Napolitano 2

Social Security & Insurance
Exploring Insurance for Social Security and Its Effect on Political Participation.
Mariah Napolitano
March 13, 2012
Prof Bryan Engelhardt


Abstract: With the political climate consistently changing, the future of social security and other government sponsored programs is always at risk. In order to reduce this risk, this paper proposes introducing a new financial product to the market that would provide insurance for social security benefits and suggests its affect on campaign contributions. This new market was modeled and a solution was found where individual purchase full insurance and reduce their political contributions aimed at continuing social security. To test the model a survey was given to individuals who were asked about their interest in this new type of insurance and how it would affect their political participation. The survey provided empirical evidence that a product like this would be attractive to some individuals and gave important feedback on ways to improve the product and the model.

The ever-changing political climate in the United States creates uncertainty in the existence and size of government-sponsored payouts, subsidies, and tax cuts. Whether it is social security, Medicare, or the capital gains rate, the futures of these political risk items are constantly in flux. Brought to the forefront of American society during the 2012 Presidential campaign due to Republican Vice-President Nominee Paul Ryan’s plan to completely reform the system, the future of social security is an issue Americans are genuinely and rightly concerned about. According to the 2012 Social Security Trustees Report, “beneficiaries will face a painful 25 percent benefit cut in 2033 when the Trust Funds are exhausted – three years sooner than projected just last year” (Paul Ryan website, 2012).

Many Americans who have paid into the social security system since they first started working are at a risk of receiving a significantly smaller or nonexistent benefit than what they had planned on for their retirement. Baring any drastic changes to the system this risk of decreasing or eliminating social security seems like a real possibility, leaving many Americans without sufficient funds for their retirement. But what if these individuals could guarantee their social security benefit independent of governmental changes to the system? This paper proposes creating a market for social security insurance, which would provide individuals the opportunity to purchase an insurance policy now that would cover any decreases to the social security benefit they receive when they retire. This type of insurance could also have an effect on the political participation of the individuals who purchase it so it is important to investigate the changes, if any, it might have on individuals’ voting or campaign contribution habits.

The paper is composed of two distinct parts; one in which a model is developed to depict the social security market in a few variations and a second part where 30 individuals were surveyed about their predictions for social security and their willingness to purchase social security insurance. Through this, I hope to show that insurance for social security (and other types of political risk) is a feasible financial product that can benefit both American citizens and insurance companies.

I.  Background/Literature Review

Political risk insurance (PRI) is not a new concept, and is commonly used when companies invest in developing nations. TheOverseas Private Investment Corporation (OPIC) an "independent" U.S. Government agency that sells investment services to assist U.S. companies investing in developing countries, offers PRI to U.S. investors in over 150 developing nations. The political risks typically insured are expropriation, political violence, and currency inconvertibility (Garver, 2009). PRI policies cover “losses to tangible assets, investment value, and earnings that result from political peril” (OPIC website, 2012). These policies allow U.S. business to invest in developing nations while hedging the risks associated with unstable governments.

Much has been written about how the PRI market is changing; books and papers detail the effects of the September 11th attacks on emerging market investment and PRI (Riordan, 2004) and other discuss the movement away from government insurance policies to private firms. (Salinger, 2008). But most relevant to the idea of insuring political risk items, like social security, within the United States, is the discussion of what products are “insurable” and how that definition changes slightly when considering items of political risk. Kathryn Gordon, of the Organization for Economic Cooperation and Development (OECD), talks about these issues in “Investment Guarantees and Political Risk Insurance: Institutions, Incentives, and Development”. Insurable risk is defined as an item clients will want to buy which the insurance industry can profitability provided. Gordon lists the conditions necessary, according to the OECD committee, to make a product insurable; “assessability (probability and severity of losses should be quantifiable); randomness (the time at which the insured event occurs should be unpredictable when the policy is underwritten, and the occurrence itself must be independent of the will of the insured); mutuality (numerous persons exposed to a given hazard should be able to join together to form a risk community within which the risk is shared and diversified)” (Gordan, 2008).

When discussing political risk items, the definition of insurable can diverge from these conditions. Political risk items may not have the greatest degree of assessability; calculating the probabilities of events happening can be challenging and there can be debate over whether an event has actually occurred. One deviation from the standard conditions, which is not as applicable to a product like social security insurance, is that many times there are no “risk communities” because each policy depends on the specifics of the investor, the country of investment and the product offered (Gordan, 2008). Within the market for social security insurance the country and the product being offered will be the same for every investment so risk communities can be formed. In reality social security insurance will create one large risk community because it is likely that any change in social security policy will affect everyone who buys the insurance (and more broadly anyone who receives social security). This does create the issue that given a policy change, the insurance company will have to payout to all of its customers. In this way, social security insurance is similar on a small scale to flood insurance; when a flood occurs, it is not typically one building or house that gets flooded but rather an entire area of buildings, resulting in insurance companies having to payout to large amounts of customers at a time. One suggestion Erwann O. Michel-Kerjan details in his paper, Catastrophe Economics: The National Flood Insurance Program, for the National Flood Insurance Program (NFIP) to stay financial sustainable in the event of catastrophe (like Hurricane Katrina) is to “transfer part of its catastrophe exposure to reinsurers or to investors in the financial markets by using alternative risk transfer instruments like a catastrophe bond (“cat bond”), a form of contingent claim” (Michel-Kerjan, 182). A similar plan could be used by insurance companies to relieve the pressure on the companies should social security get cut in the future. The key for both the NFIP and any company that provides insurance for social security is to hedge their risk whether be through reinsurers or finding an investment that is related to the item being insured. This can be through shorting an investment directly related to the insurance item or investing in an item inversely related to the item being insured.

One deviation on the definition of insurable that is important for the political risk associated with social security is that it is not “independent of the will of the insured.” Individuals have the opportunity to affect the outcome of social security through political participation, such as voting and campaign contributions. Because of this reason, this paper will focus on the effect campaign contributions might have on a product like social security insurance.

Much of the literature on campaign contributes says approximately the same thing, campaign contributions lead to policies that differ from those preferred by the median voter’s favored policies (Grossman and Helpman 1996, Prat 2002, Coate 2004, Campante, 2011). In particular, Grossman and Helpman (1996) showed in their model that a candidate is more likely to win an election if they cater to special interest groups that are more likely to donate money to their campaigns. These campaign contributions help candidates get elected because “risk-adverse voters prefer candidates with a clearer policy position” (Pratt, 2002). Because of this a banning or limiting of campaign contributions moves policies closer to the preferred policies of the median voters (Pratt, 2002).

Campante (2011) also showed that in combination with voting, contributions lead to a “wealth bias” in political policies. When wealthy individuals donate money to political campaigns, the politicians that receive the donations are encouraged to move their policies closer to those of the wealthy. So the more financial inequality that exists, the more the political system shifts in favor of the wealthy.

II.  Model

Price Discriminating Monopolist with Constant Probabilities

Assumptions

The model assumes five different possible outcomes for social security in the future; it doesn’t exist at all, it exist with benefits that are 25% of current benefits, with benefits that are 50% of current benefits, with benefits that are 75% of current benefits, and it exists with the same amount of benefits it provides today.

Each individual also has a utility function u(y) that measures the satisfaction received by the individual if event yi occurs. This model assumes that individuals are risk-adverse requiring a concave utility function. Both the firm and the individual believe with probability qi that event i will happen. Additionally (q0+q25+q50+q75+q100) =1.

The first situation which the model has been dissected for is when the market for social security insurance is controlled by a price-discriminating monopolist. In this scenario, the existence of an insurance market allows the individuals to decide on the amount of insurance they would like to purchase at the price set by an insurance company who has a monopoly on the market. As this market for social security insurance does not currently exist, it is reasonable to assume that when the market is first created it will be dominated by one firm who will have the power to price discriminate based on customers’ financials and beliefs about the future.

Model

This scenario calls for two models, one for the individual purchasing (or not purchasing) the insurance and one for the firm who is providing the insurance. The price of that insurance is represented by p. While the amounts of insurance in the individual’s model and the amounts in the insurer’s model are different (one set is quantity demanded and the other set quantity supplied) when the market is in equilibrium they will be equal so the model only uses one set of variables to represent both quantities. The ‘quantity’ insurance purchased will be represented by five different x values; x0 if social security does not exist at all when the individual retires, x25 if social security exists at 25% of its current level when the individual retires, and so forth all the way to x100 if social security exists at today’s levels when the individual retires.

Similarly the individual’s retirement portfolio will be represented by 5 variables; y0 if social security does not exist at all when the individual retires, y25 if social security exists at 25% of its current level when the individual retires, and so forth all the way to y100 if social security exists at today’s levels when the individual retires. Additionally, five different probabilities are necessary, the probability social security will not exist,q0, the probability social security will exist at 25% of current levels,q25, and so forth until the probability social security will exist at current levels, q100.

ln⁡(y) is used as the utility function (which satisfies the conditions for the utility function previously mentioned), we must assume that yiand (yi+xi-p)>0 so the consumer’s decision function will exist.

The firm is in control of the market and will look to maximize its profits, π, by optimizing all of the insurance amounts xiand the price of that insurance such that the consumer’s decision function is satisfied.

π=p-q0*x0+q25*x25+q50*x50+ q75*x75+q100*x100 such that (1)

q0*lny0+ q25*lny25+q50*lny50+q75*lny75+q100*lny100≤ q0*lny0+x0-p+q25*lny25+x25-p+q50*lny50+x50-p+q75*lny75+x75-p+q100*lny100+x100-p (2)

The firm’s profit function is equal to the price of the insurance, p, minus the expected cost of the insurance. The consumer will purchase the insurance if their expected value of not purchasing the insurance is less than or equal to their expected value of buying insurance. When the expected values are equal the consumer will be indifferent between purchasing and not purchasing the insurance.

In the firms profit equation the expected cost of the insurance is equal to q0*x0+q25*x25+q50*x50+ q75*x75+q100*x100. The consumer’s expected utility of not having insurance is the probability of having a certain retirement package multiplied by the value of that retirement package which can be described as

i=0,25,50,75,100qi*lnyi

(3)

Similarly the consumer’s expected utility of having insurance is the probability of having a certain retirement package multiplied by the value of that package plus the insurance payout the individual would receive minus the price of that insurance. It can be described as

i=0,25,50,75,100qi*ln⁡(yi+xi-p)

(4)

These conditions lead to a maximization problem with one constraint setting up a Lagrange multiplier optimization problem,

L=p-q0*x0+q25*x25+q50*x50+ q75*x75+q100*x100- λ*[q0*lny0+ q25*lny25+q50*lny50+q75*lny75+q100*lny100-q0*lny0+x0-p-q25*lny25+x25-p-q50*lny50+x50-p-q75*lny75+x75-p-q100*lny100+x100-p] (5)

This problem has been evaluated and only one solution was found.

The first order conditions of this constrained optimization with respect to xi,

∂L∂xi=-qi- λ-qiyi+xi-p=0

(6)

can be used to show that the maximizing solution to this problem is full insurance (proof in Appendix A1.1), which is shown as xi=y100-yi, meaning the insurance payout if event i occurs is equal to the difference of what the individual would have with today’s level of social security and what they would have if event i occurred. This result can be used to calculate the price of the insurance, resulting in

p= y100-y0q0y25q25y50q50y75q75y100q100 (7)