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: . The Ricardian Approach
slide 2 The Keynesian Consumption Function
퐶푡 = 푐0 + 푐푦 푌푡 − 푇푡 − consumption C function with the properties Keynes conjectured:
푐푌 = MPC cY = slope of the 1 consumption C function
Y
slide 3 Keynes’s Conjectures
1. 0 < MPC < 1
2. Average propensity to consume (APC) falls as income rises. (APC = C/Y )
3. Current disposable income is the main determinant of consumption.
slide 4 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 5 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 6 The Consumption Puzzle
Consumption function from C long time series data (constant APC )
Consumption function from cross-sectional household data (falling APC )
Y
slide 7 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 8 The basic two-period model
. Period 1: the present . Period 2: the future . Notation
Y1 is income in period 1
Y2 is income in period 2
C1 is consumption in period 1
C2 is consumption in period 2
S = Y1 - C1 is saving in period 1 (S < 0 if the consumer borrows in period 1)
slide 9 Deriving the intertemporal budget constraint
. Period 2 budget constraint:
C22 Y (1 r ) S
Y2 (1 r )( Y 1 - C 1 )
. Rearrange to put C terms on one side and Y terms on the other:
(1r ) C1 C 2 Y 2 (1 r ) Y 1
. Finally, divide through by (1+r ):
slide 10 The intertemporal budget constraint
CY CY22 1111rr
present value of present value of lifetime consumption lifetime income
slide 11 The intertemporal budget constraint
CY22 C2 CY 1111rr The budget constraint (1r ) Y Y shows all 12 Consump = combinations Saving in income in both period 1 periods of C1 and C2 that just exhaust the Y2 Borrowing in consumer’s period 1 resources.
C1 Y1
Y12 Y(1 r ) slide 12 The intertemporal budget constraint
CY C 22 2 CY11 The slope of 11rr the budget line equals -(1+r ) 1 (1+r )
Y2
C1 Y1
slide 13 Consumer preferences
Higher An indifference C2 curve shows all indifference combinations of curves represent C1 and C2 that make the higher levels consumer equally of happiness. happy. IC2
IC1
C1
slide 14 Consumer preferences
C2 The slope of an indifference Marginal rate of curve at any substitution (MRS ): point equals the amount of C the MRS 2 1 consumer would be at that point. MRS willing to substitute for one unit of C1.
IC1
C1
slide 15 Optimization
C2
The optimal (C1,C2) is At the where the budget line optimal point, just touches the MRS = 1+r highest indifference curve. O
C1
slide 16 How C responds to changes inY
An increase in Y orY C2 1 2 Results: shifts the budget line Provided they are outward. both normal goods,
C1 and C2 both increase, …regardless of whether the income increase occurs in period 1 C or period 2. 1
slide 17 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 18 How C responds to changes inr
C2 An increase in r pivots the budget line around the
point (Y1,Y2 ). B
As depicted here, A C1 falls and C2 rises. Y However, it could 2 turn out differently… C1 Y1
slide 19 How C responds to changes inr
C2 An increase in r pivots the budget line around the
point (Y1,Y2 ). B
As depicted here, A C1 falls and C2 rises. Y However, it could 2 turn out differently… C1 Y1
slide 20 How C responds to changes inr
. 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 C1 and increase C2.
. Both effects C2.
Whether C1 rises or falls depends on the relative size of the income & substitution effects. . What happens when the consumer is a borrower? slide 21 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 22 Constraints on borrowing
C2 The budget line with no borrowing constraints
Y2
C1 Y1
slide 23 Constraints on borrowing
The borrowing C2 constraint takes the form: The budget C1 Y1 line with a borrowing constraint Y2
C1 Y1
slide 24 Consumer optimization when the borrowing constraint is not binding
C2
The borrowing constraint is not binding if the consumer’s
optimal C1 is less than Y1.
C1 Y1
slide 25 Consumer optimization when the borrowing constraint is binding
C The optimal 2 choice is at point D. But since the consumer cannot borrow, the best he can do is point E E. D
C1 Y1
slide 26 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 27 The Life-Cycle Hypothesis
. The basic model:
Wt = wealth in time t
Yt = annual disposable income until retirement (income net of taxes) N = number of years until retirement T = lifetime in years . Assumptions: – zero real interest rate (for simplicity) – consumption-smoothing is optimal
slide 28 The Life-Cycle Hypothesis . Lifetime resources, calculated at time t N Wt Yt Yt1 t . To achieve smooth consumption in each period t, consumer divides her resources equally over time:
1 N Ct [Wt Yt Yt1] T t1
If we assume constant income, we can write: C = aW + bY
a = (1/T ) is the marginal propensity to consume out of wealth b = (R/T ) is the marginal propensity to consume out of income
slide 29 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 30 Implications of the Life-Cycle Hypothesis
$ The LCH implies that saving varies Wealth systematically over a person’s lifetime. Income Saving
Consumption Dissaving
Retirement End begins of life
slide 31 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 of 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 34 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 35 The Permanent Income Hypothesis
. Current income differs from permanent income P T . Yt = Yt + Yt
Yt = current income in time t YP = permanent income expected (in time t) average yearly income from human capital (earnings) and wealth YT = 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
perm perm perm Yt Yt-1 j(Yt - Yt-1 ), 0 j 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 P APC = C/Yt = aY /Y t . 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 38 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, researchers often use PILCH (an approach that combines both theories)
slide 39 The Psychology of Instant Gratification
. Modern consumption theories assume that consumers are rational and act to maximize lifetime utility. . Famous studies by David Laibson and others consider the psychology of consumers.
slide 40 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 41 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 42 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 43 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.
slide 44 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 (excess sensitivity). . 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 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