1. THE CONSUMPTION FUNCTION Looking at Aggregate Demand (closed economy) Ep = C + Ip + G Assuming G is exogenous, this leads to enquiring into determinants of Consumption and Investment Consumption is of particular interest (multipliers, etc) Previously we have: – C = (1 - s)Y (0  s < 1) – or, C = C(Y - T) We need to model the behaviour of C

2. EARLY FORMULATION: KEYNES (1936) Keynes (1936) made three main assertions: C = C(Y), (not r) 0  MPC  1, (where MPC is dC/dY) APC falls as Y increases (APC is C/Y) Taken together these imply a Consumption Function of the form: C = A + bY –where A and b are positive constants –APC = A/Y + b –MPC = b –and A/Y must fall as Y increases

3. GRAPH OF THE BASIC CONSUMPTION FUNCTION As Y increases, C/Y falls: also dC/dY  C/Y 45 O C Y0 C = A + bY A dC/dY = b

4. EARLY EMPIRICAL EVIDENCE Keynes hadn’t have much statistical evidence on consumption Early estimates in the 1940s for the USA and elsewhere were conflicting. Short-medium term annual data (1929-45) –C = A + bY; A  0; b  0.7 Long-term data (1869-1945) –C = bY: A  0, b  0.9 Which is “right”? We need a proper model to answer this.

5. LONG AND MEDUIM RUN EVIDENCE ON CONSUMPTION 1929-45: C = A + bY 1869-45; C = b*Y 45 O C Y0 C = A + bY b  0.7 C = b* Y b*  0.9

6. MODELS OF AGGREGATE CONSUMPTION Basic Intertemporal Choice model (Fisher) The Life-Cycle theory of Consumption (Modigliani, etc) The Permanent Income theory of Consumption (Friedman)

7. INTERTEMPORAL CHOICE Generally we require: PV(C)  or  PV(Y) i.e. C 1 + C 2  (1+r)  or  Y 1 + Y 2  (1+r) or  C i  (1+r) i  or   Y i  (1+r) i Households maximize Utility over expected lifetime i.e. Max: U = U (C 1,..., C i,..., C n ) s.t.  C i  (1+r) i  or   Y i  (1+r) i (i : 1  n)

8. INTERTEMPORAL CHOICE Indifference Curves represent U = U(C 1, C 2 ) 0 C2C2 C1C1

9. INTERTEMPORAL CHOICE Endowment at E: OB = PV(Y) = y 1 + y 2  (1 + r) Slope of AB is  (1 + r) 0 Y2Y2 Y1Y1 B A. E y2y2 y1y1

10. INTERTEMPORAL CHOICE Why is slope AB = - (1 + r) ? Suppose (present) savings increase by €100 i.e.  C 1 = - 100 This allows an increase in C 2 of 100(1 + r) i.e.  C 2 = +100 (1 + r) Slope AB =  C 2   C 1 = 100 (1 + r)/ - 100 = - (1 + r)

11. A CHANGE IN r An increase in r: AB pivots at E  CD 0 Y2Y2 Y1Y1 B A. E y2y2 y1y1 C D

12. OPTIMAL C Saving is (oy 1 - oc* 1 ) : future dis-saving is (oc* 2 - oy 2 ) Y1Y1 Y2Y2 0 A B. E c*c* 2 c* 1 y2y2 y1y1

13. CHANGES IN Y AND C Y 2 increases: E’  E”, AB  CD, c’ 1  c” 1 B A Y2Y2 Y1Y1 0 E’.. E” c” 1 c’ 1 D C

14. A INCREASE IN r : SAVER Income effect 1  3; Substitution effect 3  2 Y1Y1 Y2Y2 0 A B. E c11c11 y2y2 y1y1 C Dc21c21 G F c31c31 3 2 1

15. A INCREASE IN r : BORROWER Inc. effect 1  2; Sub. effect 2  3 Y1Y1 Y2Y2 0 A B. E c11c11 y1y1 C D 1 2 c21c21 3 c31c31 F G

16. IMPERFECT CAPITAL MARKETS Borrowing rate (EB) > lending rate (AE) 0 C2C2 C1C1. E Y2Y2 Y1Y1 A B

17. CREDIT (BORROWING) CONSTRAINT. 0 C2C2 C1C1 E Y2Y2 Y1Y1 A B D I” I’ Consumer cannot borrow more than Y 1 B Constraint: ADB

18. THE LIFE-CYCLE HYPOTHESIS –Income shows a marked life-cycle variation –It is low in the early years, reaches a peak in late middle age and declines, especially on retirement –Smoothing consumption over a lifetime is a rational strategy (diminishing MUy) –This implies C/Y will vary during the lifetime of an individual

19. THE LIFE-CYCLE HYPOTHESIS. 0 C1C1 C2C2 C1*C1* C2*C2* A B E’. E”. Y1’Y1’Y1”Y1” E’: low Y 1 /Y 2  high C 1 /Y 1 E”: high Y 1 /Y 2  low C 1 /Y 1

20. THE LIFE-CYCLE HYPOTHESIS Y, C and W over the life-cycle Age Y, C 6518 Age +W WW CtCt Y t Wt Wt

21. THE LIFE-CYCLE MODEL –Let retirement age = 65; life expectancy = 75 –Years to retirement = R (= 65 – present age) –Expected life = T (= 75 – present age) –Assuming no pension, no discounting: – CT = W + RY is the lifetime constraint –i.e. C = (W + RY)/T –and C = (1/T)W + (R/T)Y –or C =  W +  Y (  = 1/T;  = R/T)

22. THE LIFE-CYCLE MODEL – C =  W +  Y – MPC =  C  Y =  – APC = C  Y =  (W  Y) +  – clearly MPC < APC –for a “typical” individual, age 35 –R=30, T = 40 –  = 1/T  0.03;  (MPC) = R  T  0.75 –APC = [0.03 (W  Y) + 0.75] > MPC

23. THE LIFE-CYCLE MODEL Saving and Consumption behaviour may depend on population age-structure Does Social Security displace personal savings? What is the effect of Medicare (USA) or Medical Cards for over 70s (IRL) on Savings? Savings and Uncertainty: –“rational” behaviour: run down wealth to zero –individual circumstances unpredictable (care needs) –individual life expectancy unpredictable –on average even selfish people will die with W > 0

24. THE PERMANENT INCOME HYPOTHESIS C p = kY p (0  k  1 ) Y = Y p + Y tr C = C p + C tr Permanent income is the return to all wealth, human and non-human: Y p = rW which implies: C p = rkW NB: C is not related to Y tr i.e. dC  dY tr = 0

25. MEASURING PERMANENT INCOME AND CONSUMPTION (1) Are C p and Y p observable? E(Y tr ) = 0 E(C tr ) = 0 which imply that E(Y) = E(Y p ), etc. However this is ex ante: ex post, actual measures may reveal more (a) in a recession: Y < Y p :  Y tr < 0 (b) in a boom: Y > Y p :  Y tr > 0

26. MEASURING PERMANENT INCOME AND CONSUMPTION (2) Cross-section measurements of C and Y 45 o C Y0 Ym Cm C i = A + bY i....... C i, Y i.

27. MEASURING PERMANENT INCOME AND CONSUMPTION (3) Where Y j > Y m, Y tr > 0 and Y j > Y p j 45 o C Y0 Ym Cm C i = A + bY i C p =kY p YjYj CjCj YpjYpj Y tr j

28. MEASURING PERMANENT INCOME AND CONSUMPTION (4) Aggregate: Ytr > 0 in boom, < 0 in recession Measured C/Y should  be < in boom than in recession (Recent experience?) Aggregate C tr = 0: individual C tr is > or < 0 Average C tr = 0 for all income groups Measuring Y p : –Adaptive expectations: Y p = f(Y t, Y t - 1,...Y t-n ) –Rational expectations: only new information (shocks) change Y p –Consumption V Consumption Expenditure, which highlights the role of durables (Investment and saving rather than consumption

29. MEASURING PERMANENT INCOME AND CONSUMPTION (5) Also we may express the PYH as an error-correction model: Y p t = Y p t-1 + j(Y t – Y p t-1 ) 0 < j < 1 which with: C t = C p t = kY p t gives: C t = kY p t = kY p t-1 + kj(Y t – Y p t-1 ) Re-arranging: C t = (k – kj)Y p t-1 + kjY t j  0 implies slow adaptation, j  1 implies rapid adaptation assume k = 0.9, j = 0.3, so kj = 0.27 then: C t = (0.9 – 0.27)Y p t-1 + 0.27Y t or 0.63Y p t-1 + 0.27Y t However this is not an explicitly forward-looking model. Now suppose C = C p = kY p, then Y p = 1/k(C p ) Thus Ct = (0.63/k)C t – 1 + 0.27Y t = 0.7C t – 1 + 0.27Y t

30. PERMANENT INCOME AND RECESSION Y < Yp in short-run (mild) recession Suppose there is a shock to the system (financial crisis) Pwople expect a severe long-drawn-out recession: i.e. Yp falls, ie. E(Y) falls It is possible that initially Y > Yp C (and Cp) will fall If people anticipate a fall in Yp, then C/Y may fall Current (mid-2009) situation: big fall in W, both the Permanent and Life-cycle theories predict that this will hit C (independently of current measured Y)