Using Tobit vs' Heckman

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Using Tobit vs. Heckman

• Ken Klassen

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What to do with a bunch of zeros

• Ken Klassen

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Outline

• The problem
• The solutions
• Tobit
• Heckman
• When to use them

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The problem

• The dependent variable is constrained to be
  greater than some value c (usually 0)
• Applies equally if the variable is constrained to
  be less than some value.
• OLS cannot be used on full sample
• OLS cannot be used on positive subsample

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Examples

• LIFO liquidation
• Dhaliwal, Frankel, Trezevant (JAR 1994)
• Use stock options for compensation
• Matsunaga (TAR 1995) Klassen Mawani (CAR 2000)
• Export or use foreign subsidiaries
• Kemsley (JAR 1998)

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Examples (contd)

• Outsourcing of tax functions
• Dunbar and Phillips (JATA 2001)
• Issuing preferred shares
• Ely, Houston and Houston (JATA 2002)

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Possible solutions

• Tobit
• Used if it is a censored data set
• Heckman
• Used if it is a self-selected data set

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Tobit

• Use for censored dependent variable
• yi ?? xi ?i
• but only observe y such that
• yi yi if yi gt c
• yi c if yi c
• Key y not observed because it is less than c

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Heckman

• Use for data when self-selected
• yi ?? xi ?i
• zi ? ? wi ?i
• but only observe y such that
• zi 1 if zi gt 0 zi 0 if zi 0
• yi yi if zi 1 yi not observed if
  zi 0
• Key y not observed because choice based on z

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Using Heckman

• Another issue is specifying the models
• The choice model variables (w) should differ from
  the outcomes model variables (x)
• If the same variables are used, the second
  equation is only specified by the non-linearity
  of the probit selection equation
• Have additional variables in w

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The plot thickens

• When do you use each model?
• All examples found use Tobit
• Maddala (TAR 1991) states
• It is tempting to use the Tobit model every
  time one has a bunch of zeroobservations of y.
  p. 795
• Tobit used inappropriately most of the time, even
  in Tobins original work (Maddala 1992)

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How to decide

• Concentrate on why the zeros arise and what the
  latent variable, y, is measuring in your model
• Is it the result of a choice?
• Is it that only values below 0 are unobserved or
  could some unobserved values also be above 0

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How to decide (contd)

• If the y is the response to modeled incentives,
  then the desire could be to have a y lt 0 even
  though the observed y cannot literally be
  negative.
• Can you articulate a well-specified choice model
• Is there a set of variables w different from x?