The Cost of Corporate Subsidies

Michael E. Long, Ph.D. Research Scientist, CFC Center for Imaging Science Rochester Institute of Technology

Thomas D. Hopkins, Ph.D. Professor Emeritus, Department of Economics Rochester Institute of Technology

David L. Farnsworth, Ph.D. Professor, School of Mathematical Sciences Rochester Institute of Technology

Email: [email protected], [email protected], [email protected]

Abstract. The US government’s auto industry bailout was just one of many costly programs that target subsidies to particular firms. The merit of such programs is contentious, and more fundamentally, so too is the choice of a basis for their assessment. This short paper applies an agent-based modeling approach to such policy assessment. The result is an intriguingly suggestive perspective on subsidy programs, calling into question both their efficiency and fairness. Our hypothesis is that government subsidies affect and downgrade the entire economy, and subsidized companies that undergo bankruptcy have a higher probability of its recurrence than those that have not already gone bankrupt.

Keywords: Government Subsidies, Bailout, Agent-Based Modeling

1. INTRODUCTION farmers [3]. Many other subsidies are hidden: the price paid by US consumers for sugar is far higher Since October 2008, the federal government’s than the world price because the government Troubled Asset Relief Program (TARP) has restricts sugar imports in order to assist domestic distributed to parts of the U.S. auto industry more sugar producers; one result is that US candy than $80 billion of taxpayer funds – some $800 per manufacturers are internationally disadvantaged in American taxpaying family. While roughly $30 competing with foreign-based manufacturers [4], billion had been repaid by mid-January 2011, the [5]. Congressional Oversight Panel [1], which monitors bailout programs, concluded on January 13, 2011 One might enquire about the benefit and that full repayment is not likely ever to occur. For impact of these subsidies. As a result of these the US government to break even on the rescue, the subsidies, has a moral hazard been created? Has the market price of General Motors stock would have progress of stronger, non-subsidized producers, to exceed $50 per share at the time that the been handicapped? Has the incentive for efficient government would decide to sell its remaining business practices been blunted by the availability shares [2]. This is truly a potentially expensive of such subsidies? The problems certainly extend bailout or subsidy, but the U.S. economic structure beyond the auto industry into the fabric of society, is suffused with such subsidies, both short-term and by creating favored status for particular firms or continuing. For example, from $10 billion to $30 other entities, complicating the prospects of non- billion annually flows from the federal budget to subsidized rivals. 1 endeavors. Often, their resultant behavior has a Of course, this is a very complicated problem remarkable similarity to observed reality and can with moral and economic layers compounding it. If also lead to an understanding of emergent behavior. the purpose of the short-term subsidy is to give a loan of resources to an entity that is deemed to be This modeling technique differs from critical for the country, then the subsidy might be traditional differential-equations modeling, which warranted. However, if the cost of the subsidy uses a set of top-down equations to model a system. continues to be paid by society, while the Agent-based modeling is a type of modeling that subsidized entity continues to enjoy the free uses individual, heterogeneous agents that are given resources, independent of their unsubsidized rivals, a set of rules to follow. All of the agents follow then the merit of the subsidy might be more their instructions and interact with each other and strenuously questioned. with the simulated world based on these rules. Highly complex systems [11], [17] can thus be To initiate a preliminary inquiry into this simplified and analyzed by this simplification and complicated issue, we developed an agent-based style of modeling. model. Agent-based models (ABM) are non- deterministic in that the outcome itself is not Agent-based models are well suited for modeled and is often known. In conventional complicated systems and have the advantage over modeling, equations that fit the final state are often other methods in that aggregate results are developed and used to model not only the final state produced by modeling smaller, understandable bits but also the development thereof. However, in and allowing the agents to sort it out. Consequently, ABM individual players or agents with a set of experts can be consulted to create rules for realistic rules are turned loose in the computer-generated behavior of single agents. The agents can interact landscape to perform their appointed tasks. The with each other and their environment, and their outcome reflects the interaction of each individual behavior can be influenced and change based on agent with other agents and with the environment these interactions. that in turn acts upon the individual agent. As recently pointed out “... economic theorists 2. METHODOLOGY have increasingly resorted to mathematical systems of equations to model economic processes” [18, p. The growth of computational power in recent 76]. However, agent-based computational decades has allowed the incorporation of a economics (ACE) is evolving into a powerful tool sufficient number of agents and a large enough for evaluating economic policies [19] and studying landscape to provide interesting results by complex systems that exist in economic markets aggregating individual behavior of agents based on [18]. Indeed, the complexity of the subsidized relatively simple rules of engagement. Relatively industry—with individual actors, personalities, and recently, such ABM have been developed for a goals—led us to use an agent-based model as our number of applications such as business processes modeling tool. Other modeling methods would [6], epidemiology [7], segregation [8], civil have had difficulties handling the complexity. violence [9], development of minority opinion [10], However, like any modeling technique, there is a bank fraud [11], economics [12], tax evasion [13], trade-off between realism vs. complexity and and annuity policyholder behavior [14]. simplification vs. usefulness [20]. A complicated model that captures all the nuances of the situation Agent-based models are a collection or system may be realistic, but probably too complex to even of computer objects (agents) coupled with methods execute in a reasonable time. On the other hand, a of interaction (agent behavior). These agents are simple model with excessive assumptions is not autonomous and can be adaptive to their useful either. A reasonable tradeoff is environment, essentially learning as the model required. Although we strive for the model to be as develops [15], [16]. Agent-based models use realistic as possible, our goal is a model that can individual computer objects as players or agents. contribute to a broader study by suggesting Governed by a set of rules, these agents are turned concerns and issues warranting closer attention. loose in a computer-generated landscape to perform With this consideration ABMs are well suited to their appointed tasks such as trading, segregating, addressing complex problems. Sometimes these spreading disease, rumors, or opinions, reacting, super complex problems are called wicked creating mayhem, or any number of other problems [21]. 2 explained below. The calculations use NetLogo 2.1 Sugarscape-type Model [24].

First, we consider a simple model of a All agents’ behaviors in this model are created corporate society and examine the impact of randomly from specific distributions described taxation as a vehicle for spreading the wealth and below. subsidizing weaker enterprises. Questions are: What is the effect of the level of taxation? When Companies are created as follows: does over-taxation occur, and what is its effect on 1. A number of companies (agents) are the corporate agents? To do this, we use the created. pioneering work of Epstein and Axtell [22] to 2. Each company is given Unit develop a Sugarscape model in the computer Manufacturing Cost (UMC) of their language Python as a basic model of corporate product, determined from an exponential society. We tax the agents or corporations applying distribution with an average value a flat tax rate and redistributing the tax revenue. selected. For these and all subsequent exponential distributions, high and low In the original Sugarscape model, a 50 × 50 cutoff values are set such that if a high or matrix was constructed with the cells filled with a low value is obtained, it is discarded and a resource called sugar in various patterns [22]. This new value is generated. landscape was randomly filled with agents each with a randomly generated vision (ability to sense 3. A product cost to the customer is location and amount of sugar) and metabolic rate of established by adding a mark-up value sugar consumption. With very simple rules—look determined from a uniform random around for the best free site; go there and harvest distribution ranging from 1% to 100%. the sugar—for the agents and the landscape, the Consequently, more inexpensive products authors demonstrated concepts of environmental are created than expensive ones. carrying capacity, coherent group structures, 4. Each company's product is given a unique inequitable distribution of wealth, and evolution. product number, which is used to create the workers' shopping list to identify In order to assess the overall economic health products selected and purchased by the of the corporate society in our model, we calculate workers. the Gini coefficient, which is a measure of the 5. Each company is given a random number degree of inequality in the distribution of wealth. If of employees, again determined by an one entity had all the wealth and the rest of the exponential distribution, but independent society had none, the Gini coefficient would be of product cost. 100. If all the individual agents had exactly the same amount of wealth, then the Gini coefficient Worker agents are created next: would be 0.0. The median world country value of 1. An exponential distribution is used to the Gini coefficient is about 40, with the US at 45 randomly determine worker salaries. and Japan at 38. The largest value reported is for 2. With the workers’ salaries established and Namibia at greater than 70 and the smallest value is the number of workers per company 23 for Sweden [23]. known, each company is given cash-on- hand related to their weekly payroll 2.2 Corporate Model commitment. We develop a more detailed model. The second After the companies and workers are created, Agent-Based Model consists of companies, the simple economic environment within which the workers, products, and a government. The agents function is finalized: companies employ workers and pay them a weekly salary; each company makes and sells a single 1. A worker’s shopping list of products is unique product. The workers shop and purchase created consisting of each company’s various products made by different companies, thus unique product number. completing the economic cycle. The model is 2. The number of times the product number created with initial parameters exogenously set, as appears on the list is dependent on the company’s product cost and weekly salary 3 obligation. Hence, a company with many companies that go bankrupt and require a workers and an inexpensive product, e.g. government bailout are recorded. loaves of bread, would have its product appearing on the shopping list more 3. RESULTS frequently than a company with few employees selling more expensive items, The simpler Sugarscape-based model e.g. furniture sets. All workers have the illustrates the impact of taxation and support of same shopping list. weaker corporate identities on the environmental 3. The initial cash-on-hand for each company carrying capacity and societal wealth. The second is set at six times its weekly payroll model deals with the expected probability of repeat obligation. Payroll stands in as a surrogate company bankruptcies. for all other corporate financial obligations, such as the costs of marketing, capital, material and supplies, maintenance, and so forth.

Once all the agents are created and the simple economic environment finalized, the companies manufacture products and pay the workers. The workers purchase products made by the companies. The process proceeds as follows: 1. The economic process is started in the manufacturing step with companies making product and filling their inventory. The inventory is sufficient to support any purchases for the week. 2. Workers are paid their weekly salaries from the company’s cash on hand, which of course, is depleted by that amount. 3. Following the manufacturing phase, workers randomly select an item from the shopping list until they run out of cash. If their last purchase results in a negative balance for the week, they use a credit card and make that additional purchase. However, they start the next week with that amount less to spend. Hence, they are not allowed to carry a credit card debt beyond one week.

This produces a stable economic climate with workers randomly shopping, returning cash to the corporate environment, and getting paid weekly. However, the government now imposes a weekly tax on the workers, and therefore they have less money to spend on products. Consequently, the workers demand an annual raise to compensate for this loss and to maintain their standard of living. The lowest third of a company’s paid workers are given an annual raise. If a company runs out of money trying to meet its salary obligations, it receives a subsidy from the government. This cycle is repeated a set number of times, and the

4 3.1 Sugarscape-type Model 3.2 CORPORATE MODEL

In the simulations with increasing tax rate via The model’s default input parameters are the Sugarscape type model, the initial impact is an shown in Table 1, although these can be varied as increase in the carrying capacity of the environment discussed. —more corporations survived as the tax rate increased—as more of the less fortunate agents or Table 1: Model Default Parameters companies are supported. Concomitantly, the Gini Parameter Model coefficient initially decreases as a function of tax Number of Companies Default20 rate and then levels off, indicating an initial Company Employment redistribution of wealth and then lack of further Average Number impact (Figure 1). In contrast, the total wealth of 100 the society is initially approximately constant Employees Minimum Number followed by a decrease in the total wealth of the 5 society (Figure 2). This is undoubtedly due to the Employees redistribution of resources required to support Maximum Number 200 agents with high metabolism (high consumption of Employees (1) resources), that is, the corporations that require Average Annual $34,000 subsidies to survive. Similar behavior is realized for Salary (2) the wealth per agent, that is, all the enterprises Minimum Annual suffer to support the non-competitive corporations. $18,000 Salary (3) Maximum Annual $150,000 Salary Average Product Unit $8 Manufacturing Cost Tax Rate 0.15% Annual Worker Pay 1.0% Increase (1) 99.2% of US companies have 200 or fewer employees [25]. (2) The average 2008 annual personal income was $33,943 [26]. (3) The average annual minimum wage is about $15,000 based on 40 hour per week for 50 weeks Figure 1: Impact of Taxation on the Gini Coefficient [27].

With these input parameters, eventually, a company can run out of cash. The question is: Why, in the model, do companies go bankrupt? The following possible non-random conditions or dependencies might cause bankruptcy. 1. Time dependence, for instance, occurrence after a particular elapsed time. 2. The number of employees, for instance large or small companies might be more likely to run out of cash. 3. Particular salary obligations. 4. Product cost, such as a more expensive or inexpensive product. Figure 2: Impact of Tax Rate on Societal Wealth Table 2 shows the results of 14 simulations addressing the number of weeks before the first company ran out of cash. The simulation was 5 stopped at the first bankruptcy or at an arbitrary 17 3 129 duration without a bankruptcy. The results are for 69 69 133 the default values in Table 1, but without taxation and subsequent corporate subsidies. With repeated Table 4: The Number of Employees with Salaries below simulations, there does not appear to be a set time the Simulation Median that companies go bankrupt or a simulation time Number of Number of Median after which bankruptcy occurs. Employees of Employees with Salary Bankrupt Salaries below Table 2: Corporate Bankruptcy as a Function of Weeks Company Median of Operation 48 21 $33,135 Run Weeks of Bankruptcy 5 3 $31,280 Number Operation Observed 17 8 $30,749 4 15 Yes 69 40 $41,142 9 260 No Figure 3 considers the question of the 2 380 No dependence of bankruptcy on weekly payroll 5 400 No obligations and product costs. The instances of bankruptcies in seven simulations (runs as denoted 6 450 No in Figure 3) are indicated with a circle. For 3 473 Yes bankrupt companies, the company’s weekly payroll 1 721 No obligation does not appear to have any relationship to its consumer product’s cost. 12 764 Yes 7 791 Yes Simulation runs were also performed looking at other possible dependencies, such as frequencies 10 795 No of and time intervals between multiple bankruptcies 13 888 Yes and repeating the above summary of results for 10, 14 1900 No 20, 40, and 50 companies. One hundred simulations of the model explored different standard causes of 8 3000 No bankruptcy, but none of the resultant bankruptcies' 11 9580 No patterns showed any dependence on model input parameters. The four simulations shown in Tables 3 and 4 address the questions of bankruptcy caused by Consequently, we conclude that the occurrence number of employees and salary obligations. Each of bankruptcy in the model is a random event simulation was stopped at the first bankruptcy and dependent on the overall company configuration, as the employee information recorded. There does not defined by the model and input parameters, and not appear to be a dependence on the number of a simple dependency on a single model input employees or a preponderance of lower salaried parameter. Multiple simulations over longer time employees on the company payroll. One might periods followed this test phase. The policy of have incorrectly reasoned that bankruptcy is more government subsidies to bankrupt companies at the likely for companies with more lower-paid rate of five times their weekly salary obligations employees because they are receiving the annual was instituted allowing them to return to operation. raise and thus increasing the company’s weekly Certainly, the amount of the subsidies could salary obligation. conceivably affect future financial outcomes for a struggling company. However, the government Table 3: The Number of Employees for Bankrupt subsidies for bankrupt companies are intended as a Companies financial seed and are usually considerably less Number of Minimum Maximum than the company’s market capitalization. Employees of Number in Number in Bankrupt Simulation Simulation The simulation was stopped after 5 companies Company Run Run went bankrupt and bankrupt companies were noted. 48 10 131 This simulation with 20 companies was repeated 25 5 5 656 times. If our hypothesis that a company that goes bankrupt once has a higher probability of going 6 bankrupt again is true, then a high rate of repeat more in 25 trials is only 0.0072, which is quite bankruptcies would be expected from the corporate small. Consequently, it is safe to conclude that model compared to a random process. repeat bankruptcies in the corporate model are not random events. For the random process, consider the following probability model for bankruptcies. Consider 20 The key parameters used here (see Table 1) companies that are vulnerable to bankruptcy over a include realistic values for variables that most given number of years. Designate by k the total might agree are of central importance in number of bankruptcies in a simulation where understanding business conditions. The results repeat bankruptcies by a company are counted. To derived have sufficient plausibility to warrant compare with the model's outcomes, we require the further inquiry into the consequences of bailouts. probability P(k) that within the k bankruptcies that one or more companies will repeat the act of going 4. SUMMARY bankrupt one or more times. These results by no means prove that the auto This probability model is the same as the bailout, or any other of our myriad subsidy following for a container of 20 objects, labeled 1 programs, has produced analogous damage to either through 20. An object is selected randomly, the the level or distributional equality of societal number of the object is recorded, and the object is wealth, but they are intriguingly suggestive. There replaced in the container. This process of selection, is a common tendency for observers and advocates recording, and replacement is repeated a fixed of subsidies to point to the survival of the number of times, k. The probability that among the subsidized firm(s) as evidence of the merit of the objects selected there are any repeats is P(k). subsidy. That the new General Motors is developing a solid record of sales and profits is The solution to this problem for k = 5 is P(5) = undeniable. But, this is not sufficient grounds for 0.4186, which can be found as follows. In the first declaring the bailout a success. Although the auto selection, the probability of not getting a match is bailout may be at least a limited success in that it 20 out of 20. For the second selection, the reduced the country's despair during a difficult time probability of not getting a match is 19/20 because and eliminated a possible financial domino effect, it one has already been selected. The probability of certainly is too early to be sure of its true impact. not getting a match on the first and second selection Nevertheless, other bailouts remain questionable in is (20/20)(19/20). The probability of getting a their cost to the consumer and their effect on US match is the complement of the probability of manufacturing competitiveness on the world getting not getting a match. Consequently, the market. probability of finding one or more duplicates in k = 5 draws from 20 objects is What would occur in the absence of such bailouts, while difficult to discern, is the critical comparison state. US bankruptcy laws provide an orderly means for failing companies to be dealt This technique is used to solve the birthday with in the absence of subsidies. When we prevent problem, which asks the question: How many their operation, as subsidies do, we open the people must be at a party in order to have at lease a possibility that neither efficiency nor economic- 50-50 chance that two of them share a birthday, but, equality interests are well served. perhaps, not a birth year? The answer is 23 individuals [28]. References For 20 companies and 5 bankruptcies, the null [1] Congressional Oversight Panel, “An Update on hypothesis is p = 0.4186 from the probability model TARP Support for the Domestic Automotive with the alternative hypothesis p > 0.4186. For Industry,” 2011. twenty-five simulations of the corporate model, 17 http://cop.senate.gov/documents/cop-011311- had one or more repeated bankruptcies. The report.pdf standard normal value for this proportion is [2] "GM Weighs Cutback at Opel", The Wall Street Journal, p. B3, September 13, 2012. which gives the p-value 0.0072. The probability of getting by chance the proportion of 17 successes or [3] “Here is an Easy One”, New York Times, WK9, January 16, 2011. 7 [4] C. Cui, B. Tomson, and I. Brat, “USDA introduction,” Princeton NJ: Princeton University Says It May Relax Sugar Quotas,” Wall Street Press, 2012. Journal, April 14, 2010. [17] J. Rauch, “Seeing Around Corners,” Atlantic [5] National Confectioners Association, 2011. 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8 Figure 3: Weekly Company Payroll vs. Product Cost for Bankrupt Companies

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