EC 324: Macroeconomics (Advanced)

EC 324: Macroeconomics (Advanced) Consumption Nicole Kuschy January 17, 2011

Course Organization Contact time: Lectures: Monday, 15:00-16:00 Friday, 10:00-11:00 Class: Thursday, 13:00-14:00 (week 17-25) Course supervisor: Nicole Kuschy Email: nkusch@essex.ac.uk Office hours: Monday, 16:00-18:00

Assessment Coursework: mid-term on Friday 25th of February, 17:00 Exam: 2 hours, during the summer term Final mark: Whichever is the greater: EITHER 50% coursework mark, 50% exam mark OR 100% exam mark Details in Undergraduate Economics Handbook.

Reading Textbook: Sørensen, Peter Birch and Hans Jørgen Whitta-Jacobsen (2010): Introducing Advanced Macroeconomics: Growth and Business Cycles, McGraw-Hill. (SWJ) Supplementary readings: Romer, David (2006): Advanced Macroeconomics, 3rd Edition, McGraw-Hill. Journal articles as indicated. Lecture notes and additional material posted on the CMR.

Agenda I What we want to do: build a model of the macro economy based on solid (i.e., microeconomic) foundations build a model of the macro economy that fits the facts (e.g., in the light of time-series data) consider policy issues What we don t want to do: make ad-hoc assumptions ignore empirical data

Agenda II 1 Consumption 2 Investment 3 Monetary Policy Rules 4 Incomplete Nominal Adjustment 5 The Phillips Curve 6 An Empirical AD/AS Model 7 Rational Expectations and Policy Ineffectiveness 8 Credibility and Policy Making 9 Delegation

Lecture 1: Consumption Main reading: SWJ, chapter 15 1 Criticism of the Keynesian consumption function 2 Intertemporal consumption problem 3 Interest rates 4 Government policy and Ricardian Equivalence * Bernheim (1987), NBER Macro Annual Note: focus on total consumption throughout aggregate over goods and across individuals

Keynesian Consumption Function (KCF) Keynes 3 Conjectures on the Consumption Function 1 (Disposable) income, not the interest rate, is the primary determinant of consumption. So have C t = C(Yt d ), where Yt d = Y t T t. 2 MPC is between zero and one. 0 < dct < 1. dyt d 3 APC falls as income rises. decreasing in Yt d. C t Y d t Idea is that saving is a luxury, so rich people save more than poor. Example: C t = a + by d t, a > 0, 0 < b < 1. b is MPC wrt. disposable income

Theoretical Criticism of the KCF 1 C t = C(Yt d ) may be OK as a simple, rough approximation. But what about C t s relation to Yt+1 d, Y t+2 d etc.? 2 Why doesn t C t depend on r t in the same way savings and investment do? And what about r t+1, r t+2 etc.? 3 No distinction between permanent and temporary changes in policy.

consumption in microeconomic cross-section data Empirical Criticism of the KCF Figure: Income and consumption in microeconomic data. The McGraw-Hill Companies, 2005 Slide 1/1 Microeconomic cross-sections indicate that consumption share is lower for rich families.

consumption in macroeconomic time series data Empirical Criticism of the KCF Figure: Income and consumption in macroeconomic data. The McGraw-Hill Companies, 2005 Slide 1/2 Macroeconomic time-series indicate that aggregate consumption share is constant over time.

Empirical Criticism of the KCF. Figure 16.2: The average propensity to consume in USA and Denmark Source: National Income Accounts, Bureau of Economic Analysis and ADAM database, Statistics Denmark Figure: Average propensity to consume in USA and Denmark. The McGraw-Hill Companies, 2005 Slide 1/3

Empirical Criticism of the KCF Conclusion: KCF unsatisfactory need a more developed model We focus on the Permanent Income Hypothesis (PIH); the idea is that individuals make consumption/savings decisions across time, i.e., intertemporal choice.

Permanent Income and Life Cycle Hypotheses PIH [Milton Friedman]: Loosely states that households base consumption on average income levels (i.e., their permanent income and not year-to-year income); this implies households need to know what their income is over a long time horizon. consumption smoothing can distinguish transitory versus permanent shocks LCH [Franco Modigliani]: Suggests that households consume a constant percentage of the present value of their lifetime income; average propensity to consume (wrt. current income) is high in households that are young or old, because the former borrow against future income, while the latter run-down lifetime savings.

Intertemporal Consumption Problem Setup A Two-Period Endowment Economy Households are alive for two periods, t = 1, 2 {today, tomorrow}. There is a single good, Y t. Perfect capital markets: Households borrow and lend at the same market interest rate, r. No uncertainty.

Intertemporal Consumption Problem Consumer Preferences Household maximizes lifetime (t = 1, 2) utility, U: U = u(c 1 ) + βu(c 2 ) (1) β (0, 1) is a fixed subjective discount factor (sometimes called private discount factor) measuring the impatience to consume. Aside: SWJ put 1 1+φ C t is consumption at time t. rather than β. u is the period utility function, with u (C) > 0 and u (C) < 0. Implication: Desire to smooth consumption.

Intertemporal Consumption Problem Budget Constraint Lifetime budget constraint: C 1 + C 2 1 + r = W 0 + (Y 1 T 1 ) + (Y 2 T 2 ), (2) 1 + r where 1/ (1 + r) is the market discount factor for future consumption and W 0 is the (given) level of initial wealth. Equation (2) tells us that the present value of lifetime consumption is equal to the present value of lifetime (after tax) income, plus initial wealth.

Intertemporal Consumption Problem Optimization Problem Maximize (1) subject to (2): s.t. max C 1 U = u(c 1 ) + βu(c 2 ) C 2 = (1 + r) [W 0 + (Y 1 T 1 ) C 1 ] + (Y 2 T 2 ) First order condition: u (C 1 ) β(1 + r)u (C 2 ) = 0 Rearrange: 1 + r = u (C 1 ) βu (C 2 ) This Consumption Euler Equation tells us that the substitution of consumption across time (i.e., the intertemporal marginal rate of substitution) should be equal to the intertemporal relative price. (3)

Intertemporal Consumption Problem Figure 16.3: The consumer s optimal intertemporal allocation of consumption Equilibrium Allocation Figure: Optimal intertemporal allocation of consumption. The McGraw-Hill Companies, 2005 Slide 1/4

Intertemporal Consumption Problem Equilibrium Allocation Budget constraint: C 1 + C 2 1 + r = W 0 + (Y 1 T 1 ) + (Y 2 T 2 ) 1 + r totally differentiate to derive the slope: dc 1 + dc 2 1 + r = 0 dc 2 dc 1 = (1 + r) Indifference curve: U = u(c 1 ) + βu(c 2 ) = const. totally differentiate to derive the slope: du = u (C 1 )dc 1 + βu (C 2 )dc 2 = 0 dc 2 dc 1 = u (C 1 ) βu (C 2 )

Intertemporal Elasticity of Substitution (IES) We make some functional form assumptions on utility for the same reasons we did with the Keynesian consumption function. Suppose: C 1 σ 1 t u(c t ) =, σ > 0, σ 1 1 1 σ ln C t, σ = 1 (4) This is sometimes called power utility or CRRA.

Intertemporal Elasticity of Substitution (IES) The parameter σ determines the slope of the indifference curves and how consumption is substituted across time. High σ will be consistent with high substitution (consumption pattern sensitive to r). The parameter σ denotes the intertemporal elasticity of substitution of consumption, defined as: IES = d(c 2 /C1)/(C 2 /C 1 ) dmrs(c 2, C 1 )/MRS(C 2, C 1 ) = d log(c 2 /C 1 ) d log MRS(C 2, C 1 ) Power utility (4) has constant IES of σ.

Intertemporal Elasticity of Substitution (IES) Figure 16.7: The relation between the shape of the indifference curve and the intertemporal substitution elasticity The McGraw-Hill Companies, 2005 Figure: Indifference curves and IES. Slide 1/9

Intertemporal Consumption Function (ICF) I With functional form (4), Euler equation (3) implies: C 2 = [β(1 + r)] σ C 1 Using the budget constraint (2), we get the consumption function: C 1 = W 0 + (Y 1 T 1 ) + 1 1+r (Y 2 T 2 ) 1 + (1 + r) σ 1 β σ We call this (and the analogous expression for C 2 ) the Intertemporal Consumption Function. Accordingly, current consumption is proportional to current wealth (i.e., the PV of lifetime wealth).

Intertemporal Consumption Function (ICF) II Generic ICF: C 1 = [ θ W 0 + (Y 1 T 1 ) + 1 ] 1 + r (Y 2 T 2 ) with: θ 1 1 + (1 + r) σ 1 β, σ 0 < θ < 1 Consumption depends on r - unlike the KCF. Y 2 and T 2 also matter for C 1. expectations about the future matter for today s consumption there will be differences between permanent and temporary taxation policies

Income Effects - Comparing KCF and ICF I Recall the KCF: C t = a + b(y t T t ), where b (0, 1) measures the MPC wrt. current disposable income. Now the ICF: [ C 1 = θ W 0 + (Y 1 T 1 ) + 1 ] 1 + r (Y 2 T 2 ), where θ (0, 1) measures the MPC wrt. wealth (initial wealth plus disposable income in both periods). Cannot directly compare b and θ.

Income Effects - Comparing KCF and ICF II Let ω 0 W 0 /Y1 d and (1 + ge ) Y2 d/y 1 d and rearrange ICF: [ C 1 = θ W 0 + (Y 1 T 1 ) + 1 ] 1 + r (Y 2 T 2 ) [ = θy1 d 1 + 1 Y2 d 1 + r Y1 d + W ] 0 Y1 d [ ( ) ] 1 + g = θy1 d e 1 + + ω 0 1 + r Then have: C 1 = θy d 1 with: θ θ [1 + ( ) ] 1 + g e + ω 0 1 + r Now θ is the MPC wrt. current disposable income and comparable to b.

Income Effects - Comparing KCF and ICF III Together: 1 θ = 1 + (1 + r) σ 1 β σ [ 1 + ( ) ] 1 + g e + ω 0 1 + r In essence, we have micro-founded b. We have a solid idea of the determinants of θ: β : impatience to consume σ : intertemporal elasticity of substitution r : market rate of return g e : expected growth of future disposable income ω 0 : initial wealth to income ratio

Interest Rates The Role of Interest Rates Interest rates play a significant role in the ICF. Income, substitution and wealth effects are at work. 1 Change in r affects MPC wrt. wealth, θ = 1 1+(1+r) σ 1 β σ : θ/ r > 0 if σ < 1 θ/ r < 0 if σ > 1 If σ = 1, income and substitution effects cancel out and do not affect the MPC wrt. wealth, i.e., θ/ r = 0. 2 However, even if σ = 1, θ/ r < 0; that is, higher interest rates lower the MPC wrt. current disposable income.

Interest Rates I Tracing Out the Effect of a Change in the Interest Rate Consider the effect of an r on C 1. Substitution effect: change in relative price; swap C 2 for C 1 (higher savings) Income effect: r allows C 2 for given level of savings; increase in feasible consumption implies C 1 (lower savings) There is a tension here: When σ > 1, the substitution effect dominates the income effect. When σ < 1, things go the other way. (Assume wealth effects are absent.) When σ = 1, the fraction of lifetime income spent on C 1 does not depend on r. The income and substitution effects cancel each other.

Interest Rates II Tracing Out the Effect of a Change in the Interest Rate Interest rates and savings in the two-period case Assume: W 0 = 0, i.e., no initial wealth Three cases: 1 zero initial savings 2 positive initial savings (individual is net saver) 3 negative initial savings (individual is net borrower) Graphical illustration see Romer (2006), chapter 7.4

Interest Rates III Tracing Out the Effect of a Change in the Interest Rate In addition to income and substitution effects, there may be a wealth effect. Most transparant case is when σ = 1 (since then know that income and substitution effects offset each other). Wealth effect: Change in r does not affect MPC wrt. wealth (θ), but level of wealth itself; channel is via (1 + g e )/(1 + r) and ω 0. Specifically, r lowers MPC wrt. current disposable income ( θ), reinforcing the substitution effect. Which case is relevant, i.e., what is the likely net effect? Empirical estimations suggest σ < 1.

Government Policy Taking stock: C 1 = C( Y1 d }{{} (+), g }{{} (+), r }{{}, W 0 ) }{{} (?) (+) We have yet to consider policy implications. In the KCF case, consider a change in T. ( Y ) /( T ) r = C Y /(1 C Y ) < 0 Points we have missed out: Does the timing of taxation matter? Does the financing of a change in taxation matter? That is, does moving from a situation in which T = G to deficit financing make a difference?

Temporary and Permanent Tax Policies Recall the basic ICF: [ C 1 = θ W 0 + (Y 1 T 1 ) + 1 ] 1 + r (Y 2 T 2 ) A temporary policy here is a T 1 with T 2 = T, fixed. C 1 / T 1 = θ T 1 C 1, but as θ < 1, C 2 also; i.e., savings rise as households smooth consumption A permanent policy here is T 1 = T 2 = T, where T. ( C 1 / T = θ 1 + 1 ) 1 + r stronger effects; in special case when β = 1/(1 + r), have: C 1 / T = 1

Intertemporal Government Budget Constraint (IGBC) The funds to finance the tax cut have to come from somewhere. To think about this, we need to know the Government s Intertemporal Budget Constraint (in the same way we need to know the household constraint). Government constraint: D 0 + G 1 + G 2 = T 1 + T 2, }{{ 1 + r }}{{ 1 + r } govt. consumption govt. income where D 0 is the initial (given) level of government debt. IGBC says that PV of current and future tax revenues must cover PV of current and future government spending plus initial government debt.

Financing a Tax Cut Setup Constant Government Spending Suppose G 1 = G 2 = G; that is, government spending is constant. This has immediate implications: dt 1 = 1 1 + r dt 2 A tax cut today has to be compensated for by an increase in taxes tomorrow. But surely consumers anticipate this?

Financing a Tax Cut Intertemporal Government Budget Constraint Implications of the Intertemporal Government Budget Constraint If (t = 1) the government lowers T 1 without a change in G 1, then D 1 must rise (i.e., it issues more debt). If (t = 2) the government does not subsequently change G 2, then it has to raise T 2 to pay for the principal and interest on the extra debt. However, what if agents understand this mechanism? If T 1 without G 1 or G 2, then this implies a zero effect on the present value of total taxation: T 1 + 1 1 + r T 2 = T 1 + 1 (1 + r) T 1 = 0 1 + r }{{} extra debt burden

Financing a Tax Cut Ricardian Equivalence Formally: C 1 = θ [ W 0 + (Y 1 T 1 ) + 1 ] 1 + r (Y 2 T 2 ) implies: [ dc 1 = θ dt 1 + 1 ] 1 + r dt 2 = 0 So theory predicts that T 1 without G 1 or G 2 implies unchanged consumption. The financing of the deficit (i.e., the choice between tax financing and debt financing) has no implications for consumption. This proposition is known as Ricardian Equivalence.

More on Ricardian Equivalence Ricardian Equivalence should really be thought of as a benchmark result. It breaks down if we change our model only slightly; in particular: Government and households have different planning horizons. However, Barro (1974) provides an interesting analysis when there are bequests between generations. Intragenerational redistribution between heterogenous agents. Distortionary taxation. (The taxes we have studied are lump-sum, i.e., there are no associated distortions. Under distortionary taxation Ricardian Equivalence breaks down.) Imperfect capital markets and credit constraints. (We don t tend to borrow and lend at the same rate; some people are credit constrained.)

Ricardian Equivalence - Empirical Evidence Bernheim (1987), NBER Macro Annual Keynesian view: deficit financed tax cut increases aggregate demand Ricardian view: taxpayers understand that PV of taxes simply depends on government spending; hence, tax cuts will have no effect on aggregate demand Context: The mid 1980 s saw a high US government deficit. Main Finding: There is a short-run relationship between deficits and aggregate consumption both in cross-country data and in time-series tests of the consumption function.