Final Notes on Growth and Saving

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Final Notes on Growth and Saving
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Agenda for this week

• Paper assignment
• Simulation of increased saving experiment
• Advanced macro on optimal economic growth
• An example from economics of global warming
• Alternative schools Real Business Cycles
• Debt, deficits, and growth

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Paper Assignment

• The paper should be 3 to 5 pages (double-spaced,
  printed, plus tables, figures, and references).
  It will count as 10 percent of the course grade.
• The paper must left in the box outside Ms. Kings
  office at 28 Hillhouse Avenue before noon on
  Thursday, December 10.
•  
• Guidelines are that the paper must (a) be a
  topic in macroeconomics, (b) consider economic
  history or policy, (c) present evidence and data,
  and (d) be an application of macroeconomic
  analysis.
•  
• Some examples of topics would be the following 
• - Administration Xs theories and policies, and
  their successes and/or failures
• - The demise of the gold standard or Bretton
  Woods
• - The role of the housing price decline in the
  current recession
• - The legacy of Alan Greenspan, Paul Volcker, or
  Ronald Reagan
• - The macroeconomic effects of protectionism in
  the Great Depression.
•  
• You should consult with your Teaching Fellow
  about your topic to make sure that it makes sense
  and to get ideas for sources.
•  
• Consult rules on intellectual honesty and
  attribution, and dont procrastinate.
•  
• See notes on web site for further information.

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Numerical Example of Budget Surplus in
Neoclassical Growth Model

• Assumptions
• Production is by Cobb-Douglas with CRTS
• Labor plus labor-augmenting TC
• n 1.5 p.a. h 1.5 p.a.
• Full employment constant labor force
  participation rate.
• Savings assumption
• a. Private savings rate 18 of GDP
• b. Initial govt. savings rate minus 2 of GDP
• c. In 1992, govt. changes fiscal policy and runs
  a surplus of 2 of GDP
• d. All of higher govt. S goes into national S
  (i.e., constant private savings rate)
• Calibrate to U.S. economy of 1997

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Impact of Increased Government Saving on Major
Variables

• - Note that takes 10 years to increase C
• Political implications
• Must C increase?

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Results on Growth Rates

• Modest impact on growth in short run
• Consumption down then up
• No impact on growth in long run
• GDP v NNP (gross v. net national v. domestic)

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Return to question of whether can have too high a
savings rate

• Recall question from last time of whether C has
  to increase when S increases.
• This involves the question of whether K is above
  the Golden Rule K.
• Golden Rule maximum sustainable level of per
  capita consumption
• Simple algebra (consider only net output)
• Max f(k) nk ? f(k) n 0 ? r n
• or real interest rate growth rate

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• Find k where net interest rate equals n.
• At that point c is maximized.
• This is the golden rule savings rate.

y f(k)
y
f(k) (nd)k
Yale?
c (1-s)f(k)
(nd)k
i sf(k)
k
k
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More general approach Ramsey-Koopmans model
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Ramsey-Koopmans model (cont.)
Policy importance Say you are worried about the
damages from global warming in 2000 yrs. Say
damages are 50 of output of 50 trillion plus
growth - With conventional discounting,
.550exp(200.02)exp(-.05200) .061 - With
Stern discounting, .550exp(200.013)exp(-.01420
0) 20.5
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Example of modeling Yale RICE model

• Regional Integrated model of Climate and the
  Economy
• Integrates economic growth, CO2 emissions,
  climate change, damages, and economic policy
• Relies upon
• - Solow growth model
• - Ramsey-Koopmans optimal growth theory
• - Samuelson theory of public goods
• - wide variety of geophysical theories
• - Pigovian theory of externality taxes

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Results of Solow-Ramsey-Koopmans model
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Integration with Climate model and alternative
policies
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Growth Accounting (not covered in class)

• Growth accounting is a widely used technique used
  to separate out the sources of growth in a
  country relies on the neoclassical growth model
• DerivationStart with production function and
  competitive assumptions. For simplicity, assume a
  Cobb-Douglas production function with
  labor-augmenting technological change
• (1) Yt At Kt a Lt 1-a
• Take logarithms and time derivatives
• (2) ?ln(Yt)/?t gY gA a gK (1 - a) gL
• In the C-D, a is the competitive share of K
  sh(K) (1 - a) sh(L).
• (3) gY gA sh(K) gK sh(L) gL
• From this, we estimate the rate of TC as
• (4) TFP growth T.C. gA gY - sh(K) gK -
  sh(L) gL
• Note that this is a very practical formula. All
  terms except h are observable. Can be used to
  understand the sources of growth in different
  times and places.

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Some applications (not to be covered)

• 1. Clintons growth policy (see above)
• 2. U.S. growth since 1948
• 3. China in central planning and reform period
• 4. Soviet Union growth, 1929 - 1965The very
  rapid (measured) growth in the Soviet economy
  came primarily from growth in inputs, not from
  TFP growth.
• 5. Japanese growth, 1950-75 Japan had very large
  TFP growth after WWII. Wide variety of sources,
  including adoption of foreign
• These are contained in the slides for growth
  theory.

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Classical themes in macroeconomics Real Business
Cycle Theory
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Schools of Macroeconomics
Neo-classical growth model
Classical or non-classical? (sticky wages and
prices, rational expectations, etc.
yes
long- run
Marxist theories? Behavior growth
theories? Malthusian trap models?
no
Short run or long run? (full adjustment of
capital, expectations, etc.
Real business cycle (RBC) supply-side
economics structural models misperceptions
models
short- run
yes
Classical or non-classical? (sticky wages and
prices, rational expectations, etc.
Keynesian model (sloping AS, expectations- augme
nted PC, IS-LM, etc.)
no
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Real Business Cycles

• Basic idea cycles are caused by productivity
  shocks these are propagated by changes in prices
  and then to labor supply.
• Model Details
• Start with neoclassical growth model.
• Remember decomposition of output growth from
  growth accounting
• gY a gK (1-a) gL ?, where ? T.C.
• Changes in output come from two sources
• Technological shocks ? random.
• Changes in labor force participation assumes
  very high elasticity of labor supply with respect
  to wages.
• This then generates random output fluctuations,
  which RBC school calls business cycles.

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RBC recession
AS
Price (P)
AS
P
AD
Real output (Q)
Q
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AS2004Q4
AS2001Q1
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Policy implications of RBC models

• Output shocks are exogenous phenomena
  (earthquakes, Internet revolution, terrorist
  strikes, wars, etc.).
• No role for monetary or fiscal policies in cycle
• Economy and unemployment are efficient no need
  for policies
• Cycles are supply-driven, cannot use AD policies
  to stabilize output.
• Money is neutral (M policy cannot affect real
  output), so cannot use M policy

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Problems in RBC models

• 1. Cyclical properties of classical models of the
  business cycle
• Hard to explain deep recessions and depressions
  (1930s, 2007-09) as technological regress.
• 2. Money and output is money neutral?
• RBC predicts money neutral
• F/S and Keynesians much evidence that M is
  non-neutral
• 3. Labor market features (such as quits and
  Beveridge curve)
• Verdict Economists deeply divided.
• Personal view Keynesian approach has not
  developed a complete microeconomic justification,
  but it is most promising approach to
  understanding sources and policies for business
  cycles.

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Growth and savings in an open economy?

• For small open economy
• What happens if savings rate increases?
• In this case the marginal investment is abroad!

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• Open economy growth with mobile financial capital
  ( r world r rw)
• NX S - I

S0
r real interest rate
r rw
I(r)
Original NX deficit
I, S, NX
0
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• Higher saving
• No change I
• No change GDP
• Higher foreign saving
• Increase GNP, NNP

• Open economy growth

S1
S0
r real interest rate
Final NX surplus
r rw
I(r)
Original NX deficit
I, S, NX
0
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y f(kd)rkf
yd f(kd)
y f(kd)rkf f(kd)rw(k-kd)
(nd)k
sy
k
kd
26
k
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What if savings in an open economy?

• For small open economy
• What happens if savings rate increases?
• In this case the marginal investment is abroad!
• Therefore, same result, but impact is upon net
  foreign assets, investment earnings, and not on
  domestic capital stock and domestic income.
• No diminishing returns to investment (fixed rrw)
• Will show up in NNP not in GDP!
• (Most macro models get this wrong.)
• Large open economy like US
• Somewhere in between small open and closed.
• I.e., some increase in domestic I and some in
  increase net foreign assets

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1. Do Deficits Matter? The Ricardian Theory of
the Debt

• Robert Barro (Chicago/Harvard) introduced a
  theory in which deficits do not affect national
  saving or output.
• Chicago view of households They are "clans" or
  "dynasties" in which parents have childrens
  welfare in utility function
• Ui ui (ci, Ui1)
• where Ui is utility of generation i and
• ci is consumption of generation i
• 3. This implies by substitution
• Ui ui (ci, ui1(ci1, Ui2)) vi(ci, ci1,
  ci2, ...)
• which is just like an infinitely lived person!
• 4. Important result Barro consumers are like a
  life-cycle model with infinitely lived agents
  with perfect foresight
• there will be no impact of anticipated taxes (or
  deficits) on consumption or on aggregate demand.
• 5. Controversial, but empirically questionable.
  Reasons are myopia, singles, liquidity
  constraints, non-altruistic parents.