Negative coefficient for interaction term when interactions are positive(is this counter intuitive?)

[Chei Bukari]

Hi! everyone,
I estimated an in interaction model using OLS where I have credit, savings, remittances and insurance of households as the main policy variables. (unit of analysis is households).
Before this estimations, I validated the seven hypotheses using t-test on household expenditures (Total consumption expenditure, total food expenditure, total health expenditure and total education expenditure). The seven hypotheses were developed using combinations of the four financial products. Thus, a household that uses any two combination of these financial products have higher expenditures than those household that uses any one of the products (this was significant for all the four expenditure measures considered). While household that uses any three combinations have higher expenditures than those that use only one or two of the products.

Also, in my regression results, households with any combinations have higher magnitude of coefficients than those with only one financial product (all sign. at 1% & 5%).

NOW PROBLEM:
I generated seven interaction terms: CS CI CR SI SR CSI CSIR using the following;
credit (C)
savings (S)
remittances (R)
insurance (I)

With the syntax : gen CS = credit*savings or reg Y i.credit##i.savings since these are dummies

After I included these interaction terms in my model together with the original variables and estimated, only CSI, CR & SR have positive and significant signs as expected.
CS CI SI and CSIR have negative signs with some even significant at five percent.
I see this as counter intuitive because negative signs would mean having the products causes more harm than good to the household.

Please do any one share this opinion?
Is there any thing wrong with the way I went about the estimation regarding interaction terms?
what could be explaining the negative signs?

I would gladly appreciate your suggestions and comments. Thank you all

[Clyde Schechter]

Without seeing your actual commands and the corresponding output it is not possible to give specific advice. But it sounds like you are misinterpreting the interaction terms. For example, a the coefficient of credit#savings does not estimate the effect of using both the credit and savings products. Rather it expresses the difference between that effect and the sum of the separate effects of credit and savings product use. To see the outcome levels for various combinations of these products you should use the -margins- command after your regression.

[Chei Bukari]

Thank you very much Clyde,
Please these are the commands that I used:
[eg lconsumpovt i.credit i.saveacct i.insurance i.Remit CS CI CR SI SR ///
CSI CSIR agey agesqr i.sex hhsize Dep i.level i.HHEMPL i.land i.HHMST i.asset, robust [/CODE]

Robust
Y Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------

credit yes .2048797 .0690716 2.97 0.003 .4784 .340281

saveacct yes .3104397 .0216346 14.35 0.000 .2680294 .3528501

insurance yes .2052593 .0272796 7.52 0.000 . 1517831 .2587356

Remit yes -.0635985 .0238788 -2.66 0.008 -.1104081 -.0167888

CS -.156743 . 0753678 -2.08 0.038 -.3044868 -.0089993

CI -.2044477 .1126325 -1.82 0.070 -.4252415 .0163461

CR .0225448 .0690353 0.33 0.744 -.1127852 .1578749

SI -.0458227 .0354168 -1.29 0.196 -.1152503 .0236049

SR .0735085 .0318176 2.31 0.021 .0111364 .1358807

CSI .2967328 .1366872 2.17 0.030 .0287844 .5646811

CSIR -.2010104 .1009424 -1.99 0.046 -.3988882 -.0031326

agey .010933 .0028694 3.81 0.000 .053081 .0165578

agesqr -.0001149 .0000281 -4.09 0.000 -.0017 -.0000598

Male head -.0003233 .0177332 -0.02 0.985 -.0350857 .034439

hhsize .1310689 .0048701 26.91 0.000 .121522 .1406157

Dependents -.112103 .0181939 -6.16 0.000 -.1477686 -.076437



Nick Cox earlier suggested the same margins command given that I am interested in these interaction and their net effects but my issue is the negative signs of these coefficients.

[Chei Bukari]

Sorry every one! I was trying to use dataex but was not conversant with it.
I am still figuring out to use dataex to post the output.

[Clyde Schechter]

Try

regress lconsumpovt i.credit##i.saveacct##i.insurance##i.Remit ///
    agey agesqr i.sex hhsize Dep i.level i.HHEMPL i.land i.HHMST i.asset
margins credit#saveacc#insurance#Remit

The -margins- output will show you the expected lconsumpovt for each combination of the four products.

[Brad Anderson]

Well, if I understand your model at all correctly, and I'm not sure I do, I believe you are violating the principal of marginal homogeneity. If you include the CSRI term, then, unless you have very strong theory that would say some of the lower order terms are 0, you need to include all lower order terms in the model. You can think of this pretty simply if you consider a simple model with two predictor variables. If you model Y = X1*X2 without the main effects of X1 and X2 you can't tell whether Y changes because X1 change, or because X2 changes, or because both X1 and X2 changes, or because there is some kind of interaction. That interaction is only interpretable if you can argue that the main effect of X1 and X2 truly are 0. So you need all lower order terms in the model. E.g.,

C, S, R, I, CS, CR, CI, SR, SI, RI, CSR, CSI, CRI, SRI, and CSRI

And it's quite possible that too have + effects for main effects and - effects for interaction terms. Al it means is that the effect of 1 variable decreases as the other variable increases.

Again, using a two variable model:

Y = b0 + b1X1 + b2X2 - b3(X1*X2).

b1 gives the effect of X1 when X2 is 0, even if 0 might not be an actual value.
b2 gives the effect of X2 when X1 is 0.

b3 gives the change in the effect of X1 as X2 changes, and vice versa. So in the above model, if X2 increases by 1 unit, the effect of X1 decreases by b3 units.

[Chei Bukari]

Thank you every one for your insight suggestions. It was really helpful and I am grateful.

But for future posting of regression output on statalist, I would greatly appreciate if any one can show me how to post regression result in statalist. I had already installed dataex,
and do not actually know how to copy regression result on statalist for suggestions and comments. Thank all