Interpreting dummy variable with no constant in the model

[Siraphop Swingthong]

Hi statalist, I have a question regard to how to interpreting dummy variable with no constant in the model. For example, in this cross sectional regression

stock return_i = α₁ capital expenditure_i + α₂ employee_i + α₃Financial industry + α₄Consumer production industry + α₅Agro industryε_{i
where capital expenditure and employee are normal variables, Financial industries, consumer production industry and agro industry are dummy variable where FIN = 1 mean the stock is in financial industries and 0 for other wise, Consumer production =1 mean stock is in consumer production and 0 for other wise Agro=1 mean stock is in agro and 0 for other wise (Note that suppose there are only three industry in the market, financial, consumer production and agricultural)}

So in this case, I understand that there is no base dummy variables. Therefore, it can be interpreted that α₃ is the coefficient of financial industry (it doesn't require to sum with coefficient from constant) However, what about capital expenditure, can I interpret that α₁ is the sensitivity of "overall" stock return to capital expenditure instead of sensitivity of "base dummy variable" stock return to capital expenditure?

Edit! I also have question that if α₃ is significant how can I interpret it? Does it mean it have significant premium on financial industry?
Best regards,
Siraphop Swingthong

[Carlo Lazzaro]

Sirahop:
your query seems to be linked to a class/home assignment.
Please see https://www.statalist.org/forums/help#adviceextras #4.
If that were not the case, please post what you typed and what Stata gave you back. Thanks.

[Siraphop Swingthong]

Dear Carlo Lazzaro,
It is not class or home assignment, it is my thesis. For the full code on stata here is the following,

reg cot capex roa mv emp lev cov sale consump fin indus prop resource service tech agro $control, noconstant robust

where cot is the sensitivity of stock return on monetary policy shock that I got from SVEC model. Roa, mv, emp, lev, cov, sale are the variables that I want to know whether it can explain the heterogeneity in stock return on monetary policy shock. consump, fin, indus, prop, resource, service, tech, agro are the industry variables. (8 industries, no base dummy)

Here is the result

So from the table can I interpret the coefficient of capex that it cannot explain the sensitivity of stock return on monetary policy shock for overall stock (not any particular industry?). Second question is what is the meaning of p value that reject the null hypothesis for fin dummy variable (0.006) because in this case, it doesn't have base dummy variables. Thank you.

[Maarten Buis]

There is a discussion of that in this Stata Tip: https://www.stata-journal.com/articl...article=st0250

Additionally for regress the option should be hascons rather than nocons, as you are implicitly adding a constant manually rather than forcing the regression line through the origin. This can make a big difference for the R-squared.

[Carlo Lazzaro]

Siraphop (sorry for misspelling your name in my previous reply):
thanks for posting what you tyoed and what Stata gave you back.
As an aside to Maarten's helpful advice, I would check your regression model specification via -linktest-.

[Eric de Souza]

There is a nice article on this by Daniel Suits with a humorous passage:
Daniel Suits, Dummy Variables: Mechanics V. Interpretation, The Review of Economics and Statistics, Vol. 66, No. 1 (Feb., 1984), pp. 177-180
"In the data, of course, the United States is partitioned into four regions, but (1) is fitted by the standard procedure of omitting the dummy variable for "South." This mechanical procedure rarely calls for remark by the initiated, but to appreciate the problem of interpre- tation that might be encountered, imagine you have the job of presenting the findings to a Congressional com- mittee. If you explain in the usual language that you have "omitted the variable for 'South'," a representative from Dixie might well demand indignantly, "Now just a minute here. Let me get this straight. You did what?" To straighten out the natural confusion, you might explain that you haven't really "left out" the South. On the contrary, you have "established the South as a base line from which to measure the behavior of people in other regions as deviations." The resulting confusion and consternation among the rest of the committee can well be imagined."