7.3 The Household s Intertemporal Budget Constraint

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1 Summary Chapter 7 Borrowing, Lending, and Budget Constraints 7.1 Overview - Borrowing and lending is a fundamental act of economic life - Expectations about future exert the greatest influence on firms investment decisions - A shift of spending over time can be seen as an Intertemporal trade - An Intertemporal budget constraint is the relationship summarizing resources and opportunities available in the present and the future to a household for consumption; the present value of spending must be less than, or equal to, wealth 7.2 Thinking About the Future The Future Has a Price - Anything of value must have a price - By choosing between consuming now or in the future, we effectively decide whether to save or to borrow The Rational Expectations Hypothesis - The rational expectations hypothesis is the hypothesis asserting that agents evaluate future events using all available information efficiently so that they do not make systematic forecasting errors - The model assumes that individuals do not make systematic mistakes, not that people are flawless - We adopt the rational expectations model for three reasons: 1. There is no real alternative because of too many irrationalities in human thinking 2. Economic theory is based on optimization in the sense that agents behave rational 3. Even if people are irrational sometimes, it is unlikely that they are systematically wrong - In markets; it is enough for some to be well informed in order to drive the markets in the way that they are supposed to move 7.3 The Household s Intertemporal Budget Constraint Consumption and Intertemporal Trade - Endowment are the exogenous resources that economic agents expect to have in the present and in the future - The autarky point is the state in which a country operates when it does not trade with the rest of the world - Intertemporal trade is trade conducted by households and firms across time The Real Interest Rate - The real interest rate is the difference between the nominal interest rate and the expected rate of inflation - The price of tomorrow s consumption in terms of today is and is called the Intertemporal price - Discounting values future goods or money in terms of goods or money today - Intertemporal trade allows agents to choose combinations of consumption today and tomorrow which are different from their autarky point - The budget line is the line expressing the resource constraint of households in consuming today and tomorrow, the slope is the negative of the gross interest rate

2 7.3.3 Wealth and Discounted Values - If income in a period is greater than consumption, the individual saves, if consumption is greater, he borrows - The budget line can be expressed as: - Rearranging this formula gives: value of consumption value of income Wealth derived from income - The left-hand side is the present discounted value of consumption. It is sum of today s and tomorrow s consumption valued in terms of today s goods - The right-hand side is maximum consumption that one could enjoy today, given his resources today and tomorrow - If the individual has an initial wealth of, his budget constraint will be modified as follows: - If, he can consume more in both periods, if it s less than 0, then he starts with a debt and therefore consumes less in both periods 7.4 The Firm and the Private Sector s Intertemporal Budget Constraint Firms and the Investment Decision - Production requires that resources are diverted from consumption and use to acquire productive capital - Investment is the acquisition of productive equipment for later use in production; also called fixed capital formation - Firms can either obtain resources in the capital market or use their own funds in order to finance their investment The Production Function - The investment decision depends upon the amount of output that can be produced with the available equipment - The production function (F(K)) is the theoretical relationship linking aggregate output to inputs of factors of production - The more capital is accumulated, the additional or marginal yield declines - Diminishing marginal productivity is the tendency that, as the inputs into production are increased, the increments of output will decline The Cost of Investment - Today s investment represents the total stock of capital available for production tomorrow - When K is invested into production equipment, one will receive output F(K) tomorrow - When K is lent in the capital market, one will receive (1 + r)k tomorrow - The real interest measures the opportunity cost, the value of a resource in its best alternative use, of the resources used in investment

3 - The interest rate r is crucial for the valuation of investments - The net return V from investing K is simply the difference between the present value of output tomorrow and investment today: - An investment project is economically justifiable only if It has a positive present value, which means that either - Some investments require a reduction in interest rates or an improvements in technology to become worthwhile The Intertemporal Budget Constraint of the Consolidated Private Sector - As long as an investment project has a positive present value, the investment increases wealth - Starting from the Autarky point, one can save either by investing or by lending - If investment is the case, then savings are equal to investment which is equal to the capital stock for tomorrow s output production - The more one invests, the larger will be tomorrow s production - Tomorrow s income and consumption will now be the sum of the endowment and the produced output - The Intertemporal budget constraint determines the present value of consumption as equal to total wealth - We can rewrite the Intertemporal budget constraint as: value of consumption Total Wealth Wealth from income Value of the firm - Wealth now consists of the present discounted value of the endowment and the net value of the investment activity

4 7.5 Public and Private Budget Constraints The Public Budget Constraint - The government is little different from another economic agent. It can borrow, but is expected to repay its debt with interest - The government spends today and tomorrow. It raised net taxes of today and tomorrow. The government has an outstanding debt of in the beginning of period one which must be repaid at interest rate - A primary deficit is a budget deficit net of debt service - The governments budget constraint can be written as: -This budget constraint can be rewritten as: Public debt = value of Primary budget surpluses - For the government to obey its Intertemporal budget constraint the sum of the present value of primary budget surpluses is equal to initial outstanding debt - The budget line has a slope of - Governments with debt and deficits today must run primary surpluses tomorrow, and vice versa The Consolidated Public and Private Budget Constraint - Both households and firms have to pay taxes - The private and public Intertemporal constraints are as follows: - The private citizens pay the taxes while the government receives them - Usually the public and private sectors have different interest rates as the public sector is considered safer - Combining the private and public budget constraints yields the consolidate budget constraint: value of = value of private resources + consumption net of government spending value of the government s financing advantage - Before consolidation, private income is the present value of net of taxes income over both periods - The first part of the equation shows that the private sector can only consume what the government has not taken for itself - The second part of the private income shows the difference between the interest rates at which the government and the private sector can borrow (the more the government borrows, the better for the private sector)

5 7.5.3 The Ricardian Equivalence Proposition - If the interest rates of the private sector and the government are equal, the consolidated budget constraint will look like this: - The Ricardian equivalence proposition is a hypothesis that the time profile of taxes needed to finance a given stream of government purchases has no effect on agents Intertemporal budget constraint and therefore on real spending and saving decisions, the public debt is not considered as private wealth When Ricardian Equivalence Fails - The Ricardian Equivalence result is highly controversial - The Ricardian Equivalence implies that government borrowing and the resulting debt does not contribute to the wealth position of households - This result requires a requires a number of assumptions -These assumptions explain why the Ricardian Equivalence would fail Different interest rates - Governments are considered less risky and so their interest rates always tend to be lower than those of public firms - Interest rates are endogenous and depend on a number of factors Mortal or new citizens - Some citizens pay higher taxes than others - The private sector currently alive may factor in only a fraction of all future tax liabilities - Migration as well as others who enter later will pay taxes to reimburse the public debt issued before they arrived Restrictions on borrowing - Some households cannot borrow as much as their future expected income would let them, some cannot borrow at all - In cases like these, individuals benefit when the government runs a deficit today, causing the individual to be able to consume on a higher indifference curve Distortionary taxation and unemployment resources - People change their behaviour in response to taxes - Taxation on labour income or wages will lead to some being dissatisfied with their job and work less - If a tax cut increases economic activity and creates additional income, then the associated fiscal deficit will be associated with higher wealth Evidence - It is unlikely that the Ricardian Equivalence could ever hold in practice - It is very unlikely that the private sector would completely disregard what the government is up to - There is some evidence that the Ricardian Equivalence has some real life application, but this is only a small fracture of the whole picture

6 7.6 The Current Account and the Budget Constraint of the Nation The Primary Current Account - The consolidation of the budget constraints of the private and public sectors can be thought of as the Intertemporal budget constraint of the whole nation - The current account can be decomposed into a primary current account and net investment income: where F represents the country s net asset position in relation to the rest of the world, and r is the real interest rate - The primary current account is also the difference between GDP output and aggregate domestic spending when unilateral transfers are equal to zero - In the two-period framework, the budget constraint of the nation requires the primary current account surplus to be greater than or equal to the value of international assets in the first period: value of current and future primary accounts Existing net external debt -If a country has a net wealth of the beginning of period 1, it can run future current account deficits Enforcement of International Credit Contracts and Sovereign Borrowing - Governments, private households and firms face an international budget constraint that limits them from borrowing at any point in time to the present value of lifetime resources - There is a difference between international borrowing by private entities and sovereign borrowing by national governments - Sovereign borrowing is borrowing undertaken by national governments with foreigners, usually in the form of bond issues or loans by international banks - If governments cannot pay for their debts anymore, two things can be done, renegotiations about the terms of repayment, or debt forgiveness