Advanced Macroeconomics // Consumption

Transcription

1 Advanced Macroeconomics // Consumption Joanna Tyrowicz // (instead of Joanna Siwiska) University of Warsaw, Faculty of Economics 05/10/2008 Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

2 Introduction About 65% of GDP goes to consumption (on average in the US) In poorer countries it may even be more... Most modern consumption theories Assume consumer is forward-looking and chooses consumption for the present and future to maximize lifetime satisfaction. Consumer s choices are subject to an intertemporal budget constraint -a measure of the total resources available for present and future consumption. Mr Keynes and his contribution... Introduced the idea of marginal propensity to consume (MPC) Essentially there is some autonomous consumption and income dependent consumption. C = a + b Y D (1)... but there are some problems with it... Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

3 Modern approach to consumption Keynes model of at odds with time series a roughly constant ratio of aggregate consumption to aggregate income, despite a persistent growth of the latter Solutions: life-cycle hypothesis (LCH) and permanent income hipothesis (PIH) [respectively Modigliani (1954) and Friedman (1957)] Life-cycle hypothesis states that at different stages in life people have different needs Permanent income hypothesis states that people prefer to smooth consumption over the lifetime, so they will adapt to increases and decreases upfront. Virtually all economists have accepted the basic building blocks of both LIH and PIH: consumers are forward looking: they are concerned about the future as well as current consumption they take into account future and current income Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

4 Structure of the approach Model the behavior of a representative individual (household) assume that all individuals (households) are the same and that population size is equal to one Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

5 Structure of the approach Model the behavior of a representative individual (household) assume that all individuals (households) are the same and that population size is equal to one Time horizon is infinite... but people do not live infinitely?... uncertainty about the length of life can act much like an infinite horizon in blurring one s terminal planning date... people care about their children, who in turn care about theirs, so an economy of finite-lived individuals may behave just like one peopled by immortals Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

6 Structure of the approach Model the behavior of a representative individual (household) assume that all individuals (households) are the same and that population size is equal to one Time horizon is infinite... but people do not live infinitely?... uncertainty about the length of life can act much like an infinite horizon in blurring one s terminal planning date... people care about their children, who in turn care about theirs, so an economy of finite-lived individuals may behave just like one peopled by immortals Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

7 Structure of the approach Model the behavior of a representative individual (household) assume that all individuals (households) are the same and that population size is equal to one Time horizon is infinite... but people do not live infinitely?... uncertainty about the length of life can act much like an infinite horizon in blurring one s terminal planning date... people care about their children, who in turn care about theirs, so an economy of finite-lived individuals may behave just like one peopled by immortals For simplicity a the beginning: assume just two periods individual is maximizing utility U = U(C 1) + βu(c 2), where 0 < β < 1 (2) β is the time-preference parameter or discount factor, that measures the individual s impatience to consume Utility function at each point in time is strictly increasing in consumption, and concave: U > 0 and U < 0 Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

8 Structure of the approach - continued How much can we spend? Essentially what we will earn this and next period: What is the main problem now? Wealth = Y 1 + βy 2 (3) maxu(c 1 ) + βu(c 2 ) subject to C 1 + βc 2 = Y 1 + βy 2 (4) How to solve it? The solution is the Lagrangean maxl = maxu(c 1 ) + βu(c 2 ) λ[c 1 + βc 2 Y 1 + βy 2 ] (5) δl δu(c 1 ) =... δl =... (6) δu(c 2 ) δl δλ =... U (C 1 ) = β(1 + r)u (C 2 ) (7) Intertemporal Euler equation: This is not a consumption function (actually, it s even independent of consumption function). Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

9 Structure of the approach - continued How to do it for many periods? Finite time: start at t and end at t + T, where T > 0 Utility function is time separable Budget constraint s=t t+t U t = β s t U(C s) (8) s=t t+t 1 t+t ( ) s t 1 ( (1 + r) )s t c s = Y s + A t (9) (1 + r) Terminal condition (no Ponzi game) s=t One gets Euler equations too Grounds for mainstream LCH and PIH models ( ) T 1 B t+t +1 = 0 (10) (1 + r) Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

10 Structure of the approach - continued How to do it for infinity? Finite time: start at t and end at t + T, where T > 0 Utility function is time separable Budget constraint s=t U t = β s t U(C s) (11) s=t 1 ( ) s t 1 ( (1 + r) )s t c s = Y s + A t (12) (1 + r) Terminal condition (no Ponzi game) s=t ( ) T 1 lim B t+t +1 = 0 (13) T (1 + r) Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

11 Equivalence of debt and taxes and its consequences LCH plus infinite horizon plus some additional assumptions imply Ricardian Equivalence: the neutrality of timing of lump-sum taxes (given government spending levels) all that matters for the consumption choices of individuals is the present value of government spending government deficit cannot affect consumer choices What if future is uncertain? u(c t ) = c1 θ t 1 1 θ (14) Individuals can be surprised by unexpected events, repeatedly What they maximise is not utility, but expected utility over lifetime t+t U t = E t ( )β s t u(c s ) (15) s=t Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

12 Hall and random walk Think back about the Euler s equation U (C 1 ) = β(1 + r)u (C 2 ) (16) Let s take a quadratic utility function u(c t) = c t a 2 c2 t, then the derivative is linear: u = 1 a C s Assume β = 1/(1 + r) 1 ac s = E s(1 ac s+1 ), 1 ac s = [1 ae s(c s+1 )] C s = E s(c s+1 ) C s+1 = E s(c s+1 ) + e s+1 consumption follows C s+1 = C s + e s+1 (random walk) Changes in consumption follow from unexpected shocks Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

13 Empirical evidence Campbell and Mankiw (1990) Permanent Income, Current Income and Consumption - consumption reacts to predictable changes in income bad news for PILCH recall that according to PILCH predictable changes in income will have no effects on the growth of consumption expenditures John Shea (1995) Union Contracts and Life-Cycle/Permament-Income Hypothesis - consumption responds asymmetrically to increases and decreases, in about half of the cases reacts to actual changes in income and not to the prior information about the future change, maybe partly justified by insufficient liquidity (but this was rejected as explanation in further research by Shea). Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

14 Empirical evidence Parker J. (1999) The reaction of Household consumption to Predictable Changes in Social Security Taxes - uses household-level non-durable consumption data (USA ) and predictable changes in Social Security tax withholding, two source of variations (preannounced changes in tax rates plus when income reaches the maximum taxable amount, the take-home pay increases, because SS taxes are no longer withheld), finds that consumption responds to both these changes. Instead of looking at people choices, let s elaborate cross-country differences in savings rate? Japelli and Pagano (1994) Savings, Growth and Liquidity Constraints - look at different countries, in some credit (eg. mortgage loan) are more accessible than in others, which means you need less of your own money to buy your own place, the question is if this affects your choice of save-consume and if so, does that transmit to growth of an economy? The answer is liquidity constraints foster savings and the link between savings and growth. Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12

15 Empirical evidence - continued Possible theoretical explanation: the buffer-stock model of savings Pioneered by Deaton (1991) Savings and Liguidity Contraints, and Carroll (1992) The buffer-stock Theory of Savings. Some Macroeconomic Evidence Similar results: Souleles (1999) The response of household consumption to income tax refunds But: Browning and Callado (2001) The response of expenditures to anticipated income changes: Panel Data Estimates - majority of Spanish workers receive an automatic bonus in June and December, household consumption paths of bonus and non-bonus households are indistiquishable Possible explanation by Browning and Crossey (2001) The Life-Cycle model of Consumption and Saving the changes in income used by Parker are small hence the welfare costs of deviating from consumption smoothing are small while the changes in income used by Browingn and Crossey are large and welfare costs of deviation from consumption smoothing are large. Joanna Tyrowicz (WNE UW) Advanced Macroeconomics // Consumption 05/10/ / 12