Social Insurance and the Magic of Averages Lecture Notes

The Magic of Averages: Introduction to Social Insurance

• Historical Context and Principle: The concept of the "magic of averages" was notably described by Winston Churchill in 1932 to explain relief measures. He stated: "In the main, these relief measures are supported by insurance contributions of the unemployed, of the employers, and of the State. I have before described them as, in principle, the application of the magic of averages to the rescue of millions."

• Transition from Welfare Economics: Last week focused on the First Welfare Theorem, which posits that in a benchmark case, free exchange on a self-regulating market leads to a Pareto efficient outcome. This benchmark depends on six assumptions:

  1. Individuals are rational.

  2. Individuals have perfect information.

  3. Markets are perfectly competitive.

  4. Markets are complete.

  5. There are no public goods.

  6. There are no externalities.

• Introduction of Reality: While the benchmark case may be Pareto efficient, it can also involve significant insecurity, uncertainty, and risk. Modern study focuses on introducing risk into the economic model.

Conceptions of the Welfare State

There are four distinct conceptions regarding the role and scope of the welfare state:

• Conception 1: Welfare for the Poor: Focused on basic relief. Examples include Food Stamps in the US, Income Support in the UK, and OCMW in Belgium.

• Conception 2: Taxation and Redistribution: Includes the first conception plus mechanisms like personal income tax (e.g., in Belgium) to redistribute wealth.

• Conception 3: Social Insurance: Adds institutionalized safety nets. Examples include Social Security and Medicare in the US, the NHS in the UK, and "Sociale Zekerheid" in Belgium.

• Conception 4: Socio-economic Government Policies: The most expansive view, including labor market policies and the role of the government in actively shaping markets.

Risk and Uncertainty

• State of Nature: One possible way in which events relevant to a risky decision can unfold.

• Probability ($p$): A measure of the likelihood that a specific state of nature will occur.

• Risk vs. Uncertainty:

  • Risk: A situation where the probability of events is known.

  • Uncertainty: A situation where the probability of events is not known, often occurring when events are extremely rare or located in the far future.

• Weather Example of Risk: Based on a forecast for Sunday:

  • State 1: It rains (Probability $p = 60\%$).

  • State 2: It does not rain (Probability $100\% - 60\% = 40\%$).

Pay-off and Expected Values

• Pay-off: The outcome or value received in each specific state of nature.

• Expected Pay-off: The weighted average of all possible pay-offs, using the probability of each pay-off as its weight.

• Calculation Example:

  • Good State: Probability $= 50\%$, Pay-off $= 1000$.

  • Bad State: Probability $= 50\%$, Pay-off $= 100$.

  • $\text{Expected pay-off} = 0.5 \times 1000 + 0.5 \times 100 = 550$.

Risk Aversion and Consumption Smoothing

• Risk Averse Persona: An individual who, when comparing a situation with risk to a situation without risk with the same expected pay-off, prefers the situation without risk.

• Risk Aversion Characteristics:

  • Most people are risk-averse, particularly when the pay-offs involved are large.

  • Risk-averse individuals prefer "smoothed" pay-offs rather than volatile ones.

• Loss Defined: The difference in pay-off between the good state and the bad state.

• Central Question: How can we smooth pay-offs and reduce the loss? This often involves a transfer from the good state to the bad state.

Three Basic Institutions for Risk Management

1. Families (Informal, Non-profit, Private): Provide informal insurance.

2. Firms (Formal, For-profit, Private): Provide private insurance.

3. Government (Formal, Non-profit, Public): Provides social insurance.

Informal and Self-Insurance

• Self-insurance (Precautionary Saving): Saving money during the good state to use during the bad state.

  • Elizabeth Warren's 50/30/20 Rule: 50% for Needs, 30% for Wants, and 20% for Saving.

  • Financial Resilience Metric: Societies.be data indicates many people are unable to face unexpected expenses (e.g., being unable to pay an unexpected expense of approximately $€1100$ with own means).

• Informal Insurance (Reciprocal Transfers): Helping others in a bad state with the expectation they will return the favor when roles are reversed.

• Rotating Savings and Credit Association (ROSCA): Members pool money into a common fund, which is withdrawn by a single member each cycle. This is popular in developing countries or contexts without formal banking (e.g., under Islamic law).

• Limitations of Self/Informal Insurance: These work well only if:

  1. The probability of the bad state is small.

  2. The losses in the bad state are small.

  3. A capital market exists (for self-insurance).

  4. There is no systemic risk (for informal insurance).

Private Insurance Markets

• Definition: A contract offered by a private firm that reduces the loss (the pay-off gap between states).

• Benefit ($B$): The pay-off received from the insurer in the bad state.

  • Full Insurance: Benefit equals the loss ($B = \text{Loss}$).

  • Partial Insurance: Benefit is less than the loss (B < \text{Loss}).

• Insurance Premium ($\pi_i$): The amount the policyholder $i$ pays. The formula is:     $\pi_i = (1 + \alpha) \times p_i \times B$

  • $B$: Benefit.

  • $p_i$: Probability of the bad state for individual $i$.

  • $\alpha$: "Loading" added by the company to cover operational costs and profit.

• Numerical Examples of Private Insurance:

  • Assume Good Pay-off $1000$, Bad Pay-off $100$, $p = 0.5$, $B = 900$.

  • Scenario A (Loading $\alpha = 0$): Premium $\pi = 450$. Final income in both states is $1000 - 450 = 550$. All risk-averse individuals prefer this.

  • Scenario B (Loading $\alpha = 0.1$): Premium $\pi = 495$. Final income in both states is $1000 - 495 + 0 \text{ (good state)} = 505$ or $100 - 495 + 900 \text{ (bad state)} = 505$. Only sufficiently risk-averse individuals prefer this.

Market Failures in Private Insurance

Private insurance markets are often incomplete because they require five conditions to work effectively:

1. Individual Independent Risks (No Systemic Risk): If everyone suffers a loss at once (e.g., a financial crisis), the company cannot pay all benefits.

2. Risk (No Uncertainty): Probabilities must be known to compute premiums. Events far in the future, like Long Term Care (LTC), often fall under uncertainty.

3. Risk (No Certainty): The probability must be p < 1. If $p = 1$ (pre-existing conditions), the premium equals or exceeds the benefit.

4. No Adverse Selection: There must be no asymmetric information. If high-risk and low-risk individuals are pooled with a middle-range premium, low-risk people opt out. This cycle continues until the market collapses or low-risk individuals are uncovered.

5. No Moral Hazard: The probability $p$ should be exogenous. If insurance causes people to behave less carefully (e.g., not buying a fire extinguisher), $p$ increases, forcing premiums up. Solutions include:

   • Deductible: The user pays the first $X€$ of a claim.

   • Co-insurance: The user pays a certain percentage ($x\%$) of the cost.

Social Insurance: Principles and History

• Basics: Often called Social Security ("sociale zekerheid"). It accounts for approximately $1/3$ of government expenses in Belgium.

• Origins in the Industrial Revolution:

  • Commodification: Families became dependent on labor market earnings.

  • Urbanization: Families moved away from traditional informal support systems.

• Two Founding Models:

  • Bismarck Model (Otto Von Bismarck, Germany, ~1900): Insurance for laborers. Premiums and benefits both depend on wages (reciprocity).

  • Beveridge Model (Lord Beveridge, UK, 1942): Insurance for all citizens. Premiums paid via taxes; benefits do not depend on wages.

• The US Context: The Social Security Act was promoted via New Deal posters from Franklin D. Roosevelt, emphasizing security for widows, dependent children, and old-age retirees.

Social Insurance vs. Private Insurance

• Similarities: Eligibility is based on premium payments, and benefits are triggered by specific events (bad states).

• Key Differences:

  • Compulsory Membership: Membership is mandatory to create a large enough risk pool and prevent low-risk individuals from opting out (e.g., the "individual mandate" in the Affordable Care Act, though the fine was repealed in 2017).

  • Social Insurance Premium: Not based on individual risk ($p_i$) but often on a flat rate of earnings (e.g., $13\%$ in Belgium). This allows the system to handle uncertainty where probabilities are unknown.

Social Insurance in Belgium

• Characteristics: Largely a Bismarck-style system.

• Structure: Three separate systems for Employees, Self-employed individuals, and Civil servants.

• Management: Significant role for social partners (employers and employees).

• Reciprocity vs. Solidarity:

  • Reciprocity: Benefits like unemployment, sickness/disability, and pensions are typically wage-related (percentage of wage).

  • Solidarity: Benefits like child allowance and medical care are fixed amounts. Solidarity is achieved because:

    1. Premiums don't depend on individual risk (Solidarity between low-risk/highly educated and high-risk/low-educated).

    2. Benefits have lower/upper limits (Solidarity between high and low earners).

    3. Fixed benefits favor low earners relative to their contributions.

Evolution and Challenges

• Piggy Bank Model: Social insurance serves as a collective savings system for consumption smoothing.

• Old Social Risks: Unemployment, disability/injury, old age.

• New Social Risks: Maternity/childcare, divorce/single parenthood, part-time work, and career interruptions. These are often more vulnerable to moral hazard.

• The New Social Question: Risks are becoming less evenly distributed and more predictable, challenging the traditional solidarity model.

• Optimal Level: The generosity of benefits involves a trade-off: higher benefits provide better consumption smoothing but increase the cost of moral hazard.

Funding and Budgets (2020/2021 Data)

• Three Funding Sources: Employers, Employees, and General Taxes.

• International Context (Social Security Contributions as % of GDP, 2021):

  • OECD Average: $9.2\%$

  • Belgium: High, approximately $12.9\%$

  • Highest contributors: France, Germany, Austria, Czech Republic.

  • Lowest contributors: Australia, Denmark, New Zealand (where funding is primarily tax-based).

• Belgium Budget Breakdown (2020):

  • Total Revenue: $€151,000$ million.

    • Employer Contributions: $€54,000$ million ($36\%$).

    • Employee Contributions: $€28,000$ million ($19\%$).

    • Taxes: $€69,000$ million ($46\%$).

  • Total Expenditure: $€143,600$ million.

    • Pensions: $€56,000$ million ($39\%$).

    • Sickness: $€38,000$ million ($26\%$).

    • Unemployment: $€13,000$ million ($9\%$).

    • Invalidity: $€13,000$ million ($9\%$).

    • Family: $€10,600$ million ($7\%$).

    • Survivor Pensions: $€8,000$ million ($6\%$).

    • Social Exclusion: $€4,000$ million ($3\%$).

    • Housing: $€1,000$ million ($1\%$).

Questions & Discussion

• Potential Exam Question 1: "The main advantage of compulsory membership in social insurance is that the government collects more revenue."

  • Critique: False. While it does collect revenue, the primary economic advantage is avoiding adverse selection and the "opt-out" of low-risk individuals, ensuring the stability of the risk pool.

• Potential Exam Question 2: "'New social risks' such as divorce and career interruptions are more vulnerable to moral hazard than 'old social risks' such as industrial accidents."

  • Discussion: This focuses on the endogenous nature of the risk. Industrial accidents are largely outside a worker's choice, whereas career interruptions or lifestyle choices leading to certain new risks can be more influenced by the existence of insurance benefits.