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Matthew Gunn
Matthew Gunn
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There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $y_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear. A problem in all of macro though is that you have limited data relative to everything you'd like to estimate. If you have a twenty year sample, you only have TWO recessions! It would be like you have two subjects that got treatment.

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $y_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $y_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear. A problem in all of macro though is that you have limited data relative to everything you'd like to estimate. If you have a twenty year sample, you only have TWO recessions! It would be like you have two subjects that got treatment.

edited body
Source Link
Matthew Gunn
Matthew Gunn
  • 23k
  • 1
  • 62
  • 95

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $A_{it}$$y_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $A_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $y_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

deleted 76 characters in body
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Matthew Gunn
Matthew Gunn
  • 23k
  • 1
  • 62
  • 95

There's nothing inherently wrong with this, even if the definition of a recession is related to GDP growth (and it is).!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $A_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

There's nothing inherently wrong with this, even if the definition of a recession is related to GDP growth (and it is).

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $A_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

There's nothing inherently wrong with this!

Let $I(x_i)$ be an indicator for $x$ being greater than zero. Of course you could run the regression:

$$ y_i = b_0 + b_1 x_i + b_2 I(x_i) + \epsilon_i $$

And this would be a sensible thing to do if your conditional expectation function had a discontinuity of some unknown size at zero. For example:

enter image description here

Sure there's going to be some correlation between $x$ and $I(x)$, but that's part of the reason you run a regression with multiple regressors rather than estimating everything separately. Too correlated though and you do have a problem, but I'd think you're probably ok.

Example: estimating stock market response to earnings surprise

Let $A_{it}$ be the abnormal return of firm $i$ at time $t$. Let $x_{it}$ be the earnings surprise. You would typically run something of the type:

$$ y_{it} = b_0 + b_1 x_{it} + b_2 I(x_{it}) + \epsilon_{it} $$

because there's a sizable penalty for missing your forecast earnings! There's a big non-linearity at zero.

Appendix: Definition of a recession

There are two commonly used data sources for what's a recession:

  1. (Informal) Two consecutive quarters of GDP decline.
  2. (Formal) The expert judgement of the NBER dating committee.

GDP growth and a recession indicator aren't collinear.

added 24 characters in body
Source Link
Matthew Gunn
Matthew Gunn
  • 23k
  • 1
  • 62
  • 95
Source Link
Matthew Gunn
Matthew Gunn
  • 23k
  • 1
  • 62
  • 95