Predicting Municipal Bankruptcies: A Proposed Model from Corporate Finance

Editor’s Note: For more on this topic, purchase Municipalities in Peril: The ABI Guide to Chapter 9, Second Edition, available in the ABI Bookstore (abi.org/bookstore). Members must log in first to obtain reduced pricing.

A review of past research on municipal bankruptcies took the authors to a basic conclusion: There are some major gaps. This article attempts to fill in at least some of those gaps to assist current and future mayors, city councils, city managers, city chief financial offers, credit-ratings agencies (e.g., Standard & Poor’s), fixed-income investors, etc., in their responsibilities for the management and/or evaluation of any city. Moreover, although municipal chapter 9 bankruptcies are not as common as corporate chapter 11s, the annual trend over the last 34 years shows a definite increase in chapter 9 filings (see the graph below).[1]

Our basic approach will be to apply a methodology used in the prediction of corporate bankruptcy as developed by Prof. Edward Altman of New York University nearly 50 years ago. His Z-score model has stood the test of time and was evaluated in a previous issue of the ABI Journal.[2]

Past Research

Seven studies were reviewed,[3] and their conclusions determined that there was the need to close two gaps: (1) examine recent municipal bankruptcies beyond just one or two states (e.g., Michigan and California); and (2) develop a model with significance to specifically act as a guide to predict a chapter 9 filing. The second gap needs further discussion because it reflects many previous studies that explicitly discuss causes, trends, legal issues and implications of financial distress. These include research by Spiotto, Baldassare, Honadle, Shafroth, Brown, Park, and even Standard & Poor’s, Fitch and Moody’s. However, such past research lacks models with specific variables, tests for significance, and most important, equations with predictive capabilities to forecast a bankruptcy in advance (e.g., two years).[4] Following is a discussion of the authors’ methodology and data in an attempt to close these gaps.

Methodology and Data

The same basic statistical approach by Edward Altman (chapter 11) was employed and extended to municipal bankruptcies (chapter 9). In Altman’s 1968 study, he compared the financial data of bankrupt corporations and nonbankrupt corporations, known as a paired sample.[5] This is a common approach when multiple discriminant analysis (MDA) models are used. By this type of comparison, certain ratios can be found that separate (i.e., discriminate) between two groups — in this case, those corporations that filed for bankruptcy and ones that did not file. The authors likewise used a paired sample, discussed in more detail later, except that city populations were used because tax revenues and expenditures are somewhat aligned with the number of people who live in a city. Generally, those citizens become the tax base for revenues such as property taxes, sales taxes, etc.

First, the authors needed to obtain reliable and consistent data on recent cities that have filed for chapter 9. A good, reliable sample of 11 cities that filed for chapter 9 in recent years, which were the time frame 2008-13, was obtained. The use of population ensured a metric that was directly comparable between the cities. No paired sample is ever perfect, but cities are often compared based on the size of their populations. Table 1 shows the list of these 22 cities (11 bankrupt and 11 nonbankrupt), with their populations as reported in their respective consolidated annual financial reports, and includes the years of the chapter 9 filing. The financial data was obtained directly from the financial reports as published by the respective cities, two years prior to the chapter 9. The sample size was the best available as the authors wanted to ensure that the sample would be both current and consistent. A nonparametric test for small sample sizes (Wilcoxon Matched Pairs Signed Rank Test) was also employed.

Results

The authors tested 10 variables and found that the following four were the most significant[6] and provided a “discriminant boundary” between the bankrupt and nonbankrupt samples, as presented in Table 2. This table shows the MDA model to be at the 95 percent level of confidence. It also shows a “gray area,” like Altman did in his corporate bankruptcy model because of misclassifications. In these results, there were three such misclassifications.

The Z-score predicted Benton Harbor, Mich., as nonbankrupt (Z = 3.232), but it filed for chapter 9 in 2013. The Z-score results for nonbankrupt Tacoma, Wash. (Z = 1.543), and Scranton, Pa. (Z = 2.128), placed them in neither bankrupt nor nonbankrupt. The authors decided to still classify these two cities as an “error” (i.e., known formally as Type I/Type II errors in statistics). These three cities did not exactly fit the predictive bankruptcy equation but still produced the 95 percent level of confidence. In summary, Table 2 interprets the results of Z-score ranges for bankruptcy in two years, the gray area, and nonbankruptcy in two years.

The sample size of the 11 chapter 9 cities was rather small, but, as previously stated, the authors wanted current chapter 9 cities with reliable and consistent data for use in this research. The authors decided to additionally test the data, as reported in Table 3, by comparing the average Z-score of the bankrupt sample with the nonbankrupt sample to see if the average Z-scores were within the appropriate ranges and if the differences were significant. For this, we used the Parametric T-Test for Correlated/Paired Samples and added the Nonparametric Wilcoxon Matched Pairs Signed Rank Test, which is analogous to the aforementioned T-Test for Correlated/Paired Samples. A nonparametric test is useful when sample sizes are small.

Table 3 shows that the T-Test for Correlated/Paired Samples produced an average Z-score for the bankrupt sample of 1.041 and the nonbankrupt sample of 3.173 (p < .001), placing these averages in the correct Z-score ranges as identified in Table 2. For the Nonparametric Signed Rank Test, the results showed significant differences between the two samples (p < .004). The authors do not want to get too technical in this article. However, you need to know that this model passed critical tests, an indication that one can be confident in these results.

Sample Calculation: City of Detroit

To show how easy this model can be used, let’s take the city of Detroit and use 2011 data for the four variables in the model to produce its Z-score of -0.158, as shown in Table 4. This score is clearly in the bankrupt classification of <1.100 for predicting its chapter 9, which occurred two years later in 2013.

Conclusion

This article began citing the chapter 9 filing by Detroit in 2013. It also cited the work by Prof. Altman and how the authors were applying the use of MDA to predict a municipal bankruptcy.

As chapter 9 filings occur, the database should be expanded and retested. A prediction of two years does help, but three, four years, etc., would be even more useful. Moreover, trends in the municipal Z-scores would also help in the analysis. If a city’s Z-score annually goes from 4.2 to 3.1 to 2.3, then it is clearly headed in the wrong direction, even if it stayed above 2.2 (nonbankrupt). This should show mayors, city councils, etc. that fiscal changes might be needed before it is too late. In addition, the credit-ratings agencies (e.g., Standard & Poor’s) should also find the appeal of this Z-score model. Here’s a brief summary:

• Z-scores can be developed and applied in the public sector in addition to the corporate sector. Z-scores can be a very useful tool but clearly must be used in conjunction with other data and analysis.

• The two-year predictive chapter 9 model allows managers and decision-makers the ability to take corrective actions before it is too late. This model is an important difference from previous research. A chapter 9 filing does not occur “overnight.”

• More research and expanding databases are essential to better modeling in this important area of public finance.

• Not all states specifically authorize a chapter 9 filing. Our model applies to the 24 states where chapter 9 is authorized by state law. However, a declining Z-score would tell any general purpose government in any state that it may be headed toward financial difficulty — chapter 9 or otherwise. The predictive model described herein can be a useful tool with widespread applications.[7]