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Irving Fisher and Intertemporal Choice 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 C2 CY22 The budget CY11 constraint 11rr (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 C CY2 The slope of CY22 the budget 1111rr 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.
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