An unfunded pension liability, also known as a pension shortfall, refers to the difference between the total amount a city (or any entity that offers pensions, such as a company or a state) has promised in pensions to its current and future retirees, and the amount of money it currently has to fulfill those promises. In other words, it's the amount of money that the city owes to its pensioners, but doesn't have.

Here's how it works: when a city's employees work, the city promises to pay them a certain amount in retirement, often based on their salary and years of service. The city is supposed to set aside money each year to fund these future pension payments. This money is typically invested, with the goal of growing it over time to meet the future pension obligations.

However, if the city doesn't set aside enough money, or if the investments don't perform as well as expected, or if the city promises more in pensions than it can afford, it can end up with an unfunded pension liability.

Determining what is a "good" amount of unfunded pension liability can be tricky. Ideally, the unfunded liability should be zero, meaning that the city has enough money to meet all its future pension obligations. However, this is often not realistic due to fluctuations in investment returns, changes in the number of employees and retirees, and other factors.

A more practical goal is for a city to have a funded ratio (the ratio of the amount of money it has to the amount it owes in pensions) of at least 80%. This is often considered a healthy pension fund. However, this is a rule of thumb and not a hard and fast rule.

An unfunded pension liability becomes "excessive" when it reaches a point where the city is unlikely to be able to meet its future pension obligations without severe budget cuts, tax increases, or other drastic measures. This would typically occur when the funded ratio drops significantly below 80%, though the exact threshold can vary depending on a variety of factors, including the city's overall financial health, the structure of its pension plan, and the demographic characteristics of its employees and retirees.

It's also important to note that an excessive unfunded pension liability can have serious consequences, not just for the city's retirees, but for all its residents. To make up for a pension shortfall, a city might need to cut services, increase taxes, or take on debt, all of which can negatively impact the quality of life in the city. That's why it's crucial for cities to manage their pension liabilities carefully.