The Government Budget Constraint

The household’s budget constraints for different years are linked by the household’s choices about saving and borrowing. Over the household’s entire lifetime, these individual budget constraints can be combined to give us the household’s lifetime budget constraint. Similar accounting identities apply to the federal government (and for that matter, to state governments and local governments as well). In any given year, money flows into the government sector, primarily from the taxes that it imposes on individuals and corporations. We call these government revenues. The government also spends money. Some of this spending goes to the purchase of goods and services, such as the building of roads and schools or payments to teachers and soldiers. Whenever the government actually buys something with the money it spends, we call these government purchases (or government expenditures). Some of the money that the government pays out is not used to buy things, however. It takes the form of transfers, such as welfare payments and Social Security payments. Transfers mean that dollars go from the hands of the government to the hands of an individual. They are like negative taxes. Social Security payments are perhaps the most important example of a government transfer. Any difference between government revenues and government expenditures and transfers represents saving by the government. Government saving is usually referred to as a government surplus: government surplus = government revenues − government transfers − government expenditures. If, as is often the case, the government is borrowing rather than saving, then we instead talk about the government deficit, which is the negative of the government surplus: government deficit = −government surplus = government transfers + government expenditures − government revenues. Toolkit: and You can review the government budget constraint in the toolkit. Applying the Tools to Social Security The life-cycle model and government budget constraint can be directly applied to our analysis of Social Security. Let us go back to Carlo again. Carlo obtains pretax income and must pay Social Security taxes to the government. Carlo’s disposable income in any given year is given by the equation disposable income = income − Social Security tax. Imagine that he receives no retirement income other than Social Security. Carlo’s lifetime resources are given by the following equation: lifetime resources = working years × income − working years × Social Security tax+ retirement years × Social Security income. Now let us examine Social Security from the perspective of the government. To keep things simple, we suppose the only role of the government in this economy is to levy Social Security taxes and make Social Security payments. In other words, the government budget constraint is simply the Social Security budget constraint. The government collects the tax from each worker and pays out to each retiree. For the system to be in balance, the government surplus must be zero. In other words, government revenues must equal government transfers: number of workers × Social Security tax = number of retirees × Social Security payment. Now, here is the critical step. We suppose, as before, that all workers in the economy are like Carlo, and one worker is born every year. It follows that number of workers = working years and number of retirees = retirement years. But from the government budget constraint, this means that working years × Social Security tax = retirement years × Social Security payment, so the second and third terms cancel in the expression for Carlo’s lifetime resources. Carlo’s lifetime resources are just equal to the amount of income he earns over his lifetime before the deduction of Social Security taxes: lifetime resources = income from working. No matter what level of Social Security payment the government chooses to give Carlo, it ends up taking an equivalent amount away from Carlo when he is working. In this pay-as-you-go system, the government gives with one hand but takes away with the other, and the net effect is a complete wash. We came to this conclusion simply by examining Carlo’s lifetime budget constraint and the condition for Social Security balance. We did not even have to determine Carlo’s consumption and saving during each year. And—to reiterate—the assumption that there is just one person of each age makes no difference. If there were 4 million people of each age, then we would multiply both sides of the government budget constraint by 4 million. We would then cancel the 4 million on each side and get exactly the same result.