Micro foundations, part 1. Modern theories of consumption

Micro foundations, part 1. Modern theories of consumption Joanna Siwińska-Gorzelak Faculty of Economic Sciences, Warsaw University

Lecture overview This lecture focuses on the most prominent work on consumption. John Maynard Keynes: consumption and current income Irving Fisher: Intertemporal Choice Franco Modigliani: the Life-Cycle Hypothesis Milton Friedman: the Permanent Income Hypothesis We will also take a glimpse at: Robert Hall: the Random-Walk Hypothesis David Laibson: the pull of instant gratification slide 2

Consumption The contemporary theory of consumption was developed independently in the 1950s by Milton Friedman as the permanent theory of consumption, and by Franco Modigliani as the life cycle theory of consumption. Consumption for a foresighted consumer depends on: Financial wealth: The value of checking and saving accounts Housing wealth: The value of the house owned minus the mortgage due Human wealth: After-tax labor income over working life Nonhuman wealth: The sum of financial wealth and housing wealth

The Keynesian Consumption Function C Here s a consumption function with the properties Keynes conjectured: C C cy C 1 c c = MPC = slope of the consumption function Y slide 4

1. 0 < MPC < 1 Keynes s Conjectures 2. Average propensity to consume (APC ) falls as income rises. (APC = C/Y ) 3. Current disposable income is the main determinant of consumption. slide 5

The Keynesian Consumption Function C As income rises, the APC falls (consumers save a bigger fraction of their income). C C cy C C APC c Y Y slope = APC Y slide 6

Early Empirical Successes: Results from Early Studies Households with higher incomes: consume more MPC > 0 save more MPC < 1 save a larger fraction of their income APC as Y Very strong correlation between income and consumption income seemed to be the main determinant of consumption slide 7

Problems for the Keynesian Consumption Function Based on the Keynesian consumption function, economists predicted that C would grow more slowly than Y over time. This prediction did not come true: As incomes grew, the APC did not fall, and C grew just as fast. Simon Kuznets showed that C/Y was very stable in long time series data. slide 8

The Consumption Puzzle C Consumption function from long time series data (constant APC ) Consumption function from cross-sectional household data (falling APC ) Y slide 9

Irving Fisher and Intertemporal Choice The basis for much subsequent work on consumption. Assumes consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction (utility). Consumer s choices are subject to an intertemporal budget constraint, a measure of the total resources available for present and future consumption slide 10

The basic two-period model Period 1: the present Period 2: the future Notation Y 1 is income in period 1 Y 2 is income in period 2 C 1 is consumption in period 1 C 2 is consumption in period 2 S = Y 1 - C 1 is saving in period 1 (S < 0 if the consumer borrows in period 1) slide 11

Deriving the intertemporal budget constraint Period 2 budget constraint: C 2 Y2 (1 r ) S Y (1 r )( Y -C ) 2 1 1 Rearrange to put C terms on one side and Y terms on the other: (1 r ) C C Y (1 r ) Y 1 2 2 1 Finally, divide through by (1+r ): slide 12

The intertemporal budget constraint C C Y Y 1r 1r 2 2 1 1 present value of lifetime consumption present value of lifetime income slide 13

The intertemporal budget constraint The budget constraint shows all combinations of C 1 and C 2 that just exhaust the consumer s resources. (1 r ) Y Y 1 2 Y 2 C 2 C Saving C Y Y 1r 1r 2 2 1 1 Consump = income in both periods Borrowing slide 14 Y 1 Y Y (1 r ) 1 2 C 1

The intertemporal budget constraint The slope of the budget line equals -(1+r ) C 2 1 C (1+r ) C Y Y 1r 1r 2 2 1 1 Y 2 Y 1 C 1 slide 15

Consumer preferences An indifference curve shows all combinations of C 1 and C 2 that make the consumer equally happy. C 2 Higher indifference curves represent higher levels of happiness. IC 2 IC 1 C 1 slide 16

Consumer preferences Marginal rate of substitution (MRS ): the amount of C 2 consumer would be willing to substitute for one unit of C 1. C 2 1 MRS The slope of an indifference curve at any point equals the MRS at that point. IC 1 C 1 slide 17

Optimization The optimal (C 1,C 2 ) is where the budget line just touches the highest indifference curve. C 2 O At the optimal point, MRS = 1+r C 1 slide 18

Formal approach to optimization the method of Lagrange multipliers ] ) (1 ) (1 [ ), ( ) (1 ) (1.. ), ( 2 1 2 1 1 2 1 2 1 2 1 2 1 r C C r Y Y c c u L r C C r Y Y s t c c u U - - The solution is that: ) (1 2 1 r c U c U

How C responds to changes in Y Results: Provided they are both normal goods, C 1 and C 2 both increase, regardless of whether the income increase occurs in period 1 or period 2. C 2 An increase in Y 1 or Y 2 shifts the budget line outward. C 1 slide 20

Keynes vs. Fisher Keynes: current consumption depends only on current income Fisher: current consumption depends on the present value of lifetime income; the timing of income is irrelevant because the consumer can borrow or lend between periods. slide 21

How C responds to changes in r An increase in r pivots the budget line around the point (Y 1,Y 2 ). C 2 B As depicted here, C 1 falls and C 2 rises. However, it could turn out differently Y 2 A Y 1 C 1 slide 22

How C responds to changes in r An increase in r pivots the budget line around the point (Y 1,Y 2 ). C 2 B As depicted here, C 1 falls and C 2 rises. However, it could turn out differently Y 2 A Y 1 C 1 slide 23

How C responds to changes in r income effect If consumer is a saver, the rise in r makes him better off, which tends to increase consumption in both periods. substitution effect The rise in r increases the opportunity cost of current consumption, which tends to reduce C 1 and increase C 2. Both effects C 2. Whether C 1 rises or falls depends on the relative size of the income & substitution effects. slide 24

Constraints on borrowing In Fisher s theory, the timing of income is irrelevant because the consumer can borrow and lend across periods. Example: If consumer learns that her future income will increase, she can spread the extra consumption over both periods by borrowing in the current period. However, if consumer faces borrowing constraints (aka liquidity constraints ), then she may not be able to increase current consumption and her consumption may behave as in the Keynesian theory even though she is rational & forward-looking slide 25

Constraints on borrowing C 2 The budget line with no borrowing constraints Y 2 Y 1 C 1 slide 26

Constraints on borrowing The borrowing constraint takes the form: C 1 Y 1 Y 2 C 2 The budget line with a borrowing constraint Y 1 C 1 slide 27

Consumer optimization when the borrowing constraint is not binding C 2 The borrowing constraint is not binding if the consumer s optimal C 1 is less than Y 1. Y 1 C 1 slide 28

Consumer optimization when the borrowing constraint is binding The optimal choice is at point D. But since the consumer cannot borrow, the best he can do is point E. C 2 E D Y 1 C 1 slide 29

The Life-Cycle Hypothesis due to Franco Modigliani (1950s) Fisher s model says that consumption depends on lifetime income, and people try to achieve smooth consumption. The LCH says that income varies systematically over the phases of the consumer s life cycle, and saving allows the consumer to achieve smooth consumption. slide 30

The Life-Cycle Hypothesis The basic model: W t = wealth in time t Y t = annual disposable income until retirement (income net of taxes) R = number of years until retirement T = lifetime in years Assumptions: zero real interest rate (for simplicity) consumption-smoothing is optimal slide 31

The Life-Cycle Hypothesis Lifetime resources Wt Yt Yt 1 t1 To achieve smooth consumption, consumer divides her resources equally over time: R C t 1 [ Wt T Y t t1 t1 If we assume constant income, we can write: C = aw + by where a = (1/T ) is the marginal propensity to consume out of wealth b = (R/T ) is the marginal propensity to consume out of income Y ] R slide 32

Implications of the Life-Cycle Hypothesis The Life-Cycle Hypothesis can solve the consumption puzzle: The APC implied by the life-cycle consumption function is C/Y = a(w/y ) + b Across households, wealth does not vary as much as income, so high income households should have a lower APC than low income households. Over time, aggregate wealth and income grow together, causing APC to remain stable. slide 33

Implications of the Life-Cycle Hypothesis The LCH implies that saving varies systematically over a person s lifetime. $ Income Wealth Saving Consumption Dissaving Retirement begins End of life slide 34

Implications of the Life-Cycle Hypothesis

Implications The saving rate changes over the life-time of the consumer Consumption is not very responsive to changes in current income Consumption may change even if current income does not Important role for expectations

The Permanent Income Hypothesis due to Milton Friedman (1957) The PIH views current income Y as the sum of two components: permanent income Y P (average income, which people expect to persist into the future) transitory income Y T (temporary deviations from average income) slide 37

The Permanent Income Hypothesis Consumers use saving & borrowing to smooth consumption in response to transitory changes in income. The PIH consumption function: C = ay P where a is the fraction of permanent income that people consume per year. slide 38

The Permanent Income Hypothesis Current income differs from permanent income Y t = Y t P + Y t T Y t = current income in time t Y P = permanent income expected (in time t) average yearly income from human capital (earnings) and wealth Y T = transitory income transitory deviations of current income from permanent income

The Permanent Income Hypothesis Consumers have to somehow estimate the amount of permanent income Friedman assumed an adaptive formula Y t perm Y perm perm t - j( Y - Y ), 0 j 1-1 t t 1 Consumers correct their previous estimates of permanent income by the j amount of deviation of current income from previous period estimated permanent income

The Permanent Income Hypothesis The PIH can solve the consumption puzzle: The PIH implies APC = C/Y = ay P /Y To the extent that high income households have higher transitory income than low income households, the APC will be lower in high income households. Over the long run, income variation is due mainly if not solely to variation in permanent income, which implies a stable APC. slide 41

PIH vs. LCH In both, people try to achieve smooth consumption in the face of changing current income. In the LCH, current income changes systematically as people move through their life cycle. In the PIH, current income is subject to random, transitory fluctuations. Both hypotheses can explain the consumption puzzle. In applied work, reseraches often use PILCH (an approach that combines both theories) slide 42

The Random-Walk Hypothesis due to Robert Hall (1978) based on Fisher s model & PIH, in which forwardlooking consumers base consumption on expected future income Hall adds the assumption of rational expectations, that people use all available information to forecast future variables like income. slide 43

The Random-Walk Hypothesis If PIH is correct and consumers have rational expectations, then consumption should follow a random walk: changes in consumption should be unpredictable. A change in income or wealth that was anticipated has already been factored into expected permanent income, so it will not change consumption. Only unanticipated changes in income or wealth that alter expected permanent income will change consumption. slide 44

Implication of the R-W Hypothesis If consumers obey the PIH and have rational expectations, then policy changes will affect consumption only if they are unanticipated. slide 45

The Psychology of Instant Gratification Theories from Fisher to Hall assumes that consumers are rational and act to maximize lifetime utility. Famous studies by David Laibson and others consider the psychology of consumers. slide 46

The Psychology of Instant Gratification Consumers consider themselves to be imperfect decision-makers. E.g., in one survey, 76% said they were not saving enough for retirement. Laibson: The pull of instant gratification explains why people don t save as much as a perfectly rational lifetime utility maximizer would save. slide 47

Two Questions and Time Inconsistency 1. Would you prefer (A) a candy today, or (B) two candies tomorrow? 2. Would you prefer (A) a candy in 100 days, or (B) two candies in 101 days? In studies, most people answered A to question 1, and B to question 2. A person confronted with question 2 may choose B. 100 days later, when he is confronted with question 1, the pull of instant gratification may induce him to change his mind. slide 48

Summing up Keynes suggested that consumption depends primarily on current income. More recent work suggests instead that consumption depends on current income expected future income wealth interest rates Economists disagree over the relative importance of these factors and of borrowing constraints and psychological factors. slide 49

Summing up 2. Fisher s theory of intertemporal choice Consumer chooses current & future consumption to maximize lifetime satisfaction subject to an intertemporal budget constraint. Current consumption depends on lifetime income, not current income, provided consumer can borrow & save. 3. Modigliani s Life-Cycle Hypothesis Income varies systematically over a lifetime. Consumers use saving & borrowing to smooth consumption. Consumption depends on income & wealth. slide 50

Summing up 4. Friedman s Permanent-Income Hypothesis Consumption depends mainly on permanent income. Consumers use saving & borrowing to smooth consumption in the face of transitory fluctuations in income. 5. Hall s Random-Walk Hypothesis Combines PIH with rational expectations. Main result: changes in consumption are unpredictable, occur only in response to unanticipated changes in expected permanent income. slide 51

Chapter summary 6. Laibson and the pull of instant gratification Uses psychology to understand consumer behavior. The desire for instant gratification causes people to save less than they rationally know they should. slide 52

Saving motives in Poland Florczak & Jabłonowski, 2016 https://www.nbp.pl/publikacje/materialy_i_studia/252_en.pdf

Research on consumption Johnson & Parker & Souleles (2006); Household expenditure and the income tax rebates of 2001 ; Am. Econ. Rev. 96: They study the US large income tax rebate program provided by the Economic Growth and Tax Relief Reconciliation Act of 2001. The program sent tax rebates, typically $300 or $600 in value, to approximately two-thirds of U.S. households. According to the PI hypothesis, a single rebate would have little effect on spending. Furthermore, in the absence of liquidity constraints, spending should increase as soon as consumers begin to expect the tax cut, and not increase only after they actually have received the rebate check. The rebate checks were mailed out over a 10-week period from late July to the end of September 2001. The particular week in which a check was random.

Research on consumption This randomization allows the authors to identify the causal effect of the rebate by comparing the spending of households that received the rebate earlier with the spending of households that received it later. The authors find that the average household spent 20% 40% of its 2001 tax rebate on nondurable goods during the three-month period in which the rebate was received. The authors also find that the expenditure responses are largest for households with relatively low liquid wealth and low income, which is consistent with liquidity constraints

Research on consumption A paper that stands in contrast to these is Browning & Callado (2001) The response of expenditures to anticipated income changes: Panel Data Estimates AER, vol.91(3) They use Spanish micro data to examine the consumer response to the payment of institutionalized June and December extra wage payments to full-time workers & compare it to consumption of workers witouht the extra wage payments. Browning & Collado detect no evidence of excess sensitivity there is no significant difference in consumption profiles of both groups They argue that the reason why earlier researchers found a large response of consumption to predicted income changes is because of bounded rationality: Consumers tend to smooth consumption and follow the theory when expected income changes are large but are less likely to do so when the changes are small

Ricardian equivalence approach The focus is on the effects of budget deficits on consumption and private savings Assumptions: fully rational consumers Infinite time horizon Taxes are lump-sum Conclusion: the timing of taxes does not matter for consumption Private consumption is not on by way that that government spending is financed (by taxes or by public borrowing) Hence, tax cuts (keeping government spending unchanged) do not make any difference

Two period model ) (1 ) ( ) ( ) (1 2 2 1 1 2 1 r T Y T Y r C C - - ) (1 ) (1 ) ( 2 1 2 1 2 1 1 1 2 1 2 1 2 2 1 r T T r G G T T T G r G G T T rb G G - 1. Private budget constraint 2. Government s budget constraint Plug 2 into 1 to get the private sector s budget constraint ) (1 ) (1 ) (1 2 1 2 1 2 1 r G G r Y Y r C C - -

Intuition Let s assume that government spending are unchanged, but the government cuts taxes Will private consumption change? Current disposable income increases, but future disposable income decreases, as the government will have to increase taxes in the future to pay back the public debt Rational consumers, expecting an increase in taxation will not increase consumption, but will increase savings (they will save the current increase in income) Current decrease in taxation does not have any effect on total, disposable income, so it does not affect consumption

Ricardian equivalence approach Conclusions: when the government cuts taxes and runs a budget deficit, the government saving falls In the same time, private sector savings increases, implying that: Total amount of savings does not change Consumption is not affected; Aggregate demand is not affected