Economic Growth and Business Cycles

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Economic Growth and Business Cycles

• The Real Business
• Cycle Model

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Contents

• Beyond monetary explanations, real terms
• RBC treats growth and cycles as being
  integrated, not as a sum of two components driven
  by different factors.
• How much would productivity shocks explain output
  fluctuations in the postwar US economy?
• NGM can be modified to study business cycles

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Real Business Cycles Model

• RBC models business cycles in real terms
• output fluctuations can be accounted for by
  productivity shocks, roughly 2/3rds
• The model also displays other behaviors of the
  actual economy, i.e.
• Investment Volatility gt Output Volatility
• Consumption smoothing
• model explains both long term growth and short
  term fluctuations in output with same factors.

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Business Cycles

• Business Cycles are not cycles, forget about sin
  and cos functions
• TFP shocks can be modeled using a stochastic
  process
• Example of stochastic process flip a coin a 100
  times, say heads is 1 and tails is -1, plot the
  result over time
• The aggregate of small shocks create depressions
  or booms
• Business Cycles output minus trend

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Neoclassical Growth Model

• Same process as we went through in class

Notice that

• Balanced Growth path was smooth
• Completely deterministic, knowing kt gave you
  kt1
• Does not exhibit business cycles

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Neoclassic Growth Model

• Smooth lines
• Steady state
• deterministic

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Actual Data

• Not Smooth !
• The model needs to reflex this

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Quantitatively Defining Business Cycles using HP
Filter
Business Cycles (bottom line) Output - Trend
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Adding Shocks

• In the deterministic model we have
  YtAKt ?
  Ht1-?
• Remember we just set the productivity factor A
  1
• Econometric analysis shows that this productivity
  factor actually follows a stochastic process,
  specifically an AR(1). Lets make A vary over
  time, stochastically, like flipping a coin.

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Adding Shocks

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Adding Shocks

• zt ?zt-1 et
• ? (rho) is the persistence of the time series
• 0 lt ? lt 1
• et (epsilon) is the innovation term
• et is a normal variable with mean 0 and standard
  deviation sigma
• We can calibrate epsilon and sigma

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Calibration

• Most parameters same as learned in class, but
  what about our new stochastic factor in the
  production function.
• Use Solow residuals, that is calculate the
  technological change as the difference between
  changes in the output and the changes in the
  inputs K and H.

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Derivation of z

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Calibration
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Calibration

• Let s do the calibration of zt in excel.
• Also we can generate a zt series in excel.

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HP Filter

• Business cycles are thought to be 3 to 5 years
• The HP Filter filters out low frequency long term
  fluctuations in GDP (changes over 5 periods
  long), and medium frequency (3 to 5 years)
  changes in the growth rate.
• The filter separates the long term growth rate
  from the short term business cycles.

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HP Filter Program

• Program using Prescotts HP Filter equation to
  single out business cycles

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Figure 1.1 Log of Real GNP and its Growth
Component

• Procedure for finding SD and Cross Correlations
  using HP Filter
• Take natural log of time series
• Find trend and deviation with HP Filter
• Calculate standard deviation of deviation time
  series points
• Find covariance of point at t and t1, t2, t3

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Figure 1.2 H-P-Filtered Cyclical Component and
Log-Differenced Real GNP
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Ratios

• Ratio of standard deviations

• Ratio of variances

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Conclusions

• Both the model and the data show that the
  consumption is much less volatile than investment
• Why?
• People want to smooth consumption overtime
• Therefore, according to the equation C I wH
  rK, investment is the only factor left to account
  for the fluctuating economy
• Correlation of variances between the model and
  the real data
• Correlation of output variances was 62
• Therefore according to Prescotts model, 62 of
  the business cycles can be accounted for by the
  shock in productivity.
• Significance
• Not monetary
• Productivity shock can account for much more than
  previously expected

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Conclusions

• Model disagreements with data
• Hours and productivity in the model economy go up
  and down together, in the data they do not.
• In the artificial economy, output fluctuates less
  than in the data, conclude that not all
  fluctuations can be explained by productivity
  shocks.
• Labor input in model fluctuates only about half
  as much as in the data.

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Solving the Model

• Review of Dynamic Programming
• Dynamic Programming under uncertainty
• Computing the fixed point