GRA 6639 Topics in Macroeconomics

Lecture 9 Spring 2012 An Intertemporal Approach to the Current Account Drago Bergholt (Drago.Bergholt@bi.no) Department of Economics

INTRODUCTION Our goals for these two lectures (9 & 11): - Establish an intertemporal (microfunded) equilibrium model suitable for a systematic and rigorous study of the current account. - Use the model to address the following issues: a. What determines current account surpluses and deficits? b. How does the current account respond to shocks? c. Are current account deficits always bad? d. How is the current account affected by fiscal policy? e. What determines the world interest rate? f. What explains the global imbalances that have emerged the last decade? g. How long can deficits be sustained, and when is a country bankrupt (last lecture)? 2.

INTRODUCTION Case studies: - Hopefully, we will also have the time conduct a number of interesting case studies: a. Why has Norway s current account grown so much over the last decades? b. How could (can) the U.S. current account deficit be so large, while the U.S. (and world) real interest is so low? c. Why did the world interest rate rise so much in the 1980 s? d. What s up with the Greeks (the current financial crises)? Or what separates Greece from Australia? e. What is the optimal fiscal policy rule in Norway (handlingsregelen)? 3.

INTRODUCTION Readings - Main reference: Obstfeld, M. and K. Rogoff (1996): Foundations of international macroeconomics, ch. 1.1-1.3 and 2.1-2.3. - Others: a. Bernanke, B. S. (2005): The Global Saving Glut and the U.S. Current Account Deficit, speech March 10, 2005. b. Blanchard, O. and G. M. Milesi-Ferretti (2009): Global Imbalances: In Midstream?, IMF Staff Position Note 09/29. c. IMF World Economic Outlook Sept. 2011: Slowing Growth, Rising Risks, ch. 1-2. Link: http://www.imf.org/external/pubs/ft/weo/2011/02/pdf/text.pdf. 4.

WHAT IS THE CURRENT ACCOUNT? Definition of the current account - The change in the value of net claims on the rest of the world. - The net increase in foreign asset holdings. Current account = + Trade account Exports imports of goods and services + Primary income account Payments for use of labor and financial resources + Secondary income account Redistribution (foreign aid, etc.) 5.

WHAT IS THE CURRENT ACCOUNT? The canonical current account equation - Let denote the value of an economy s net foreign assets at the end of period (in what period is a state variable?). - Then, the current account at time,, is defined as: or - Net export:. - Gross national product (GNP):. - The accumulation equation updated: 6.

GLOBAL IMBALANCES A bird s view of global imbalances Source: IMF World Economic Outlook, September 2011 7.

A cross-country perspective GLOBAL IMBALANCES 8.

GLOBAL IMBALANCES A historical perspective: Current accounts in U.S. as share of GDP 9.

THE SIMPLEST POSSIBLE MODEL Environment - Small open economy where agents can borrow and lend at a world market interest rate (the interest rate is given). - The economy exists for two periods,. - One (macro) consumption good in each period. - Endowment economy, output in each period is given as and. - No investments, no public sector. - Representative household, population normalized to one. - Perfect foresight economy (no uncertainty, no shocks). - Several of these assumptions will be relaxed later. 10.

THE SIMPLEST POSSIBLE MODEL The representative household s problem - Lifetime utility:, (1) where is the discount factor, and, and. - Financial wealth after first period (assume ):. - Financial wealth after second period:. - Why is? - The intertemporal budget constraint (combine the two above): (2) 11.

THE SIMPLEST POSSIBLE MODEL The representative household s problem - The representative household s problem is to maximize (1) subject to (2). - Solve (2) for : - Insert into (1): ( ) - First order condition with respect to : (3) - Equation (3) is the familiar (consumption) Euler equation. 12.

GRA 6639 Topics in Macroeconomics THE SIMPLEST POSSIBLE MODEL The representative household s problem - Notice that (3) can be written as: (4) - Increasing consumption path if and only if (why?). - Optimal consumption level can in principle be found by combining the Euler equation and the intertemporal budget constraint. - Special case: If, the Euler equation implies and the BC yields: (5) 13.

THE SIMPLEST POSSIBLE MODEL Determination of the current account - The accumulation equation in our simple model:, (6) - Remember the period budget constraints: Period 1: Period 2: - Current account period 1: - Current account period 2: - Implied lifetime trade balance: 14.

THE SIMPLEST POSSIBLE MODEL The autarky interest rate - Imagine the economy were closed (autarky). - Equilibrium conditions: and. - The interest rate that satisfies the Euler equation when is called the autarky interest rate: (7) - A decline (increase) in (with fixed) raises (lowers) the autarky interest rate. - Comparative advantage: Countries tend to import present consumption when autarky interest rates (the price of present consumption) are high. - Special case: implies. 15.

THE SIMPLEST POSSIBLE MODEL Gains from open capital markets 16.

THE SIMPLEST POSSIBLE MODEL Gains from open capital markets - Suppose : - Consumption levels in both periods are given by (5). - The current account becomes: - The difference between present and future income (i.e. economic growth) is the main determinant of the current account. - depends on the growth rate, not on the absolute income level. 17.

THE SIMPLEST POSSIBLE MODEL Summing up - The absolute income level should not be an important determinant of the current account. - Countries with high expected income growth would tend to have current account deficits, countries with low (negative) growth would tend to have surpluses. - Patient countries (high ) would run surpluses, impatient ones deficits. - Current account deficits are not necessarily a bad thing! - Gains from intertemporal trade as long as. - Intertemporal trade makes consumption smoothing possible (why is that good?). - Gains are obtained by trade with someone different from oneself. 18.

THE SIMPLEST POSSIBLE MODEL Does the model help explain - Big deficits in the U.S., large surpluses in China? - Large surpluses among oil producers? Extensions - Investments. - A public sector. - Large economies (China and the U.S. are not small economies, they may affect the world interest rate). 19.

GOVERNMENT CONSUMPTION AND TAXES Environment - Now we add a public sector. Assume that public spending is financed by a lumpsum tax. The government can lend and borrow just as households. - Household s (period) utility is separable in private and public consumption (is this a strong assumption?): - need not be equal to, but the lifetime public budget must be balanced. - The government s intertemporal budget constraint: - Disposable (after tax) income:. 20.

GOVERNMENT CONSUMPTION AND TAXES Household s intertemporal budget constraint - Financial wealth after first period:. - Financial wealth after second period:. - Household s intertemporal budget constraint: (8) - The Euler equation is unaffected because utility is separable. - The current account: 21.

GRA 6639 Topics in Macroeconomics GOVERNMENT CONSUMPTION AND TAXES Fiscal policy and the current account - Assume. The Euler equation then implies and the BC yields: - The current account: (9) - Temporarily high (low) public spending will reduce (increase) the current account. - Taxes or the government budget does not matter (Ricardian equivalence). 22.

INVESTMENT Motivation - So far we have treated output as an exogenous variable. This very unrealistic assumption can be relaxed. - Mechanism: Investment in factors used in production increases current output possibilities. - An important motivation for borrowing abroad is to finance investments. Norway in the 1970 s is one example. 23.

INVESTMENT Environment - Production function: (10) with, and - Assume that initial capital, which is given by nature, fulfills (realistic?). - Law of motion for capital (we ignore depreciation): (11) - Remarks: a.. Why? b.. - Everything else is the same. 24.

INVESTMENT The current account - Change in total domestic wealth, i.e. national saving: - The current account (from the equation above and (11)): (12) - Saving: (13) - Combining (12) and (13), the current account can be written as: (14) - Equation (14) is yet another way to define the current account. Countries with lower (higher) savings than investments run current account deficits (surpluses). 25.

INVESTMENT The current account, saving and investment 2006 (percent of GDP) 26.

INVESTMENT The intertemporal budget constraint - Financial wealth after first period:. - Financial wealth after second period:. - Household s intertemporal budget constraint: (15) - Now the representative household must decide how much to invest in addition to how much to consume. 27.

INVESTMENT The representative household s problem - Notice that the intertemporal budget constraint can be rewritten as: ( ) - Lifetime utility of the representative household,, becomes: [( ) ](16) - First order conditions: : : (17) 28.

INVESTMENT The optimal saving plan - Now there is two ways of saving for the future: a. Lending in international financial markets with constant returns. b. Investing in productive capital at home with diminishing returns. - Equation (17),, suggests investing at home until the marginal return on that investment is equal to returns in the capital market. - Remark: The desired capital stock is independent of preferences. 29.

INVESTMENT The production possibilities frontier - The production possibilities frontier (assume ): - Interpretation: Available technological possibilities for transforming period 1 consumption into period 2 consumption in autarky. - Rewrite to a function of period 1 variables only: ( ) (18) - Notice that:, 30.

INVESTMENT Investment and the current account - TBA 31.

INVESTMENT Comparative statics in the model with investments - What happens to the current account if: a. The interest rate increases. b. There is a positive productivity shock in, the productivity level in period 1. c. There is a positive productivity shock in, the productivity level in period 2. d. There is a higher predetermined capital stock (exogenous increase in wealth). - Preliminaries: Assume. Then (10), (13), (14) and the capital law of motion yields a current account with capital growth: ( ) - This current account identity will be used for comparative statics. 32.

( ) INVESTMENT Case a: A raise in the interest rate - Substitution effect on saving: Relatively cheaper consumption in period 2 higher saving - Income effect on saving: a. Net borrowers : Income b. Net lenders : Income - Investment effect: (from (17)) - Net effect: for borrowers, for lenders. 33.

( ) INVESTMENT Case b: Positive productivity shock in - Saving effect: Case c: Positive productivity shock in - Consumption smoothing effect: - Investment effect: (from (17)) - Net effect: - Lesson: Higher future productivity lowers today s current account. 34.

( ) INVESTMENT Case d: Higher initial capital (exogenous increase in wealth) - Income effect: Increases total wealth, parts of which give - Investment effect: unaffected, so - Last effect dominates because changes one for one with while changes less than one for one. - Net effect: - Lesson: Countries with high capital stocks should tend to have surpluses. 35.

A TWO-REGION WORLD ECONOMY Introduction - So far we have looked at a small open economy which, by being small, takes the world interest rate as given. - Now it is time to abandon the small economy assumption and study how the world interest rate is determined, and how it interacts with the current account. Environment - The world consists of two countries (regions), Home and Foreign (*) - We ignore the public sector. - We look at endowment economies first, but reintroduce production and saving later. - The period utility, the Euler equation, and the budget constraint are as before (in both countries). 36.

Global market clearing A TWO-REGION WORLD ECONOMY - Market clearing in the endowment economy: - Implied world saving: - Implied world current account ( and without investment): - Walras law: Consider an economy with markets. If markets are in equilibrium, then the last market must also be in equilibrium. - By Walras law the world economy is in equilibrium if: (19) 37.

A TWO-REGION WORLD ECONOMY Savings and the world interest rate - The world interest rate is determined by and (the two countries net supply of period 1 consumption). For now, we assume and. - This gives the following world interest rate in equilibrium : 38.

A TWO-REGION WORLD ECONOMY Savings and the world interest rate - Notice that represents the price of present consumption in terms of future consumption, i.e. the price of a period 1 surplus country s export good in terms of its import good. - In the figure, clears markets in the sense that Home s supply (lending) of period 1 consumption to Foreign is equal to Foreign s demand (borrowing) for period 1 consumption from Home. - Comparative statics: What happens if increases? What happens if increases? (Hint: refer to case b. and c. in the small economy model) - Remark: When drawing the figure, we assumed that and. That assumption is analyzed next. 39.

A TWO-REGION WORLD ECONOMY Consumption and the world interest rate - is Home s net supply of period 1 consumption to Foreign, while is the equivalent supply from Foreign. - Since, the relationship between (Home) saving and the world interest rate in our two-period model is: - Thus, to find, we need to identify how consumption depends on the interest rate ( is treated as exogenous for now). 40.

A TWO-REGION WORLD ECONOMY A small detour: The elasticity of intertemporal substitution - From the Euler equation (derivation in class): - Definition of the elasticity of intertemporal substitution : (20) - The elasticity of intertemporal substitution is constant when utility is isoelastic: (21) where and (22) 41.

A TWO-REGION WORLD ECONOMY The shape of the savings schedule - From the budget constraint (2) and the Euler equation (4): [ ] - Implicitly differentiating with respect to gives (derivation in class): (23) - Assume that period utility is given by (22). Then (23) becomes (derivation in class): (24) - Result: A rise in the world interest rate has an ambiguous effect on Home s period 1 consumption. 42.

A TWO-REGION WORLD ECONOMY The effects on saving and consumption of a rise in - Note that: - If Home is a borrower in period 1,, then a rise in unambiguously leads to higher saving and lower consumption. - As rises however, Home must eventually become a lender, i.e.. If is not that much higher than, a rising still increases saving and lowers consumption. - When becomes sufficiently high, saving can actually drop and consumption increase. 43.

A TWO-REGION WORLD ECONOMY Saving, the current account and the world interest rate revisited 44.

A TWO-REGION WORLD ECONOMY Optimal consumption growth path - When utility is isoelastic the Euler equation (3) can be written as: - Note that the implied optimal growth rate of consumption is: (25) Remarks: a. Optimal consumption growth is positive if. b. Optimal consumption growth is high in absolute value if is high. What is the intuition behind these results? 45.

A TWO-REGION WORLD ECONOMY Substitution, income and wealth effects of an interest rate change - Insert (25) into the budget constraint (2) to find optimal period 1 consumption: (26) - Substitution effect: Higher means that the price of current consumption in terms of future consumption rises. That reduces consumption today (i.e. more saving). - Income effect: Higher allows higher future consumption. Some of this positive income effect is spilled over to period 1 through higher consumption today. - The tension between the two effects above is reflected in. - Wealth effect: Higher lowers lifetime income and reinforces the substitution effect in lowering current consumption and raising saving. 46.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Environment - We now introduce investment to the two-region world economy model. - Production in Home and Foreign: and - We continue to abstract from government sector. - Besides being large economies, everything else is the same (as in the small economy model with investment). 47.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Equilibrium - Equilibrium requires: - Using (13) this is equivalent to: - Using (14) there is an implied mutual consistency between current accounts: 48.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Investment schedules - The investment schedules are given as in (17) (where we use that ): and - A rise in leads to lower and ( and are predetermined as before). 49.

INVESTMENT, SAVING AND THE METZLER DIAGRAM The shape of the savings schedule - The intertemporal budget constraint in Home is still (15) (but no government sector). - The budget constraint (15) combined with the Euler equation gives: {[ ] } - Implicitly differentiating with respect to in the general case (derivation in class): [ ] - In the isoelastic utility case this becomes very similar to (24): - Thus, given current account balances, the slope of the savings schedule identical to its counterpart in the endowment case. 50.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Saving, the current account and the world interest rate revisited 51.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Application 1: An increase in Home s impatience - Suppose households in Home become more impatient, represented by a fall in. - By inspecting the Euler equation we find that lower implies less period 2 consumption relative to period 1 consumption. - in figure shifts to the left. - increases to restore equilibrium in financial markets. - Home saving and investment falls, Foreign investment falls, Foreign saving increases. 52.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Application 2: A rise in Home s future productivity - Suppose suddenly is expected to be higher. - What is the effect on the investment schedule? The investment schedule skifts outwards. - What is the effect on the saving schedule? responds to shifts in productivity as if there are purely exogenous output changes. Higher leads to a shift in inwards. 53.

INVESTMENT, SAVING AND THE METZLER DIAGRAM Application 2: A rise in Home s future productivity - Assume initially balanced current accounts. - Home s current account becomes negative. - Foreign s current account becomes positive due to more saving and less investment. - The world interest rate increases. 54.

GLOBAL IMBALANCES REVISITED Case study: The global saving glut and the U.S. deficit - Puzzle: How can the U.S. current account deficit be so large, while the U.S. (and world) real interest rate is so low? 55.

GLOBAL IMBALANCES REVISITED Case study: The global saving glut and the U.S. deficit - Traditional view: U.S. consumers save too little. - But why then the low interest rates? - Bernanke (2005): A significant increase in global supply of savings can explain the low level of world interest rates and the U.S. current account deficit. 56.

GLOBAL IMBALANCES REVISITED Case study: The global saving glut and the U.S. deficit - Bernanke (2005): The global saving glut and the U.S. current account deficit a. Increase in global saving due to: - Strong motives for saving in countries with ageing populations (e.g. Germany and Japan). - High commodity prices has triggered savings in many (developing) countries. - Low prospective returns to domestic investment in many industrialized countries (due to e.g. slowly growing workforces and high capital-labor ratios). b. Low U.S. saving because of high equity and house prices. Also, anticipations of high productivity in the U.S. based on experiences from the 1990 s. - How can we understand this using our two-country model (sketch in class)? 57.

GLOBAL IMBALANCES REVISITED Case study: The global saving glut and the U.S. deficit - Important issue: Is the U.S. current account deficit sustainable? - That is one of the topics next time. 58.

EXERCISES 1. Discuss reasons why a country may find it optimal to run a current account deficit. 2. Consider the two-country endowment model studied in class. Home s utility is: a. Show that Home consumption in period 1 is: b. Show that Home saving in period 1 is: c. Compute the interest rate when Foreign has the same preferences, but possible different endowments and. 59.