Topic6-Consumption_Rev

Topic6-Consumption_Rev - Consumption and Saving A Micro...

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Unformatted text preview: Consumption and Saving A Micro Foundation Micro Intertemporal Choice and the 2-Period Model, 2The Life-Cycle Model, LifePermanent Income Hypothesis, Rational Expectations Topic 6 (Text: 4.1, Appendix 4.A; Pres Topic #4) 1 9000 10000 11000 The Effects of the Recent Tax Rebates Tax rebate After-tax income Consumer expenditures 2006 2007 2008 savrt 012345 month 2006 Saving rate 2007 2008 month 5 Household saving rates in many OECD OECD countries have fallen sharply in recent years (U.S. is at -0.5%) (U.S. Economist, April 7 2005. 7 Ja n- 62 07 04 01 98 95 92 89 86 83 80 77 74 71 68 65 25.0% Ja n- 53 56 59 30.0% Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Ja n- Percent 19 76 -I 20 08 -I 20 06 -I 20 04 -I 20 02 -I 20 00 -I 19 98 -I 19 96 -I 19 94 -I 19 92 -I 19 90 -I 19 88 -I 19 86 -I 19 84 -I 19 82 -I 19 80 -I 19 78 -I 19 20 20 20 20 20 19 19 19 19 19 19 19 19 19 19 19 76 08 06 04 02 00 98 96 94 92 90 88 86 84 82 80 78 -I -I -I -I -I -I -I -I -I -I -I -I -I -I -I -I -I 10.0% Ja n- Ja n- 50 47 -2.5% Ja n- Ja n- Savings Behavior 22.5% U.S. Savings 20.0% 17.5% 15.0% 12.5% Pers Sav/GDP Private Sav/GDP 7.5% 5.0% 2.5% 0.0% Consumption Trends 72.5% U.S. Consumption 70.0% 67.5% Cons/GDP 65.0% 62.5% 60.0% Components of Consumption 45.0% 40.0% Components of Consumption 35.0% Cons Dur Cons Non Dur 20.0% Cons Serv Gov Cons 15.0% 10.0% 5.0% 0.0% Intertemporal Choice • Keynes hypothesized that consumption and therefore saving depend on the current level of income alone Recall that Saving = Income – Consumption – Taxes Recall • But sensible consumers know they are really trading off present for future consumption What is not consumed today is saved to be consumed What tomorrow, and vice versa • Irving Fisher formalized this tradeoff, and introduced the interest rate as an important determinant of consumption and saving consumption saving 11 The Two-Period Model Two• Assume that consumer lives only for two periods Period 1: youth Period Period 2: old age Period • Y1, Y2: income in periods 1 & 2 • C1, C2: consumption in periods 1 & 2 • r: real interest rate at which consumer real can borrow or lend in period 1 12 The Two-Period Model (cnt.) cnt.) Two• Budget constraints in the two periods: Uses = Resources Resources C1 + S = Y1 C2 = (1 + r) S + Y2 If S > 0, the consumer is saving If C >=< Y If S < 0, the consumer is borrowing If 13 The 2-Period Model Example #1 2• Let Y1 = 150, Y2 = 220, C1 = 120 220, • What would be maximum C2 if r = 10%? 14 The Two-Period Model (cnt.) cnt.) Two• Substitute for S from the second equation into the first to get a single intertemporal budget constraint: S = Y1 - C1 C2 = (1 + r) S + Y2 ⇒ S = C1 + C2 Y −2 1+ r 1+ r Y C2 = Y1 + 2 1+ r 1+ r PV (Cons) = PV (Income) 21 The Two-Period Model (cnt.) cnt.) Two• If there is initial financial wealth, AA0 ≥ 0, AA the PV of income is augmented C1 + C2 Y = Y1 + 2 + AA 0 1+ r 1+ r PV (Cons) = PV (Income) + Initial Wealth 22 Example #1 Repeated (cnt.) cnt.) • You can see that her total resources PV of income PV are allocated to the PV of consumption 150 + 220 C = 350 = C1 + 2 1.10 1.10 24 The Two-Period Model (cnt.) cnt.) TwoC2 Y = Y1 + 2 1+ r 1+ r 1/(1+r) unit of goods today = 1 unit of good tomorrow Today’s price of consuming a unit of good Today’ tomorrow is 1/(1+r) Can represent the above budget constraint budget graphically C1 + • • • It makes things clearer (hopefully) It 25 The Two-Period Model (cnt.) cnt.) TwoHow do consumers choose how to choose consume? • Consumer’s preferences over 1st and 2nd Consumer’ period consumption can be represented with indifference curves indifference • An indifference curve gives combination of consumption bundles that makes consumer equally happy Higher curves (NE) represent higher utility than Higher lower curves 26 The Two-Period Model (cnt.) cnt.) TwoHow do consumers choose how to choose consume? • The budget constraint line gives all the possible consumption combinations On the line no resources are wasted! On Below the line resources are wasted Below Above the line points are unattainable Above unattainable • The optimum is the highest utility that can be attained with the given budget constraint The optimum is where the indifference curve is The tangent to the budget constraint 27 The Two-Period Model (cnt.) cnt.) TwoMain point: • Consumption depends on the present value of present income It doesn’t matter if the higher income is in the first or second It doesn’ period • Critical: the ability to borrow and lend • The consumer tends to smooth consumption smooth She spreads consumption relatively evenly over both periods, She regardless of the income profile Think of retirement and short unemployment spells Think 28 The 2-Period Model Examples 2• What happens when: 1. Y1 ⇑ ? 2. Y2 ⇑ ? Consumption smoothing Consumption 29 The Relative Price of Future Consumption Relative • 1 Why is the relative price of C2 1 + r ? If you save 1 unit of output in period 1, you are forgoing If this consumption in period 1 But you get 1+r units of output (consumption) in period 2 But The trade-off is 1 to 1+r The trade1+ • To get 1 unit of output in period 2, you need to save 1 units of output in period 1 1+ r 30 The Two-Period Model Again TwoAn ↑ in “r” has two effects on saving (S): • Relative price of period 2 consumption ↓ $1 saved in 1st period gives more consumption in $1 2nd period So reduce today’s consumption by saving more to So today’ increase tomorrow’s consumption tomorrow’ Substitution effect tends to ↑ S Substitution • But there is an income effect! income 32 The Two-Period Model Again TwoSome things to keep straight • Around what point does the budget line rotate? • What about the Income Effect? Income When the interest rate rises • If you are a borrower, you You are worse off You Substitution effect consume less now Substitution consume Income effect consume less now and later Income consume Income effect reinforces the substitution effect for C1 Income 33 The Two-Period Model Again TwoWhen the interest rate rises • If you are a lender, You are better off You Substitution effect consume less now Substitution consume Income effect consume more now and later Income consume The income effect fights the substitution effect for C1 The • The further away you are from autarky, the bigger the income effect will be • We assume the substitution effect dominates 34 The Two-Period Model Again TwoAn ↑ in “r” has two effects on saving (S): • Relative price of period 2 consumption ↓ $1 saved in 1st period gives more consumption in $1 2nd period So reduce today’s consumption by saving more to So today’ increase tomorrow’s consumption tomorrow’ Substitution effect tends to ↑ S Substitution • But there is an income effect! income 40 The Two-Period Model Again TwoSome things to keep straight • Around what point does the budget line rotate? • What about the Income Effect? Income When the interest rate rises • If you are a borrower, you You are worse off You Substitution effect consume less now Substitution consume Income effect consume less now and later Income consume Income effect reinforces the substitution effect for C1 Income 41 The Two-Period Model Again TwoWhen the interest rate rises • If you are a lender, You are better off You Substitution effect consume less now Substitution consume Income effect consume more now and later Income consume The income effect fights the substitution effect for C1 The • The further away you are from autarky, the bigger the income effect will be • We assume the substitution effect dominates 42 Review Income & Substitution Effects Saver r⇑ r⇓ Substitution Effect C1 ⇓ C1 ⇑ Income Effect C1 ⇑ C1 ⇓ Borrower r⇑ r⇓ Substitution Effect C1 ⇓ C1 ⇑ Income Effect C1 ⇓ C1 ⇑ 43 Consumption Behavior in Recessions Real Consumption Growth Rate in Recessions (per quarter) 4% Rec81 Rec07 Ground 0 3% Mean P1Sd M1Std 2% 1% 0% -2 -1% -2% 0 2 4 6 8 10 12 14 16 Complementary Models • The two-period model provides all the twonecessary intuition on how intertemporal consumption decisions are made • There are 2 complementary models we’ll complementary we’ discuss next The Life Cycle model (Modigliani) The Insights into the life cycle of earnings Insights The Permanent Income hypothesis (Friedman) The Primacy of wealth in the consumption decision Primacy • There are no new principles here 46 The Life-Cycle Model Life• The two-period model suggests that an twoindividual Saves when income is high (e.g., while working), Saves and Dissaves when income is low (e.g., while retired) Dissaves • Franco Modigliani extended the two-period twomodel to many periods to understand lifetime patterns of income, consumption, and saving 47 The Life-Cycle Model (cnt.) cnt.) Life• The typical real income path is inverse U-shaped, with peak earnings occurring between the ages of fifty and sixty • Consumers dislike changes in their consumption levels they spread their lifetime resources to maintain a they fairly even standard of living over time smooth consumption smooth • They borrow while young, save in middle age, and dissave while old 48 Figure 4.A.5 Life-Cycle Consumption, LifeIncome, and Saving 49 The Life-Cycle Model (cnt.) cnt.) Life• Therefore, national savings rates depend on the country’s age distribution country’ • Countries with unusually young or unusually old populations have low saving rates Saving rate = Amount saved / Income Saving rate Amount 50 The Life-Cycle Model (cnt.) cnt.) Life• The decline in the US personal saving rate from 9% in the 50s and 60s to 3% in the 90s, and to 1% or from 9% 3% 1% less (even negative) currently negative is attributed to: Ageing population Ageing Increase in taxation of the younger workers to pay for Increase Social Security and Medicare Increases consumption of the old more than it decreases Increases consumption of the young Increase in old-age security causes people to save less for Increase oldretirement Increase in the share of income used for medical Increase expenditures (are medical expenditures consumption?) Non-medical consumption shares have stayed roughly Nonconstant 51 How Is Amount Saved Defined? • S = Y – C – G at the national level Personal Saving rate = Disposable personal income – consumption – interest and transfer payments 52 Saving Example Example: • A person earns $100,000 in a year and consumes exactly $100,000 • This person started the year with a portfolio worth $500,000 which increased to $2,500,000 because of capital gains How much did she save? How By how much did her wealth increase? By 53 Permanent Income Hypothesis • Milton Friedman used the idea that consumption depends on the present value of income to study the effect of temporary and permanent changes in temporary permanent income on consumption and saving He called the PV of income Permanent Income He PV Permanent • A permanent 1-unit ↑ in income raises permanent 1permanent income more than a temporary 1-unit ↑ 1A temporary ↑ in income is an increase in Y1, with Y2 held temporary fixed A permanent ↑ in income is an ↑ in both Y1 and Y2 permanent both 54 Permanent-Income Hypothesis (cnt.) cnt.) Permanent• Therefore, a permanent 1-unit increase in income 1increases current and future consumption more and than a temporary 1-unit increase 1Amount saved from a permanent increase in income will be Amount saved less than amount saved from a temporary increase in income • Temporary income increases would be mostly saved, permanent increases mostly consumed This explains why aggregate consumption is smoother than This income 55 Permanent-Income Hypothesis (concl.) concl.) Permanent• The algebraic statement of this idea is: C = λ * P.Income, 0 < λ < 1 λ is endogenous, it increases as the person ages endogenous It converts your “Permanent Income” or your “wealth” to an It Income” wealth” annuity (it could be made to grow over time) annuity You consume the annuity yield of your wealth each period You i.e., the annual payment that you can get from the annuity i.e., If your annuity increases you increase your consumption If increases only by the increase in the “yield” of your annuity yield” It is calculated exactly like the payment to a mortgage that It exactly is required to pay it off by a certain date 56 Rational Expectations and Consumption • Consumption theory highlights the important role of expectations about future expectations income (and policies) in determining current consumption current • The rational expectations hypothesis maintains that people use all available information to make optimal forecasts about the future 57 Rational Expectations and Consumption (cnt.) cnt.) • The permanent income and rational expectations hypotheses combined lead to the conclusion that: only unexpected changes in income and unexpected policies will change current consumption current All anticipated changes to income are already All programmed into the consumption plan What if you want to borrow when young but can’t? What can’ 58 What Is the Evidence? DispI = 0.89 C • MPC out of disposable income is ~ 85% - 95% Maybe higher Maybe • Souleles (1999) finds that people consume 9 % of their tax rebates in strictly non-durable form but non54% in consumer durables form • Johnson, Parker, Souleles (2005) report somewhat higher numbers for the 2001 tax rebates All report higher MPCs for liquidity-constrained All MPC liquidityhouseholds 59 Example #3 • Suppose the permanent-income consumption for permanentan individual with 20 years of remaining life is 1 given by C= P.Income 10.00 Interest rate is 7.75469% Interest How much will she consume this year if her P. Income How or PV(Y) = $500,000? If she receives an unanticipated $1,000 additional If income this year, by how much will her current consumption increase? Use a spreadsheet to verify for yourselves that she can Use indeed consume this amount every year for 20 years! Hint: Her current wealth at any point in time earns interest 62 Example #4 • Y = 9,000, G = 2,000 r 2% 3% 4% 5% 6% Cd 6,100 6,000 5,900 5,800 5,700 Id 1,500 1,400 1,300 1,200 1,100 1. Why does Cd & Id fall as r rises? rises? 2. What are the equilibrium values for r, S and I ? 66 Appendix 1 • Given a PV(Y), what is the current Permanent Income consumption? Let r be the real interest rate g the rate at which desired consumption grows N the number of periods of life remaining • Then we have ⎧ 1 ⎡ ⎛ 1 + g ⎞N ⎤⎫ ⎪ ⎪ PV0 (Y ) = C0 ⎨ ⎟ ⎥⎬ ∀ r > g ⎢1 − ⎜ ⎪ r − g ⎢ ⎝ 1 + r ⎠ ⎥⎪ ⎣ ⎦⎭ ⎩ • Consumption will start at C0 and grow at g 68 Glossary of Terms Y 1, Y 2 C1, C2 r S P.Income Income in the two periods, 1 and 2 Consumption in the two periods Interest rate on saving Consumer saving Permanent Income 69 THE END 86 ...
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