TFP without capital stocks

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TFP without capital stocks

• By Ralf Martin (CEP CeRiBA)
• r.martin_at_lse.ac.uk
• For CAED Cardiff, 2005

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Business Microdata and capital stocks

• Often only have investmenttherefore
• Interpolate missing periods in ad hoc way
• Makes ad hoc guesses about initial capital
  stocks. Error does not die out
• Assume depreciation
• PIM
• Estimate prod function and thus TFP pretending
  that capital was observed

3
What I propose instead

• Estimate TFP and capital stock simultaneously
• Instead of ad hoc assumption use a consistent
  framework based on behavioural assumption
• Account properly for all randomness and
  uncertainty which is implied by the procedure

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How do I do this

• Estimate production function and investment
  equation simultaneously

where
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What is the difficulty?

• Problem can be seen in simple example
• suppose we have only 2 periods
• plants only observed in second period when they
  produce
• Try to identify from a production function
  regression of the second period variables (note
  lower case denotes log of the upper case
  variables)

where all shocks are iid (log) normal
This would lead to regression equation
which is non separable between observed vars and
non observed shocks
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so what can we do?

• In order to estimate integrate out shock

• Problem if we have more periods t, then this
  expression depends on all shocks in periods ltt. ?
  computationally not tractable
• Solution simulation based approach

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Generic idea and current implementation

• Use both output and investment equation
• Use simulation based approach to handle all
  errors
• Framework I actually implement is more simplistic
  than what is required for this idea
• Key simplifying assumptions
• All in terms of gross investment i.e. Do not
  take disposals into account
• Adjustment process is exogenous i.e. no formal
  modelling of adjustment costs

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Key equations
Investment
Production
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Point estimate results

• Persistence in revenue prod func shock
• High depreciation rate
• Little extra persistence in investment
• Low trend growth

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New and old capital estimates
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Summary and the way forward

• New method to estimate capital stock which
• Tries to interpolate all data gaps consistently
• Takes account of uncertainty of the procedure
• Plans to move forward include
• Use different optimisation method more robust to
  local maxima
• Extend model to account for disposals and zero
  investment and adjustment costs
• Estimate with data where (at least for some years
  and plants) capital stocks are available (e.g.
  Chilean plant level data)