Policy Research Report: Risk-Based Budgeting Review and Recommendations

Transcription

1 Nebraska Transportation Center Report SPR-P1 (15) M51 Final Report Policy Research Report: Risk-Based Budgeting Review and Recommendations John E. Anderson, Ph.D. Baird Family Professor of Economics Department of Economics University of Nebraska-Lincoln Laurence Rilett, Ph.D, PE Director, Nebraska Transportation Center Professor Department of Civil Engineering University of Nebraska-Lincoln 216 Nebraska Transportation Center 262 WHIT 22 Vine Street Lincoln, NE (42) This report was funded in part through grant[s] from the Federal Highway Administration [and Federal Transit Administration], U.S. Department of Transportation. The views and opinions of the authors [or agency] expressed herein do not necessarily state or reflect those of the U.S. Department of Transportation.

2 Policy Research Report: Risk-Based Budgeting Review and Recommendations John E. Anderson, Ph.D. Baird Family Professor of Economics Department of Economics University of Nebraska-Lincoln Laurence Rilett, Ph.D, PE Director, Nebraska Transportation Center Professor Department of Civil Engineering University of Nebraska-Lincoln A Report on Research Sponsored by Nebraska Department of Roads University of Nebraska-Lincoln March 216

3 Technical Report Documentation Page 1. Report No. SPR-P1 (15) M51 2. Government Accession No. 3. Recipient's Catalog No. 4. Title and Subtitle Policy Research Report: Risk-Based Budgeting Review and Recommendations 5. Report Date March Performing Organization Code 7. Author(s) John E. Anderson and Laurence Rilett 9. Performing Organization Name and Address University of Nebraska-Lincoln Nebraska Transportation Center 22 Vine St. 262 Whittier Research Center PO Box Lincoln, NE Sponsoring Agency Name and Address Nebraska Department of Roads 15 Hwy. 2 Lincoln, NE Performing Organization Report No Work Unit No. (TRAIS) 11. Contract or Grant No. 13. Type of Report and Period Covered May 215 February Sponsoring Agency Code 15. Supplementary Notes 16. Abstract This report summarizes our analysis of NDoR historic budget data with an eye toward making practical suggestions for managing budget risks. We first report on our analysis of the statistical properties of revenue and expenditure series, identifying the major sources of budget risk. Then, we suggest a budget risk management approach that employs Monte Carlo simulations using readily available software and illustrate the use of that approach for key NDoR expenditures. Finally, we provide additional recommendations for managing budget risk. 17. Key Words 18. Distribution Statement 19. Security Classif. (of this report) Unclassified 2. Security Classif. (of this page) Unclassified 21. No. of Pages Price ii

4 Table of Contents Disclaimer... iv Executive Summary... viii Chapter 1 Introduction and Background Deterministic vs. Stochastic Budgets Analyzing Sources of Budget Risk An Approach for Dealing with Budget Risk... 4 Chapter 2 Data Analysis: Graphs and Descriptive Statistics Revenue Series Expenditure Series Seasonal Patterns of Expenditure Lettings Analysis Unit Root Tests Stochastic Budgeting using Monte Carlo Simulations Some Caveats... 5 Chapter 3 Business Practices Review Question One: Question Two: Question Three: Question Four: Question Five: Question Six: Chapter 4 Budgeting Recommendations References... 7 Appendix A Augmented Dickey-Fuller (ADF) Unit Root Tests Appendix B Crystal Ball Simulations Full Details... 1 Appendix C Autoregressive Moving Average (ARIMA) Models Appendix D Project Cost Analysis iii

5 List of Figures Figure 2.1 Diesel net revenue series...8 Figure 2.2 Gasoline net revenue series...9 Figure 2.3 Total fuel taxes revenue series...9 Figure 2.4 Total registrations revenue series...1 Figure 2.5 Total federal receipts series...1 Figure 2.6 Grand total NDOR receipts series...11 Figure 2.7 Comparison of selected revenue series...11 Figure 2.8 Administration expenditure series...17 Figure 2.9 Support services expenditure series...17 Figure 2.1 Business technology services expenditure series...18 Figure 2.11 Payroll clearing expenditure series...18 Figure 2.12 Capital facilities expenditure series...19 Figure 2.13 Highway maintenance expenditure series...19 Figure 2.14 System preservation expenditure series...2 Figure 2.15 Operations expenditure series...2 Figure 2.16 Snow and ice control expenditure series...21 Figure 2.17 Unusual and disaster operations expenditure series...21 Figure 2.18 Equipment operations expenditure series...22 Figure 2.19 Indirect charges expenditure series...22 Figure 2.2 Highway construction expenditure series...23 Figure 2.21 Preliminary engineering expenditure series...23 Figure 2.22 Right-of-way expenditure series...24 Figure 2.23 Construction expenditure series...24 Figure 2.24 Construction engineering expenditure series...25 Figure 2.25 Construction related expense expenditure series...25 Figure 2.26 Construction related expense-overhead series...26 Figure 2.27 Category 81, Preliminary Engineering, Figure 2.28 Category 815, Right-of-Way, Figure 2.29 Category 82, Construction, Figure 2.3 Category 83, Construction Engineering, Figure 2.31 Lettings forecast by year, Figure 2.32 Lettings analysis by month, Figure 2.33 Shocks to trend-stationary and unit root processes [source: Nielsen (25)]...41 Figure 2.34 Monte Carlo simulation for the sum of expenditure categories Figure 2.35 Total budget simulation sensitivity analysis...45 Figure 2.36 Expenditure category 8 simulation sensitivity analysis...47 Figure 2.37 Expenditure category 8 PDF forecast simulation (95% certainty)...47 Figure 2.38 Expenditure category 8 CDF forecast simulation (95% certainty)...48 Figure 2.39 Expenditure category 8 PDF forecast simulation (99% certainty)...48 Figure 2.4 Expenditure category 8 CDF forecast simulation (99% certainty)...49 Figure 2.41 Category 753 snow and ice control simulation...49 Figure 3.1 Bridge project cumulative cost...53 Figure 3.2 New road construction project cumulative cost...54 Figure 3.3 4R maintenance resurfacing project cumulative cost...54 iv

6 Figure 3.4 Comparison of seasonal cost shares with seasonal factor codes...55 Figure 3.5 Comparison of cumulative seasonal cost shares with cumulative seasonal factor codes...55 Figure 3.6 Estimated work phase 5 (construction engineering) share of award by project...63 Figure 3.7 Estimated work phase 5 (construction engineering) share of award by project; actual, fitted, and residual...63 v

7 List of Tables Table 2.1a Revenue series descriptive statistics...12 Table 2.1b Revenue series descriptive statistics, continued...13 Table 2.2a Expenditure series descriptive statistics...27 Table 2.2b Expenditure series descriptive statistics, continued...28 Table 2.2c Expenditure series descriptive statistics, continued...29 Table 2.2d Expenditure series descriptive statistics, continued...3 Table 2.3 Correlations among key expenditure categories...31 Table 2.4 Correlations among highway construction subcategories...31 Table 2.5 Unit root tests--summary...4 Table 2.6 Fitted probability distributions for key budget categories...44 Table 3.1 Project cost and budget contingency simulations...61 vi

8 Disclaimer The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the U.S. Department of Transportation s University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. vii

9 Executive Summary This report summarizes our analysis of NDoR historic budget data with an eye toward making practical suggestions for managing budget risks. We first report on our analysis of the statistical properties of revenue and expenditure series, identifying the major sources of budget risk. Then, we suggest a budget risk management approach that employs Monte Carlo simulations using readily available software and illustrate the use of that approach for key NDoR expenditures. Finally, we provide additional recommendations for managing budget risk. Highlights of the report: Where are the budget risks? o Data analysis of NDoR revenue and expenditure series reveals the important statistical properties of all series, including the degree of variability in each series and correlations among the series. Graphical representations are provided to illustrate the variability of each series over time. Detailed descriptive statistics are presented revealing the properties of the probability distributions for each series. o Analysis of expenditure series indicates that a few series are mean-preserving, where shocks have transitory effects but no permanent effects. Expenditure series: 7, 75, 753, 754, 755, 81, 815 o But, many of the revenue and expenditure series have unit roots, where transitory shocks cause permanent effects in the series. All of the revenue series have this property viii

10 Expenditure series with this property: 5, 6, 642, 655, 751, 752, 756, 8, 82, 83, 85, What can be done to Deal with the Budget Risks? o A budget estimation tool for incorporating risk management into budget planning is presented and applied to NDoR historic data for both the sum of expenditure categories 5-85 and for the components of category 8 (highway construction). Monte Carlo simulations for key monthly expenditure series are presented to illustrate how this tool can be used to manage risk. Implementation of this tool is demonstrated using readily available software: Oracle s Crystal Ball. A three-step process is described by which budget analysts can implement a risk-based budgeting approach. o Additional budget management ideas and perspectives are presented. What is a prudent budget cash-flow contingency rate? o Based on analysis of NDoR project-level cost data provided, our recommendation is to reduce the current ten percent cash-flow budget contingency practice to five percent. ix

11 Chapter 1 Introduction and Background This policy report has been prepared at the request of the Nebraska Department of Roads (NDoR), whose budget is subject to various random shocks that make budget implementation challenging. The objective of this study is to analyze the various stochastic risks faced by NDoR in both revenues and expenditures and to recommend methods of budget management in the face of those risks. To do that, we carry out extensive analysis of NDoR data to identify the key sources of budget risk and characterize the data series according to their risk properties. We then propose ways of dealing with that risk, focusing on the use of Monte Carlo simulations for critical budget categories. Those simulations provide critical information on the likelihood of positive expenditure shocks which can then be used to inform budget plans incorporating riskbased assessments. This analysis is based on data provided by NDoR, which included detailed revenue and expenditure historical series in the form of monthly data. Revenue data cover the period CY 1995 through 215 (April). Expenditure data cover the period FY 2 through FY 215. Letting data were provided for FY 22 through FY214. Project-specific data were provided for 24 completed projects. For budget background, the 214 NDoR budget for total system costs was $757 million, of which $565 million was for construction and $149 was for maintenance. Overhead expenses of $34 million accounted for the remainder of the system costs, representing 6 percent of combined construction and maintenance costs. Demonstrating concern for the accuracy of project cost forecasts, and the challenges of budgeting in the face of uncertainty, the 214 NDoR Annual Report provides a table (p.6) that reports the accuracy of forecasts for one-year program costs. The NDoR stated goal is to make

12 sure project cost forecasts are within 5 percent of actual costs. The data provided for the period reveal a maximum project underestimate of $31.6 million in 29, and a maximum overestimate of $19,9 million in Deterministic vs. Stochastic Budgets The usual approach to budget development and implementation assumes that all quantities involved on both the revenue and expenditure sides of the budget are known with a reasonable degree of certainty. So, the budget is developed and implemented from a deterministic point of view. When essential elements of the budget are subject to risk, however, we are in a situation where the budget becomes stochastic. For context, we can begin with a conventional deterministic budget with no risk associated with any of the revenue sources or expenditure categories. Suppose that at time t there are j revenue sources denoted R(t), and k expenditure categories denoted E(t). Total revenues minus total expenditures in year t cannot be negative so the budget balance equation is given by, j k i=1 R i (t) i=1 E i (t). (1) In this budget environment there is no risk and therefore no risk-related difficulty in assuring budget balance. If some of the revenue sources and expenditure categories are subject to risk, however, the budget balance equation must be modified. 1 Denoting revenue risk terms as ρ i and 1 We generally use the term risk in this report, but sometimes use the term uncertainty to mean the same thing. Knight (1921) originally made a distinction between risk and uncertainty, using risk to refer to the situation where one is able to calculate probabilities on the basis of some objective classification of situations, whereas uncertainty 2

13 expenditure risk terms as ε i, including them in an additive fashion for expositional purposes, the budget balance equation becomes, j k i=1 (R i (t) + ρ i ) i=1 (E i (t) + ε i ). (2) Each error term may follow a distinct probability distribution and the error terms may be correlated with one another. That is, ρ i follows a probability density function (PDF) with mean zero and variance σ 2 i, while ε i follows another PDF, and their joint distribution has a non-zero covariance. As a consequence, budgeting in this context is more complex due to the risks involved. An unusually large negative revenue error or positive expenditure error can cause an unexpected budget deficit. On the other hand, an unexpected revenue windfall or cost reduction can create a situation where a budget surplus must be spent rapidly at the end of a fiscal year. The literature on stochastic budget approaches to planning and implementing government budgets is limited, but several useful studies are available and inform the approach taken in this report. Chou (29) presents an expert systems approach to estimating the cost of transportation projects. Chou, Yang, and Chong (29) provides an overview of the use of probabilistic simulations for engineering projects. Dillon, Pate-Cornell and Guikema (25) review the use of budget reserves to manage complex project budgets. Iyer and Jha (24) illustrate approaches to identifying specific factors affecting the cost of projects. Muthukrishnan, Pal, and Svitkina (27) apply a stochastic approach to budget optimization in the context of search-based is used to refer to the situation where no objective classification can be made. Hirshleifer and Riley (1992) contend that Knight s distinction has proven to be, a sterile one, so we use the terms interchangeably. 3

14 advertising. Yang (25) shows how to conduct simulations with proper regard for correlated cost elements. Having reviewed this literature, we incorporate all of these elements in the stochastic budget approach we outline below. 1.2 Analyzing Sources of Budget Risk In order to analyze the sources of budget risk for NDoR, our statistical approach implement the following steps. First, we analyze the statistical properties of key revenue and expenditure line items (time series) in the NDoR budget using historic budget data provided to us. We compute relevant descriptive statistics including mean, median, mode, maximum, minimum, standard deviation, coefficient of variation, skewness, and kurtosis for each series. We test for normality and estimate the best-fit probability distribution for each series. We also test for the presence of unit roots in each series to distinguish series that are mean-reverting after a shock from those where transitory shocks have permanent effects. 1.2 An Approach for Dealing with Budget Risk Elkjaer (2) addresses the fundamental problem of project budgeting in the context of complex environments in which there are economic uncertainties. His approach combines stochastic simulation using Monte Carlo methods with elements of the successive principle. 2 While the Stochastic Budget Simulation (SBS) method presented in Elkjaer (2) involves use of a proprietary simulation model, the underlying steps implemented in that model can be followed using publicly available software. 2 The successive principle is attributed to Lichtenberg (1989) and summarized in Elkjaer (2) as, a tool for project management and decision-makers who require the inclusion of not only regular cost items, but also of all the relevant fuzzy factors affecting their work. The steps required to implement the successive principle involve identifying sources of uncertainty, estimation of statistical properties of each budget element, and critical examination of a priority list of sources of budget risk. 4

15 In the remainder of this report we will follow the five essential steps of the SBS method: 1. Identify and group all relevant issues that have an influence on the project 2. Quantify the conditional cost effects of the relevant issues identified in (1). Generate a group of generic risks or overall influences having impacts on all cost categories. 3. Quantify the cost items and generic risks that influence the cost uncertainties. 4. Calculate total project cost and the local uncertainty for each budget item. A key issue in estimation is to avoid stochastic dependencies among budget items. 5. Present results in a manner usable to inform stakeholders about potential economic outcomes. 5

16 Chapter 2 Data Analysis: Graphs and Descriptive Statistics In this section we begin with graphical illustrations of key revenue and expenditure series along with descriptive statistics for each of the series. Figures 2.1 through 2.7 illustrate the revenue series and Figures 2.8 through 2.26 illustrate the expenditure series. Tables 2.1 and 2.2 report measures of central tendency, including the mean and median. Indicators of range and variation reported include the minimum, maximum, standard deviation, and coefficient of variation (standard deviation divided by the mean). Measures of the shape of each PDF are also included. Skewness measures the symmetry of a distribution (a perfectly symmetric distribution has a zero skewness statistic; an asymmetric distribution with a long right-hand tail has a larger skewness statistic while a distribution with a long left-hand tail has large negative skewness statistic). Kurtosis measures the degree to which a distribution is peaked or flat relative to a normal distribution (a Gaussian, or normal, distribution has kurtosis of zero; a flatter distribution has a negative kurtosis and a more peaked distribution has a positive kurtosis). We also report a Jarque-Bera (JB) test for each distribution which is a goodness-of-fit test indicating whether the distribution has skewness and kurtosis that match a normal distribution. The JB test statistic is used to jointly test whether skewness and kurtosis match a normal distribution (i.e. skewness measure of zero and excess kurtosis measure of zero). Any deviation from zero skewness and/or zero kurtosis causes the JB statistic to increase. Along with the JB test statistic we report the associated probability value where a prob-value near zero (conventionally.1,.5, or.1) indicates that we can reject the null hypothesis of a normal distribution. That is, if the distribution is normal, there is a very small probability that we would obtain such a large JB statistic. Hence, we reject the null hypothesis of a normal distribution. 6

17 2.1 Revenue Series Figures 2.1 through 2.7 illustrate the revenue series over the time period Diesel net revenue is illustrated in Figure 2.1 which reveals a structural shift in Since that time, the series fluctuates around a flat trend. Gasoline net revenue is illustrated in Figure A notable feature to observe in that figure is the change in the series variability that took place in approximately 21. Since that time, the degree of variability in the series is more moderate. Once again, the series appears to fluctuate around a flat or even slightly falling trend since Figure 2.3 combines the fuel tax sources with the graph appearing very similar to the gasoline revenue in Figure 2.2, reflecting the dominance of gasoline tax revenue in the total fuel tax revenue. The coefficients of variation for the revenue series indicate that the greatest variability occurs in the federal receipts series (CV =.71), illustrated in Figure 2.5. Federal receipts are the largest single source of revenue for NDoR, with a mean value of nearly $2 million over the time period of analysis, compared to the mean for the grand total of NDoR receipts of approximately $5 million. While the mean level of federal receipts is approximately $2 million per month, the peaks illustrated in that figure are in the range of $5 to $65 million, reflecting a high degree of variability. That pattern is not surprising given the dramatic changes in federal funding related to the ARRA stimulus in recent years, but it is evident that there have been other episodes and idiosyncratic factors in previous years with peaks in the same high range (1996, 2, and 22). 3 It should be noted that the July 1, 29 change in the gasoline tax rate structure (reducing the fixed and variable components and adding a wholesale ad valorem component of 5%) did not have an appreciable effect on NDoR revenues. The total fuel tax and the NDoR revenue distribution were unaffected, at least initially. Source: Chronology of Nebraska Motor Fuel Tax Rates, 1993 thru Current. 7

18 Registrations revenue is also highly variable, as illustrated in Figure 2.4, with a CV of.45, but that series has clear and predictable seasonality contributing to the variability. Skewness measures for the revenue series reveal that the fuel tax series are skewed leftward, while the registrations, federal receipts, and grand total NDoR receipts series are skewed rightward. The revenue series all have probability distributions that are more peaked than the normal distribution, as indicated by the kurtosis measures. The JB statistics indicate that we can reject the null hypothesis of a normal distribution for all of the revenue series except for diesel-net revenue. 8,, Diesel Net 7,, 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.1 Diesel net revenue series 8

19 Gasoline Net 18,, 16,, 14,, 12,, 1,, 8,, 6,, Figure 2.2 Gasoline net revenue series TOTAL FUEL TAXES 26,, 24,, 22,, 2,, 18,, 16,, 14,, 12,, 1,, Figure 2.3 Total fuel taxes revenue series 9

20 TOTAL REGISTRATIONS 8,, 7,, 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.4 Total registrations revenue series TOTAL FEDERAL RECEIPTS 7,, 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.5 Total federal receipts series 1

21 GRAND TOTAL NDOR RECEIPTS 11,, 1,, 9,, 8,, 7,, 6,, 5,, 4,, 3,, 2,, Figure 2.6 Grand total NDOR receipts series 36,, 32,, 28,, 24,, 2,, 16,, 12,, 8,, 4,, DIESELNET GASNET TOTSTATERECEIPTS Figure 2.7 Comparison of selected revenue series 11

22 Table 2.1a Revenue series descriptive statistics Diesel-Net Gasoline-Net Total Fuel Taxes Total Registrations Mean 5,357,631 12,442,595 18,14,97 2,67,166 Median 5,387,553 12,674,135 18,324,837 2,377,578 Maximum 7,741,455 16,817,753 24,597,62 7,241,774 Minimum 1,789,55 6,528,38 11,14,63 819,982 Std. Dev. 1,63,586 1,85,348 2,663,392 1,197,559 Skewness Kurtosis Coefficient of Variation Jarque-Bera Probability <.1 Augmented Dickey- Do not reject unit Do not reject unit Do not reject unit Do not reject unit Fuller (ADF) test root root root root Observations

23 Table 2.1b Revenue series descriptive statistics, continued Total Federal Receipts Grand Total NDOR Receipts Mean 19,66,638 5,49,169 Median 16,97,31 47,91,924 Maximum 66,277,15 11,421,68 Minimum 25,224,34 Std. Dev. 13,892,259 16,328,521 Skewness.91.7 Kurtosis Coefficient of Variation Jarque-Bera Probability <.1 <.1 Augmented Dickey- Fuller (ADF) test Do not reject unit root Do not reject unit root Observations

24 2.2 Expenditure Series Figures 2.8 through 2.26 illustrate the expenditure series over the time period The largest expenditure categories are category 8 (highway construction) with a mean of nearly $35 million per month and sub-category 82 (construction) with a mean of approximately $29 million. The third largest category is 75 (highway maintenance) with a mean of $9.6 million per month. The estimated coefficients of variation reveal that far and away the most variable expenditure series is category 655 (payroll clearing). This series high CV is as much a reflection of the small mean as it is of a high standard deviation, however. Hence, it is not as concerning as several of the other expenditure series that comprise a larger share of the NDoR budget. Other categories with large CVs (exceeding one) include category 6 (support services), category 642 (business technology services), category 7 (capital services), category 753 (snow and ice control), and category 755 (equipment operations). It should be noted, however, that much of the variation in some of these series is simply a reflection of the seasonal nature of NDoR activity. Figure 2.16 illustrates the category 753 snow and ice control expenditures. That figure reveals a sequence of three winters in succession from 27-8 through 29-1 with unusually high expenditures which contribute to the large CV for that category. Whereas the usual peak expenditures were in the range of $4 to $5 million per month, during those years the peaks were in the range of $8 to $14 million per month. Starting with the winter of 21-11, the expenditure pattern appears to be more typical (i.e. similar to winters prior to 27). Unusual and disaster operations expenses are illustrated in Figure Here again, unusual conditions in the years 21 through 212 are indicated in the graph, reflecting factors 14

25 such as the rain and extreme flooding in 211. While the peaks illustrated for those years are dramatic, the dollar amounts involved are relatively small (approximately $.5 million) as a share of the NDoR budget. For the important highway construction category (8), Figure 2.2 reveals a high degree of variability. Peaks are in the range of $7 to $8 million per month, whereas troughs are in the range of $1 million. Similarly, Figure 2.23 illustrates the important category 82 construction expenditures. Here again, peaks are in the range of $5 to $7 million per month, whereas troughs are less than $1 million. Of course, it is important to recognize that NDoR has direct influence on these series, given its ability to alter the timing of projects. These expenditure series are not entirely exogenous. Our estimated JB statistics indicate that for all of the expenditure series reported we can reject the null hypothesis of a normal distribution. The skewness statistics are positive for all of the expenditure series indicating that the distributions are asymmetric and have long right-hand tails. Hence, we know that these expenditure series are subject to positive shocks causing expenditures to sometimes be much larger. The two series with the highest skewness measures are expenditure categories 754 (unusual and disaster operations) and 815 (right-of-way). The kurtosis statistics are also all positive indicating that these distributions are all more peaked than a normal distribution. The two series with the highest kurtosis measures are, once again, expenditure categories 754 (unusual and disaster operations) and 815 (right-of-way). Table 2.3 reports the pairwise correlations among key expenditure categories in the NDoR budget. These correlation coefficients reflect the strength of linear association between budget items. The first thing to notice is that most of the correlations are positive, indicating that when one budget item rises or falls, so does the other. There are direct positive relationships 15

26 between most budget items. The size of the correlations is also important to note. Most of the correlations are modest, with values less than.5, reflecting relatively weak linear associations between variables. The strongest correlations (greater than.5) are between 75 (Highway maintenance) and 5 (Administration) and 85 (Construction related expense). These budget series are positively correlated with one another to a substantial degree. Three of the correlation coefficients are negative, indicating an inverse relationship. Category 6 (Support services) is negatively correlated with 5 (Administration) and 7 (Capital facilities). Category 7 (Capital facilities) is also negatively correlated with 85 (Construction related expense). These budget items move in opposite directions as one rises the other falls, and vice versa. These estimated correlation coefficients are used in the Monte Carlo simulations that follow in order to account for co-movements among the budget variables. Table 2.4 reports correlations among the highway construction subcategories. These expenditure components are all positively correlated with one another, with the strongest correlation being that between construction and construction engineering. 16

27 5 Administration 2,4, 2,, 1,6, 1,2, 8, 4, Figure 2.8 Administration expenditure series 6 Supportive Services 12,, 1,, 8,, 6,, 4,, 2,, -2,, -4,, Figure 2.9 Support services expenditure series 17

28 642 Business Technology Services 4,, 3,, 2,, 1,, -1,, -2,, -3,, Figure 2.1 Business technology services expenditure series 655 Payroll Clearing 3,, 2,, 1,, -1,, -2,, -3,, Figure 2.11 Payroll clearing expenditure series 18

29 7 Capital Facilities 2,, 1,6, 1,2, 8, 4, -4, Figure 2.12 Capital facilities expenditure series 75 Highway Maintenance 2,, 16,, 12,, 8,, 4,, Figure 2.13 Highway maintenance expenditure series 19

30 751 System Preservation 16,, 14,, 12,, 1,, 8,, 6,, 4,, 2,, -2,, Figure 2.14 System preservation expenditure series 752 Operations 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.15 Operations expenditure series 2

31 753 Snow and Ice Control 14,, 12,, 1,, 8,, 6,, 4,, 2,, -2,, Figure 2.16 Snow and ice control expenditure series 754 Unusual & Disaster Oper 9, 8, 7, 6, 5, 4, 3, 2, 1, Figure 2.17 Unusual and disaster operations expenditure series 21

32 755 Equipment Operations 6,, 4,, 2,, -2,, -4,, -6,, Figure 2.18 Equipment operations expenditure series 756 Indirect Charges 4,, 3,5, 3,, 2,5, 2,, 1,5, 1,, 5, Figure 2.19 Indirect charges expenditure series 22

33 8 Highway Construction 8,, 7,, 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.2 Highway construction expenditure series 81 Preliminary Engineering 8,, 7,, 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.21 Preliminary engineering expenditure series 23

34 815 Right-Of-Way 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.22 Right-of-way expenditure series 82 Construction 8,, 7,, 6,, 5,, 4,, 3,, 2,, 1,, Figure 2.23 Construction expenditure series 24

35 83 Construction Engineering 4,, 3,5, 3,, 2,5, 2,, 1,5, 1,, 5, Figure 2.24 Construction engineering expenditure series 85 Construction Related Expense 24,, 2,, 16,, 12,, 8,, 4,, -4,, Figure 2.25 Construction related expense expenditure series 25

36 85-85 Construction Related Expense - Overhead 5,, 4,, 3,, 2,, 1,, -1,, -2,, -3,, Figure 2.26 Construction related expense-overhead series 26

37 Table 2.2a Expenditure series descriptive statistics Administration Support Business Payroll Capital Services Technology Clearing Facilities Services Mean 1,31,926 1,771,6 494,516 42,8 282,683 Median 1,259,33 1,697,26-53, ,87 Maximum 2,161,842 1,99,75 3,612,76 2,634,556 1,642,23 Minimum 239,48-2,99,8-2,81,285-2,158,65-125,116 Std. Dev. 257,35 1,996, , ,672 32,756 Skewness Kurtosis Coefficient of Variation Jarque-Bera Probability <.1 <.1 <.1 <.1 <.1 Augmented Dickey- Fuller (ADF) test Do not reject unit root Do not reject unit root Do not reject unit root Do not reject unit root Reject unit root Observations

38 Table 2.2b Expenditure series descriptive statistics, continued 75 Highway Maintenance 751 System Preservation 752 Operations 753 Snow and Ice Control 754 Unusual and Disaster Operations Mean 9,627,393 2,894,398 2,846,92 1,831, ,95 Median 9,37,823 1,778,992 2,719,68 921,345 17,553 Maximum 19,36,71 13,899,18 5,531,768 13,782, ,687 Minimum 2,14, ,77 934, ,39 8,521 Std. Dev. 2,862,652 2,664, ,476 2,176, ,5 Skewness Kurtosis Coefficient of Variation Jarque-Bera Probability <.1 <.1.3 <.1 <.1 Augmented Dickey- Fuller (ADF) test Reject unit root Do not reject unit root Do not reject unit root Reject unit root Reject unit root Observations

39 Table 2.2c Expenditure series descriptive statistics, continued 755 Equipment Operations 756 Indirect Charges 8 Highway Construction 81 Preliminary Engineering 815 Right-of-Way Mean 477,545 1,473,177 34,822,813 2,812,483 1,31,285 Median 437,56 1,43,759 32,72,77 2,72, ,898 Maximum 5,869,644 3,547,99 78,73,569 6,975,553 5,586,445 Minimum -5,5, ,594 8,346,487 1,92,37 171,62 Std. Dev. 1,28, ,673 17,793,59 926, ,344 Skewness Kurtosis Coefficient of Variation Jarque-Bera Probability <.1 <.1 <.1 <.1 <.1 Augmented Dickey-Fuller (ADF) test Reject unit root Do not reject unit root Do not reject unit root Reject unit root Reject unit root Observations

40 Table 2.2d Expenditure series descriptive statistics, continued 82 Construction 83 Construction Engineering 85 Construction Related Expense 85_85 Construction Related Expense-- Overhead Mean 28,936,75 2,42,657 5,566,264 1,567,341 Median 27,58,743 2,6,16 3,971,12 1,527,773 Maximum 72,863,217 3,777,557 21,22,632 4,718,9 Minimum 3,522,752 25,781-1,39,173-2,81,352 Std. Dev. 17,212,9 661,144 3,786, ,551 Skewness Kurtosis Coefficient of Variation Jarque-Bera Probability <.1.4 <.1 <.1 Augmented Dickey- Do not reject unit Do not reject unit Do not reject unit Do not reject unit Fuller (ADF) test root root root root Observations

41 Table 2.3 Correlations among key expenditure categories Budget Category Administration Support Capital Highway Highway Construction Services Facilities Maintenance Construction Related Expense 5 Administration 1. 6 Support Services Capital Facilities Highway Maintenance Highway Construction Construction Related Expense Table 2.4 Correlations among highway construction subcategories Budget Category Preliminary Engineering 81 Preliminary Engineering 1. Right-of-Way Construction Construction Engineering 815 Right-Of-Way Construction Construction Engineering

42 2.3 Seasonal Patterns of Expenditure The nature of the road construction and maintenance activities carried out by NDoR are inherently seasonal and weather-dependent. Consequently, statistical measures of variability in the data may simply reflect the seasonality of NDoR activities. There is also seasonality introduced by the annual budget cycle. Each fiscal year begins in July and ends in June, superimposing a fiscal seasonal expenditure cycle on top of the seasonal weather cycle. In order to examine seasonal patterns of expenditure, from both potential sources, Figures 2.27 through 2.3 illustrate the monthly expenditure patterns for sub-categories of budget category 8. These figures graph monthly expenditure data by calendar year. Preliminary engineering expenditures have clearly peaked in the spring (April and May) and fall (October) for each of the last two years graphed, 213 and 214. Right-of-way expenditures have typically been clustered in the first have of the calendar year (January through June) most years. A notable exception is 214 with a large spike in September. For the largest expenditure category, construction, the seasonal patterns are quite consistent across the years. Expenditures are low during the first quarter (January through March) and rise rapidly in the second quarter (April through June). The third quarter of the year (July through September) sees the highest level of expenditure, which carries over into the first part of the fourth quarter (October), but then falls off dramatically at the end of the year (November and December). Construction engineering generally has peaks in the second quarter (April through June), and again in the fourth quarter (October). When viewed against the backdrop of the NDoR fiscal year, which runs from July through June, there is some evidence of expenditure bunching at the end of the fiscal year (April- May-June) in the preliminary engineering, right-of-way, and construction engineering patters. 32

43 There may also be end-of-fiscal-year spending in the larger construction (82) category, but evidence of that is clouded by the normal seasonal uptick in construction activity. 6,, 5,, 4,, 3,, 2,, 1,, Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Figure 2.27 Category 81, Preliminary Engineering,

44 2,5, 2,, 1,5, 1,, 5, Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Figure 2.28 Category 815, Right-of-Way, ,, 7,, 6,, 5,, 4,, 3,, 2,, 1,, Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Figure 2.29 Category 82, Construction,

45 4,, 3,5, 3,, 2,5, 2,, 1,5, 1,, 5, Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec Figure 2.3 Category 83, Construction Engineering, Lettings Analysis In order to obtain a view at the project level, we provide analysis of the lettings data provided by NDoR in this section. Using the aggregate annual lettings data over the period , a time series model was developed and its forecast is illustrated in Figure The blue forecast line is bracketed by the red dashed confidence interval lines (+/- two standard errors). Over this time period total annual lettings have risen from approximately $269 million to $451 million. There is a noticeable dip in the pattern during due to the recession. 35

46 6,, 5,, 4,, 3,, 2,, 1,, LETTINGSF ± 2 S.E. Figure 2.31 Lettings forecast by year, Further insight can be gained by examining project-level letting data. Figure 2.32 graphs the letting data by month over the period for which data are available. Lettings appear to be highly idiosyncratic, with little evidence of seasonal patterns. There is something of a fall-winter pattern evident with lettings increasing in the fall of the year, into the early months of the following calendar year. There is only weak evidence of an occasional May-June effect. If data were available enabling tracking of individual projects from letting through completion, further analysis could be conducted in order to determine the extent to which project budgets have implicit cushions built into them. The aggregate of those over-estimates can result in substantial funds remaining at the end of a fiscal year. Without more specific project-level data, however, such analysis is not feasible. 36

47 1-Feb 1-Mar 1-Apr 1-May 1-Jun 1-Jul 1-Aug 1-Sep 1-Oct 1-Nov 1-Dec 1-Jan 1-Feb 1-Mar 1-Apr 1-May 1-Jun 1-Jul 1-Aug 1-Sep 1-Oct 1-Nov 1-Dec 1-Jan 1-Feb 1-Mar 1-Apr 1-May 1-Jun 1-Jul 1-Aug 1-Sep 1-Oct 1-Nov 1-Dec 1-Jan 1-Feb 1-Mar 1-Apr 1-May 1-Jun 14,,. 12,,. 1,,. 8,,. 6,,. 4,,. 2,,. - Figure 2.32 Lettings analysis by month,

48 2.5 Unit Root Tests As with any time series data, it is necessary to check for unit roots in order to ascertain whether the series are mean-reverting or subject to temporary shocks that cause permanent changes. Parzen (1962) classifies stochastic processes as either stationary or evolutionary. A stationary process is one whose probability density function (PDF) remains the same over time, indicating that the stochastic process is not changing. For a series that is stationary, shocks have transitory effects, but not permanent effects. Figure 2.33 illustrates in the top panel a shock to a trend-stationary process. The blue line shock dissipates and the series reverts to the previous red-line trend. The process is said to be mean-reverting. On the other hand, an evolutionary process is one which is not stationary. A unit root is a characteristic of a stochastic time series model where a variable evolves over time. The series is non-stationary. It has a stochastic trend and shocks have permanent effects. Figure 2.33 illustrates a shock to a unit root process in the lower panel where the blue-line shock clearly has a permanent effect. For example, a series that follows a first-order autoregressive model AR(1), y t = a 1 y t 1 + ε t, (3) has a unit root if a 1 = 1. That is, if the value of the variable today is last period s value plus an error term. In such a process, the variance of y t diverges to infinity over time: j=t VAR(y t ) = j=1 σ 2 = t σ 2. (4) If a unit root is found in any of the data series analyzed in this report, there is a stochastic trend in the series which makes any regression models using the usual ordinary least squares 38

49 (OLS) estimator unreliable in terms of hypothesis testing due to a non-normal distribution. An AR(1) process with a unit root can be first-differenced, and the process y t is stationary. Appendix A1 reports the details of the Augmented Dickey-Fuller (ADF) unit root tests conducted for each series. In each case the null hypothesis is that a unit root exists. Table 2.5 below provides a summary of the unit root test results with expenditure category names. Tests indicate that we can reject the null hypothesis of a unit root processes for some expenditure series, but not for others. Series for which we can reject the null hypothesis of a unit root include: 7, 75, 753, 754, 755, 81, and 815. Hence, we have strong evidence that there are no unit roots in these series. These are mean-reverting series where shocks have transitory effects but no permanent effects. The top panel of Figure 2.1 illustrates this type of series. Those series for which we cannot reject the hypothesis of a unit root include: 5, 6, 642, 655, 751, 752, 756, 8, 82, 83, 85, and 85_85. For these series, transitory shocks cause permanent effects. The lower panel of Figure 2.33 illustrates this type of series. Any regression analysis using these series may be unreliable as a result of the unit root properties of the series. Differencing is required in order to obtain reliable results. NDoR analysts conducting time series analysis of these data should take care to know the unit root properties of the data series and conduct analysis using differencing where needed. On the revenue side, the ADF tests indicate that the null hypothesis of a unit root cannot be rejected for any of the series. Hence, we have evidence that there are unit roots in these series. These are not mean-reverting series, so shocks have permanent effects. The lower panel of Figure 2.33 illustrates this type of series. After first differencing, all of the revenue series become stationary. 39

50 Table 2.5 presents a summary of unit root tests for revenue and expenditure series, identifying those series which are mean-reverting and those for which transitory shocks cause permanent effects. Table 2.5 Unit root tests--summary Series for which ADF test indicates rejection of unit root Series for which ADF test indicates no rejection of unit root These are mean-reverting series where shocks For these series, transitory shocks cause permanent have transitory effects but no permanent effects effects Expenditure Series 7 Capital facilities 2 5 Administration 75 Highway maintenance 6 Support services 753 Snow and ice control Business technology services Unusual and disaster operations Payroll clearing 755 Equipment operations System preservation 3 81 Preliminary engineering 752 Operations Right-of-way Indirect charges 8 Highway construction 82 Construction 83 Construction engineering 85 Construction related expense 85_85 Construction related expense-overhead 9 Revenue Series Diesel-net Gasoline-net Total fuel taxes Total registrations Total federal receipts Grand total NDoR receipts Notes provided by NDoR: (1) redistribution of funds ended in 211, (2) appropriations by legislature ended in 29, with subsequent expenditures coming from previous funds allocated (3) normal fluctuations in highway surface preservation expenses, (4) includes expenses such as striping with increasing paint cost, (5) weather related expenses and the 29-1 winter from hell, (6) 211 extreme rain and flooding, (7) new equipment and repair, (8) fluctuates based on major projects, particularly for expanded roadways, (9) business policy change after 29. 4

51 Figure 2.33 Shocks to trend-stationary and unit root processes [source: Nielsen (25)] 41

52 2.6 Stochastic Budgeting using Monte Carlo Simulations In this section we describe the use of a Monte Carlo simulation approach that can be used in budget analysis and planning. 4 The objective is to simulate the likely distribution of expenditures given a specified risk level in order to inform budget implementation. Monte Carlo simulations generate draws from probability distributions to simulate the likely outcome of a system being analyzed. In our application, use draws from various probability distributions associated with each budget category to simulate a total budget outcome. We also use Monte Carlo simulations for the key expenditure series in budget category 8 to simulate the likely costs of highway construction. In order to conduct Monte Carlo simulations for NDoR budget data, we used the Oracle Crystal Ball software. 5 This software works in conjunction with Microsoft Excel spreadsheets in order to implement Monte Carlo simulations. We use the Crystal Ball software to draw 1, repeated estimates and generate probability distributions for the budget totals being simulated. In order to illustrate the value of Monte Carlo simulations for assessing budget risks, our first simulation presented below is for the combination of NDoR expenditure categories 5 through 8 using monthly data over the period Monte Carlo simulations require specification of probability distributions for each of the budget category series and the correlations among those series. Table 2.6 reports the fitted probability distributions for key budget categories, including the monthly data for budget 4 Kriz (22) indicates that Monte Carlo simulation is infrequently used in the field of public finance, but it is, one of the core methods used to assess optimal strategies in the face of uncertainty It should be noted that the sum of expenditure categories 5-8 does not replicate the full NDoR budget. Rather, the sum of these main budget categories is used in simulations to be suggestive of the approximate monthly budget totals. 42

53 categories 5 through 85 used in this Monte Carlo simulation. The correlations among budget categories reported in Table 2.3 were also used in generating the simulations. Figure 2.34 illustrates the simulated expenditure totals with their associated frequencies. Given the historic nature of the data series, the range of simulated expenditure totals is very broad. Monthly totals range from less than $2 million to more than $1 million. For practical analysis of likely current budget totals, the simulated range would need to be narrowed. A slider tool along the horizontal axis in the probability distribution graph generated by Crystal Ball permits adjustment of the confidence level associated with the simulations. By adjusting the confidence level, the simulation provides insight on the sensitivity of the total expenditures to sub-categories of expenditure. Figure 2.34 Monte Carlo simulation for the sum of expenditure categories

54 Table 2.6 Fitted probability distributions for key budget categories Budget Category Revenues: Diesel net Gasoline net Total fuel taxes Total registrations Total federal receipts Grand total NDoR receipts Fitted Probability Distribution Beta Weibull Weibull Lognormal Gamma* Beta Expenditures: 5 Administration Logistic 6 Supportive services Lognormal* 7 Capital facilities Lognormal* 75 Highway maintenance Lognormal 8 Highway construction Beta 85 Construction related expense Lognormal* Expenditure Category 8 Detail: 81 Preliminary engineering Logistic 815 Right-of-way Gamma 82 Construction Triangular 83 Construction engineering Lognormal 85 Construction related expense Not enough observations Note: An asterisk * indicates that Crystal Ball is not able to find a best fit distribution for the series. In such cases, Crystal Ball still provides a list of distributions, sorted by the Anderson-Darling (AD) statistics which measure the goodness of fit for each distribution. The smaller the AD statistics, the better the distributional fit. In each such case we selected the distribution with the lowest AD statistic. 44

55 Note: E195=Category 8, D195=Category 75, F195=Category 85, A195=Category 5, B195=Category 6, C195=Category 7 Figure 2.35 Total budget simulation sensitivity analysis Figure 2.35 illustrates the sensitivity analysis conducted as part of the Monte Carlo simulation, identifying the expenditure categories most responsible for variations in the simulated totals. The sensitivity analysis indicates that most of the forecast risk (59%) is related to expenditure category 8 (highway construction). Expenditure categories 75 (highway maintenance) and 85 (construction related expense) also contribute another 3% of the sensitivity. Given the sensitivity results reported above, additional analysis of category 8 and its subcomponents is required and is presented below. Figure 2.36 illustrates the sensitivity analysis for categories 81 (preliminary engineering), 815 (right-of-way), 82 (construction), and 83 (construction engineering). Based 45

56 on the sensitivity analysis shown in the figure it is clear that expenditure categories 82 (construction) and 83 (construction engineering) account for nearly all of the forecast risk. Figure 2.37 illustrates the 95% forecast for the sum of category 8 expenditures. This figure presents the probability distribution function (PDF) for expenditures and the forecast shows that expenditures are expected to fall below $68.2 million 95 percent of the time. In only five percent of the simulations does the sum exceed that amount. Figure 2.38 presents similar information using the cumulative probability distribution function (CDF), which indicates that expenditures fall below $69.7 million 95 percent of the time. Figure 2.39 illustrates the 99% forecast for the sum of category 8 expenditures using the fitted PDF. This forecast indicates that the sum of expenditures in this category falls below $76.2 million 99 percent of the time. In only one percent of the simulated cases does the expenditure exceed that amount. Figure 2.4 illustrates the CDF simulation, which indicates that expenditures fall below $78.3 million 99 percent of the time. Hence, for planning purposes budget analysts using this simulation tool can specify the level of risk tolerance and then simulate the maximum expenditure associated with that level of risk and plan the budget accordingly. With precise estimates of likely expenditures, given the amount of risk the budget planner is willing to take, a budget can be constructed that incorporates informed risk-taking. 46

57 Note: B197= Category 81, C197=Category 815, D197=Category 82, E197=Category 83 Figure 2.36 Expenditure category 8 simulation sensitivity analysis Figure 2.37 Expenditure category 8 PDF forecast simulation (95% certainty) 47

58 Figure 2.38 Expenditure category 8 CDF forecast simulation (95% certainty) Figure 2.39 Expenditure category 8 PDF forecast simulation (99% certainty) 48

59 Figure 2.4 Expenditure category 8 CDF forecast simulation (99% certainty) Figure 2.41 Category 753 snow and ice control simulation 49

60 Consider another example of an expenditure category that has been problematic in recent years. In this case we illustrate an alternative use of the Monte Carlo simulation, asking the question: What if we budget for an episode with an $8 million expenditure? Is that likely to be sufficient, with a reasonable probability? Figure 2.41 illustrates the 95 percent simulation for category 753 snow and ice control. This category of expenditure proved to be highly variable during the period 27-8 through For this simulation, suppose that we plan on a maximum expenditure of $8 million and ask the question: How likely is it that the actual expenditure is that amount or less? The probability density function simulation indicates that snow and ice control expenditures fall below $8 million 96 percent of the time. Hence, budget planning that includes a winter with a cost episode of that amount will be sufficient in all but 4 percent of the cases. 2.7 Some Caveats There are several caveats to keep in mind when using this type of data analysis. First, the analysis in this report has been conducted in nominal terms, or in current dollars. That means inflation is incorporated in the data. Since most budgeting is done in nominal terms the use of nominal data here should be familiar. But, as expenditures in particular are subject to inflationary increases, NDoR analysts will have to apply their own specific cost adjustments over time. Neither the consumer price index (CPI) nor the GDP deflator are really appropriate for NDoR expenditure categories. The CPI measures inflation related to consumer goods and services as measured by the Bureau of Labor Statistics (BLS). The GDP deflator measures inflation for all of the elements of GDP, including consumption, investment, government spending, and net exports. More specific estimates of cost increases are needed for the purposes of NDoR estimation if inflation adjustments are required. 5

61 Second, the Monte Carlo simulations presented above use historic NDoR data, which means that forecasts reflect historic experience. The simulations presented above are constrained in the sense that they are conditional on past experience. Future events may be out of the realm of previous experience. Out-of-sample forecasts should be considered with caution. 51

62 Chapter 3 Business Practices Review In this section we respond to six specific questions posed by the Controller Division Finance Administrator of the Nebraska Department of Roads (NDoR). Answers given here are based on analysis of data provided on 24 individual projects concluded in 214. Each question is listed below followed by responses that are informed by analysis of the project-level data provided. Data were provided for 24 projects selected by NDoR. The majority of projects (17 of the 24) are 4R maintenance resurfacing projects. Three projects are bridge projects. Another three projects are 4R maintenance restore and rehabilitation projects. The final project is a reconstruction project with added capacity. It should be noted that the authors of this review were not involved in the selection of projects used in this analysis. Consequently, results reported here may be subject to small sample and/or selection bias. 3.1 Question One: Should different payout and seasonal factors be established for various types of construction projects? For example, major interstate reconstruction, asphalt overlay, new major bridge, etc. Yes, analysis of project data indicate that projects of different types have markedly different cost trajectories over time. Payout factors should depend on the type of project. To illustrate the difference, consider Figures which plot the cumulative construction costs for three projects: bridge replacement with no added capacity, new roadway construction, and 4R maintenance resurfacing, respectively. (Payout trajectories have been graphed for all 24 projects and will be provided in the final supplemental report.) The cumulative cost trajectories clearly differ, with the bridge project having a nearly linear trajectory while the road construction 52

63 trajectory is concave and the 4R maintenance resurfacing project has a logistic curve pattern. The horizontal red line in each figure records the award amount. Payout factors should be developed that reflect not only the length of the project (as they currently do) but also depend on the type of project. Further analysis of cost data for a large number of projects of each type can reveal typical patterns to inform development of payout factors specific to each project type. The seasonal factor codes used for work phase 4 (construction) appear to correlate well with the project data provided. Figure 3.4 illustrates the monthly cost shares based on the data and the seasonal factor codes. While there are monthly variances, the cumulative pattern illustrated in Figure 3.5 reveals that over the calendar year the actual cost shares track well with the seasonal factor codes. In the aggregate (for all 24 projects) the seasonal factor codes appear to be relatively accurate. Figure 3.1 Bridge project cumulative cost 53

64 Figure 3.2 New road construction project cumulative cost Cumulative construction cost, Project NH-26-1(157) 6,,. 5,,. 4,,. 3,,. 2,,. 1,, Figure 3.3 4R maintenance resurfacing project cumulative cost 54

65 seasonal cost share seasonal factor code Figure 3.4 Comparison of seasonal cost shares with seasonal factor codes cumulative cost shares cumulative seasonal factor codes Figure 3.5 Comparison of cumulative seasonal cost shares with cumulative seasonal factor codes 55

66 3.2 Question Two: What is the best contingency rate to be used in order to maximize project delivery yet ensure adequate cash balance availability? In order to answer question two, we analyzed the data for the 24 projects provided by NDoR. Those projects included 17 4R projects for maintenance resurfacing, and maintenance restore and rehabilitation. The remaining projects wee for bridge preservation and maintenance, bridge replacement, and bridge rehabilitation. One project was for new roadway construction and another was for safety. We note that with NDoR selection of these projects we have no assurance that they are fully representative of the full project portfolio. To the extent that these projects may not be fully representative, any conclusions that follow from our analysis may not be appropriate. With that caveat, we proceed to analyze the selected projects. Note: It was assumed that the 24 projects that were provided were representative of a typical NDoR project profile. All recommendations in this report are predicated on this assumption. If they are not representative it may be that the conclusions are not correct. Of the 24 projects, 13 had final cost exceeding the award amount, with an average of 5.5 percent overage. The maximum overage for a project was 18.3 percent for bridge preservation project. The remaining 11 projects had final cost below award amount, with an average underage of 4.71 percent. The maximum underage was percent for the safety project. For each project phase four expenditure data were used to statistically estimate the trajectory of cumulative total project cost. The estimating equation in each case is a third degree polynomial in the number of months. That is, the cumulative cost is regressed on time, measured in months, time squared, and time cubed. The estimated trajectories are illustrated in the Appendix. Actual cumulative cost, fitted values, and residuals are both illustrated in graphs and provided in tables in the Appendix. 56

67 Consider, for example, the project with control number 7696, data for which is illustrated on pages In that case the estimated cumulative cost function rises at a decreasing rate, over the 32 months of the project, following the actual cost pattern over time quite closely. The final period fitted cost is $5,642,76 compared to the actual final cost of $5,87,845, yielding a residual of $165,769 indicating an underestimate of the final actual cost of 2.9 percent. For each project the Theil inequality coefficient is reported. This coefficient lies between zero and one, where a value of zero indicates a perfect fit. The mean squared forecast error can be decomposed into three components that are used to judge the quality of the forecast. The bias proportion of the mean squared forecast error indicates how far the mean of the forecast is from the mean of the actual data series. The variance proportion indicates how far the variation of the forecast is from the variation in the actual data series. Finally, the covariance proportion measures remaining unsystematic forecast errors. The fitted cost trajectories track the actual data very well, as reflected in these statistics and as is clear from the visual presentations. In order to develop a standard by which to assess the likelihood that a cash-flow budget contingency will be sufficient to cover the variability in project cost a target error amount two measures of error in estimating cumulative project cost are used. First, we use the mean absolute error which is reported for each fitted project equation, reflecting the average monthly error in estimating the cumulative project cost. This statistic is computed as the mean of the absolute value of the monthly residuals, or estimating errors. Absolute values of residuals are used in this statistic to treat positive residuals (indicating estimated cost above actual cost) and negative residuals (indicating estimated cost below actual cost) symmetrically. Second, we use the mean of fitted standard errors. The estimated standard errors are recovered from the estimated cost equations (as illustrated in the top graph for each project) and their mean is 57

68 computed. We compute the mean of (1) the mean of absolute fitted errors, and (2) the mean of fitted standard errors. Our suggested target error, based on the estimated cost functions and their errors for these projects, is half of that mean. Table 3.1 reports project data, fitted cost equation information, and simulated budget contingencies. The final period fitted residual indicates the difference between the total cumulative cost and the estimated cost. A positive residual reflects actual cost that exceeds estimated cost while a negative residual reflects actual cost below estimated cost. Eleven of the final period fitted residuals are negative while the remaining thirteen are positive. The final period fitted residuals as a percent of actual project cost range from a positive eight percent to a low of minus eleven percent. Our fitted cost equations have a sum total of final period fitted residuals of $456,7 for the 24 projects with total costs of $184,212,947, or two-tenths of one percent. We compute three alternative budget contingency amounts as a percentage of the actual total cost of each project and then compare those contingency amounts to our suggested target error based on the estimated cost equations. The three contingencies analyzed are: (1) the current ten percent contingency, (2) a seven percent alternative contingency, and (3) a five percent alternative contingency. The current ten percent contingency is sufficient to cover the target amount in 21 of the 24 projects. In all three cases where the estimated cost equations do not achieve the target standard, with total cost exceeding total awards, the projects are short-term lasting nine months or less. With so few monthly data points, statistical estimation is imprecise. Hence, the estimating equations have more uncertainty. Computing a seven percent contingency, we find that similar performance. In 21 cases the seven percent contingency is sufficient to cover the target amount. This level of contingency performs as well as the current ten percent contingency. 58

69 Finally, we simulate a five percent contingency. This contingency rule is sufficient to cover the target amount in 18 cases. Most importantly, comparing the five percent rule to the ten percent rule, we find that the five percent rule performs as well (or, no worse) in 21 project cases. The ten percent rule misses in three cases, and the five percent rule does no worse. For the 24 projects listed in the table, the reduced budget contingency rule frees up $9.2 million in funds to be used for additional projects, without increasing the risk of cash-flow problems. We also analyzed a 2.5 percent contingency but found that in that case the contingency was only able to cover the target amount in seven of the 24 projects. Based on that analysis we are not comfortable recommending contingency levels below five percent given the limited nature of the data (24 projects selected by NDoR) analyzed. For the 24 projects listed in Table 3.1, the total cost overage is $1,984,512. In comparison, a ten percent contingency provides an extra $18,412,195 to cover that overage. But that contingency amount leaves approximately $16 million unused. By reducing the contingency amount to five percent of awards, the amount available to cover overage is $9,26,97, which is still well more than adequate. On the basis of this analysis, our recommendation is to reduce the current ten percent cash-flow budget contingency practice to five percent. Example Project: In order to explain the analysis summarized in Table 3.1, consider the project with control number 7696 (shown in the seventh row of project data). That project took 32 months to complete at a phase four actual cost of $5.8 million. That cost was $156,267 over the award amount. Our estimated cost, based on the statistical model for the project, concluded with a total cost that is $165,769 below the actual cost. The mean absolute fitted error for the model is $17,39 and the mean of fitted standard errors is $237,468. The mean of those two measures is $23,889. Our suggested target error is half that amount, or $118,734. The current NDoR 59

70 contingency for this project, at 1 percent of the award amount, is $58,785, which is well in excess of that needed to cover the cost overage. The alternative contingencies considered, at 7 percent and 5 percent respectively, are $46,549 and $29,392. In this case, the recommended contingency of 5 percent is adequate to cover the cost overage. 6

71 Table 3.1 Project cost and budget contingency simulations Project control number Over/under (award amount minus cost amount) Final period phase 4 actual cost Final period fitted residual Final period fitted residual percent Mean absolute fitted error Mean of fitted standard errors Mean of mean absolute fitted error and mean of fitted standard errors Does a ten percent contingency cover half the mean of absolute fitted error and the mean of fitted standard error? Does a seven percent contingency cover half the mean of absolute fitted error and the mean of fitted standard error? Does a five percent contingency cover half the mean of absolute fitted error and the mean of fitted standard error? Number of periods Ten percent contingency Seven percent contingency Five percent contingency 12381SA 5-91,991 16,, 478, ,91 77, ,579 1,6, 1 1,12, 1 8, , ,336-28, , ,86 26,835 72,534 5,774 36, ,89 2,779,715-14, , , ,39 277, , , ,87 4,57,29-247, ,18 383,424 35,221 45, ,1 1 22, ,887 2,217,56 89, , ,124 49, , ,225 11, ,324,38 5,289, , ,657 49, , , , , ,267 5,87, , ,39 237,468 23,889 58, , , ,247 4,946,177-13, , , , , , , ,729 7,484,86-86, , , ,3 748, , , ,44 2,52, , , ,15 3,91 252, , , ,732 1,34,9-34, ,59 74,849 59,954 13, , , ,17 3,443,191 86, ,36 35, , , , , ,647 5,214,9-242, , ,347 56, , , , ,65 4,294,65-72, , , , ,47 1 3, , ,58 8,99, , ,358 77,63 67,494 89, , , ,332 2,712,445 4, ,965 88,461 65, , , , ,621 2,251, , , , ,32 225, , , ,22 11,, 413, , , ,178 1,1, 1 77, 1 55, ,423 5,618,72 14, ,59 62, , , , , ,376 8,562,98 33, ,988 42,29 357,9 856, , , A 57 78,99 19,, -47, ,6 551, ,366 1,9, 1 1,33, 1 95, ,8 4,117, , ,86 272,22 227,31 411, , , ,959 4,675,48-28, ,44 44,222 32, , , , ,324 52,, -13, ,233,4 3,15,689 2,624,347 5,2, 1 3,64, 1 2,6, 1 1 Sum total: 1,984, ,121, ,7 18,412, ,888, ,26, When does a five percent contingency perform as well? 61

72 3.3 Question Three: What is the best construction engineering percentage to be applied on each project? Should the percentage have more categories for different project costs? The construction engineering cost as a share of contract awards ranges from 2 percent to 8 percent for the projects analyzed (from 3 to 7 percent of total cost). Analysis of the project data indicates that the engineering cost depends both on the contract amount and the type of project. Award size is not a major factor in explaining the share, however. Award size and type of project are highly correlated. New road construction and reconstruction with added capacity projects tend to involve larger awards and also require more construction engineering. The current practice of allocating 12 percent to construction engineering for contracts under $2 million and 5 percent for contracts over $2 million is biased upward. Data analysis indicates that the phase 5 award share forecast (see Figure 3.6 below) for the 24 projects analyzed is generally in the range of 4 to 6 percent, depending on the award size and type of project. The two standard deviation forecast range (+ 2 S.E.) does not exceed 1 percent for any of the projects. The phase 5 award share rises with project award size at a decreasing rate. The largest shares (in the range of 6 to 8 percent) occur for reconstruction projects with added capacity, new roadway construction, and occasional 4R maintenance resurfacing projects. Figure 3.7 illustrates the actual, fitted, and residual shares. The fitted values are generally in the range of four to five percent and the residuals are generally plus or minus two percent. Based on this analysis, a policy of allocating 8 percent for new road construction projects and reconstruction with added capacity projects, and 5 percent for other projects, may well be 62

73 adequate to cover construction engineering costs. This is substantially less than the current allocation Forecast: PHASE5AWARF Actual: PHASE5AWARDSHARE Forecast sample: 1 25 Adjusted sample: 1 24 Included observations: 24 Root Mean Squared Error Mean Absolute Error.123 Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion. Variance Proportion Covariance Proportion PHASE5AWARF ± 2 S.E. Figure 3.6 Estimated work phase 5 (construction engineering) share of award by project Residual Actual Fitted Figure 3.7 Estimated work phase 5 (construction engineering) share of award by project; actual, fitted, and residual 63

74 3.4 Question Four: Should the payout estimates be more closely tied to actual construction delivery, not tied only to dollars paid out to date? Yes, as indicated in question 1, answer (a), payout rates vary with project type and therefore should depend on actual construction delivery rather than dollars paid out to date. 3.5 Question Five: How should funds be set aside for unplanned contingencies? The remaining question five asks how funds should be set aside for unplanned contingencies. Rather than the appropriate amount, this question asks how funds should be set aside. Potential answers to this question may be related to the type of project or its timing. Analysis of project over/under amounts indicates that they are unrelated to the length of the project and the award amount. Hence, there is no reason to make the contingency amount related to the length of the project or the size of the award. 3.6 Question Six: What is the best way to project payout of estimated balances that remain after construction end date, but contract not completed? 1. Current cash flow practice is to set an end date 15 days after the project construction end date. Analysis of the project data indicates that the payouts after the construction end date are highly variable, depending upon the type of project. The share of total cost paid out after the end of construction ranges from less than one percent to 98 percent. The outlier project at 98 percent is the one safety project in the data where significant additional contracts were added to the project. Other projects with higher than typical payouts after the end of construction included the two bridge projects, with payouts of 24 and 11 percent for the bridge replacement and preservation projects, respectively. While 64

75 4R maintenance resurfacing projects typically show payouts in the range of 3-6 percent, there are several projects where the payout after construction end is significantly higher, in the range of 25-4 percent. In each of the 4R project cases with higher late payouts there are additional contracts involved. 2. Estimation of balances to be paid after the construction end date should be primarily based on the type of project, with bridge, safety, and major road construction projects having larger payouts after construction end dates. In addition, the payouts after construction end are contingent on the addition of contracts during the life of the project. When additional contracts are let during project implementation, a rolling cash flow period should be extended depending on the dates on which the additional contracts are let. 65

76 Chapter 4 Budgeting Recommendations Our primary recommendation is that NDoR use the statistical properties of revenue and expenditure series provided in this report along with Monte Carlo simulation methods to determine likely budget outcomes and plan budgets accordingly. Given the nature of the data available for this analysis, which is in the form of monthly data by expenditure category, this is the most reasonable approach. If additional project-level data were made available, analysis could be conducted by following each project from letting through completion. That approach can provide information on the implicit assumptions being made in the project budgeting process revealing implicit incorporation of risk factors that may result in under-spending relative to budgeted expenditures. There are additional ways of thinking about coping with budget risk. First, it is always possible to set aside a portion of an expenditure budget category as a contingency fund for those categories subject to the greatest risk. At the beginning of a fiscal year, a portion of the expenditure category is set aside in case of cost overruns or unanticipated cost increases. This approach is a form of planned underspending. At a later point in the fiscal year when budget uncertainties are clearer, the funds can be freed to spend before the end of the fiscal year. Often, simple budget rules are suggested to cover contingencies. NDoR budget practices may already incorporate implicit contingency funds, although we are unable to model that possibility with the data available. To the extent that projects are let with built-in contingency funding in the form of over-estimates of project costs, the situation can arise where positive balances occur near the end of a fiscal year. In that case, additional projects can let, or the timing of planned projects can be accelerated. In any case, such budget practices leave the agency with funds to be spent late in the fiscal year. Resolution of this budget timing issue requires project-level data to determine the implicit contingency factors involved. 66

77 Second, NDoR could consider establishment of its own budget stabilization fund. Most states have such funds, often called rainy day funds. Payments are made into the fund during the upturn in the business cycle, and withdrawals are made during a downturn. Guidelines for the amount to pay in during good years are often simplistic. For example, a simple rive percent pay-in rule is often suggested. Both Kriz (22) and Joyce (21) indicate, however, that a simple five percent rule is oversimplified and inadequate to cover the risks involved, with high confidence. Rather, their analysis indicates that more specific information is needed on the budget risks involved in order to determine an appropriate fund balance. 7 Once again, however, if current NDoR budget practices are resulting in positive balances near the end of a fiscal year, those practices are already incorporating a form of budget stabilization fund, albeit without formal fund rules. It is important to investigate the nature of the informal practices that may result in positive balances near the end of fiscal years. Finally, in some cases, it may be possible to take advantage of the fungibility of funds and move funds across budget lines. Movement of funds across budget lines provides a ready mechanism for dealing with risk. When one budget category is hit with an unexpected increase in expenditures, that event can be offset by moving funds from an underutilized budget category. The flexibility to do this, however, is often limited by state and federal regulations that prevent dedicated funds from being used for other purposes. While federal limitations may be difficult to override, it may be feasible to consider transfers across budget lines involving state funds. This approach may require NDoR to seek authority from the state to move funds across budget lines, however. 7 In fact, Kriz (22) suggests the use of Monte Carlo simulations using Crystal Ball software and demonstrates the application of that software for modeling optimal budget reserves in Minnesota. 67

78 Answers to the six specific business practice questions posed by NDoR are summarized below: Question 1: Should different payout and seasonal factors be established for various types of construction projects? For example, major interstate reconstruction, asphalt overlay, new major bridge, etc. Yes, analysis of project data indicate that projects of different types have markedly different cost trajectories over time. Payout factors should depend on the type of project. Question 2: What is the best contingency rate to be used in order to maximize project delivery yet ensure adequate cash balance availability? Our recommendation is to reduce the current ten percent cash-flow budget contingency practice to five percent. Question 3: What is the best construction engineering percentage to be applied on each project? Should the percentage have more categories for different project costs? Our recommendation is for a policy of allocating 8 percent for new road construction projects and reconstruction with added capacity projects, and 5 percent for other projects, may well be adequate to cover construction engineering costs. This is substantially less than the current allocation. Question 4: Should the payout estimates be more closely tied to actual construction delivery, not tied only to dollars paid out to date? Yes, payout rates vary with project type and therefore should depend on actual construction delivery rather than dollars paid out to date. Question 5: How should funds be set aside for unplanned contingencies? 68

79 Analysis of project over/under amounts indicates that they are unrelated to the length of the project and the award amount. Hence, there is no reason to make the contingency amount related to the length of the project or the size of the award. Question 6: What is the best way to project payout of estimated balances that remain after construction end date, but contract not completed? Estimation of balances to be paid after the construction end date should be primarily based on the type of project, with bridge, safety, and major road construction projects having larger payouts after construction end dates. In addition, the payouts after construction end are contingent on the addition of contracts during the life of the project. When additional contracts are let during project implementation, a rolling cash flow period should be extended depending on the dates on which the additional contracts are let. 69

80 References Chou, J.S. (29). Generalized linear model-based expert system for estimating the cost of transportation projects. Expert Systems with Applications 36: Chou, Jui-Sheng, I-Tung Yang, and Wai Kiong Chong. (29). Probabilistic simulation for developing likelihood distribution of engineering project. Automation in Construction 18: Dillon, Robin L., M. Elisabeth Pate-Cornell, and Seth D. Guikema. 25. Optimal use of budget reserves to minimize technical and management failure risks during complex project development. IEEE Transactions on Engineering Management 52(3): Elkjaer, Martin. (2). Stochastic budget simulation. International Journal of Project Management 18: Hiershleifer, Jack, and John G. Riley. (1992). The analytics of uncertainty and information. Cambridge, UK: Cambridge University Press. Iyer, K.C. and K.N. Jha. (24). Factors affecting cost performance: evidence from Indian construction projects. International Journal of Project Management 23: Joyce, Philip G. 21. What s so magical about five percent? A nationwide look at factors that influence the optimal size of state rainy day funds. Public Budgeting & Finance 21(2): Knight, Frank H. (1921). Risk, uncertainty, and profit. New York, NY: Houghton Mifflin. Kriz, Kenneth A. (22). The optimal level of local government fund balances: a simulation approach. Proceedings of the Ninety-Fifth Annual Conference of the National Tax Association 95: Lichtenberg, S. (1989). New project management principles for the conception stage. Proceedings, INTERNET 88 and Journal of Project Management 7:

81 Muthukrishnan, S., Martin Pal, and Zoya Svitkina. (27). Stochastic models for budget optimization in search-based advertising. Internet and Network Economics, Lecture Notes in Computer Science 4858: Nebraska Department of Roads. (213). Annual Financial Report, Fiscal Year Ending June 3, 213. Nielsen, Heino Bohn. (25). Non-stationary time series and unit root tests. University of Copenhagen. Parzen, Emanuel. (1962). Stochastic processes. San Francisco, CA: Holden-Day, Inc. State of Nebraska Department of Roads Annual Financial Report. State of Nebraska Department of Roads Annual Report. Yang, I.T. (25). Simulation-based estimation for correlated cost elements. International Journal of Project Management. 23:

82 Appendix A Augmented Dickey-Fuller (ADF) Unit Root Tests Notes: In this appendix, we include some basic time series properties and statistical analyses for the following activity categories and lines: Activity Categories: 5 Administration, 6 Supportive Services, 7 Capital Facilities, 75 Highway Maintenance, 8 Highway Construction, 85 Construction Related Expense Activity Lines: 642 Business Technology Services 655 Payroll Clearing 751 System Preservation 752 Operations 753 Snow and Ice Control 754 Unusual & Disaster Operations 755 Equipment Operations 756 Indirect Charges 81 Preliminary Engineering 815 Right-Of-Way 82 Construction 83 Construction Engineering 72

83 85-85 Construction Related Expense Overhead A1 provides bar charts for all the series listed above, plotting from January 2 to December 215. A2 provides some descriptive statistics for all the series listed above. Note that different series may have different number of observations due to missing data (or null values). A3 presents tables of results of the Augmented Dickey-Fuller (ADF) tests, after nulling data that are in NBER-published recessions. The two NBER-published recessions in the timeframe (2-215) are March to November of 21 and December of 27 to June of 29. A p-value greater than.1 suggests failure to reject the null hypothesis of unit root. At that point the series may need first-differencing or second-differencing. A p-value smaller than.1 signifies rejection of the unit root null hypothesis, thus suggests the series is stationary at different significance level. All the data and statistical analyses are presented based on fiscal year, where July to the next June is considered a full fiscal year. 73

84 Null Hypothesis: DIESEL_NET has a unit root Exogenous: Constant Lag Length: 12 (Automatic - based on SIC, maxlag=14) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(DIESEL_NET) Method: Least Squares Date: 8/14/15 Time: 15:13 Sample (adjusted): 1997M2 215M1 Included observations: 225 after adjustments Variable Coefficient Std. Error t-statistic Prob. DIESEL_NET(-1) D(DIESEL_NET(-1)) D(DIESEL_NET(-2)) D(DIESEL_NET(-3)) D(DIESEL_NET(-4)) D(DIESEL_NET(-5)) D(DIESEL_NET(-6)) D(DIESEL_NET(-7)) D(DIESEL_NET(-8)) D(DIESEL_NET(-9)) D(DIESEL_NET(-1)) D(DIESEL_NET(-11)) D(DIESEL_NET(-12)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 6.99E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 74

85 Null Hypothesis: GASOLINE NET has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=14) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GASOLINE NET) Method: Least Squares Date: 8/14/15 Time: 15:13 Sample (adjusted): 1997M1 215M1 Included observations: 226 after adjustments Variable Coefficient Std. Error t-statistic Prob. GASOLINE NET(-1) D(GASOLINE NET(-1)) D(GASOLINE NET(-2)) D(GASOLINE NET(-3)) D(GASOLINE NET(-4)) D(GASOLINE NET(-5)) D(GASOLINE NET(-6)) D(GASOLINE NET(-7)) D(GASOLINE NET(-8)) D(GASOLINE NET(-9)) D(GASOLINE NET(-1)) D(GASOLINE NET(-11)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 3.48E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 75

86 Null Hypothesis: GRAND_TOTAL_NDOR_RECEIPT has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=14) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GRAND_TOTAL_NDOR_RECEIPT) Method: Least Squares Date: 8/14/15 Time: 15:13 Sample (adjusted): 1997M1 215M1 Included observations: 226 after adjustments Variable Coefficient Std. Error t-statistic Prob. GRAND_TOTAL_NDOR_RECEIPT(-1) D(GRAND_TOTAL_NDOR_RECEIPT(-1)) D(GRAND_TOTAL_NDOR_RECEIPT(-2)) D(GRAND_TOTAL_NDOR_RECEIPT(-3)) D(GRAND_TOTAL_NDOR_RECEIPT(-4)) D(GRAND_TOTAL_NDOR_RECEIPT(-5)) D(GRAND_TOTAL_NDOR_RECEIPT(-6)) D(GRAND_TOTAL_NDOR_RECEIPT(-7)) D(GRAND_TOTAL_NDOR_RECEIPT(-8)) D(GRAND_TOTAL_NDOR_RECEIPT(-9)) D(GRAND_TOTAL_NDOR_RECEIPT(-1)) D(GRAND_TOTAL_NDOR_RECEIPT(-11)) C R-squared.5548 Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 2.51E+16 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 76

87 Null Hypothesis: TOTAL_FEDERAL_RECEIPTS has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=14) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(TOTAL_FEDERAL_RECEIPTS) Method: Least Squares Date: 8/14/15 Time: 15:14 Sample (adjusted): 1997M1 215M1 Included observations: 226 after adjustments Variable Coefficient Std. Error t-statistic Prob. TOTAL_FEDERAL_RECEIPTS(-1) D(TOTAL_FEDERAL_RECEIPTS(-1)) D(TOTAL_FEDERAL_RECEIPTS(-2)) D(TOTAL_FEDERAL_RECEIPTS(-3)) D(TOTAL_FEDERAL_RECEIPTS(-4)) D(TOTAL_FEDERAL_RECEIPTS(-5)) D(TOTAL_FEDERAL_RECEIPTS(-6)) D(TOTAL_FEDERAL_RECEIPTS(-7)) D(TOTAL_FEDERAL_RECEIPTS(-8)) D(TOTAL_FEDERAL_RECEIPTS(-9)) D(TOTAL_FEDERAL_RECEIPTS(-1)) D(TOTAL_FEDERAL_RECEIPTS(-11)) C R-squared.5411 Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 2.3E+16 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 77

88 Null Hypothesis: TOTAL_FUEL_TAXES has a unit root Exogenous: Constant Lag Length: 12 (Automatic - based on SIC, maxlag=14) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(TOTAL_FUEL_TAXES) Method: Least Squares Date: 8/14/15 Time: 15:14 Sample (adjusted): 1997M2 215M1 Included observations: 225 after adjustments Variable Coefficient Std. Error t-statistic Prob. TOTAL_FUEL_TAXES(-1) D(TOTAL_FUEL_TAXES(-1)) D(TOTAL_FUEL_TAXES(-2)) D(TOTAL_FUEL_TAXES(-3)) D(TOTAL_FUEL_TAXES(-4)) D(TOTAL_FUEL_TAXES(-5)) D(TOTAL_FUEL_TAXES(-6)) D(TOTAL_FUEL_TAXES(-7)) D(TOTAL_FUEL_TAXES(-8)) D(TOTAL_FUEL_TAXES(-9)) D(TOTAL_FUEL_TAXES(-1)) D(TOTAL_FUEL_TAXES(-11)) D(TOTAL_FUEL_TAXES(-12)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 5.45E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 78

89 Null Hypothesis: TOTAL_REGISTRATIONS has a unit root Exogenous: Constant Lag Length: 13 (Automatic - based on SIC, maxlag=14) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(TOTAL_REGISTRATIONS) Method: Least Squares Date: 8/14/15 Time: 15:14 Sample (adjusted): 1997M3 215M1 Included observations: 224 after adjustments Variable Coefficient Std. Error t-statistic Prob. TOTAL_REGISTRATIONS(-1) D(TOTAL_REGISTRATIONS(-1)) D(TOTAL_REGISTRATIONS(-2)) D(TOTAL_REGISTRATIONS(-3)) D(TOTAL_REGISTRATIONS(-4)) D(TOTAL_REGISTRATIONS(-5)) D(TOTAL_REGISTRATIONS(-6)) D(TOTAL_REGISTRATIONS(-7)) D(TOTAL_REGISTRATIONS(-8)) D(TOTAL_REGISTRATIONS(-9)) D(TOTAL_REGISTRATIONS(-1)) D(TOTAL_REGISTRATIONS(-11)) D(TOTAL_REGISTRATIONS(-12)) D(TOTAL_REGISTRATIONS(-13)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 4.59E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat

90 Prob(F-statistic). Fail to reject the null of unit root for all selected revenue series. Hence unit root for all selected series. After first-differencing all series become stationary. 8

91 Null Hypothesis: NUM5 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM5) Method: Least Squares Date: 8/1/15 Time: 23:31 Sample (adjusted): 21M1 215M5 Included observations: 121 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM5(-1) D(NUM5(-1)) D(NUM5(-2)) D(NUM5(-3)) D(NUM5(-4)) D(NUM5(-5)) D(NUM5(-6)) D(NUM5(-7)) D(NUM5(-8)) D(NUM5(-9)) D(NUM5(-1)) D(NUM5(-11)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 3.97E+12 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 81

92 Null Hypothesis: NUM6 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM6) Method: Least Squares Date: 8/1/15 Time: 23:28 Sample (adjusted): 21M1 215M12 Included observations: 128 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM6(-1) D(NUM6(-1)) D(NUM6(-2)) D(NUM6(-3)) D(NUM6(-4)) D(NUM6(-5)) D(NUM6(-6)) D(NUM6(-7)) D(NUM6(-8)) D(NUM6(-9)) D(NUM6(-1)) D(NUM6(-11)) C R-squared Mean dependent var Adjusted R-squared.8222 S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.42E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 82

93 Null Hypothesis: NUM642 has a unit root Exogenous: Constant Lag Length: 3 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM642) Method: Least Squares Date: 8/1/15 Time: 23:31 Sample (adjusted): 2M5 215M12 Included observations: 147 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM642(-1) D(NUM642(-1)) D(NUM642(-2)) D(NUM642(-3)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 4.4E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 83

94 Null Hypothesis: NUM655 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM655) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 21M1 215M5 Included observations: 121 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM655(-1) D(NUM655(-1)) D(NUM655(-2)) D(NUM655(-3)) D(NUM655(-4)) D(NUM655(-5)) D(NUM655(-6)) D(NUM655(-7)) D(NUM655(-8)) D(NUM655(-9)) D(NUM655(-1)) D(NUM655(-11)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 5.67E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 84

95 Null Hypothesis: NUM7 has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM7) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 2M3 215M12 Included observations: 122 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM7(-1) D(NUM7(-1)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 8.45E+12 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 85

96 Null Hypothesis: NUM75 has a unit root Exogenous: Constant Lag Length: (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM75) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 2M2 215M12 Included observations: 161 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM75(-1) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.6E+15 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 86

97 Null Hypothesis: NUM751 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM751) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 21M1 215M5 Included observations: 121 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM751(-1) D(NUM751(-1)) D(NUM751(-2)) D(NUM751(-3)) D(NUM751(-4)) D(NUM751(-5)) D(NUM751(-6)) D(NUM751(-7)) D(NUM751(-8)) D(NUM751(-9)) D(NUM751(-1)) D(NUM751(-11)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.5E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 87

98 Null Hypothesis: NUM752 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM752) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 21M1 215M5 Included observations: 121 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM752(-1) D(NUM752(-1)) D(NUM752(-2)) D(NUM752(-3)) D(NUM752(-4)) D(NUM752(-5)) D(NUM752(-6)) D(NUM752(-7)) D(NUM752(-8)) D(NUM752(-9)) D(NUM752(-1)) D(NUM752(-11)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 4.41E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 88

99 Null Hypothesis: NUM753 has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM753) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 2M12 215M5 Included observations: 124 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM753(-1) D(NUM753(-1)) D(NUM753(-2)) D(NUM753(-3)) D(NUM753(-4)) D(NUM753(-5)) D(NUM753(-6)) D(NUM753(-7)) D(NUM753(-8)) D(NUM753(-9)) D(NUM753(-1)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.48E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 89

100 Null Hypothesis: NUM754 has a unit root Exogenous: Constant Lag Length: (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM754) Method: Least Squares Date: 8/1/15 Time: 23:32 Sample (adjusted): 2M2 215M12 Included observations: 159 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM754(-1) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 2.69E+12 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 9

101 Null Hypothesis: NUM755 has a unit root Exogenous: Constant Lag Length: (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM755) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 2M2 215M12 Included observations: 161 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM755(-1) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 2.6E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 91

102 Null Hypothesis: NUM756 has a unit root Exogenous: Constant Lag Length: 5 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM756) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 2M7 215M12 Included observations: 146 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM756(-1) D(NUM756(-1)) D(NUM756(-2)) D(NUM756(-3)) D(NUM756(-4)) D(NUM756(-5)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.31E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 92

103 Null Hypothesis: NUM8 has a unit root Exogenous: Constant Lag Length: 12 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM8) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 21M2 215M5 Included observations: 118 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM8(-1) D(NUM8(-1)) D(NUM8(-2)) D(NUM8(-3)) D(NUM8(-4)) D(NUM8(-5)) D(NUM8(-6)) D(NUM8(-7)) D(NUM8(-8)) D(NUM8(-9)) D(NUM8(-1)) D(NUM8(-11)) D(NUM8(-12)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 5.29E+15 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 93

104 Null Hypothesis: NUM81 has a unit root Exogenous: Constant Lag Length: (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM81) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 2M2 215M12 Included observations: 159 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM81(-1) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.1E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 94

105 Null Hypothesis: NUM815 has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM815) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 2M3 215M12 Included observations: 155 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM815(-1) D(NUM815(-1)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.1E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 95

106 Null Hypothesis: NUM82 has a unit root Exogenous: Constant Lag Length: 12 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM82) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 21M2 215M5 Included observations: 118 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM82(-1) D(NUM82(-1)) D(NUM82(-2)) D(NUM82(-3)) D(NUM82(-4)) D(NUM82(-5)) D(NUM82(-6)) D(NUM82(-7)) D(NUM82(-8)) D(NUM82(-9)) D(NUM82(-1)) D(NUM82(-11)) D(NUM82(-12)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 4.25E+15 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 96

107 Null Hypothesis: NUM83 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM83) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 21M1 215M5 Included observations: 121 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM83(-1) D(NUM83(-1)) D(NUM83(-2)) D(NUM83(-3)) D(NUM83(-4)) D(NUM83(-5)) D(NUM83(-6)) D(NUM83(-7)) D(NUM83(-8)) D(NUM83(-9)) D(NUM83(-1)) D(NUM83(-11)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 1.89E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 97

108 Null Hypothesis: NUM85 has a unit root Exogenous: Constant Lag Length: 11 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM85) Method: Least Squares Date: 8/1/15 Time: 23:33 Sample (adjusted): 21M1 215M5 Included observations: 121 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM85(-1) D(NUM85(-1)) D(NUM85(-2)) D(NUM85(-3)) D(NUM85(-4)) D(NUM85(-5)) D(NUM85(-6)) D(NUM85(-7)) D(NUM85(-8)) D(NUM85(-9)) D(NUM85(-1)) D(NUM85(-11)) C R-squared Mean dependent var Adjusted R-squared.5542 S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 6.66E+14 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 98

109 Null Hypothesis: NUM85_85 has a unit root Exogenous: Constant Lag Length: 5 (Automatic - based on SIC, maxlag=13) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(NUM85_85) Method: Least Squares Date: 8/1/15 Time: 23:34 Sample (adjusted): 2M7 215M5 Included observations: 139 after adjustments Variable Coefficient Std. Error t-statistic Prob. NUM85_85(-1) D(NUM85_85(-1)) D(NUM85_85(-2)) D(NUM85_85(-3)) D(NUM85_85(-4)) D(NUM85_85(-5)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid 3.82E+13 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic). 99

110 Appendix B Crystal Ball Simulations Full Details Run preferences: Number of trials run 1, Extreme speed Monte Carlo Random seed Precision control on Confidence level 95.% Run statistics: Total running time (sec).22 Trials/second (average) 4,558 Random numbers per sec 27,347 Crystal Ball data: Assumptions 6 Correlations 15 Correlation matrices 1 Decision variables Forecasts 1 Crystal Ball Report - Full Simulation started on 215/8/18 at 下午 11:42 Simulation stopped on 215/8/18 at 下午 11:42 Forecasts Worksheet: [no dropping recession simulation test.xlsx]activity Categories_Lines Forecast: Total Cell: F26 Summary: Entire range is from 13,582, to 119,9,314.6 Base case is. After 1, trials, the std. error of the mean is 681,

111 Statistics: Forecast values Trials 1, Base Case. Mean 53,22, Median 5,427, Mode --- Standard Deviation 21,535, Variance ################# Skewness.4152 Kurtosis 2.43 Coeff. of Variation.462 Minimum 13,582, Maximum 119,9,314.6 Range Width 16,317, Mean Std. Error 681,19.95 Forecast: Total (cont'd) Cell: F26 Percentiles: Forecast values % 13,582, % 26,834, % 32,366, % 38,44,55.5 4% 44,89, % 5,345, % 57,97, % 65,125, % 71,922, % 83,933, % 119,9,314.6 End of Forecasts 11

112 12

113 Assumptions Worksheet: [no dropping recession simulation test.xlsx]activity Categories_Lines Assumption: Category 5 Logistic distribution with parameters: Mean 1,282,45.73 Scale 136, Correlated with: Coefficient Category Category 7.1 Category Category 8.21 Category Assumption: Category 6 Lognormal distribution with parameters: Location -11,188,92.25 Mean 1,772, Std. Dev. 1,993,62.29 Correlated with: Coefficient Category Category Category Category 8.2 Category Assumption: Category 7 Lognormal distribution with parameters: Location -164, Mean 28, Std. Dev. 29,

114 Correlated with: Coefficient Category 5.1 Category Category Category 8.15 Category Assumption: Category 75 Lognormal distribution with parameters: Location. Mean 9,648,416.8 Std. Dev. 3,27,972.5 Correlated with: Coefficient Category 5.51 Category 6.17 Category 7.15 Category 8.27 Category Assumption: Category 8 Beta distribution with parameters: Minimum 7,4,72.52 Maximum 75,733, Alpha Beta Assumption: Category 8 (cont'd) Correlated with: Coefficient Category 5.21 Category 6.2 Category 7.15 Category Category

115 Assumption: Category 85 Lognormal distribution with parameters: Location -2,95,89.28 Mean 5,534, Std. Dev. 3,532, Correlated with: Coefficient Category 5.25 Category 6.35 Category Category Category 8.15 End of Assumptions 15

116 Note: E195=Category 8, D195=Category 75, F195=Category 85, A195=Category 5, B195=Category 6, C195=Category 7 The sensitivity analysis indicates that most of the forecast risk (59%) is related to expenditure category 8. Expenditure categories 75 and 85 also contribute another 3% of the sensitivity. For this reason, additional analysis of category 8 and its subcomponents is presented below. 16

117 Category 8 Simulation Assumption: Category 81 Logistic distribution with parameters: Mean 2,766,29.14 Scale 499, Correlated with: Coefficient Category Category 82.5 Category Assumption: Category 815 Gamma distribution with parameters: Location 169, Scale 716, Shape Correlated with: Coefficient Category 81.6 Category 82.2 Category 83.6 Assumption: Category 82 Triangular distribution with parameters: Minimum 3,341,76.27 Likeliest 3,522, Maximum 77,67, Assumption: Category 82 (cont'd) Correlated with: Coefficient Category 81.5 Category Category

118 Assumption: Category 83 Lognormal distribution with parameters: Location -2,278,84.14 Mean 2,42,91.12 Std. Dev. 661,8.79 Correlated with: Coefficient Category Category Category 82.7 Note: B197= Category 81, C197=Category 815, D197=Category 82, E197=Category 83 Based on the sensitivity analysis shown in the figure above, it is clear that expenditure categories 82 (construction) and 83 (construction engineering) account for nearly all of the forecast risk. The following two figures illustrate the 95% and 99% forecasts for the sum of category 8 expenditures. The 95% forecast shows that category 8 expenditures are expected to fall 18