OLS, problems of estimation, error structure

[Sarah Edlund]

Hello everyone!

I would like to run an analysis about the effect of the Corona crisis on the happiness of people that live alone.

I’m using two data sources: 1. Panel data and 2. a survey that were conducted during the Corona crisis. The panel data offer information about the general level of happiness for each individual before the Corona crisis. The same individuals were asked during the Corona crisis about how much the Corona crises affected their happiness. Since the questions are not exactly the same I cannot run DID estimations. That's why I’m running OLS regressions to see how much single living people are affected by the Corona crises compared to people living with other people together.

My depend variable: “how much does the Corona crises affect your own happiness”

Independent variables: “living alone” + control variables

Does it make senses to use “level of happiness before the Corona crisis”as an additional independent control variable? Or does this lead to problems with the correct estimation (e.g. because of the error structure)? I'm considering using this variable to control for differences in the level of happiness between the individuals. I would be very thankful for any answer.

[Jared Greathouse]

I suppose you could lag your dependent variable and include it in the model......... without seeing your data, I don't know though.

Do they really use the words "Corona crisis"? They don't just say "pandemic"?

[Sarah Edlund]

Thanks for your answer.
They do not use "Corona crisis". They use Covid 19 pandemic. And we also use Covid 19 pandemic in the paper.

[Roman Mostazir]

Does it make senses to use “level of happiness before the Corona crisis”as an additional independent control variable? Or does this lead to problems with the correct estimation (e.g. because of the error structure)? I'm considering using this variable to control for differences in the level of happiness between the individuals. I would be very thankful for any answer.

Yes it does. It is like pre-post intervention. You have data on happiness before and after Covid. I therefore would tend to think of Covid as an exposure/intervention and you would like to see the change in happiness as a function of time+control variables. If you have multiple waves of data, mixed-model will be a good choice and the data for pre-covid hapiness should be there where row for time-1 should correspond to pre-covid happiness in the outome column. This will allow the model to estimate the change in happiness from baseline (pre-covid).

See help for -mixed-. Alternatively, if you have only pre-Covid and post-Covid data on hapiness i.e., two time points, you can fit baseline adjusted analysis of covariance (ancova) model (OLS) where the outcome is post-Covid happiness and the baseline happiness is one of the adjusting variables. But I suspect, since you have mentioned panel data, -mixed- is the way to go.

[Sarah Edlund]

Thanks for your answer. I don't think I can estimate mixed models as the pre-pandemic happiness question and the pandemic happiness question are different. Before the pandemic, people were asked about their general level of happiness. The survey conducted during the pandemic asked how much the pandemic had affected respondents' happiness. So I don't have two time points where the same question was asked.

[daniel klein]

My depend variable: “how much does the Corona crises affect your own happiness”

If this is the exact question, then Sarah is right: it does not measure happiness (at all). It measures the subjective belief of how the pandemic affects happiness. Strictly speaking, there is not even a direction here. Does "very much" as an answer imply that happiness decreases or increases? Perhaps singles are happier during the pandemic because they do not constantly run into happy couples, reminding them that they are still singles. Anyway, I would be very cautious interpreting those results.

Even if the question measured happiness, I am not sure I fully understand the research question or better: the implied data-generating process. Do you want to know whether the effect of the pandemic was different for singles and non-singles? If so, then being single seems to moderate the pandemic's effect on happiness. Unless you assume that happiness before the pandemic somehow affects the status of being single (which would imply quite a complex process), I do not immediately see the need "to control" for prior happiness. Also, you could reasonably argue that the pandemic is orthogonal to both being single and the level of happiness before the pandemic hit. So, again, no need to "control" for prior happiness. Of course, the main problem is that we, unfortunately, cannot observe the counterfactual as everyone gets the same pandemic treatment.