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Permanent Income Hypothesis, a two period application

MBA 681 Economics for Strategic Decisions

Prepared by Yun Wang

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Basic facts (Figure 1.1):

Gross domestic saving rates in developing countries are higher than the rates in industrial countries (highest in Asia).

Investment rate follows similar pattern (highest in Asia).

Foreign saving is particularly large in Sub-Saharan Africa.

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Consumption and Saving

Keynesian Approach

Permanent Income Hypothesis

The Life-Cycle Model

The Basic Framework

Age and Dependency Ratio

Other Determinants

Income Levels and Income Uncertainty

Intergenerational Links

Liquidity Constraints

Inflation and Macroeconomic Stability

Government Saving

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The Debt Burden and Taxation

Social Security, Pensions and Insurance

Changes in the Terms of Trade

Financial Deepening

Household and Corporate Saving

Empirical Evidence

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Keynesian Approach

Consumption is a function of disposable income:

C = (1 - s)(Y - T),

C current consumption, Y - T disposable income;

0 < s < 1 marginal propensity to save.

Merits:

First approximation in empirical macroeconomic models.

A reflection of the behavior of consumers subject to liquidity constraints.

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The Permanent Income Hypothesis

Consumption is a function of permanent income.

Example : Consumers are identical and live for only two periods, 1 and 2. Assume perfect foresight.

Budget constraint for period 1:

A1 - A0 = Y1 - T1 + rA0 - C1 (1)

A: stock of financial assets, Y - T disposable income;

r: real interest rate (constant).

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Budget constraint for period 2, in the absence of bequest:

C2 = Y2 - T2 + (1+r)A1 (2)

Eliminate A1 from (1) by using (2).

Yield the household’s intertemporal budget constraint:

C2 Y2 - T2

C1 + ––––– = (1+r)A0 + (Y1 - T1) + ––––––––

1+r 1+r

(3)

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Simple version of the model:

Household’s objective is to maintain a perfectly stable (or smooth) consumption path, C1 = C2.

Divide its lifetime resources equally among each period of life.

Amount consumed by the household in each period is equal to its permanent income, Yp .

Yp : level of income that gives the household the same present value of its lifetime resources as that implied by its intertemporal budget constraint.

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Using equation (3) intertemporal budget constraint is

Then Yp becomes:

Yp Y2 - T2

Yp + ––– = (1+r)A0 + (Y1 - T1) + –––––

1+r 1+r

1+r Y2 - T2

Yp = (–––––){(1+r)A0 + (Y1 - T1) + ––––––– }

2+r 1+r

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(Y1 - T1 )+ (Y2 - T2 )

Yp = –––––––––––––––––––––

If A0 = 0 and r = 0, YP becomes an exact average of present and future disposable income.

Implications:

Saving (in period 1) is the difference between disposable income and permanent income.

S1 = Y1 - C1 = Y1 - Yp

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Transitory income :

YT = Y1 - Yp

This forms the basis for a number of empirical tests.

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Importance of variations in the structure of income during life cycle.

Figure 1.2: stylized pattern of income, consumption, and savings predicted by the standard life-cycle model.

The Life-Cycle Model

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Basic Framework:

Two period framework.

Life time budget constraint :

C1 + ––––– = W1 (4)

1+r

W1: life-time wealth.

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Suppose that the household’s preferences are intertemporally additive :

u(C2)

U = u(C1) + –––––– (5)

1+

U: life-time utility;

: rate of time preference which measures the degree of impatience.

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L = U + [C1 + ––––– - W1]

1+r

u’(C2) 

u’(C1 ) = , ––––––– = ––––.

1+ 1+r

Maximization of (5) with respect to C1 and C2 subject to the life-time budget constraint (4).

By forming the Lagrangien expression:

: Lagrange multiplier.

The first order optimality conditions are given by:

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Combining these two equations obtain Euler equation :

1+r

u’(C1 ) = –––u’(C2)

1+

- - -1/

U = {C1 + C2 /(1+)}

where  > 1.

When  = r, we obtain C1 = C2. The model becomes the simple version of permanent income hypothesis.

Assume constant elasticity of substitution :

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-1/ 1+r -1/

C1 = (–––––)C2

1+

Taking logarithms of both side

1+r

ln(C2/C1) = ln(––––)  (r - )

1+

The elasticity of substitution between period 1 and period 2 consumption, , is :

 = 1/(1+).

Euler equation becomes :

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 measures the responsiveness of the change in consumption between the two periods to changes in interest rate, r.

The effect of the change in r on consumption and saving (in period 1) is indeterminate.

Conflict between income and substitution effects.

The greater is , the greater will be the reduction in C1 (relative to C2) induced by a rise in r.

If  is sufficiently large: effect of substitution dominates; an increase in r reduces consumption and raises saving.

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Predictions of life-cycle model

The young will save relatively little as they anticipate increases in their future income.

Middle-aged individuals, who are nearing the peak of their earnings, tend to save the most, in anticipation of relatively low incomes after retirement.

The elderly tend to have a low, or even negative, saving rate, although the desire to leave a bequest or to cover the contingency of living longer than expected could provide motivation for saving even after retirement.

Age and Dependency Ratio

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Implication: Aggregate saving rate will tend to fall in response to dependency ratio, measured as

youth dependency ratio (ratio of under-20 age group to the 20-64 age group);

ratio of the elderly to the working age population.

Distribution of assets among the population affects the consumption and saving patterns at the aggregate level.

The larger the share of total wealth held by the middle-aged households, the higher the saving rate, and the higher the growth rate of income in a given country.

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Remark : demographic factors such as the share of the working population relative to the that of retired persons are likely to explain only the long-term trends in saving.

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Other Determinants

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Income levels and income uncertainty

Recent empirical research has highlighted the fact that at low or subsistence levels of income, the saving rate is also low.

Two implications:

in low-income countries the response of saving to changes in real interest rate is likely to be weak;

changes in income distribution can have important effects on measured saving rates at the aggregate level.

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Increased uncertainty regarding future income will enhance the precautionary motive for saving.

Sources of income uncertainty :

Many households in developing countries derive their incomes from agriculture.

In that sector, incomes can be subject to relatively large fluctuations resulting from variations in climatic conditions or changes in domestic and the world prices of agricultural commodities.

Macroeconomic instability.

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Intergenerational links are likely to be strong in developing countries (role of extended family).

These links can affect consumption and saving in two ways:

lengthen the effective planning horizon over which households make their consumption and saving decisions;

affect household preferences (by affecting, for example, the degree to which the marginal utility of consumption).

Intergenerational Links

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Liquidity Constraints

Consumption smoothing requires well-functioning financial markets to allow agents to borrow and lend across periods.

In many developing countries, well-developed financial markets either do not exist, or not function very well.

Households often have limited access to credit markets, and credit rationing may be pervasive.

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Liquidity constraints affect the ability of households to transfer resources across time periods as well as across uncertain states of nature relative to income.

Consequence : consumption tends to be highly correlated with current income, rather than permanent income or life-cycle wealth.

In the presence of liquidity constraints, financial liberalization can have an adverse effect on saving rates.

Increased access to these markets will allow individuals to bring forward their consumption (reduce saving).

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If households are net creditors, an increase in the inflation rate may lower real value of wealth. To offset this, they raise their saving rate.

The variability of inflation (measure of macroeconomic stability) may affect saving by increasing uncertainty about future income.

Precautionary motive : a high degree of price variability may lead to an increase in the saving rate.

Inflation and Macroeconomic Stability

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Key feature of the life-cycle model: saving behavior is directly influenced by households’ assessments of their future disposable income.

Key variable that affects these assessments is government policy, particularly government saving or dissaving.

Three major interpretations of the relationship between government and private saving:

Government Saving

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Conventional view:

Assume a fall in government saving (resulting from a tax cut or a bond-financed increase in government spending).

This will tend to raise consumption and reduce saving by myopic households (that is, households who care solely about the present).

Reason: they shift the tax burden from present to future generations .

Decline in government saving will lead to a decline in national saving.

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The Keynesian view

Higher temporary government dissaving.

Consumption and income increase in the presence of under-utilized production capacity: multiplier effect.

Higher income will raise private saving.

Whether or not this increase in private saving is large enough to offset the initial decline in government saving is a priori ambiguous.

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The Ricardian equivalence view

Predicts that a rise in the budget deficit resulting from a tax cut will have no effect on the national saving rate because private saving will rise by an equivalent amount in anticipation of future tax liabilities.

If individuals are rational and far-sighted, they will realize that a permanent rise in government spending today must be paid for either now or later.

They will increase saving by an equivalent amount.

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Critics for the assumptions of Ricardian equivalence from the analytical point of view:

consumers are far-sighted;

successive generations are linked by altruistically motivated bequests;

consumers do not face liquidity constraints;

taxes are nondistortionary.

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Empirical results for developing countries is against Ricardian equivalence.

Reason: although individuals may form expectations about their future tax liabilities in a systematic way, liquidity constraint may prevent them from acting on these expectations.

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Social Security, Pensions, and Insurance

The availability of formal public pension and social security schemes may cause to lower the private saving rate.

Channels implied by the life-cycle model:

by redistributing income to the elderly;

by reducing the need to save for retirement (if there is no reduction of the retirement age);

by curbing the need for precautionary saving to cover the contingency of living longer than expected.

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The impact of increased social security benefits on national saving depend on the effect that such changes on public saving.

Private pension plans have been developed in many developing countries in recent years.

In principle, individuals should view their contributions to funded private pensions as a perfect substitute for other forms of saving.

But, in practice, individuals do not seem to fully take into account their pension contributions in determining their saving behavior.

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Result : introduction of private pension plans is often accompanied by an increase in national saving rates.

Conclusion of Holzmann (1997) in the case of Chile.

Availability of various kinds of insurance:

health insurance ;

unemployment insurance ;

personal loss and liability insurance.

They influence saving behavior.

To the extent that insurance plans limit expected outlays for contingencies and emergencies, they tend to reduce income uncertainty and therefore the need for precautionary saving.

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Movements in terms-of-trade has an important effect on saving.

Harberger-Laursen-Meltzer Effect: predicts a positive relationship between changes in the terms-of-trade and saving, through their positive effect on wealth and income.

Predictions:

Temporary decrease in terms of trade leads to decrease in current income compared to future income thus leads to a decrease in saving.

If permanent deterioration in the terms of trade leads to reduction in both permanent and transitory income, no effect on saving.

Changes in the Terms of Trade

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Financial Deepening

Financial development may affect saving both directly and indirectly:

reduction in cost of intermediation leads to increase in the return to saving;

increased efficiency in the process of financial intermediation leads to an expansion of investment and stimulates the rate of economic growth;

increase in income leads to an increase in saving.

Figure 1.3: positive relationship between gross domestic saving rates and an indicator of financial deepening.

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Forgoing discussion focused only on saving by households.

This focus justified in the many developing countries where private saving rates are essentially determined by household behavior.

However corporate saving (retained earnings) may also be significant.

They may respond to different variables than those affecting the decisions of households.

Household and Corporate Saving

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Importance of this distinction in the aggregate private saving depends on households’ responses to higher corporate saving.

If firms retain more earnings, households may have less by a corresponding amount:

In such conditions, households pierce the corporate veil.

Aggregate private saving behavior will largely reflect household behavior.

Example: Colombia (Figure 1.4).

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Masson, Bayoumi, and Samiei (1995)

Edwards (1996c)

Dayal-Gulati and Thimann (1997)

Loayza, Schmidt-Hebbel and Servén (1999).

Empirical Evidence

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Masson, Bayoumi, and Samiei (1995)

Used cross-country database (developing countries) to study determinants of private saving.

Results:

increase in public saving associated with higher national saving, suggesting Ricardian equivalence does not hold;

decrease in age dependency ratio raises private saving;

increase in per capita income raises private saving;

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changes in real interest rate had no significant effect on saving;

increases in foreign saving increases both investment and consumption;

terms-of-trade windfalls have a positive but transitory effect on saving.

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Edwards (1996c)

Used both developing and industrialized countries.

Significant determinants of private saving rate:

rate of growth of per capita income;

monetization ratio (indicator of financial deepening);

foreign saving (negative effect);

government saving (negative effect);

social securities (negative effect).

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Dayal-Gulati and Thimann (1997)

Used both Southeast Asia and Latin America countries.

Determinants of private saving rate:

terms of trade shock: positive effect;

government saving: partially crowd out private saving;

social security expenditures: negative effect;

fully funded pension schemes: positive effect;

macroeconomic stability: positive effect;

financial deepening: positive effect;

per capita income: positive effect.

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Loayza et al. (1999)

Used an extensive cross-country database to study determinants of private saving.

A novelty of the analysis : distinction between short- and long-term determinants of saving rate.

This distinction is highly significant in their empirical results.

Main findings:

Macroeconomic uncertainty (the variance of inflation) had a positive effect on private saving rates. Consistent with the precautionary motive.

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Public sector saving had a negative but less than proportional effect on private saving. Ricardian equivalence does not hold in strict terms.

Real interest rates had no significant effect on saving.

Terms-of-trade improvements were positively associated with private and national saving rates.

Limitations:

Effect of interest rates on saving may be nonlinear.

Asymmetric effects of terms-of-trade.

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Figure

1.1

Saving and Investment Rates, 1976-97

(Percentage of GDP)

United States

European

Union

Japan

Developing

countries

Africa

Asia

Middle East

and Europe

Latin America

and Caribbean

Gross domestic savings (S)

Gross domestic investment (I)

1976-83

1984-91

1992-97

S-I

-0.9

-2.2

-1.5

0.2

0.3

0.5

0.6

2.8

2.4

-0.8

-1.9

-4.6

-3.0

-4.4

0.5

-1.7

-1.3

3.4

-4.4

-1.6

-3.1

-0.4

-2.6

Source: International Monetary Fund.

Figure 1.2

Income, Consumption, and Saving

in the Life-Cycle Model

Source: Adapted from Deaton (1999, p. 42).

Age

Income

Retirement

Death

Consumption

Borrowing

Income, Consumption, and Saving

Saving

Dissaving

Retirement

income

Consumption

Dissaving

Figure

1.3

Financial Deepening and Saving Rates

(Averages over 1980-95)

Source: World Bank.

Ratio of quasi money to broad money stock

Gross Domestic savings (% of GDP)

Ghana

Malays

Algeria

Korea

Indonesia

Thailand

Bangladesh

Venezuela

Costa Rica

Chile

Brazil

Tunisia

Panama

Peru

India

Nigeria

Zimbabwe

Côte d'Ivoire

Pakistan

Nepal

Jamaica

Bolivia

Philippines

Morocco

Colombia

Zambia

Tanzania

Source:López-Mejía and Ortega (1998).

Household Saving

Corporate Saving

Total Private Saving

Figure

1.4

Colombia: Components of Private Saving, 1950-93

(Percent of GNP)

1950

1952

1954

1956

1958

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

0.05

0.1

0.15

0.2