The economics of consumption
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The economics of consumption. From: President Ella Eli To: Yale Students Re: Generous Gift My dear students, I am delighted to report that a generous alumna has made a gift of $1000 per Yale student, available immediately. You can come by the office and pick up your check any time.

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From: President Ella Eli

To: Yale StudentsRe: Generous Gift

My dear students,

I am delighted to report that a generous alumna has made a gift of $1000 per Yale student, available immediately. You can come by the office and pick up your check any time.

Professor Nordhaus has requested that you detail how you would spend the funds. Would you please write this down in your notebooks in class today. You will find it instructive as you discuss Consumption in class this week.

With best wishes,

President Ella Eli

P.S. Professor Nordhaus has told me about “elevator quizzes,” which are a great idea. This is not an elevator quiz, but you should hold on to your answers for later reference. EE

Importance of consumption in macro
Importance of consumption in macro

1. Consumption is two-thirds of GDP – understanding its determinants is major part of the ball game.

2. Consumption is the entire point of the economy:

3. Consumption plays two roles in microeconomics:

a. AD: It is a major part of AD in the short run: recall IS curve in which

Y = C(Yd) + I + G + NX

b. AS: What is not consumed is saved and influences national investment and economic growth

Growth in c and gdp quarterly
Growth in C and GDP (quarterly)

  • Chicken or egg:

  • ΔC causes recession?

  • Recession causes ΔC?

Alternative theories of consumption
Alternative Theories of Consumption

The basic Keynesian insight is that consumption depends fundamentally on personal income (“consumption function”)

This enters into the Keynesian models as C = α + βYd

On a closer look, a major puzzle: the short-run and cross-sectional consumption functions looked very different from the long-term consumption function.

Alternative theories of consumption1
Alternative Theories of Consumption

There are four major approaches in macroeconomics:

*1. Fisher's approach: sometimes called the neoclassical model

2. Keynes original approach of the consumption function

*3. Life-cycle or permanent income approaches (Modigliani, Friedman)

4.Rational expectations (Euler equation) approaches (in Jones)

*We will do in class, but more Fisher in section.

Intertemporal consumption choice fisher s model
Intertemporal Consumption Choice: Fisher’s model

Basic idea:

People have expectations of lifetime income; they determine their consumption stream optimally; this leads consumers to “smooth” consumption over their lifetime.

Assumptions of two period model:

Periods 1 and 2

Income Y1 and Y2

Maximize utility:

Budget constraint:

We will do graphical case now and calculus later.

Budget constraint:


[no income in retirement]


Indifference curve between current and future consumption






Key result: consumption independent of timing of income!!!

Called “consumption smoothing”





Summary to here
Summary to here

Income over life cycle is the major determinant of consumption and saving.

In idealized case, have consumption smoothing over lifetime.

Now move from two-period (Fisher model) to multi-period (life cycle model).

Basic assumptions of life cycle model
Basic Assumptions of Life Cycle Model

Basic idea:

People have expectations of lifetime income; they determine their consumption stream optimally; this leads consumers to “smooth” consumption over their lifetime.


“Life cycle” for planning from age 1 to D.

Earn Y per year for ages 1 to R.

Retire from R to D.

Maximize utility function:

Budget constraint:

Discount rate on utility (δ) = real interest rate (r) = 0 (for simplicity)

Techniques for finding solution
Techniques for Finding Solution

1. Two periods:

Maximizing this leads to U’(C1)=U’(C2). This implies that C1 = C2 , which is consumption smoothing. The Cs are independent of the Ys.

2. Lagrangean maximization (advanced math econ):

Maximizing implies that U’(C1)=U’(C2)=-λ. This implies that

which again is consumption smoothing independent of Y.


Since U’(C1)=U’(C2)=… = -λ, C is constant over time.

Note: this assumes diminishing marginal utility or U”(C)<0. Make sure you know what this means.


Review of last time
Review of last time

Life-cycle model:

People plan their consumption over the future


“Life cycle” for planning from age 1 to D.

Earn constant Y per year for ages 1 to R.

Retire from R to D.

Maximize discounted utility:

For simplicity, assume r = δ = 0.

Initial Solution

C, Y, S

Diagram of Life Cycle Model Showing Consumption Smoothing

Income, Y

Consumption, C

Saving, S







Anticipated change in timing of income

C, Y, S

Income “splash” (Y’) with no W increase

Income, Y

Anticipated income change of ΔY.

Because it is anticipated, no change in lifetime income, so no change in (smoothed) consumption. MPC = 0; MPS = 1.

Consumption, C’=C

Saving, S’







What about anticipated taxes?

C, Y, S

Income “splash” from tax cut

Income, Y

No C change!

Saving, S’







Unanticipated change in permanent income

C, Y, S

Y’ =unanticipated increase; W increases.

  • Unanticipated windfall of ΔY in period z.

  • Leads to smoothing the windfall over remaining lifetime.

  • one time splash: MPC = ΔY/(D-z). For life expectancy of 40 years, would be MPC = .025.

  • Permanent income increase: MPC = ΔY(R-z)/(D-z) = .6 to .8










Example of the life cycle model at work
Example of the Life Cycle Model at Work:

  • How would the consumption and saving of people with volatile or stable income streams look?

  • See figure for Internet Entrepreneur and Yale Professor.

Major result of LCM: consumption smoothing


C of both!




Vector auto regressions var
Vector auto-regressions (VAR)

Nobel prize in Economics for 2011 won by Chris Sims (Princeton) in part for development of VAR technique.

Vector autoregression (VAR) is a statistical model used to capture the linear interdependencies among multiple time series (vector Yt ):

Yt = A0 + A1Yt-1 + A2Yt-2 + A2Yt-2 + et

Sims emphasized it as “theory-free estimation.”

Example of short run MPC using VAR:

MPC = 0.16 ( + 0.04)

Smaller than other estimates because of autoregressive properties.

Summary: Econometric estimates of short-run MPC > life-cycle theory.

How about a nice car?

  • What is your favorite car?

  • What do you have?

  • Why not smooth consumption to get your favorite car?

    Liquidity constraints

  • Case of Yale students where income growing rapidly.

  • Here consumption is limited by borrowing constraint.

  • In class: A picture of the model with liquidity constraints.

  • Is this reason for MPC higher than life cycle prediction? (Partially, but cannot explain response of non-constrained consumers)

Behavioral economics
Behavioral economics

Basic idea: That people are not optimizers:

- Draw upon behavioral psychology: anchoring, loss aversion, hyperbolic discounting, and similar phenomena

Real-world examples for all of us:

- Procrastination (as in procrastinate saving for the future).

- Addictive substances (shop until you drop)

Why is it “behavioral”? Because lead to inconsistent decisions that are regretted later

- cheating, hangovers, unwanted pregnancies, jail

Examples from macroeconomics:

- MPC too high; low savings for retirement; subprime mortgages; sticky housing prices; too high discount rate in energy use

Press button

for Econ 122

Elevator quiz
Elevator quiz

  • Look back to your answer from Monday on how you would allocate your $1000 unexpected generous gift.

  • Explain how this decision fits into the economics of consumption that we discussed in class and in the textbook.

  • We will discuss our answers when you are done.

  • Then hand it in at the end of class.

Taxes interest rates and saving
Taxes, interest rates, and saving

“Raise the tax on the returns for saving, and people will save less. We can argue the magnitude, but to argue that saving does not respond at all is simply to argue that incentives and disincentives are irrelevant to behavior.”

“Of Course Higher Taxes Slow Growth,” J.D. Foster and Curtis Dubay

Impact of higher interest rates on saving
Impact of higher interest rates on saving

Important question for economics

A common theme:

- The country need to reduce taxes to increase savings

- Examples: lower marginal tax rates, lower capital gains taxes, move to consumption taxes,

- Mechanism: ra = rb (1-τ)

What is the economic theory of this?

What is econometric evidence on this?



Higher interest rate leads to lower saving because income effect outweighs substitution effect.

[Pension example]







Opposite case: higher r increases savings as substitution effect dominates




If we estimate the impact of changes in interest rates on consumption, we get paradoxical case (δs/δr < 0):

The impact is essentially zero (and not robust to changes in specifications, samples, etc.)

Econometric savings schedule s r
Econometric savings schedule: S(r) consumption, we get paradoxical case (

Fiscal policy tax cuts and the life cycle
Fiscal policy, tax cuts, and the life cycle consumption, we get paradoxical case (

When the economy is in a liquidity trap and recession, major available policy tool is fiscal policy (remember IS-MP)

But, fiscal policy is controversial inside and outside economics:

Purchases (G):

- Controversial because increases size of government

- Long lags (recognition, decision, implementation)

- Infrastructure and other programs have long gestation periods.

Tax Cuts (T) and transfers (-T):

- One view: people will smooth consumption, and even anticipate a future tax increase, and there will be little or no response.

- Other view: people are short-sighted and/or liquidity constrained, and they will spend a substantial fraction of increased incomes

Further extensions
Further Extensions consumption, we get paradoxical case (

Wealth effects:

  • Examples: Suppose the alumna gives you $1000. Or the stock market collapsed? What would be the effect?

    Life cycle model predicts that initial wealth (or surprise inheritances) would be spread over life cycle.

    • Intuition: an inheritance is just like an income splash.

      So the augmented life cycle model is

      Ct = β0 + β1Ypt + β2 Wt

      where Ypt is permanent or expected labor income and Wt is wealth.

What is the Effect of Stock Market consumption, we get paradoxical case (Booms and Busts on Consumption?

The stock market the housing market and consumption
The stock market, the housing market, and consumption consumption, we get paradoxical case (

  • Economists think that the bursting of the stock market bubble in 2000 or the housing market today contributed to recessions.

  • Reasons? Decline in consumption (today) and investment (later)

  • Rationale: the “wealth effect” on consumption

  • Analysis in the life-cycle model:

    • In augmented life-cycle model Ct = β0 + β1 Ypt + β2 Wt standard estimates are that β2 = .03 - .06 (example in a minute)

    • Effect in the “Roaring 90s” and the housing crash today.

  • This is often called “deleveraging” but is more a “wealth effect”

Regression consumption, we get paradoxical case (

Dependent Variable: Real consumption expenditures

Method: Least Squares with AR correction

Sample: 1960.1 2011.2

VariableCoefficientStd. ErrorP

Real Disposable income 0.73 0.025 .0000

Real wealth 0.035 0.0041 .0000

R-squared 0.9997

Wealth and Consumption through Two Bubbles consumption, we get paradoxical case (

Loss of wealth and savings rate increase consumption, we get paradoxical case (

Key ideas on consumption and saving
Key ideas on consumption and saving consumption, we get paradoxical case (

  • Consumption derived from consumer maximization

  • Pure model leads to consumption smoothing

  • All kinds of important predictions

  • But pure model has “anomolies” and shows too large a short-run MPC relative to theory

  • Reasons are probably liquidity constraints and behavioral frictions.

  • Remember the wealth effect