I am looking at the effect of sport participation on happiness. Happiness is my dependent variable, between integers 1 to 10, and sport participation is my independent variable which is binary; I also have controls commonly used in happiness economics (age, marital status, work etc). I wanted to use an instrumental variable approach in order to limit endogeneity concerns and I have a relevant instrument: a binary variable on whether sports facilities existed in close proximity to the respondent.

Using a two step instrumental variable approach yielded consistent, statistically significant results. However, when using ivregress or ivreg2, using the same instrument, the resulting standard error on my sport participation variable is huge (~1.2, which is over 10x that of any other variables) and the p value is now 0.6. What could be the reasons for this and is there a way to resolve this?

Furthermore, are there any other models which would be useful to employ and applicable for my data and how would I go about applying them?

Many thanks!