[Richard Goller]

What was the regression code used here? The coefficient on this variable will be that a white individual after 2008 receives a higher odds of being a home-owner than the counterfactual. I can't see clearly what the counterfactual is from the output presented

logistic TEN1 WHITE##POS08 BLACK##POS08 ASIAN##POS08 Year POS08 NORE##POS08 NO
> RW##POS08 MERS##POS08 YOHU##POS08 EASM##POS08 WESM##POS08 EAST##POS08 LOND##PO
> S08 SOUE##POS08 SOUW##POS08 WALE##POS08 SCOT NORI##POS08

[Richard Goller]

Because from what I can tell, black people had the lowest probability out of all to be homeowners after 2008

[Richard Goller]

What was the regression code used here? The coefficient on this variable will be that a white individual after 2008 receives a higher odds of being a home-owner than the counterfactual. I can't see clearly what the counterfactual is from the output presented

logistic TEN1 WHITE##POS08 BLACK##POS08 ASIAN##POS08 Year POS08 NORE##POS08 NO
> RW##POS08 MERS##POS08 YOHU##POS08 EASM##POS08 WESM##POS08 EAST##POS08 LOND##PO
> S08 SOUE##POS08 SOUW##POS08 WALE##POS08 SCOT NORI##POS08

Because I would assume from the results that since BLACK##POS08 has the lowest ratio, it is the least likely that a black person is a home owner after 2008

[Rhys Williams]

What is the omitted ethnicity? In your dataset you have white, asian, black and what?
Unless I am mistaken, the coefficient on 0.8999 on white-post2008 tells you that compared to the baseline group, a white person post-2008 has a higher odds ratio of buying a house.
You aren't comparing this with a black person.
The fact that you see black-post2008 has the lowest odds ratio tells you that black people are less likely to own a house, post 2008, than whites or asians but it is still positive relative to the baseline group. Therefore, whatever ethnicity the baseline group is, has the lowest odds ratio of owning a house.

[Richard Goller]

The omitted ethnicity is any other ethnicity, I think I didn't include it because I though it would get rid of it because of collinearity.

[Richard Goller]

What is the omitted ethnicity? In your dataset you have white, asian, black and what?
Unless I am mistaken, the coefficient on 0.8999 on white-post2008 tells you that compared to the baseline group, a white person post-2008 has a higher odds ratio of buying a house.
You aren't comparing this with a black person.
The fact that you see black-post2008 has the lowest odds ratio tells you that black people are less likely to own a house, post 2008, than whites or asians but it is still positive relative to the baseline group. Therefore, whatever ethnicity the baseline group is, has the lowest odds ratio of owning a house.

When I put the command:
. logistic TEN1 WHITE##POS08 BLACK##POS08 ASIAN##POS08 OTHER##POS08 Year POS08 N
> ORE##POS08 NORW##POS08 MERS##POS08 YOHU##POS08 EASM##POS08 WESM##POS08 EAST##P
> OS08 LOND##POS08 SOUE##POS08 SOUW##POS08 WALE##POS08 SCOT NORI##POS08

I get:

------------------------------------------------------------------------------
TEN1 | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.WHITE | 2.453621 .0366737 60.05 0.000 2.382784 2.526563
1.POS08 | 1.118408 .0268547 4.66 0.000 1.066993 1.172301
|
WHITE#POS08 |
1 1 | .8999048 .0193903 -4.89 0.000 .8626918 .938723
|
1.BLACK | .881083 .0192605 -5.79 0.000 .8441304 .9196531
|
BLACK#POS08 |
1 1 | .8385081 .0264014 -5.59 0.000 .7883266 .891884
|
1.ASIAN | 2.30365 .0418028 45.99 0.000 2.223158 2.387057
|
ASIAN#POS08 |
1 1 | .9322237 .0240025 -2.73 0.006 .8863469 .9804751
|
1.OTHER | 1 (omitted)
|
OTHER#POS08 |
1 1 | 1 (omitted)
|
Year | .9486771 .0020399 -24.50 0.000 .9446874 .9526836
POS08 | 1 (omitted)
1.NORE | .7671352 .0148891 -13.66 0.000 .7385011 .7968795
|
NORE#POS08 |
1 1 | .9722931 .0158421 -1.72 0.085 .9417336 1.003844
|
1.NORW | .9388538 .0175828 -3.37 0.001 .905017 .9739557
|
NORW#POS08 |
1 1 | .9436468 .0136144 -4.02 0.000 .9173368 .9707115
|
1.MERS | .7622664 .0168705 -12.27 0.000 .7299077 .7960596
|
MERS#POS08 |
1 1 | 1.054149 .0236808 2.35 0.019 1.008742 1.1016
|
1.YOHU | .8699577 .0165543 -7.32 0.000 .8381094 .9030162
|
YOHU#POS08 |
1 1 | .9824224 .0150215 -1.16 0.246 .9534176 1.012309
|
1.EASM | .9351591 .0187676 -3.34 0.001 .8990893 .9726759
|
EASM#POS08 |
1 1 | .9272235 .0166278 -4.21 0.000 .8951998 .9603928
|
1.WESM | .9032103 .0173062 -5.31 0.000 .8699198 .9377748
|
WESM#POS08 |
1 1 | .8954941 .0139077 -7.11 0.000 .8686462 .9231717
|
1.EAST | .9574156 .0186856 -2.23 0.026 .9214841 .9947481
|
EAST#POS08 |
1 1 | 1.0158 .0168379 0.95 0.344 .9833286 1.049343
|
1.LOND | .5142871 .0097574 -35.05 0.000 .4955142 .5337712
|
LOND#POS08 |
1 1 | .943466 .0142507 -3.85 0.000 .9159446 .9718144
|
1.SOUE | 1.021406 .0189112 1.14 0.253 .9850051 1.059152
|
SOUE#POS08 |
1 1 | .9518513 .0133686 -3.51 0.000 .9260066 .9784173
|
1.SOUW | .9391315 .0181032 -3.26 0.001 .9043117 .9752919
|
SOUW#POS08 |
1 1 | .977764 .0155584 -1.41 0.158 .9477407 1.008738
|
1.WALE | .8722455 .0161878 -7.36 0.000 .8410882 .904557
|
WALE#POS08 |
1 1 | 1.002142 .0141358 0.15 0.879 .9748155 1.030234
|
SCOT | .8737091 .0158135 -7.46 0.000 .8432585 .9052594
1.NORI | 1 (omitted)
|
NORI#POS08 |
1 1 | 1.011829 .0267934 0.44 0.657 .9606546 1.06573
|
_cons | .8986184 .0206509 -4.65 0.000 .8590414 .9400188

The OTHER races get omitted, guess because from the information in the other variables you are ables to estimate whether a person belongs to the OTHER group. Same with NORI, or Northern Ireland

[Rhys Williams]

Yes, completely, it is known in the literature as the dummy variable trap.

But it is not omitted, it is the baseline group.

To see this, consider the regression Y = a + bX + c(Male)
Where Male is a dummy variable which equals 1 if an individual is male and 0 otherwise. The coefficient c tells us how much more of Y a male gets compared to a woman (who is the baseline group). In other words, the output of a woman with X=0 is equal to a (the constant), whilst the output for a man with X=0 is equal to a+c.

Extending this example to your case, all your coefficients are compared to the baseline group of "other ethnicity". You see a positive value on all your interaction terms for Asian, Black and White. This means that these groups all have higher odds of buying a house than does the group "other". So in fact, the lowest odds is not black but other.
You could of course include "other" but omit "black" and then you will be using black as the baseline group. Hence, you should see a negative coefficient on the interaction term with other.

This should help you better understand the effect of your interaction term. If it doesn't make sense then I suggest you read up on it as it will help you interpret your own case

Best,
Rhys