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Home , Consumption function, Intertemporal choice, Robert Hall (economist)

In this chapter, you will learn… C H A P T E R 16 an introduction to the most prominent work on , including: Consumption . : consumption and current income . : . : the life-cycle hypothesis . : the permanent income hypothesis SIXTH EDITION SIXTH EDITION . : the random-walk hypothesis N. GREGORY MANKIW PowerPoint® Slides by Ron Cronovich

© 2007 Worth Publishers, all rights reserved CHAPTER 16 Consumption slide 1

The Keynesian consumption Keynes’s conjectures function

1. 0 < MPC < 1 C

2. Average propensity to consume (APC ) C = C + cY falls as income rises. (APC = C/Y ) c c = MPC = slope of the 3. Income is the main determinant of 1 consumption. consumption C function

Y

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The Keynesian consumption Early empirical successes: function Results from early studies As income rises, consumers save a bigger . Households with higher incomes: C fraction of their income, so APC falls. . consume more, ⇒ MPC > 0 C = C + cY . save more, ⇒ MPC < 1 . save a larger fraction of their income, ⇒ APC ↓ as Y ↑ C C . Very strong correlation between income and APC = = + c Y Y consumption: slope = APC ⇒ income seemed to be the main Y determinant of consumption

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1 Problems for the The Consumption Puzzle Keynesian

Based on the Keynesian consumption function, Consumption function . C from long time series predicted that C would grow more data (constant APC ) slowly than Y over time. . This prediction did not come true: . As incomes grew, APC did not fall, Consumption function and C grew at the same rate as income. from cross-sectional

. showed that C/Y was household data very stable in long time series data. (falling APC )

Y

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Irving Fisher and Intertemporal The basic two-period model Choice . Period 1: the present . The basis for much subsequent work on consumption. . Period 2: the future . Assumes consumer is forward-looking and . Notation chooses consumption for the present and future Y1, Y2 = income in period 1, 2 to maximize lifetime satisfaction. C1, C2 = consumption in period 1, 2 . Consumer’s choices are subject to an S = Y − C = saving in period 1 intertemporal budget constraint, 1 1 a measure of the total resources available for (S < 0 if the consumer borrows in period 1) present and future consumption.

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Deriving the intertemporal The intertemporal budget budget constraint constraint

C Y . Period 2 budget constraint: C + 2 = Y + 2 1 1 + r 1 1 + r C 2 = Y2 + (1 + r )S

= Y2 + (1 + r )(Y1 ! C 1) present value of present value of . Rearrange terms: lifetime consumption lifetime income

(1 + r )C 1 + C 2 = Y2 + (1 + r )Y1

. Divide through by (1+r ) to get…

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2 The intertemporal budget The intertemporal budget constraint constraint

C 2 Y2 C 2 Y2 C2 C + = Y + C2 C + = Y + 1 1 + r 1 1 + r 1 1 + r 1 1 + r The slope of (1 + r )Y +Y the budget 1 2 Consump = line equals 1 Saving income in −(1+r ) (1+r ) The budget both periods constraint shows all combinations Y2 Y2 Borrowing of C1 and C2 that just exhaust the consumer’s C C Y 1 Y 1 resources. 1 1 Y1 +Y2 (1 + r ) CHAPTER 16 Consumption slide 12 CHAPTER 16 Consumption slide 13

Consumer preferences Consumer preferences

Higher The slope of C2 C2 An indifference indifference Marginal rate of an indifference curve shows curves substitution (MRS ): curve at any represent all combinations the amount of C2 point equals higher levels of C1 and C2 the consumer the MRS that make the of happiness. would be willing to 1 at that point. consumer substitute for MRS IC equally happy. 2 one unit of C1.

IC1 IC1

C1 C1

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Optimization How C responds to changes in Y

C C 2 Results: 2 An increase The optimal (C1,C2) in Y or Y At the optimal point, Provided they are 1 2 is where the shifts the MRS = 1+r both normal goods, budget line budget line C and C both just touches 1 2 outward. the highest increase, indifference curve. O …regardless of whether the income increase occurs in period 1 C1 or period 2. C1

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3 Keynes vs. Fisher How C responds to changes in r

C2 . Keynes: As depicted here, An increase in r pivots the budget Current consumption depends only on C falls and C rises. 1 2 line around the current income. However, it could point (Y1,Y2 ). . Fisher: turn out differently… B Current consumption depends only on the present value of lifetime income. A The timing of income is irrelevant Y2 because the consumer can borrow or lend C1 between periods. Y1

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How C responds to changes in r Constraints on borrowing

. income effect: If consumer is a saver, . In Fisher’s theory, the timing of income is irrelevant: Consumer can borrow and lend across periods. the rise in r makes him better off, which tends to increase consumption in both periods. . Example: If consumer learns that her future income will increase, she can spread the extra consumption . substitution effect: The rise in r increases over both periods by borrowing in the current period. the opportunity cost of current consumption,

which tends to reduce C1 and increase C2. . However, if consumer faces borrowing constraints (aka “liquidity constraints”), then she may not be . Both effects ⇒ ↑C . 2 able to increase current consumption Whether C1 rises or falls depends on the relative …and her consumption may behave as in the size of the income & substitution effects. Keynesian theory even though she is rational & forward-looking. CHAPTER 16 Consumption slide 20 CHAPTER 16 Consumption slide 21

Constraints on borrowing Constraints on borrowing

C C 2 The borrowing 2 The budget constraint takes line with no the form: The budget borrowing line with a constraints C ≤ Y 1 1 borrowing constraint Y2 Y2

C1 C1 Y1 Y1

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4 Consumer optimization when the Consumer optimization when the borrowing constraint is not binding borrowing constraint is binding

C2 C2 The borrowing The optimal constraint is not choice is at point D. binding if the consumer’s But since the

optimal C1 consumer cannot borrow, is less than Y1. E the best he can D do is point E.

C1 C1 Y1 Y1

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The Life-Cycle Hypothesis The Life-Cycle Hypothesis

. due to Franco Modigliani (1950s) . The basic model: W = initial wealth . Fisher’s model says that consumption depends Y = annual income until retirement on lifetime income, and people try to achieve (assumed constant) smooth consumption. R = number of years until retirement The LCH says that income varies systematically . T = lifetime in years over the phases of the consumer’s “life cycle,” and saving allows the consumer to achieve . Assumptions: smooth consumption. . zero real rate (for simplicity) . consumption-smoothing is optimal

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Implications of the Life-Cycle The Life-Cycle Hypothesis Hypothesis . Lifetime resources = W + RY The LCH can solve the consumption puzzle: . To achieve smooth consumption, . The life-cycle consumption function implies consumer divides her resources equally over time: APC = C/Y = α(W/Y ) + β C = (W + RY )/T , or . Across households, income varies more than C = W + Y α β wealth, so high-income households should have where a lower APC than low-income households. α = (1/T ) is the marginal propensity to . Over time, aggregate wealth and income grow consume out of wealth together, causing APC to remain stable. β = (R/T ) is the marginal propensity to consume out of income CHAPTER 16 Consumption slide 28 CHAPTER 16 Consumption slide 29

5 Implications of the Life-Cycle The Permanent Income Hypothesis Hypothesis $ . due to Milton Friedman (1957) P T The LCH . Y = Y + Y Wealth implies that where saving varies Y = current income systematically Income P over a Y = permanent income person’s Saving average income, which people expect to lifetime. persist into the future Consumption Dissaving T Y = transitory income Retirement End temporary deviations from average income begins of life CHAPTER 16 Consumption slide 30 CHAPTER 16 Consumption slide 31

The Permanent Income Hypothesis The Permanent Income Hypothesis

The PIH can solve the consumption puzzle: . Consumers use saving & borrowing to smooth consumption in response to transitory changes . The PIH implies P in income. APC = C / Y = α Y / Y . The PIH consumption function: . If high-income households have higher transitory income than low-income households, P C = α Y APC is lower in high-income households. where α is the fraction of permanent income . Over the long run, income variation is due mainly that people consume per year. (if not solely) to variation in permanent income, which implies a stable APC.

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PIH vs. LCH The Random-Walk Hypothesis

. Both: people try to smooth their consumption . due to Robert Hall (1978) in the face of changing current income. . based on Fisher’s model & PIH, . LCH: current income changes systematically in which forward-looking consumers base as people move through their life cycle. consumption on expected future income . PIH: current income is subject to random, . Hall adds the assumption of transitory fluctuations. , that people use all available information . Both can explain the consumption puzzle. to forecast future variables like income.

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6 The Random-Walk Hypothesis Implication of the R-W Hypothesis

. If PIH is correct and consumers have rational expectations, then consumption should follow a random walk: changes in consumption should If consumers obey the PIH be unpredictable. and have rational expectations, . A change in income or wealth that was anticipated has already been factored into then policy changes expected permanent income, will affect consumption so it will not change consumption. only if they are unanticipated. . Only unanticipated changes in income or wealth that alter expected permanent income will change consumption.

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Summing up Chapter Summary

. Keynes: consumption depends primarily on 1. Keynesian consumption theory current income. . Keynes’ conjectures . Recent work: consumption also depends on . MPC is between 0 and 1 . APC falls as income rises . expected future income . current income is the main determinant of . wealth current consumption . interest rates . Empirical studies . Economists disagree over the relative importance . in household data & short time series: of these factors and borrowing constraints. confirmation of Keynes’ conjectures . in long-time series data: APC does not fall as income rises

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Chapter Summary Chapter Summary

2. Fisher’s theory of intertemporal choice 3. Modigliani’s life-cycle hypothesis . Consumer chooses current & future . Income varies systematically over a lifetime. consumption to maximize lifetime satisfaction of . Consumers use saving & borrowing to smooth subject to an intertemporal budget constraint. consumption. . Current consumption depends on lifetime . Consumption depends on income & wealth. income, not current income, provided consumer can borrow & save.

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7 Chapter Summary Chapter Summary

4. Friedman’s permanent-income hypothesis 5. Hall’s random-walk hypothesis . Consumption depends mainly on permanent . Combines PIH with rational expectations. income. . Main result: changes in consumption are . Consumers use saving & borrowing to smooth unpredictable, occur only in response to consumption in the face of transitory fluctuations unanticipated changes in expected permanent in income. income.

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