ECONOMETRIC MODELING

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• ECONOMETRIC MODELING
• OF
• TECHNICAL CHANGE

Copenhagen May 30, 2007
by Dale W. Jorgenson Harvard University
http//post.economics.harvard.edu/faculty/jorgenso
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ECONOMETRIC MODELING OF TECHNICAL CHANGE

• Substitution vs. Technical Change
• Jorgenson (2000)

• Index Number Approach
• Jorgenson, Ho, and Stiroh (2005)

• Parametric Approach
• Jorgenson and Fraumeni (2000)

• State-Space Approach
• Jorgenson and Jin (2006)

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STATE-SPACE MODELING OF TECHNICAL CHANGE

• Production Function

• Accounting Identity

• Price Function

• Translog Price Function
• i,kK,L,E,M

• Input Demand Equation

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SUMMARY STATE-SPACE MODELING

• Stochastic Specification

• Observable Variables

• Latent Variables

• Random Variables

• Parameters

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RESTRICTIONS FROM PRODUCTION THEORY

• Homogeneity
• for k K, L, E, M

• Symmetry

• Concavity
• positive semi-definite

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DEFINITION OF TECHNICAL CHANGE

• Rate of Technical Change
• Rate of change in the price of output, holding
  input prices constant

• Biases of Technical change
• Change in the value shares of inputs, holding
  input prices constant

• Transition Equation

where
is stationary. The transition equation is a
vector auto-regressive scheme (VAR).
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TWO-STEP KALMAN FILTER

• Kalman Filter, Hamilton (1994)

• State Equation

where

• Observation Equation

where
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FILTERING AND SMOOTHING

• Filtering

where

consists of observations up to time t and
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ECONOMETRIC MODEL

where
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TWO-STEP KALMAN FILTER

• Instrumental Variables

• New Observation Equation

or

• Wooldridge (2002, Chapter 12) shows that the
  estimator is consistent and asymptotically normal.

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LIST OF SECTORS

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TESTS FOR OVER-IDENTIFICATION

Note (1) The number of degrees of freedom for
the LR test for each sector is 8. (2) The null
hypothesis is that the instrumental variables are
exogenous. (3) High p-values indicate that we
cannot reject the null hypothesis of
exogeneity. (4) The last column presents p-values
adjusted for simultaneous inference.
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TESTS OF VALIDITY OF THE INSTRUMENTAL VARIABLES

Note (1) Number of degrees of freedom for the
LR test for each sector is 99. (2) The null
hypothesis is that instrumental variables are
uncorrelated with the endogenous independent
variables. (3) Low p-values indicate that we can
reject the null hypothesis of no correlation.
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EMPIRICAL RESULTS
Latent biases of technical change for capital,
1958-2004, and projections for 2005-2025

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EMPIRICAL RESULTS
Latent biases of technical change for labor,
1958-2004, and projections for 2005-2025

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EMPIRICAL RESULTS
Latent biases of technical change for energy,
1958-2004, and projections for 2005-2025

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EMPIRICAL RESULTS
Latent biases of technical change for material,
1958-2004, and projections for 2005-2025

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EMPIRICAL RESULTS
Latent levels of technology, 1958-2004, and
projections for 2005-2025

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SUMMARY AND CONCLUSIONS

• Observable Variables Prices of Output and
  Inputs, Value Shares Describe Substitution.

• Latent Variables Rate and Biases of Technical
  Change Describe Technical Change.

• Rate of Technical Change is the Sum of Induced
  and Autonomous Components

• Induced Technical Change Results from the
  Interactions of Biases of Technical Change in
  Input Prices.

• Autonomous Technical Change is the Change in the
  Level of Technology.

• Future Research Agenda Model the Diffusion of
  Technologies through Investments that Embody
  These Technologies.

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