Columbia University Department of Economics Lecture 21 Economics UN3213 Intermediate Macroeconomics Professor Mart ´ ın Uribe Spring 2019
Announcements Homework 6 due now Homework 7 will be posted today, due April 22 in class. Recitations: – review of hwk6 – Numerical example in lecture 20 (fiscal deficit and the inflation tax).
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Topics Today • Fiscal Policy and Ricardian Equivalence – Motivating Questions - How does a tax cut affect consumption, the real interest rate, and investment? - Do tax-cut induced fiscal deficits drive up interest rates and crowd- out investment? 3
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 View I: Tax cuts generate fiscal deficits. More government bor- rowing drives up interest rates. This crowds out investment. And tax cuts by increasing households’ disposable income stimulate con- sumption spending. ( r ↑ , I ↓ , C ↑ .) View II: Because tax cuts lead to higher public debt, sooner or later, the government must increase taxes to repay that debt (including interest). Hence tax cuts today lead to tax increases in the future. Households understand this, so they do not spend the tax cut on consumption goods. Instead, they save the tax cut in the bank to be able to pay for the future expected increases in taxes. So current spending does not increase, the interest rate does not increase, and investment does not fall. (∆ r = ∆ C = ∆ I = 0). This result is known as Ricardian Equivalence. 4
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Goal To evaluate views I and II, we will build a model of the equilibrium de- termination of consumption, investment, and the real interest rate. The model will be a two-period economy like in the lectures on the short-run effects of monetary policy. However, now, we abstract from nominal price rigidity. Instead we assume that prices are fully flexible. We will drop nominal prices all together and focus on the determination of real quantities only. 5
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 A Two-Period Model of Consumption, Investment, Savings and the Interest Rate The economy lasts for only two periods, period 1 and period 2. Basic Units of the Model 1. The Government 2. Firms 3. Households 6
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 1. The Government T 1 = taxes in period 1 T 2 = taxes in period 2 The government chooses T 1 and T 2 . Taxes are lump sum, in the sense that they do not depend on the household’s level of income, spending, or any other manifestation of wealth. G 1 = government spending in period 1 G 2 = government spending in period 2 G 1 , G 2 , are exogenously given. 7
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Government Debt, the Primary Deficit, and the Secondary Deficit Let B t denote government debt (bonds) issued in period t and ma- turing in period t + 1, for t = 1 , 2, r = denote the interest rate, The primary fiscal deficit is the difference between government spending and tax revenue, Primary Fiscal Deficit = G t − T t and the secondary fiscal deficit is the primary deficit plus interest payments on the public debt Secondary Fiscal Deficit = rB t − 1 + G t − T t . The negative of the secondary fiscal deficit is known as the secondary fiscal surplus or government savings. Thus, Government Savings = T t − rB t − 1 − G t . How do government spending, taxes, and the primary and secondary fiscal deficits look like in the real world? The next two figures displays U.S. data over the period 1929 to 2017. 8
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Taxes and Government Spending: U.S. 1929−2017 35 30 25 Percent of GDP 20 15 10 1930 1940 1950 1960 1970 1980 1990 2000 2010 T t /Y t G t /Y t (G t +r B t−1 )/Y t 9
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Primary and Secondary Fiscal Deficit, U.S. 1929−2017 12 10 8 6 Percent of GDP 4 2 0 −2 −4 1930 1940 1950 1960 1970 1980 1990 2000 2010 (G t −T t )/Y t (G t +r B t−1 −T t )/Y t 10
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Observations on the Graphs – Steady increase in the shares of government spending and taxes in GDP since 1930, from around 10% to near 30%. – Large increases in government spending and fiscal deficits are observed during World War II and during the great contraction of 2007-2009. – Protracted fiscal deficits during Reagan (1981-1989), Bush senior (1989-1993), and Bush junior (2001-2009). – Only time of secondary fiscal surpluses in recent history: Clinton (1993-2001). Let’s go back to our two-period model and see what we can say about the macroeconomic effects of changes in fiscal policy 11
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 The Government Budget Constraint in Period 1 Let S g 1 denote government savings in period 1. Then, the budget constraint of the government in period 1 is S g 1 = T 1 − rB 0 − G 1 We assume that the government starts period 1 with no debt, B 0 = 0. Thus, the government budget constraint in period 1 is given by S g 1 = T t − G t (1) Government savings can be positive or negative. When S g 1 is positive, government debt goes down, and when S g 1 is negative, it goes up, that is, B 1 = B 0 − S 1 . Since we assume that B 0 = 0, we have that the amount of debt outstanding at the beginning of period 2 is B 1 = − S g 1 . 12
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 The Government Budget Constraint in Period 2 In period 2 (the last period of this economy), the government uses its tax revenue, T 2 , plus all of its period-1 savings including interest, (1+ r ) S g 1 , to purchase goods, G 2 . The government’s budget constraint in period 2 is then given by G 2 = T 2 + (1 + r ) S g (2) 1 Notice that the government does not issue debt in period 2 ( B 2 = 0). This is because after period 2 the world ends, so no one would buy it. 13
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 The Intertemporal Budget Constraint of the Government Combining the period-1 and period-2 government budget constraints yields the intertemporal or present-value budget constraint of the government: G 2 T 2 G 1 + 1 + r = T 1 + (3) 1 + r This constraint says that the present discounted value of tax rev- enues (given by the right-hand side) must equal the present dis- counted value of government expenditures (given by the left-hand side). 14
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Summary of Government: Period 1 budget constraint: G 1 + S g 1 = T 1 (1) Period 2 budget constraint: G 2 = T 2 + (1 + r ) S g (2) 1 Present value government budget constraint: G 2 T 2 G 1 + 1 + r = T 1 + (3) 1 + r 15
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 Tax Cuts Today Imply Tax Increases in the Future Consider now a tax cut in period 1, that is, ∆ T 1 < 0. Suppose that the government does not change government spending in either period (i.e., ∆ G 1 = ∆ G 2 = 0). Then, to satisfy the intertemporal budget constraint, the government must raise taxes in period 2 by ∆ T 2 = − (1 + r )∆ T 1 > 0 The interpretation is that if neither current nor future government spending changes, a tax cut now (that is, in period 1) leads to a tax increase in the future (that is, in period 2). There’s no such thing as a free lunch. 16
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 2. Firms • Suppose that in period 1 firms borrow I 1 units of goods and convert them into capital goods (machines, structures, etc.) • In period 2, firms use the capital to produce final goods using the technology f ( I 1 ). The production function f ( · ) is assumed to be positive, f ( I 1 ) > 0, increasing, f ′ ( I 1 ) > 0 , and concave, f ′′ ( I 1 ) < 0 . Here, f ′ and f ′′ denote, respectively, the first and second derivatives of the function f ( · ). • In addition, in period 2 firms must repay their loans in the amount (1 + r ) I 1 . • In period 1, firms choose the level of investment, I 1 , so as to maximizes profits. 17
Intermediate Macro Ricardian Equivalence M. Uribe, 2019 The Firm’s Profit Maximization Problem We denote the profits of the firm in period 2 by Π. Profit is given by the difference between output, f ( I 1 ), and the cost of investment, including interest, (1 + r ) I 1 . That is Π = f ( I 1 ) − (1 + r ) I 1 ( ∗ ) Firms choose investment so as to maximize profits. That is, the optimization problem of the firm is max [ f ( I 1 ) − (1 + r ) I 1 ] I 1 We assume that each firm borrows an amount of funds that is too small to affect the interest rate. Therefore, it makes sense to assume that in choosing I 1 firms take the interest rate, r , as exogenously given. 18
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