Consumption & Saving Chapter 13

East Asian Savings Rates  As a region, East Asia has high savings rates. These high savings rates have helped finance high rates of capital accumulation and growth.  Why have East Asian savings rates been so high? Culture? Luck?  Will it last?

Objectives  Explain high East Asian Savings rates.  Calculate Present Value & Annuity Value of a series of present and future payments.  Calculate Real and Nominal Present Values  Calculate the Multiplier for an open economy.

Consumption in Hong Kong

Pro-cyclical Consumption

Durables

Consumption Facts  Consumption movements are closely correlated with GDP. In other words, consumption is pro-cyclical.  Consumption volatility is overall somewhat less than output volatility.  The volatility of consumer durables purchases is much greater than the volatility of services or non-durables.

Why do People Save?  Life Cycle Motives – Income is Not Smooth Across Time. Households save, in part, to transfer income from high income periods to low income periods.  Precautionary Motives – Households like to achieve a buffer stock of wealth in the case of a possible bad outcome. If households have a buffer stock of saving, bad outcomes in terms of income don’t result in really bad outcomes in terms of consumption.

Life Cycle Motives: Two Period Model  To examine life-cycle theory, we use simplest possible model.  One good consumed by a household that lives two periods, C 1 and C 2.  Money price of goods is P 1 and P 2.  Household lives and earns money income PY 1 and PY 2 in each period.  Household can buy/sell bonds, B, at nominal interest rate i.

Temporal Budget Constraints  First period, period 0. B = PY 0 – P 0 C 0 1)  Second period, period 1. P 1 C 1 =PY 1 +(1+i)B2)  Note B can be either > or 0, household is a saver. If B < 0, household is a borrower.

Intertemporal Budget Constraint  Combine two budget constraints Multiply 2) by the inverse of the budget constraint. Rearrange terms. Set left side of 2.2) equal to right side of 2.1). Rearrange terms of 3).  Present Discounted Value of Lifetime Income equals Present Discounted Value of Lifetime Consumption. 2.1) 2.2) 3) 4)

Present Value  Many assets can be described as an income stream paying a certain amount of dollars in each period in the future: $Y 1, $Y 2, $Y 3 …..$Y N.  Q: How much is the current value of such an income stream? A: Current payments are worth more than future payments, since current money can be saved at interest.

Value of a Future Payment  Consider two payments. I could pay you $Y N in N periods or pay you a smaller value today,.  You put the smaller amount in the bank at interest rate i. After 1 period you will have. After 2 periods you will have.  After N periods you will have  The two payments have equal value.

Present Discounted Value  The present value of a payoff N periods in the future is the dollar payoff divided by the interest rate raised to the N power.  The present value of a stream of payments is equal to sum of the present values of each payment

Real Intertemporal Budget Constraint  Convert the model to real terms. Define real income Y. Divide both sides by P 1. Remember the definition of the real interest rate.  Real Present Discounted Value of Lifetime Income, W, equals Real Present Discounted Value of Lifetime Consumption. 4.1) 4)

Graph the Budget Constraint C1C1 C0C0 (1+r)∙W W

Preferences  People prefer some combinations of present and future consumption. More is better. If two combo’s have equal future consumption, choose the combo with more present consumption. Smooth over time. Households have diminishing returns to consumption in any period.  Preferences are represented by indifference curves – Smooth sets of combo’s amongst which the household is indifferent.

C1C1 C0C0 ABC

Optimal Choice  Preferences represent combo’s the household would like to have.  Budget represents combo’s the household can have.  Optimal choice is to choose the point on the budget constraint which is part of the highest available indifference curve.  This indifference curve will be exactly tangent to the budget at the optimal point.

Optimal Point C1C1 C0C0 (1+r)∙W W

Implications  Because of diminishing returns to consumption, will lie in the middle. That is consumption will be smooth over time.  Optimal current consumption will depend only on lifetime present wealth, not on income in any time period.

Income Stream & Consumption  Consider three hypothetical increases in income of $ A Temporary Increase – Y 0 increase by 100, but Y 1 is unchanged. This will increase W by A Future Increase – Y 1 increases by 100, but Y 0 is unchanged. W increases by 100/1+r≈100 3.A Permanent Increase – Y 0 & Y 1 increase by 100. W increases by 100(2+r/1+r) ≈200  Cases 1 & 2 increase W by nearly identical amounts. But current consumption depends only on W. Thus, cases 1 & 2 will increase by similar amounts.  Case 3 increases W by nearly double the amount.

Optimal Point C1C1 C0C0 (1+r)∙W W W+100W+200

Income Stream and Savings  In the first case, future income does not rise but optimal future consumption, C 2 * does. Current savings must rise.  In the second case, current income does not rise, but optimal current consumption. Current savings must fall.  What happens to savings with a permanent change in income?

Annuity Value  Just as any stream of future payments has a present value, so does it have an annuity value.  An annuity is an asset that makes a constant payment every period, for a number of years, N. Such an annuity has a present value.  The annuity value of any amount is the size of the payment of an annuity whose present value is equal that amount.

Present Value of an Annuity Payment  The real present value of an annuity with payment Y.  Off-the-shelf formula for geometric sum  Solve for present value of an annuity Y5)

Annuity Value of a Present Value  If you have some current lump sum, PV, payment and you want to buy a annuity for T periods.  Q: How big an annuity payment Y can you get.  A: Invert Equation 5)

Permanent Income Theory  The permanent income theory says that households keep consumption smooth consuming the annuity value of their financial wealth, F, plus the present value of lifetime income, W.

Example  The fractionis referred to as the propensity to consume out of wealth.  A household lives for = 40 periods and the real interest rate is.02. In every period they would consume a fraction of their wealth equal to

Applications: Wealth Effect  Changes in asset prices will change the current value of financial wealth.  The effect of an increase in financial wealth on consumption is called the wealth effect.  According to the PIH, a one dollar increase in the value of a stock portfolio should lead to an increase in consumption equal to the propensity to consume out of wealth.  Econometricians estimate that the wealth effect to be less than $.05 consistent with our theory.

Application: Life Cycle of Saving  Permanent Income Hypothesis suggests that households like to keep a constant profile of consumption over time.  Age profile of income however is not constant. Income is low in childhood, rises during maturity and reaches a peak in mid- 1950’s and drops during retirement.  This generates a time profile for savings defined as the difference between income and consumption.

Time Path of Savings time C,Y S>0 S<0 C Y

East Asian Demographics  During last 25 years, East Asian Nations had a sharp decrease in their ‘dependency ratio’.  Dependency ratio is the % of people in their non-working years (children & seniors.  Dependents are dis-savers and non- dependents are savers.

East Asian Demographics  Due to plummeting birth rates, East Asia had a plummeting ratio of youths as a share of population  This put a large share of population in high savings years.  Share of prime age adults has hit its peak in most Asian countries and will fall over the next half century.

Interest Rates: Incentives and Effects  A rise in interest rates increases the payoff to savings and increases the incentive to save. Substitution Effect (Plus Factor for All)  A rise in the interest rate reduces the amount of savings you need to do to meet target level of future consumption. Income Effect (Minus Factor for Net Savers).  A rise in the interest rate reduces the amount of borrowing you can do and still meet some target lever of future consumption. Income Effect (Plus Factor for Net Borrowers)

Aggregate Savings & Interest Rates  Interest rates have a positive impact on savings by borrowers, i.e. borrowers reduce their borrowing.  Interest rates have an ambiguous effect on savings by savers.  Since there is positive net savings, interest rates have ambiguous effect on aggregate savings.  Empirically, impact of interest rates on savings are hard to detect.

Consumption & Business Cycles  Consumption fluctuates more over the business cycle than can be accounted for permanent income hypothesis.  Two Explanations for co-movement of consumption with current income Borrowing Constraints Permanent Income Hypothesis

Borrowing Constraints  Though dollar changes in financial wealth may have relatively small effects on optimal consumption, for some people current income matters more.  If your optimal consumption is greater than your income you need to borrow to reach that consumption.  But if you cannot borrow the most you can consume is your income.  In this case, your present income is very important for current consumption.

Borrowing Constraints C1C1 C0C0 (1+r)∙W WY1Y1

Precautionary Savings  Many people are buffer stock savers holding a stock of savings to protect against a rainy day.  When the economy gets worse, the likelihood of a rainy day increases and people tend to save more.  Again this suggests a stronger relationship between current income and consumption than indicated by permanent income theory.

Consumption, Income & the Multiplier Effect  Real consumption is a function of current income which is a function of GDP.  Consumption is a major component of GDP.  There is positive feedback between consumption and GDP which is called the multiplier effect.

Open Economy Multiplier  Consumption is a linear function of current GDP. C = A + mpc ∙Y  Some consumption is imports, so imports are also a function of current GDP. IM = B + mpim ∙Y (Assume mpim < mpc)  By accounting identity, GDP is a function of consumption and imports Y = C + I + G – IM + EX

Multiplier Effect  We can calculate the effect of an autonomous increase in demand Y = A + mpc ∙Y + I + G + EX – B-mpim ∙Y Y = A-B + (mpc-mpim) ∙Y + I + G+ EX  Define mpd = mpc-mpim ( 1-mpd) ∙Y =A – B+ I + G+ EX

Multiplier Effect  An exogenous change in demand has a larger effect on total demand, the larger is the effect of current GDP on consumption of domestic goods.  If budget constraints or precautionary savings are important then mpc may be high and mpd high.  If economy is very open, like HK mpim may be high and mpd low.