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What is the correct way to test for significant differences in parameter estimates in the following case:

I have a dependent variable (height for age) and a independent variable (household state pension benefits). These are observed in two years.

To see if there is an endogeneity problem I want to include pension benefits in year two in the regression of year 1.

The equation I want to estimate is thus:

$$y_1 = b_0 + b_1 * x_1 + b_2 * x_2 + e$$

I then want to test if $b_1$ is significantly different from $b_2$ (in stead different from zero). I found this previous question, but I am not sure if this is exactly the same problem. Also, is there a standard way of implementing this in R?

This is my first post, so sorry if I didn't post correctly, please feel free to edit.

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Bastiaan Quast
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1 Answers1

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The easiest way to test whether both variables are statistically significantly different is to use an interaction term:

$y_1 = b_0 + b_1 * x_1 + b_2^* * ( x_2 \times x_1 ) + e$

$b_2^*$ shows you whether the interaction term is statistically significantly and you can just use the t-statistics (see Matts answer: https://stats.stackexchange.com/a/13113/9866)

The z-test is another approach (for larger sample sizes):

$Z = \frac{b_1-b_2}{\sqrt{\sigma_{b_1}^2 + \sigma_{b_2}^2 }}$

Under $H_0$ (equality of regression coefficients) $Z$ should be standard normal distributed.

For more information, see:

http://www.udel.edu/soc/faculty/parker/SOCI836_S08_files/Paternosteretal_CRIM98.pdf

http://www.jstor.org/stable/2782277

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Arne Jonas Warnke
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