Abstract
Building on work done earlier this chapter illustrates our use of the Analytic Hierarchy/Network Process to produce a December 2008 forecast of when the U.S. economy would begin to recover from the contraction that, according to an announcement dated December 1, 2008, from the Business Cycle Dating Committee of the National Bureau of Economic Research (NBER), began during the month of December, 2007. Here we illustrate two approaches.
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Notes
- 1.
The authors were asked by a reviewer why we did not include a fifth alternative time period (e.g., 36–48 months)? As part of our exercise, we had concluded that we would have no confidence in attempting to project that far out into the future. Moreover, some grounding for the shorter four alternatives chosen is that, according to the NBER, the longest post-World War II contractions were each 16 months (November 1973 to March 1975, and July 1981 to November 1982) (NBER no date).
- 2.
This led to borrowing-fueled speculative spree especially in the housing market, similar to the internet-stock mania in the 1990 s. The rules and regulations governing these financial companies were generally less restrictive than those for banks, mutual funds, and other financial institutions.
- 3.
Thus, these investment banks essentially transformed their role from being underwriters to becoming sellers of loans. In the process, they shared the risks of mortgage loans with other investors. At the same time they collected a large sum of “new loans” from those investors. Many of the buyers of the securities were wealthy and reputable individuals, as well as institutions including educational institutions, local governments, charitable organizations, and banks.
- 4.
Practically non-existent until late in the 1990 s, CDS market grew very rapidly, reaching a staggering $62 trillion in 2008, more than 4 times the U.S GDP!.
- 5.
The defining moment was really when holders of high-risk portfolios had to face a double whammy: investors demanding their money back, and lenders shutting the door in their face.
- 6.
The importance of ‘Confidence’ in causing a crisis and influencing the pace of recovery is well discussed in Akerlof and Shiller (2009).
- 7.
For more discussion about the policy response, see Azis (2009).
- 8.
Recent estimates show that seized properties account for almost one in four sales, and about a quarter of homes with mortgages are underwater. Deutsche Bank estimated that the negative equity will peak at 48 % of total homes by 2011.
References
Akerlof, George and Robert Shiller (2009). Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism, Princeton University Press.
Azis, Iwan J (2009). Crisis, Complexity and Conflict, Emerald Group Publishing Limited.
Belsky, E., & Prakken, J. (2004). Housing wealth effects: Housing’s impact on wealth accumulation, wealth distribution and consumer spending. Joint Center for Housing Studies’ Report of a study commissioned and supported by the National Association of Realtors, Harvard University (W04–13). Cambridge, MA: National Center for Real Estate Research.
Blair, A.R., Nachtmann, R. and Saaty, T.L., “Incorporating Expert Judgment in Economic Forecasts: The Case of the U.S. Economy in 1992,” Chapter 12 in the book: Saaty, T.L. and L.G. Vargas, Models, Methods, Concepts and Applications of the Analytic Hierarchy Process, Kluwer Academic Publishers, London, 2001.
Blair, A.R., Nachtmann, R., Saaty, T.L. and Whitaker, R., “Forecasting the Resurgence of the US Economy in 2001: An Expert Judgment Approach,” Socio-Economic Planning Sciences, Vol. 36, 2002, pp. 77–91, and also Chapter 2 in Saaty, T.L. and L.G. Vargas, Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks, Springer, New York, 2006.
Greenspan, A. (2003, March 4). Remarks at the annual convention of the Independent Community Bankers of America, Orlando, Florida (via satellite).
Hilsenrath, Jon E., “Despite Job Losses, the Recession is Finally Declared Officially Over,” The Wall Street Journal, July 18, 2003.
National Bureau of Economic Research, Business Cycle Dating Committee, “Determination of the December 2007 Peak in Economic Activity,” Dec. 1, 2008, NBER web site (www.nber.org).
National Bureau of Economic Research, “Business Cycle Expansions and Contractions,” NBER web site (www.nber.org).
National Bureau of Economic Research, no title, link “announcement of business cycle trough/end of last recession,” July 17, 2003, NBER web site (www.nber.org).
NBER (2008b). Determination of the December 2007 Peak in Economic Activity, in http://www.nber.org/cycles/dec2008.html.
Organization for Economic Cooperation and Development, “Economic Outlook No. 84,” November 2008, web site (www.oecd.org).
Roubini, N., & Menegatti, C. (2007, March). The US housing recession is still far from bottoming out. RGE Monitor, pp. 1–22.
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The Judgment Matrices, the Supermatrix and the Limit Supermatrix for the Holarchic Approach
The Judgment Matrices, the Supermatrix and the Limit Supermatrix for the Holarchic Approach
The pairwise comparison judgments and the priorities derived from them are given in Tables 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 and 37. The caption of each table gives the parent element with respect to which the comparisons are being made; the derived priority is in the rightmost column of the table. The derived priorities are placed in their appropriate position in the supermatrix in the column labeled with the name of the parent element. The derived priorities in Tables 9–37 are used to form the supermatrix shown in three parts in Table 7. The supermatrix is raised to powers until it converges; that is, its values remain the same from one power to the next resulting in the limit supermatrix shown in Table 8.
1.1 Posing the Question When Comparing Criteria
In this paper we use the terms criteria and factors interchangeably. The caption for Table 9 reads “Judgments for the importance of its subfactors to the main factor Aggregate Demand”. The Aggregate Demand main factor is the parent element with respect to which its six subfactors in the Aggregate Demand cluster in Fig. 1 are compared. They are Consumption, Net Exports, Investment, Confidence, Fiscal Policy, Monetary Policy and Expected Inflation. The Fundamental Scale of the AHP is used to express the pairwise comparison judgments: [1-Equal, 3-Moderate, 5-Strong, 7-Very Strong, 9-Extreme; numbers in-between and decimals are also allowed]. The question posed is: “Which subfactor is more important in determining the time to recovery with respect to the Aggregate Demand main factor and how much more important?” The pair involved in a comparison is indicated by the (row, column) headings for the cell into which the judgment is placed. The judgment indicates how much more important the row element is than the column element in the opinion of the judge. For example, the value of 7 in the (Consumption, Exports) cell in Table 9 means Consumption is considered to be very strongly more important than Exports in determining the time to recovery. If instead the judgment was that Exports were very strongly more important than Consumption, the inverse value of 1/7 would be entered. An example of such an inverse value is the (Net Exports, Investment) judgment of 1/5 which means Investment is strongly more important than Net Exports in determining when the economy will turn around. The lower part of each matrix in a table has the reciprocal values of the entries of the transpose judgments in the upper part of the matrix.
1.2 Entering the Derived Priorities in the Supermatrix
The priorities in Table 9, determined by computing the principal eigenvector of the matrix of judgments, are: (0.355, 0.025, 0.053, 0.104, 0.208, 0.227, 0.029). The priorities may be interpreted as meaning that Consumption at .355 and Monetary Policy at .227 are the most important Aggregate Demand Factors. Put another way, Consumption is 35.5 % of what drives an economic recovery among aggregate demand factors while Net Exports is the least important at 2.5 %. These priorities are entered into the supermatrix in Table 9 under the Aggregate Demand column heading.
1.3 Posing the Question When Comparing Time Periods with Respect to Criteria
The time periods are compared according to which is the more likely period for recovery due to the influence of the factor with respect to which the comparisons are made. In Fig. 1 the Fiscal Policy criterion in the Aggregate Demand Factors cluster has the subfactors (or subcriteria): Tax Policy and Government Expenditure, so the time periods are pairwise compared with respect to each of these two subfactors rather than directly with respect to the factor Fiscal Policy. The time periods are compared directly with respect to the factors in the cluster that have no subfactors such as Consumption. The question posed would be: Is the 0–6 Months time period or the 6–12 Month time period more likely to be the turnaround time because of Consumption and how strongly more? Here 0–6 Months is not more likely than 6–12 Months; it is the other way around so a 1/3 is entered in Table 9 in the (0–6 Months, 6–12 Months) cell.
In all the tables involving time periods the names are abbreviated as follows: 6 Months means 0–6 Months, 12 Months means 6–12 Months, 24 Months means 12–24 Months and 36 Months means 24–36 Months.
1.4 Posing the Question When Comparing the Primary Factors with Respect to Time Periods
The final type of comparison arises because of the links back from the time periods to the primary factors. In this case the question posed is: For the turnaround to occur in the 6 Months time period which would have greater influence, and how strongly greater, the primary factor Aggregate Demand or Aggregate Supply? The judgment is that Aggregate Demand would be very strongly dominant over Aggregate Supply for the turnaround to occur in 6 months, so a 7 is entered in the (Aggregate Demand, Aggregate Supply) cell in Table 34.
1.5 Computing the Limit Supermatrix
Overall priorities for the alternative time periods are obtained by raising the supermatrix to powers until it converges to the limit supermatrix shown in Table 9. In the limit supermatrix all the columns are the same. The raw values for the alternative time periods are the same in every column of the limit supermatrix. These four values are shown in column 2 of Table 6 below. They are normalized by dividing each by their sum to obtain the priorities for the time periods shown in the third column. These priorities may be interpreted as the likelihood of a turnaround occurring during these time periods.
1.6 Computing the Expected Number of Months Until the Turnaround
To compute the expected time to the turnaround, as is traditionally done in economics, multiply the mid-point of each time period by the likelihood of the turnaround occurring during that time period. For example, the 0–6 Month time period runs from 0 to 6 months so its midpoint is 3 months. The 6–12 Month time period runs from 6 to 12 months so its midpoint falls at 9 months; the 12–24 time period runs from 12 to 24 months, so its midpoint falls at 18 months, and the 24–36 Month time period runs from 24 to 36, so its midpoint is at 30. Using an expected value calculation, in months, from December 2008: Expected turnaround = 3 × 0.0967 + 9 × 0.1997 + 18 × 0.3001 + 30 × 0.4035 = 19.5898
The exercise was done in early December 2008, so this means the turnaround is expected to occur around late July or early August 2010.
The pairwise comparison matrices are shown in Tables 9–37. A set of priorities or weights is obtained from each pairwise comparison matrix as its principal eigenvector. These derived priorities are placed into the supermatrix in the appropriate column. For example Table 9 gives the priorities or weights for the main factor Aggregate Demand, so they are placed in the supermatrix in Table 7 in the first column under “Aggregate Demand” beginning in the fourth row.
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Saaty, T.L., Vargas, L.G. (2013). Forecasting the Resurgence of the U. S. Economy in 2001: An Expert Judgment Approach. In: Decision Making with the Analytic Network Process. International Series in Operations Research & Management Science, vol 195. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-7279-7_2
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