level, such as in assessing the performance of the construction market at the national level. The NHCCI might not represent local construction markets effectively. As noted in Section 1.6, “local historic cost data and experience with cost inflation are valu- able data sources for use in projecting future rates” (FHWA 2017b). Using their own historical Index Components Applicability Frequency FHWA: NHCCI • Bid data from highway construction contracts executed by STAs National Quarterly RSMeans: CCI • 9 types of buildings • 66 construction materials • Wage rates for 21 different trades • 6 types of construction equipment National and regional Annual ENR: Building cost index • Cement • Structural steel • Lumber • Labor National and regional Monthly ENR: Building cost index (CCI) • Cement • Structural steel • Lumber • Labor (Combined in different proportions than the building cost index) National and regional Monthly Table 3-1. External traditional construction cost indexes.

Cost Indexing Alternatives 17 bid data to develop in-house CCIs enables STAs to indirectly account for the unique conditions of the local construction market (to a certain extent): “Pricing changes in any single state can be affected by influences that are muted or lost in national prices and price indexes. One example of this is contractor competition, which has a strong influence on prices but has only a local or regional effect” (Molenaar et al. 2013). 3.5 Limitations of Traditional Construction Cost Indexes As recommended by FHWA (2017a), preference should be given to the use of in-house historical bid data in making inferences about the future of local construction markets. However, traditional methods of processing these data into the calculation and maintenance of CCIs limit their capacity to handle the complexities of the construction market. Many of those traditional CCIs are calculated with one of the three price index equations shown in Equations 3-1 to 3-3 (FHWA 2017b). Laspeyres Price Index: Eq. 3-1 , ,01 ,0 ,01 L p p q p q j t jj n j jj n ∑ ∑ ( ) = = = Paasche Price Index: Eq. 3-2 , ,1 ,0 ,1 P p p q p q j t j tj n j j tj n ∑ ∑ ( ) = = = Fisher Price Index: Eq. 3-3 , ,01 ,0 ,01 , ,1 ,0 ,1 F p p q p q p q p q j t jj n j jj n j t j tj n j j tj n ∑ ∑ ∑ ∑ ( ) = ×= = = = where pj,t is the prevailing price of item j in period t and qj,0 is the quantity of item j purchased in period 0. Research results from NCHRP 10-101 revealed a significant issue associated with these typical procedures for calculating a price index (Rueda-Benavides et al. 2020). These equations are not able to factor the economies of scale principles into the cost indexing process. “Economies of scale refers to a reduction in total cost per unit as output increases” (Betts 2007); that is, lower unit prices should be expected for larger quantities of work, and vice versa. It is important to understand that these traditional price index equations were proposed in the 1920s, or even earlier (Fisher 1922)—before the era of computers, when the estimation of index values was limited to hand-made calculations, which constrained data processing and analysis capabilities. This could explain the simplicity of these equations and the reason why they are unable to consider the principles of economies of scale. Their limited ability to factor the relationship between unit prices and quantities is better illustrated with the following simple example.

18 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies Figure 3-1 shows two curves that represent the market conditions for two commodities for a given STA: asphalt and concrete. These curves were created with historical cost data from a given indexing period (Period 1). To illustrate, the highlighted point in the asphalt curve in Figure 3-1 indicates that the average unit price for 200 tons of asphalt during that period was around $135 per ton. For the purposes of this example, it is assumed that market conditions remain unchanged during the next indexing period (Period 2). Thus, the same curves would also represent the market in Period 2, as shown in Figure 3-2. Since the market has not changed in between these two indexing periods, an effective composite cost index calculated with two inputs should show no change in Period 2 with respect to Period 1. In order words, the index values for both periods should be the same. However, if only the four data points shown in Figures 3-1 and 3-2 are used in the calculation of the index values in their respective periods, the traditional cost indexing equations would perceive an inexistent overall decrease of about 23% [(1.00 – 0.77)/100%] in market prices, as shown in Table 3-2. There are other limitations to traditional CCIs in addition to their inability to consider quantity–unit price relationships. Rueda-Benavides and Gransberg (2015) introduced two prin- ciples that are repeatedly violated when traditional CCIs are used for cost estimating purposes at the program or project level: the matching principle and the proportionality principle. (200, $134.06) 0 500 1,000 1,500 2,000 $0 $200 $400 $600 $800 $1,000 Pr ic e [U SD ] Quantity [tons] Asphalt (250, $495.24) $300 $400 $500 $600 $700 $800 $900 $1,000 Pr ic e [U SD ] 0 1,000 2,000 3,000 Quantity [CY] Concrete Note: CY = cubic yards. Figure 3-1. Asphalt and concrete quantity versus unit price curves for Period 1. (2,000, $91.96) $0 $200 $400 $600 $800 $1,000 Pr ic e [U SD ] 0 500 1,000 1,500 2,000 Quantity [tons] Asphalt (3,000, $392.63) $300 $400 $500 $600 $700 $800 $900 $1,000 Pr ic e [U SD ] 0 1,000 2,000 3,000 Quantity [CY] Concrete Figure 3-2. Asphalt and concrete quantity versus unit price curves for Period 2.

Cost Indexing Alternatives 19 The matching principle refers to the degree of similarity between the components used in the calculation of a CCI and the scope to be forecast. Once the matching principle has been reasonably met, the proportionality principle comes into play. It refers to the degree of consistency between the relative weights of index components and the actual contribution of the same components to the total cost of the intended program/project. Therefore, an ideal, but unlikely, scenario would be one in which each cost element in the program is represented by an input element in the CCI, and the relative weight of each element is the same in the CCI as in the program. It should be noted that a violation of the matching principle implies a violation of the proportionality principle, since not sharing the same components would make it impossible to match the weights. Moreover, while there is considerable variability in the scope and configuration of programs and projects within an STA during the planning and programming phases, the set of input components in a typical CCI usually remains unchanged over time. This means that the matching principle cannot always be met. The lack of ability to meet the matching and proportionality principles is preventing STAs from developing scope-based CCIs such as those required by the ideal cost forecasting pro- cess proposed in Section 1.6. The MCCI methodology discussed in the next section not only addresses this issue by offering a high degree of flexibility to adapt to the specific needs of each program or project, but also allows the consideration of the economies of scale principle into the cost forecasting process. Likewise, an MCCI has the capacity to address another problem faced by STAs in the calculation of cost indexes: the absence or lack of sufficient data with which to calculate index values at some indexing periods. The following section has more information about the process of developing MCCIs and about the capabilities of this alternative cost indexing approach. 3.6 Multilevel Construction Cost Index An MCCI consists of a group of indexes organized in a multilevel arrangement. Thus, each cost element in a program/project can be individually represented by its closest matching MCCI index. After the most relevant group of MCCI indexes for the scope of work under consideration is selected, they are mathematically combined into a single scope-based CCI, which is then used to generate annual inflation rates. Costs for different programs/projects are forecast with different sets of indexes, which offers great flexibility to customize the forecasting process to the specifics of each program or project. The rest of this section provides additional information about this alternative cost indexing approach and details the MCCI development process, starting with procedures for data collection and cleaning. Some parts of this section use examples from the case studies conducted under NCHRP 10-101 (Rueda-Benavides et al. 2020), to better illustrate the MCCI develop- ment process. Period Asphalt Concrete Traditional Index Quantity (tons) Price ($) Price ($) Laspeyres Paasche Fisher P1 200 134.06 250 495.24 1.00 1.00 1.00 P2 2,000 91.96 3,000 392.63 0.774 0.777 0.775 Quantity (CY) Table 3-2. Traditional cost indexing approaches.

20 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies 3.6.1 Collection and Cleaning of Historical Bid Data If the intended MCCI is anticipated to be used for long-range forecasting purposes, the STA should make efforts to collect and clean at least 20 years of historical bid data, since that is the suggested lookback period for long-range forecasts. To the maximum extent possible and practical, efforts should be made to collect data from all unit price projects awarded during that period of time. Doing so would facilitate a considerable amount of data to better identify the basket pay items discussed in the next section. All collected data should then be formatted into a tidy format that merges all projects into a single data set. Figure 3-3 shows a screen capture of a small portion of the tidy data set created for the Minnesota Department of Transportation (DOT). This was one of the case studies conducted under NCHRP 10-101 (Rueda-Benavides et al. 2020). “Tidy data sets are easy to manipulate, model and visualize, and have a specific structure: each variable is a column, each observation is a row, and each type of observational unit is a table” (Wickham 2014). There is only one observational unit in this study: pay items included in the collected projects. Thus, there is only one table, with each row referring to a single pay item used in a given project. The columns show all the available information associated with each pay item and its respective contract. Information provided for each pay item on each row includes, but is not limited to, item identification number, item description, awarded quantity, unit of measure- ment, contract identification number, project location (e.g., county, district), and unit price submitted by each bidder. Any efforts to create a tidy data set are greatly rewarded with easier and more expedited data manipulation and processing procedures. Although some of the information included in the tidy data set will not be immediately used for the development of the MCCI, it could be required for future market or financial analysis or to optimize MCCIs by modeling additional cost influencing factors. Data cleaning efforts should also include the identification and removal of outliers, which would also be considerably easier with a tidy data set. “Usually, the presence of an outlier indicates some sort of problem. This can be a case that does not fit the model under study, or an error in measurement” (Cho et al. 2010). Two outlier detection filters strategically selected and applied to serve different purposes are used in this guidebook. The first filter is the modi- fied Z-score method (Iglewicz and Hoaglin 1993), which is applied at the pay item level (i.e., to each row) to identify outliers among the unit prices received for the same item under the same contract. While some of those errors could correspond to typographical mistakes or the mis- interpretation of the scope contained within the unit price, a number of them are the result of unbalanced bids (Rueda-Benavides 2016). “A bid is considered unbalanced if the unit rates are substantially higher or lower, in relation to the estimate and the rates quoted by other bidders” (JICA 2000). There are three main reasons that could lead a contractor to unbalance a bid: 1. To protect its intended profit or fixed cost, which could be partially lost if actual quantities of work are less than the bid quantities; 2. To maximize profits by taking advantage of errors in the quantities of work listed in the solicitation documents; or 3. To inflate prices for early activities to reduce financial costs (the cost of borrowing money). Regardless of the ethical implications usually associated with unbalanced bids, this is a common practice among construction contractors and could mislead STAs when tracking market changes over time.

Figure 3-3. Excerpt of Minnesota DOT’s tidy data.

22 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies Equation 3-4 is used to apply the modified Z-score method. The reason behind the use of this method is that outliers are identified by using the sample median (x̃) and the median absolute deviation, which makes it more suitable for small samples. Since this method is used on bids submitted by different contractors under the same contract, it is applied to relatively small samples. The average number of bids received by some agencies for a single contract is between three and four. Other more commonly used outlier detection methods rely on the sample mean and standard deviation to identify outliers. However, these two statistics are more sensitive to extreme values in small samples, which increases the risk of not detecting outliers that should be discarded (Iglewicz and Hoaglin 1993). On the basis of Iglewicz and Hoaglin’s guidelines, all unit prices with an absolute modified Z-score greater than 3.5 (|Mi| > 3.5) were removed from the data set. 0.6745 MAD Eq. 3-4M X x i i ( )= − where Mi = modified Z score for observation i, MAD = median absolute deviation = {|Xi – median|}, Xi = value of observation i, and x̃ = median of all observations. The second outlier detection approach is used as a secondary filter to remove outliers over- looked by the modified Z-score method. The missed outliers could have resulted from unusual project requirements that may have forced all contractors to bid outside the typical unit price ranges. Since the modified Z-score method compares unit prices for the same item under a given contract, it may find no outliers if all bidders are forced to submit unit prices substantially higher (or lower) than those typically paid by the agency for the same pay item in other projects. The robust regression and outlier removal (ROUT) method (Motulsky and Brown 2006) is a suitable second detection filter. This method combines robust regression and nonlinear regression techniques to identify values that could be significantly apart from the regression equation, similar to those shown in Figures 3-1 and 3-2. The ROUT method can be applied with GraphPad Prims 7, a statistical software equipped with a ROUT function that can be activated during the development of nonlinear regression models. Figure 3-4 shows an example of the output yielded by this software. All red data points are outliers detected by the ROUT method and excluded from the regression analysis. 10,000 20,000 30,000 40,000 50,000 Quantity U ni t P ric e 0 0 200 400 600 800 Figure 3-4. Example of GraphPad Prims 7 output.

Cost Indexing Alternatives 23 3.6.2 Defining Basket of Pay Items for the Multilevel Construction Cost Index When the data collection and cleaning are completed, the process of developing the MCCI continues with the selection of the pay items that will become the foundation of the indexing system. The larger the basket of MCCI pay items, the better. However, not all items are suitable to become part of this process, either because they are not relevant or are not frequently used or because their unit prices are not comparable between projects. The following steps help in the identification of the largest possible group of significant repetitive MCCI pay items: 1. Discard items whose units do not consistently refer to the same set of specifications or amounts work (e.g., each, lump sum), and keep those units that are comparable between projects (e.g., linear feet, cubic yards, tons). Pay items measured on an “each” or “lump sum” basis are usually not comparable between projects; therefore, it is not appropriate to use historical unit prices to track price changes in these items. 2. Identify pay items frequently used by the agency, ideally, but not necessarily, at least once in the first and second halves of each year. Although items used on a semiannual frequency are preferred, that should not be a strict requirement, since it could lead to the dismissal of relevant items whose frequency of use might skip a few periods. MCCI systems are able to handle missing values. 3. Discard items that show no apparent correlation between their unit prices and their respec- tive quantities of work, as that would be a violation of the economies of scale principle, which could mean that unit prices for those items are not comparable between projects. The MCCI methodology has the capacity to consider economies of scale in the calculation of index values. 3.6.3 Configuration and Calculation of the Multilevel Construction Cost Index Historical bid data from the selected basket of pay items is then used to develop several cost indexes organized in a multilevel arrangement like the one shown in Figure 3-5. This figure illustrates the five-level arrangement with 96 cost indexes developed for the Colorado DOT, another of the case studies agencies in NCHRP 10-101. The 96 indexes shown in Figure 3-5 were developed with a basket of 40 pay items. The lowest level in the MCCI is the pay item level, which contains one cost index for each of those 40 pay items. This level has the most specific cost indexes. Each of the 40 cost indexes at this level is only intended to be used on its respective pay item. A bottom-up calculation approach was used, and the Colorado DOT’s indexes at the pay item level were used to calculate the 28 indexes at Sub-Division Level 1, which are less specific. Similarly, the indexes at Sub-Division Level 1 were used to calculate 22 broader indexes at 40 Indexes 28 Indexes 22 Indexes 5 Indexes 1 Index Agency Level Division Level Sub-Division Level 2 Pay Item Levels Bo tto m -U p Ca lc ul ati on Sub-Division Level 1 Figure 3-5. Example of MCCI configuration—Colorado DOT.

24 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies Sub-Division Level 2, and so on, until the top level was reached, where a single general index was calculated at the agency level. All indexes were developed with a semiannual updating frequency, with index values updated twice every year, once on June 30 and again on December 31. A semiannual recalculation approach was selected because an exploratory data analysis anticipated an inconsistent quarterly supply of data for some of the chosen pay items. Likewise, a semiannual updating frequency was preferred over annual updates because shorter periods can better reflect the volatility of the construction market (Molenaar et al. 2013). Even though STAs execute hundreds of contracts per year, it is not possible to ensure that every item in a representative group of cost items will be used during each index period, which could result in missing index values. Unlike traditional CCIs, the multilevel arrangement of MCCIs facilitates a mechanism to avoid missing index values by allowing the use of correspond- ing upper indexes to fill the gaps. Calculations to develop MCCIs are divided into two major steps: (1) calculation of all indexes at the pay item level and (2) bottom-up calculation of indexes at upper levels. 3.6.3.1 Step 1: Calculation of Indexes at the Pay Item Level Since indexes at the pay item level are single-component indexes (calculated with a single pay item), there is no need to deal with the challenges associated with the combination of different types of index inputs. Nevertheless, to effectively track unit price fluctuations at the pay item level, it is necessary to consider the economies of scale principle, which is done by tracking the average movements of the regression curve that defines the quantity–unit price relationship. The following steps summarize the calculation of indexes at the pay item level: Step 1.1 Extract all historical bid data from the tidy data set (after removing outliers) for all selected MCCI pay items. Step 1.2 Identify a 5-year period with sufficient data to effectively model the relationship between quantities and unit prices for each item. The selection of the same 5-year period for all items would simplify the calculation process. Quantity–unit price relationships can be modeled with power regression curves like the one shown in Figure 3-6. Power regression y = 29.338x-0.165 0 5 10 15 20 25 30 35 40 U ni t P ric e ($ /C Y) Quantity (CY) 350,00050,0000 100,000 150,000 200,000 250,000 300,000 Figure 3-6. Minnesota DOT unit price model for common excavation 2008–2012.

Cost Indexing Alternatives 25 curves are commonly used to explain the reduction in construction prices as the quantities of work increase (Rueda-Benavides 2016, Pakalapati 2018, Molenaar et al. 2013). Power regression models are defined by Equation 3-5: unit price quantity Eq. 3-5A B( )= × where A and B are constant values determined for each set of observations to be modeled. The power regression models developed with the selected 5-year periods are hereinafter referred to as “base curves.” Step 1.3 Base curves are assumed to represent average unit prices for their respective items at the midpoint of the selected five-year period. It would be June 30, 2010, for the curve shown in Figure 3-6 (midpoint between January 2008 and December 2012). Thus, the price variation at each indexing period is calculated as the average deviation from the base curve. There could be indexing periods before and after the selected 5-year period. For example, Figure 3-7 shows the average deviation between the same base curve shown in Figure 3-6, in June 2010, and recorded unit prices for the same item during the first index- ing period of 1999 (P1 = January to June 1999). The calculation of the average deviation in Figure 3-7 was performed with Equation 3-6. This equation was applied to each indexing period for each pay item. AD 100% Eq. 3-6 1n P A Q A Q ij ijk i ijk B i ijk Bk n i i ∑= − × ×= where ADij = average deviation for item i in index period j, Pijk = unit price for observation k for item i in index period j, Qijk = quantity for observation k for item i in index period j, Ai and Bi = constant values for base curve for item i, and n = number of observations for item i at index period j. Step 1.4 Use calculated average deviations to define index values for each item at each indexing period. Starting the index for each item with a value of 100 at the first indexing period 0 2 4 6 8 10 12 14 16 U ni t P ric e ($ /C Y) Quantity (CY) Unit Prices 1999-P1 Base Curve 2010-P1 50,0000 100,000 150,000 200,000 250,000 300,000 Average change: –36% Figure 3-7. Example of base curve and calculation of price fluctuations.

26 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies in the available data would facilitate a future development of scope-based cost indexes. In the Minnesota DOT case study, the first indexing period was P1-1999. Thus, this period was assigned a value of 100 for all pay items. This value was set at the end of that period, June 30, 1999. The average deviation shown in Figure 3-7 indicates that P1-1999 for that item should be 36% lower than P1-2010. Therefore, the index value for P1-2010 would be 156.25 [(100/(1 – 0.36)]. The rest of the index values for all pay items can now be calculated by using their respective P1-2010 index value and the average deviations measured at each index period. Step 1.5 All four steps detailed above would produce a cost index for each of the MCCI pay items by using the available historical bid data. After that, the agency needs to establish a system to constantly update all indexes at the end of each indexing period by repeating the same calculation process. 3.6.3.2 Step 2: Bottom-Up Calculation of Indexes at Upper Levels The second major step in the development of an MCCI refers to bottom-up calculations to define indexes at the upper levels. To calculate the Colorado DOT indexes at Sub-Division Level 1 (see Figure 3-5), indexes at the pay item level were grouped on the basis of similar characteristics and aggregated to produce a single overall cost index per group. It means that, for the Colorado DOT’s MCCI, 28 groups were formed out of the 40 pay item cost indexes, which resulted in the 28 indexes at Sub-Division Level 1. In a similar way, these 28 indexes were divided into 22 groups to produce the 22 indexes at Sub-Division Level 2, and so on until the calculation of a single agency level index with the five indexes from the division level. Indexes at all levels are grouped according to the coding scheme used by each STA to classify its pay items. Pay item identification numbers could communicate information about the scope, materials, and activities associated with each item. Thus, pay items with similar identi- fication numbers can be assumed to be closely related. STAs’ pay item coding schemes, which usually align with their standard specification books, can also be used to label each of the cost indexes in the MCCI. Table 3-3 shows how some of the indexes were grouped and labeled for the Colorado DOT’s MCCI. This table only shows identification labels for indexes across the bottom-up pathways of the 13 pay item indexes under Division 2. Divisions 3 to 6 also have downward ramifications, but those are not shown in Table 3-3. In moving from the pay item level to the agency level, the number of digits used to identify the MCCI indexes is reduced, which means that now the index represents a broader scope of work; that is, the degree of detail of an index is given by its MCCI level, with the scope becoming increasingly broader at upper levels. For example, cost indexes 203-00010 and 203-00060 in Table 3-3 only represent these two specific pay items. Bid data from these two indexes were then used to calculate Cost Index 203-000 at Sub-Division Level 1, which is intended to represent all items that start with 203-000. In the same way, Index 203 represents all pay items that start with 203, and Index 2 represents all pay items starting with 2. Division Level indexes in Colorado DOT’s MCCI align with actual construction divisions from its standard specification book. All the construction divisions in the Colorado DOT Standard Specification Book are listed below (Colorado DOT 2019). Thus, in the case of the Colorado DOT, Index 2 represents the overall market behavior of earthwork activities, comprising all pay items starting with 2. • Division 2: Earthwork, • Division 3: Bases, • Division 4: Pavements, • Division 5: Structures, and • Division 6: Miscellaneous construction.

Cost Indexing Alternatives 27 MCCIs developed for different agencies would have different configurations from the one shown in Table 3-3, but the bottom-up calculation process and upward ramifications would follow the same general principles. Each STA’s MCCI configuration should be adjusted to its unique pay item classification system. A complete version of Table 3-3 as well as examples of MCCI configurations for two other agencies can be found in Appendix B of the NCHRP Web-Only Document 283: Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting for State Transportation Agencies (Rueda-Benavides et al. 2020). The bottom-up process for producing higher-level indexes is just a weighted average calcula- tion of the grouped items at the lower levels, as shown in Figure 3-8. This figure shows how two of the Colorado DOT’s pay item indexes (203-00010 and 203-00060) are combined to generate Pay Item Level Sub-Division Level 1 Sub-Division Level 2 Division Level Agency Level 202-00035 202-000 202 2 1 202-00210 202-002 202-00220 202-00240 202-00250 203-00010 203-000 203203-00060 203-00100 203-001 206-00000 206-000 206 206-00065 206-00100 206-001 206-00360 206-003 207-00205 207-002 207 — — — 3 — — — 4 — — — 5 — — — 6 Table 3-3. Colorado DOT’s MCCI levels and configuration. Note: Icomi = combined index value at index period i, I ji = index value for item j at index period i, and Wji = weight for item j at index period i. Figure 3-8. MCCI bottom-up calculation approach.

28 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies their corresponding index at Sub-Division Level 1 (230-000). Weights for this calculation are proportional to the dollar amounts awarded on the items under consideration during each indexing period within the group. It means that during Index Period 1, 203-00010 contributed to 25% of the combined awarded amount and 203-00060 contributed to the remaining 75%. 3.6.4 Development of Scope-Based Construction Cost Indexes This section presents the process for generating scope-based CCIs from an MCCI at both the project and the program levels. This ability gives MCCIs the flexibility to adapt to different scopes of work. 3.6.4.1 Project-Specific Cost Indexes The process of generating a project-specific CCI is illustrated with the asphalt paving project shown in Table 3-4. This is a real project awarded by Minnesota DOT. In summary, a project-specific cost index was developed through the combination of individual relevant MCCI indexes (one MCCI index for each anticipated pay item). Each pay item was paired with the MCCI index that best represented its scope. Item identification numbers were used to find matching indexes. Item Number Description Units Weight (%) MCCI Index 2021501/00010 Mobilization LS 2.3781 2 2051501/00010 Maintenance and restoration of haul roads LS 0.0001 2 2104509/00055 Remove twisted end treatment EACH 0.1203 2104 2104521/00220 Salvage guard rail-plate beam LF 0.1077 2104521/00220 2104601/01011 Haul salvaged material LS 0.0595 2104 2105501/00010 Common excavation CY 0.0773 2105501/00010 2221501/00010 Aggregate shouldering Class 1 TON 1.9326 2 2221604/00010 Aggregate shouldering SY 0.1231 2 2232501/00040 Mill bituminous surface (1.5 inches) SY 0.3325 2232501/00040 2232602/00010 Milled rumble strips EACH 0.3266 2232602/00010 2357606/00010 Bituminous material for shoulder tack GAL 0.0195 2357606/00010 2360501/22200 Type SP 12.5 wearing course mixture (2,b) TON 82.7320 2360501/22200 2411507/00060 Concrete end post EACH 1.5658 2411 2540602/00150 Mail box support EACH 0.1359 2 2554501/00001 Traffic Barrier Design Special LF 0.6992 2554501 2554501/02007 Traffic Barrier Design B8307 LF 0.3703 2554501/02007 2554501/02038 Traffic Barrier Design B8338 LF 0.6268 2554501/02038 2554521/00020 Anchorage assembly-plate beam EACH 0.1364 2554 2554523/00028 End treatment-tangent terminal EACH 0.2610 2554 2563601/00010 Traffic control LS 4.1618 2 2580603/00010 Interim pavement marking LF 0.5916 2580603/00010 2582501/03008 Pavement message (stop ahead) epoxy EACH 0.1567 258 2582502/41104 4-inch solid line white epoxy LF 2.4801 258 2582502/41524 24-inch stop line white epoxy LF 0.0266 258 2582502/42104 4-inch solid line yellow epoxy LF 0.3017 258 2582502/42204 4-inch broken line yellow epoxy LF 0.2770 258 TOTAL 100.00 Table 3-4. Minnesota DOT sample of asphalt paving project.

Cost Indexing Alternatives 29 The final project-specific CCI is just the weighted average of the selected MCCI indexes. The weighted average calculation is similar to the one shown in Figure 3-8 for the bottom-up calculation process. However, this time weights were calculated for each item and not for each indexing period. The weight for each pay item is proportional to its contribution to the total engineer’s estimate. Actual awarded prices cannot be used to calculate weights because they will only be known after the project has been awarded. Engineer’s estimates are calculated on the basis of current prices observed at the moment of developing the project-specific CCI. It should be noted that, at this point in the process, the relative relevance of each item is more important than predicting the actual prices to be submitted by the successful contractor at the letting date. Table 3-4 shows the weight and MCCI index selected for each item. The latter refers to the index identification labels in the last column of the table [see the configuration of the Minnesota DOT’s MCCI in Appendix B of NCHRP Web-Only Document 283 (Rueda-Benavides et al. 2020)]. Those labels are equivalent to the labels shown in Table 3-3 for the Colorado DOT. For example, an item such as 2580603/00010, interim pavement marking, (Table 3-4) has its own index at the pay item level. On the other hand, item 2582502/41104, 4-inch solid line white epoxy, had to move up to the MCCI division level to find its best-matching index. It should be noted that cost indexes at the Minnesota DOT’s division level are identified with three-digit labels (e.g., 258). Likewise, the identification number for all Minnesota DOT pay items always starts with 2; therefore, that is the single-digit label for the Minnesota DOT’s agency level index. Some indexes in Table 3-4 are used to represent more than one item. For example, MCCI Index 258 represents five items. Table 3-5 and Figure 3-9 show an example of a project-specific CCI generated for the asphalt paving project in Table 3-4. All project- and program-specific CCIs developed with the proposed methodology were set to start with an index value of 100. Therefore, all the selected indexes in the last column of Table 3-4 should start with an index value of 100 in order to produce the index shown in Table 3-5. 3.6.4.2 Program-Specific Cost Indexes The first step in the creation of program-specific cost indexes is to understand the compo- sition of the scope of work associated with the program. Some programs, such as bridge or pavement management programs, are aimed at planning construction activities for specific types of work. In those cases, the program-specific cost index could be a project-specific index for a carefully selected sample project intended to represent the scope of the intended program. For Date Index Date Index Date Index Date Index P1-1999 100.00 P1-2004 98.33 P1-2009 167.73 P1-2014 206.80 P2-1999 95.56 P2-2004 107.63 P2-2009 154.21 P2-2014 234.74 P1-2000 104.65 P1-2005 111.53 P1-2010 180.67 P1-2015 232.07 P2-2000 102.32 P2-2005 129.98 P2-2010 211.10 P2-2015 208.51 P1-2001 103.47 P1-2006 137.55 P1-2011 176.54 P1-2016 250.10 P2-2001 119.04 P2- 2006 160.08 P2-2011 135.62 P2-2016 174.95 P1-2002 114.94 P1-2007 146.38 P1-2012 202.39 P1-2017 223.16 P2-2002 100.77 P2-2007 170.48 P2-2012 168.01 P2-2017 236.04 P1-2003 100.13 P1-2008 158.46 P1-2013 205.13 P1-2018 245.06 P2-2003 104.46 P2-2008 162.91 P2-2013 224.80 P2-2018 278.82 Table 3-5. Example of project-specific CCI for the Minnesota DOT’s asphalt paving project.

30 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies example, the asphalt paving project in Table 3-4 was initially identified as a good representative of the Minnesota DOT’s typical asphalt paving activities. Thus, a planning program focused only on asphalt paving could use the index shown in Table 3-5 to determine a program-specific inflation rate. The process for developing program-specific indexes for programs that involve various types of work has a few additional steps but is still a simple four-step process: 1. Identify the different types of work contained in the program. 2. Approximate the percentage of the total program that corresponds to each type of work. These percentages will be used as weights in Step 4. 3. Identify a sample project that reasonably represents each type of work and develop project- specific CCIs for those projects. This step may not always be required, since the agency could create and maintain a library of generic cost indexes for typical types of work. 4. Using the weights defined at Step 2, combine all project-specific indexes through a weighted average calculation. This weighted average calculation is also similar to the one shown in Figure 3-8, but this time it is used to combine multiple project-specific indexes into a single program-specific CCI. The simplicity of this methodology also facilitates sensitivity analyses with which to evaluate multiple scenarios or to quantify the risk of having drastic changes in the anticipated distribution of work within the program. For example, Figure 3-10 shows three possible program-specific indexes that could be developed by the Minnesota DOT for a statewide pavement program that combines asphalt paving and concrete paving activities. The three program-specific indexes in Figure 3-10 correspond to three different distributions of the amounts of work associated with each pavement material (50%–50%; 30%–70%; and 70%–30%). These hybrid indexes are the result of a weighted average calculation between an asphalt paving and a concrete paving CCI. The asphalt paving CCI is the same project-specific CCI shown in Figure 3-9, which is assumed to represent all asphalt paving activities. Similarly, the concrete paving CCI in Figure 3-10 is a project-specific CCI for a representative concrete paving project. 50 100 150 200 250 300 6/ 30 /1 99 9 6/ 29 /2 00 0 6/ 29 /2 00 1 6/ 29 /2 00 2 6/ 29 /2 00 4 6/ 29 /2 00 5 6/ 30 /2 00 6 6/ 30 /2 00 3 6/ 30 /2 00 7 6/ 30 /2 00 9 6/ 30 /2 01 0 6/ 30 /2 01 1 6/ 30 /2 01 3 6/ 30 /2 01 4 6/ 30 /2 01 5 6/ 30 /2 01 6 6/ 30 /2 01 7 6/ 30 /2 01 8 6/ 29 /2 00 8 6/ 29 /2 01 2 In de x Va lu e Date Figure 3-9. Example of project-specific CCI for the Minnesota DOT’s asphalt paving project.

Cost Indexing Alternatives 31 3.6.5 Regional Considerations and Price Inputs for Multilevel Construction Cost Index One of the objectives of NCHRP 10-101 was testing the hypothesis that different geographic regions within a state could be affected by different inflationary trends, so that different inflation rates should be applied to different regions. The study confirmed that hypothesis and found that different MCCI versions would better represent local construction markets for different regions within the case study agencies. All MCCI versions developed for the Colorado DOT followed the same configuration shown in Table 3-3 and Figure 3-5. The difference between versions lies in their geographic scope (statewide or regional) and their type of price input: awarded unit prices (submitted by the selected contractors); average unit prices per project; median unit prices per project; and all unit prices received from both successful and unsuccessful contractors. Table 3-6 shows the 20 different MCCI versions developed and evaluated for the Colorado DOT, and Figure 3-11 shows the Colorado DOT’s four geographic regions. The different MCCI versions in Table 3-6 correspond to additional partitions to the available data in an attempt to analyze price volatility at the regional level and to determine the most suit- able index calculation input. For example, the Colorado DOT’s “statewide MCCI with awarded unit prices” was developed with historical data from all available projects across the state and using only unit prices submitted by the awarded contractors. On the other hand, the Colorado DOT’s “northeast MCCI with awarded unit prices” was also built with low-bid proposals, but only with bid data from the northeast region in Colorado. Therefore, this MCCI is only applicable to this region. Similar geographic classifications and MCCI versions were developed and evaluated for the other case study agencies in NCHRP 10-101 (Rueda-Benavides et al. 2020). Case study results showed that statewide MCCIs tend to outperform regional MCCIs, which could be explained by 80 100 120 140 160 180 200 220 240 260 280 6/ 30 /1 99 9 6/ 29 /2 00 0 6/ 29 /2 00 1 6/ 29 /2 00 2 6/ 30 /2 00 3 6/ 29 /2 00 4 6/ 29 /2 00 5 6/ 30 /2 00 6 6/ 30 /2 00 7 6/ 29 /2 00 8 6/ 30 /2 00 9 6/ 30 /2 01 0 6/ 30 /2 01 1 6/ 29 /2 01 2 6/ 30 /2 01 3 6/ 30 /2 01 4 6/ 30 /2 01 5 6/ 30 /2 01 6 6/ 30 /2 01 7 6/ 30 /2 01 8 In de x V al ue Date Aphalt Paving CCI Concrete Paving CCI Program-Specific CCI (50% AP; 50% CP) Program-Specific CCI (30% AP; 70% CP) Program-Specific CCI (70% AP; 30% CP) Figure 3-10. Example of program-specific CCI—Minnesota DOT Paving Program.

32 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies Figure 3-11. Colorado DOT geographic regions. Geographic Classification Description Statewide MCCIs Statewide MCCI with awarded unit prices Statewide MCCI with average unit prices per project Statewide MCCI with median of unit prices per project Statewide MCCI with all unit prices Regional MCCIs Region Description Northwest Northwest MCCI with awarded unit prices Northwest MCCI with average unit prices per project Northwest MCCI with median of unit prices per project Northwest MCCI with all unit prices Northeast Northeast MCCI with awarded unit prices Northeast MCCI with average unit prices per project Northeast MCCI with median of unit prices per project Northeast MCCI with all unit prices Southwest Southwest MCCI with awarded unit prices Southwest MCCI with average unit prices per project Southwest MCCI with median of unit prices per project Southwest MCCI with all unit prices Southeast Southeast MCCI with awarded unit prices Southeast MCCI with average unit prices per project Southeast MCCI with median of unit prices per project Southeast MCCI with all unit prices Table 3-6. Classification of the Colorado DOT’s multilevel construction cost indexes.

Cost Indexing Alternatives 33 the fact that statewide indexes are developed with larger data sets that allow for a more effective representation of construction market changes. The only region that showed an overall better performance of regional indexes was Colorado’s northeast region. This could be because this region is the most densely populated in Colorado; it leads the Colorado DOT in spending large portions of its annual construction budget in that part of the state and in making its regional historical bid database sufficiently large to produce reliable cost indexes. Although regional MCCIs were not the best option for most regions, it was found that different statewide MCCI versions were more suitable for different regions within the same state. This finding still allowed the study to conclude that construction activities in different geographic regions could be affected by different inflation patterns. In other words, it would be reasonable to consider the use of different inflation rates for different regions across the state. Those different regional inflation rates would be the result of using a different construction cost index in each region. Thus, as part of the MCCI development process, this guidebook suggests the development of and evaluation of various MCCI versions, mimicking the case study methodology in NCHRP 10-101 (Rueda-Benavides et al. 2020). To optimize implementation efforts, STAs could evaluate only statewide MCCIs, considering regional versions only for those parts of the state that consume considerable portions of the construction budget. Implementa- tion efforts could be further optimized by considering only MCCIs developed with awarded unit prices and with all the unit prices received by the agencies. The most suitable MCCIs for 10 of the 11 regions evaluated in the case studies were built with those two price inputs. After it has developed all MCCI versions under consideration, an STA can proceed to perform a comparative suitability analysis by using the protocol presented in the next section. This protocol helps in identifying the most suitable MCCI alternative for each region. It can also be used to assess and compare the performance of traditional cost indexing alternatives. In fact, the case study methodology in NCHRP 10-101 included the application of this protocol to a large group of alternatives, including various MCCIs and a number of traditional CCIs (Rueda-Benavides et al. 2020). 3.7 Identification of Suitable Construction Cost Index NCHRP 10-101 designed a protocol to assess the degree of suitability of available cost indexing alternatives. The proposed protocol is not aimed at finding the best possible CCI (Rueda-Benavides et al. 2020). It is instead intended to facilitate a comparative analysis to identify the most suitable alternative among a set of available options, even if all options are traditional CCIs affected by the limitations discussed in Section 3.5. This means that the protocol can still be used by STAs that decide not to implement MCCIs. It should be noted that the proposed protocol for the assessment of cost indexes is not intended to evaluate their cost forecasting capabilities. Those capabilities are ultimately provided by the forecasting methodologies discussed in the next chapter. The protocol is instead intended to identify the indexing alternative that most closely resembles the observed behavior of the construction market, which should be the most suitable source of historical pricing data for the intended cost forecasting process. Figure 3-12 illustrates the proposed comparative suitability analysis protocol. Each step in this protocol is discussed in the following sections. 3.7.1 Representative Pay Items and Analysis Period The pay items used for the comparative analysis of cost indexing alternatives do not neces- sarily need to include all the pay items used for the development of MCCIs. The analysis could involve only the most relevant pay items—ideally, a group of pay items representing the most

34 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies relevant construction division. Table 3-7 shows the items selected for the Minnesota DOT’s case study. These items were selected to represent the three main construction activities performed by the Minnesota DOT: asphalt paving, concrete paving, and earthwork. Likewise, the analysis period used for the identification of the most suitable cost indexing alternative does not need to be the same 20-year period suggested for the development of MCCIs. The analysis period for the proposed protocol should be long enough to include a good amount of cost indexing data, but not too long, so that the indexing alternatives are still evaluated on their suitability to the current construction industry. If a given cost index shows the best effectiveness at tracking price fluctuations over the past 20 years but a different one is found to be more effective over the past 10 years, preference should be given to the latter. Thus, the guidebook suggests an analysis period of about 10 years. 3.7.2 Bid Data Point Clouds The bid data point clouds are created with actual awarded unit prices recorded for each selected pay item along the analysis period. This results in a set of separate three-dimensional clouds, one per selected pay item. The three parameters that give the location of each point in the cloud are (1) letting data, (2) bid quantity, and (3) recorded awarded unit price. 3.7.3 Base Power Regression Curves and Base Unit Price Estimates The base power regression curves used in the comparative analysis of cost indexing alter- natives are similar to those used to develop the MCCI in Section 3.6.3, but they are built with bid data from projects awarded during the first year of the analysis period. In the case of the Identify a set of representative pay items and define the analysis period Create a bid data point cloud for each selected pay item Develop a power regression curve for each selected pay item for the first year of the analysis period Use power regression curves to estimate the unit price for each bid quantity advertised along the analysis period Adjust estimated unit prices to their respective bid dates using each of the cost indexing alternatives under consideration Compare adjusted estimated unit prices and actual awarded prices with a weighted MAPE value for each indexing alternative Identify the cost indexing alternative with the lowest adjusted MAPE Figure 3-12. Cost indexing comparative suitability analysis protocol. Item ID Description Relative Weight (%) 2106507/00010 Excavation—common 17 2301507/00010 Structural concrete 33 2360509/23200 Type SP 12.5 wearing course mixture (3,B) 21 2360509/23300 Type SP 12.5 wearing course mixture (3,C) 19 2360509/24500 Type SP 12.5 wearing course mixture (4,E) 10 Table 3-7. Selected relevant items for Minnesota DOT comparison analysis.

Cost Indexing Alternatives 35 Minnesota DOT case study, one power regression curve was developed for each of the items listed in Table 3-7. The analysis period for that case study started in January 2007 and ended in December 2018; therefore, base power regression curves were created with historical bid data from 2007. Those curves are then used to estimate base unit prices for all bid quantities awarded for each of the selected pay items throughout the analysis period. Since the regression curves were devel- oped with data from the first year of the analysis period, all unit price estimates produced with those curves are assumed to yield average unit prices in the middle of that year. Thus, the Minnesota DOT’s base power regression curve for structural concrete (second item in Table 3-7) was used to estimate a unit price for a quantity awarded in 2018, but the output corresponded to the average price for that amount of structural concrete in mid-2007. 3.7.4 Index-Based Data Point Clouds All base unit price estimates from the previous step are then adjusted to their respective letting dates, creating another data point cloud for each pay item called the index-based data point cloud. Each cost indexing alternative under consideration is used to create a separate set of index-based data point clouds. Each point in the index-based data point clouds has a cor- responding point in the original bid data point clouds created with the actual historical bid data. Equations 3-7 to 3-9 define the location for each point in its respective index-based data point cloud. Equations 3-7 and 3-8 show that the letting data and quantity for each observation (each recorded awarded unit price) remain unchanged for all cost indexing alternatives. Those are given by their actual letting dates and awarded quantities. Equation 3-9 shows the calculation of the based unit price estimate described in the previous section and the subsequent adjustment with each indexing option. Eq. 3-7 Eq. 3-8 Eq. 3-9 0 L L Q Q P A Q I I kij ki kij ki kij i ki B jt j i( ) = = = × × where Lkij = location in letting date axis for observation k for item i with index j, Lki = actual letting date for observation k, Qkij = location in quantity axis for observation k for item i with index j, Qki = actual awarded quantity for observation k, Pkij = location in unit price axis for observation k for item i with index j, Ai and Bi = constant values for base curve for item i, Ijt = index value for index j at letting date, and Ij0 = base index value for index j. 3.7.5 Average Distance Between Bid Data and Index-Based Data Point Clouds and Identification of the Most Suitable Cost Indexing Alternative The next step is the calculation of the average distance between corresponding points for the cost indexing option. The shorter the average distance, the larger the overlap between the bid

36 Improving Mid-Term, Intermediate, and Long-Range Cost Forecasting: Guidebook for State Transportation Agencies data and the index-based data point clouds and the more suitable the cost indexing alternative. It should be noted that corresponding points have the same letting date and awarded quantity. Thus, the average distance between them is only the difference between the actual awarded unit price and the index-based unit price. Average distances between the bid data and the index-based data point clouds were quan- tified in the form of mean absolute percentage error (MAPE) values: one MAPE value per pay item per indexing alternative. MAPE values are commonly used in the cost estimating literature to measure and compare accuracy between cost estimating approaches (Gransberg et al. 2015), but in this study, those values were aimed at indicating the degree of overlap between data point clouds for each selected pay item. For instance, for the Minnesota DOT case study, five MAPE values (one per pay item listed in Table 3-7) were calculated for each cost indexing alternative under consideration. Equation 3-10 was used to calculate the MAPE for value under each cost index. MAPE 100% Eq. 3-10 1n P P P ij aki ekij aki k n∑= −= where MAPEij = mean absolute percentage error for item i with index j, Paki = awarded unit price for observation k for item i, Pekij = index-based unit price for observation k for item i with index j, and n = number of observations for item i. The MAPE values associated with each cost indexing approach are then combined into a single overall MAPE that takes into consideration the relative weight of each pay item shown in Table 3-7 for the Minnesota DOT’s case study. The result of this combination is a weighted MAPE, which is just the weighted average of all pay item MAPE values, as shown in Equation 3-12. The relative weight for each item is calculated with Equation 3-11. Eq. 3-11 _MAPE MAPE Eq. 3-12 1 W T T W W i ai a j iji n i∑ = = ×= where Wi = relative weight for item i, Tai = total amount ($) awarded for item i during analysis period, Ta = total amount ($) awarded for all items i during analysis period, MAPEij = MAPE for item i with index j, W_MAPEj = weighted MAPE for index j, and n = number of items. After the steps explained above are repeated to generate a weighted MAPE for each cost indexing alternative in each region, the most suitable alternative for each region is then assumed to be the one with the lowest-weighted MAPE.