Let' say I have a regression model:
Suppose $x$ is income and $y$ is consumption. The hypothesis is that higher income leads to higher consumption and hence, the coefficient on $x$ should be positive, other things remaining the same.Let's also say the estimated coefficient is 0.60. This model obviously suffers from omitted variable bias. Please ignore this issue. My question:
a) Does this model suffer from reverse causality? In other words, is it the case that the relationship is because higher consumption is driving down income? My first guess is that this is not the case because coefficient is positive which means correlation between income and consumption is positive. See here.
b) Given (a), can I use this as a rule-of-thumb to rule out the reverse causality in this case? Is this generalizable to other cases with two variables?
Thanks. P.S. One can also just use correlation rather than running a simple regression as mentioned earlier.