Appendix: budget constraints

Summary

In the following, I will use simple concepts and notation to clarify a few details on the functioning of budgetary constraints.

A growing fiscal deficit can be financed by increasing taxes, reducing expenditure or increasing the amount of money in circulation

The government deficit can be written as follows:

where Dt indicates the government deficit at time t. C_t ^g are current public expenditures, I_t ^g those for investment, while Tt represents the total revenue. The government also has debt that involves interest expenses; L_t ^bg is the debt of the government to the central bank (for example, with QE of recent years, the central banks of the main countries of the world have purchased large amounts of government bonds); L_t ^cg is the debt placed with commercial banks, investment funds and the public, that is, the debt not held by the central bank. This debt pays an interest rate equal to i, so that the product between (L_t ^bg + L_t ^cg) and the sum of the two debts indicates the annual cost of the debt in terms of expenditure for interest (note that the symbol “·” indicates the operation of multiplication between two terms). The government usually also issues debt in foreign currency L_t ^fg whose interest is indicated by i. E represents the exchange rate translating the debt issued in foreign currency in the domestic currency. For example, if the debt is issued in dollars and the government deficit is expressed in euros, it represents how many euros it takes to buy a dollar (at the time of writing, it requires fewer euros to buy a dollar). Mt represents the money issued by the central bank and (M_t −M_t−1) its variation. It basically indicates the share of the deficit that can be financed by the printing of currency (“seigniorage”). In writing the budget constraint in this way we are assuming that the central bank pays its profits to the state coffers, as usually happens even in countries where the central bank is independent.