Class 10 Stat701 Fall 1997

Fitting the Nerlove data.

Key points from the econometric models

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All multiplicative models - giving percentage change interpretations on the log scale.
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Learning is proxied by the cumulative output.
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Level of technology is also proxied by the cumulative output
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Models have some obvious limitations - returns to scale does not depend on the level of X.
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Can still value the models if you buy into them as approximations to a ``local'' reality.
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Models manufactured to mirror economic theory.
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A possible more hard-nosed approach. If your only objective is to predict cost, FORGET the theory, use and manipulate the explanatory variables in anyway that lets you do ``good'' prediction - closer to the Stat621 regression project view of the world.

Statistical points from Berndt

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Underspecification - what's the impact of leaving out a variable that should be in the model?
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What's the impact of fitting

displaymath65

when the true model is

displaymath67

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Answer: typically it biases the estimates of those that are left in - unless
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The left out variable is uncorrelated with those that are in.
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tex2html_wrap_inline69

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If you can design an experiment, it is often a good idea to build this feature in - make the X-s uncorrelated (aka orthogonal).
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In the underspecified model RMSE is biased upwards - so you tend to be conservative - p.values too big, PI's too wide.
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Berndt on p.75 (3.35) recovers the returns to scale parameter r by using the relationship tex2html_wrap_inline71 and likewise for tex2html_wrap_inline73 . He then goes on to say that one cannot in general directly employ the estimated standard errors of tex2html_wrap_inline75 and tex2html_wrap_inline77 to compute confidence intervals for r and tex2html_wrap_inline73 .
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However, there is a very computer intensive way of finding standard errors and confidence intervals for just about any ``smooth'' function of the original parameters. It is called the BOOTSTRAP.
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Idea behind the bootstrap.
  • Resample your data - take a random sample with replacement of rows from your spreadsheet.
  • Recompute the regression and related statistics from this resampled dataset.
  • Repeat many times, obtaining a bootstrap sample of parameter estimates.
  • Estimate the standard error by calculating the standard deviation of the resampled estimates.
  • Obtain bootstrap confidence intervals from the quantiles of the resampled estimates


Richard Waterman
Mon Oct 6 23:04:14 EDT 1997