ADVANCED MACROECONOMICS I MSC Alemayehu Geda Email: ag112526@gmail.com Web Page: www.alemayehu.com Lecture 2 Consumption and Saving Theories Addis Ababa University Departement of Economics MSc/MA Program 2014
Lecture on Consumption/Saving Theories (MSc/MA Class) (i) Background about Consumption Theory (ii) The General Formulation (Micro Foundation): Intertemporal Optimization (iii) Theories of Consumption & Saving (a) The Anod-Modigliani Approach [LC Hypothesis] (b) The Friedman Approach [PI Hypothesis] (c) The Duesenenberry Approach [RI Hypothesis] Alemayehu Geda Dept. of Economics, Addis Ababa University, 2014-2015 E-mail AG112526@gmail.com & web : www.alemayeh.com
I. Background to the Theories Following Keynes (1936) the relationship b/n consumption and Income is central for macroeconomics (C is over 75% of GDP) Three theories are suggested to explain this relationship: The Ando-Modigliani (1950s) Theory (Life-Cycle Hypothesis) The Friedman (1957) Theory (Permanent Income Hypot.) The Duesenberry (1949) Theory (Relative Income Hypot.)
Background to the Theory..Cont d Recall that Keynes [Keynesian Theory] argues that C= C0 + cy, with C0 > 0 and the average propensity to consume (APC = C/Y) is greater than the marginal propensity to consume (MPC = c): C/Y = (C0 + cy)/y > c, or (1) APC > MPC (2) Moreover, the APC should not be a constant if C0 is not zero.
Background to the Theory..Cont d Keynes followers estimated the consumption function for the U.S. using the data from 1929-1941: C = 26.5 + 0.75Yd C0=26.5 billion > 0 APC > MPC Increases in consumer spending seemed to be less than increases in disposable income, supporting MPC < 1 This implies: As Y increase APC declines (see next Diagram)
Background to the Theory..Cont d Real Consumption C(Y) APC (C/Y) Y (Real Income)
Background to the Theory..Cont d Keynes noted: As income declines people will protect their habit by not cutting consumption proportionally (& the converse is true) Cross-sectional data in the 1930 verified this (rich people proportionally saved more, Keynes claimed) A. The STAGNATION thesis Acceptance of this theory [ie MPC<APC as Y rises] led to the formulation of what is called the STAGNATION thesis in 1940s The argument says in C demand (relative to Y; ie C/Y) declines this will pose a problem for fiscal policy
Background to the Theory..Cont d Y=C+I + G or 1= C/Y+I/Y+G/Y implies, if there is no reason for I/Y to rise as income increased G/Y must increase more that proportionately otherwise the economy will stagnate. B. WWII & the STAGNATION thesis Following WWII in the west gov t spending was rising sharply and economists were worried the economy will stagnate following the end of war time spending Following the war, however, it is inflation not recession that has occurred. Why? One plausible explanation was the role of wealth
Background to the Theory..Cont d C. The Role of Wealth During war peopls has earned large increase in income but consumption was currbed by rationing. This led to forced saving held in bonds [wealth]. The latter is converted to consumption following the end of the war. Implication: Consumption is a function of BOTH income and wealth [we did that in Kenyan macro model]
Background to the Theory..Cont d A. The KUZNET Study/ Hypothesis [Kuznet s results are being questioned by Pikette 2014 though] Kuznets, Simon. Uses of National Income in Peace and War, Occasional Paper 6. NY: NBER, 1942. Time series estimates of consumption and national income Overlapping decades 1879-1938, 5 year steps (Each estimate is a decade average) Results: (1946 study) Between 1869-1938, real income expanded to seven (7) times its 1869 level ($9.3 billion to $69 billion) But the average propensity to consume ranged between 0.838 and 0.898. That is, APC did not vary significantly in the face of vastly expanding income.
Kuzent s Result:
By the way!: don t believe Kuzent: see Piketty, 2014. Be careful! No Kuznet inverted-u!... but just Piketty s U.
Kuznet s result... Cont d He also found that C/Y is below trend or long run average during Boom; and above trend during slum [C/Y>Trend in Slum & C/Y<Trend in boom] Implies the ratio varies inversely with income (basically similar to the short-run Keynesian hypothesis) Thus by 1940s a theory of consumption is expected to account for three observed facts: [1] Cross-section (budget) studies shows that as Y increases C/Y declines (or S/Y increase). That is MPC<APC and APC declines as Y increase
Kuznet s result... Cont d [2] Business cycle, short-run, data shows the C/Y<Average in boom and >Average in slum. [As income fluctuate MPC<APC] [3] Long-run data show no tendency for C/Y raton to change over time. [So, as Y grows along trend MPC=APC]. Short-run functions A consumption theory should thus explain this short-run and long-run phenomenal as well as the effect of wealth (asset) on consumption
II. The General Formulation (Micro Foundation): Intertemporal Optimization The theories to be discussed in the rest of the lecture assume a rational optimizing agent to deal with their theory of consumption/saving. In this section we will develop the micro foundation before exploring the three major theories of consumption/saving. The intertemporal optimization consumption models below is done for two periods but can readily be extended to finite or infinite horizon.
. Micro Foundation...Cont d
Micro Foundation...Cont d
Micro Foundation...Cont d
. Micro Foundation...Cont d
Micro Foundation...Cont d
Micro Foundation...Cont d
II. The Life-Cycle Hypothesis: The Ando- Modigliain Theory Franco Modigliani, Albert Ando, and Richard Bloomberg Assumes that each representative agent will die, and knows: when he/she will die, how many periods T he/she will live, and How much his/her life-time income will be. The consumer smooths consumption expenditure over his/her life, spending 1/T of his/her life-time income each period The constraint is that her/his life time consumption doesn t exceed the present value of his/her total income. See nxt diagram (early &let year dissaving )
The Life-Cycle hypothesis...cont d
The Life-Cycle hypothesis...cont d Thus for a representative consumer i if PV rises C rises more or less proportionately, thus: Cti=ki(PVi) where 0<ki<1 ki=fraction of PV that she wants to consume in period t ki depends: (a) shape of the indifferent curve embodied in the utility function [section I above on micro foundation ] (b) the [market] interest rate (r), and (c) the personal discount rate [d]
The Life-Cycle hypothesis...cont d If popn distn by age and income is constant, test b/n current and future (shape of indiff curve) are stable we can add all the individual ( i ) consumptions to generate a stable aggregate consumption function given by [2]. Ct=k(PV) [2] Note: theory refers to expected income and we operationalized it in [2] by PV. Ando and Modigliani further operationalize PV for their empirical work into: (a) labour, YL and (b) property or asset related income, Yp. Thus,
The Life-Cycle hypothesis...cont d PV 0 = T 0 Y L (1 + r) t + T 0 Y P (1 + r) t If capital market is efficient the PV income from asset will be equal to the value of the asset itself, a; ie T 0 Y p (1 + r) t = a 0 We can also divide the labour income into the known and unknown (expected) labour income PV 0 = Y L0 + Y Lt T 1 +a (1+r) t 0
The Life-Cycle hypothesis...cont d The next step is how to relate expected labour income [YL1..YLT] to current observable variables. We will assume there exists average expected labour income at time 0 which is Yo[expected], given by: Y e 0 = 1 (T 1) From this we can write (T 1)Y e 0 = T 1 T 1 Y LT (1 + r) t Y LT (1 + r) t Substituting this expected income in the PVo definition above, we get:
The Life-Cycle hypothesis...cont d We can also divide the labour income into the known and unknown (expected) labour income PV 0 = Y L0 + T 1 Y 0 e +a 0 This has now one remaining variable that is not measurable, the average expected labour income, Y e Many assumptions can be used to link this expected income [Y e ] to current labour income [YL0]. The simplest assn is average expected labour income is just a multiple of present labour income: ie Y e 0 = βy L0 where β > 0
The Life-Cycle hypothesis...cont d Thus, if the current income rises people adjust their expectation up so Y e rises by β of the increase in YL Ando and Modigliani found that this formulation fits the data well. Thus, substituting βyl for Y e, we obtain PV 0 = Y L0 + T 1 βy L0 +a 0 PV 0 = 1 + β(t 1) Y L0 +a 0 The Ando-Modigliani consumption function is given by the diagram on next slide. In the diagram: In the short run asset remaining constant consumption & income move along the consumption line. In the long run the function shifts as assets changes & consn and income move along the ray from the origin.
The Life-Cycle hypothesis...cont d YL
The Life-Cycle hypothesis...cont d Illustration and conclusion: The estimation for the US by Anod and Modigliani gave this result. Assuming 45 years average remaining life time, T C t = k 1 + β(t 1) Y L0 +ka 0 0.7Y Lt +0.06a t Note here that 0.7=k[1+β(T-1)]; 0.06[1+β(44)]=>β=0.25 If we divide both sides of the estimated eqn by Yt: (Ct/Yt)=0.7(YL/Yt)+0.06(at/Yt) The C/Y ratio will be constant as the economy grwoth if (YL/Yt) & (at/yt) are roughly constant. The observed data for the US shows they are fairly constant (being 0.75 &3. If these values are inserted in the above estimation we get:
The Life-Cycle hypothesis...cont d Illustration and conclusion: (Ct/Yt)=0.7(0.75)+0.06(3)=0.53+0.18=0.71 A spot check at 1987 shows C= 3 trillion & income 3.7 trillion gives C/Y ratio to be 0.80. Note that this theory explains all three of the observed consumption phenomena: (a) Explains MPC<APC result of budget/cross-section studies (b) Explains the cyclical behaviour of consumption with C/Y ratio inversely related to Y along short-run function (c) It also explains the long-run constancy of C/Y ratio (d) It explicitly includes assets as an explanatory variable (a role observed in post WWII situation).
The Life-Cycle hypothesis...cont d Criticisms of LCH The households, at all times, have a definite, conscious vision of: The family s future size and composition, including the life expectancy of each member, The entire lifetime profile of the labor income of each member after the applicable taxes, The present and future extent and terms of any credit available, and The future emergencies, opportunities, and social pressures which might affect its consumption spending. It does not take into account liquidity constraints
The Life-Cycle hypothesis...cont d Policy Implication [Criticisms of LCH] Changes in current income have a strong effect on current consumption ONLY if they affect expected lifetime income. In Q2 1975 in the US, a one-time tax rebate of $8 billion was paid out to taxpayers to stimulate AD. The rebate had little effect.
III. The Friedeman Approach or the Permanent Income Hypothesis Milton Friedman (A Theory of the Consumption Function. Princeton Univ. Press, 1957). Here he developed the Permanent Income Hypothesis/Theory Employs the following Assumptions: Perfect certainty about: Future receipts; Future interest rates; Future prices, etc. People save to reduce fluctuations in expenditures People are immortal (or leave bequests) Like Modigliani and Ando he noted consumption shouldn t depend on current income alone. With this, the Individual s utility function is given by u = u(c,c1) similar to our micro-foundation discussion.
III. The Friedeman Approach or the Permanent Income Hypothesis Unlike Life-Cycle Hypothesis (which hold income follows regular pattern) the PIH hold that people face random and temporary changes to their income from year to year Friedman holds that, thus, current income (Y) could be divided between permanent (Yp) and transitory (YT) component. Y=YP + YT Permanent Income: part of the income people expected to persist into the future. Transitory Income: part of income that is not expected to persist (is random: deviation from the average) Friedman maintained consumption primarily depends on YP & Consumer use Saving/borrowing to smooth consumption for change in Y.
III. The Friedeman Approach or the Permanent Income Hypothesis Similarly consumers do save rather than spend their transitory income (so as to distribute it over time). Thus, the consumption function is given by: C = αy P where α is a constant consumption is proportional to permanent income. NB also that we can arrive at this relationship using optimization as discussed in part I (Micro foundation) too [Read! The Textbook]. What are the implications of such formulation: (A) The PI solves the consumption puzzle by stating that: the Keynesian function uses the wrong variable (ie current income). This error-in-variable explains the seemingly contradictory findings; ie Thus, the APC will be given by:
III. The Friedeman Approach or the Permanent Income Hypothesis Thus, the APC will be given by: APC = C Y =[αy P] Y -When current income temporary rises above permanent, APC declines When the reverse holds, APC temporarily rises. Regarding the HH data it combines permanent and transitory income; so If all variation comes from the permanent component, we observe no different in APC across HHs But if the variation comes form the transitory component, HH with higher transitory income will NOT have higher consumption and hence we find such [high income] HH having lower/declining APC. Regarding the Time Series data
III. The Friedman Approach or the Permanent Income Hypothesis Regarding the Time Series data Friedman argues year to year fluctuation are dominated by transitory income, therefore: Years of high income with see a declining APC But over the long-run (say decade to decade) variation in income comes from the permanent component hence the APC is almost constant. (ie the PI varies with C) Rational Expectation and Consumption [The HALL Approach: Read Branson, 1989, PP. 266-) The PI builds its idea on the assumption of forward looking agents who form expectation about their future income. Thus, PI maintains consumption depends on expectation.
III. The Friedman Approach or the Permanent Income Hypothesis Recent research that begins with Hall combines PIH with rational expectation (people use all information to forecast future events). Hall showed that if PIH is correct and consumer use rational expectation then change in consumption over time should be unpredictable so consumption follows a random walk. Hall s Reasoning: According to the PIH consumers smooth consumption based on their current expectation of their future income Over time they change consumption if they revise their expectation based on news or new information Thus, change in consumption reflects surprise about life time income If consumers use rational expectation (optimally use news) surprises and hence consumption will be unpredictable.
III. The Friedman Approach or the Permanent Income Hypothesis Implications of Hall s formulation Has implication not only for forecasting but also for policy. That is if consumers use PIH and rational expectation, only unexpected policy changes do influence consumption. Eg announcing tax cuts next year to reduce consumption next year leads to revision of expectation and hence may reduce consumption TODAY (not next year). Thus, policies influence not only through policy makers action but through public expectation of their action thus hard to know how policies alter aggregate demand. -- ----end of PIH..
IV. The Duseneberry Approach or the Relative Income Hypothesis/Habit Persistent Models The Duesenberry (1949) model is based on two relative income related hypotheses. [see also Brown. Habit Persistence and Lags in Consumer Behavior, Econometrica 20 (July 1952)]. [A] Consumers are concerned not so much with their absolute consumption as that of the level relative to the rest of the population [B] Consumption is influenced not merely by present levels of absolute or relative income but also by level of consumption attained in the previous period (habit persistence or habit formation) Following the first hypothesis he wrote the related utility function: U = u C 0 R 0. C t R t C T R T. Where R is weighted average of the rest of the population s consumption
IV. The Duseneberry Approach or the Relative Income Hypothesis/Habit Persistent Models In this formulation U increase only if individuals consumption relative to the average increase. Thus individuals APC depends on her position in the income distribution. That is, Individuals with income <average tend to increase C/Y [to keep up] Individual with income > average will have lower C/Y [takes a small portion of his income to buy consumption basket] This explains the cross-section MPC<APC as Y increase and the long-run constancy of the APC [C/Y]. Following the 2 nd hypothesis: it is difficult for a family to reduce consumption in the face of declining income than to reduce the proportion of income [to be] saved
IV. The Duseneberry Approach or the Relative Income Hypothesis/Habit Persistent Models This implies the saving-income ratio depends on the level of present income relative to previous peak income, Ypeak
Relative Income hypothesis...cont d This savaging function could be converted into a consumption: function
Relative Income hypothesis...cont d The above result shows the following points: [A] As income grwoth steadily, the peak income equals last years income. In the long run Y equals Ypeak because in the long run the ΔY is zero. At that point APC=MPC, both constant hence the Kuznet s result. [B] But as income fluctuates around the trend, the C/Y will vary inversely with income owing to the negative coefficient of C in Y/Ypeak. In the above formulation. To get the MPC, multiply the C/Y in the previous slide by Y, then take the partial derivative of the resulting equation wrt to Y.. This will give you. (1-a)-2b(Y/Ypeak). This MPC is < the APC [which is (1-a)-a(Y/Ypeak) ] This combination of long and short run behaviour gives what is called the Ratchet effect, shown in the next diagram.
Relative Income hypothesis...cont d The ratchet effect says when income falls off consumption drop less than it rises (along the short-run curve) as income grwoth along trend.
End of Lecture