Wald test explained: restrictions on coefficients (Excel)

We all know how to use a simple t-test to figure out whether a coefficient is statistically different from zero. Turns out this logic can be elegantly generalised to test for any linear restriction on coefficients! This is what Wald test is designed for! Today we are investigating the Wald test and learning how to calculate it in Excel based on the example of constant versus increasing returns to scale of a production function.
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[@NEDLeducation]

You can find the spreadsheets for this video and some additional materials here: drive.google.com/drive/folders/1sP40IW0p0w5IETCgo464uhDFfdyR6rh7
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[@kdwalker1656]

This application of the Wald test, migrating from the raw data --> coefficient analysis --> Wald test, is exactly what I was looking for. My personal preference that draws me to statistics tutorials is when the lecturer or tutor can show me the application of the data analysis over simply showing the equations and matrix multiplications (for me, the math is easier to understand than knowing the scenarios to apply a particular test and how to interpret it).

[@NEDLeducation]

Hi, and thanks so much for the feedback! Happy to hear you enjoyed the approach!

[@erdincaltay9495]

Hi, how can we test the difference of the parameters of two independent that are estimated by two different regressions where the dependent vaiable is the same?

[@yanjin189]

Thanks a million for the video. Super clear. I am wondering how to manually test joint zero, e.g. alfa=beta=0 in your example? Thanks!

[@jure4835]

Isn't the Wald test designed specifically for unrestricted models?

[@NEDLeducation]

Hi, and thanks for the question! It is essentially designed (in part) to choose between unrestricted and restricted models: if Wald test shows the coefficients on two variables are the same in the unrestricted model (say, the effect of short-term debt and long-term debt on ROA is the same), for example, why not use the sum of the variables *say, total debt) as the regressor instead? On the other hand, if the Wald test shows the coefficients are significantly different, a restricted model would lose information/explanatory power/suffer potentially from heterogeneity bias. Hope it helps!

[@willmccubbin3240]

Excellent as usual, and clearly explained. Cheers, Savva

[@NEDLeducation]

Cheers Will, glad you are enjoying the videos! Stay tuned for more econometrics stuff :)

[@thezorrinofromgemail6978]

Excellent as usual.