Skip to main content
5 votes
Accepted

Rubin Causal Model and Selection Bias

I recommend you read my answer here and answers to linked questions and remember to consider $y_0$ as an unmeasured pre-treatment confounder. Then the quantity $E[y_0|T=1] - E[y_0|T=0]$ refers to pre-...
Noah's user avatar
  • 34.2k
5 votes
Accepted

Omit continuous variable in categorical by continuous interaction

If you feed your model $(\text{woman}, 50000)$, $(\text{man}, 50000)$, $(\text{woman}, 150000)$, $(\text{man}, 150000)$, you will get three distinct net worth values, not four (assuming $\hat\beta_2\...
Dave's user avatar
  • 63.7k
5 votes
Accepted

Deriving a conditional joint probability model for the data in a Bayesian linear model

The left-hand side of your final equation, $p(y,X|\beta$), can be written as $p_y(y|X,\beta)p(X|\beta)$, and writing the right-hand side more explicitly then gives $$ p_y(y|X,\beta)p(X|\beta) = p_\...
Durden's user avatar
  • 1,522
2 votes
Accepted

how to summarize moving average

A moving average is already some kind of a summary statistic. It smooths out larger moves of the original data that could be noisy. I have 2 suggestions that might help you: Simply compare the 5-year ...
Gustavo Amarante's user avatar
2 votes
Accepted

Granular difference-in-differences with non-repeating unit of observation

I recommend the following notation, $$ Y_{pst} = \beta_1 T_s + \beta_2 A_t + \beta_3 (T_s \times A_t) + \epsilon_{pst}, $$ where you observe some characteristic of job posting $p$ in state $s$ and ...
Thomas Bilach's user avatar
2 votes
Accepted

Event study regression specification: interacting covariates with leads and lags

As indicated in the comments, $p_t$ is time-varying but exhibits the same pattern across the $j$ units. If you're estimating the standard difference-in-differences equation, adjusting for time effects,...
Thomas Bilach's user avatar
2 votes

Omit continuous variable in categorical by continuous interaction

I guess I am reiterating Dave's answer, but with a little more details for future readers. One way to look at a linear model with one categorical and one continuous variable, NW = b0 + b1xGender + ...
AAE's user avatar
  • 21
1 vote

Omit continuous variable in categorical by continuous interaction

Technically, what Dave posted was right. I was confused about the notation OARC was using in Stata. Their notation in Stata (changed to this example) is ...
Atreya Dey's user avatar
1 vote

can add of interaction term makes a third term insignificant?

There is no reason this can't happen. Unless the variables are orthogonal (and yours are not) then we expect changes in parameter estimates when we add nee variables, whether main effects or ...
Peter Flom's user avatar
  • 122k
1 vote

Can using Fisherian inference help me to be more confident of an underpowered result?

Your core question is "Can the same logic be applied when you the results are underpowered not because of a small sample size, but due to imperfect compliance?" The "logic" of ...
num_39's user avatar
  • 1,589
1 vote

Only first differencing the independent variable?

I'll start with your second question. The most flexible (linear) version of the CEF model says the expected rating depends on income today and income in the last period: $$E[y_{t} \vert i_t, i_{t-1}] =...
dimitriy's user avatar
  • 35.9k

Only top scored, non community-wiki answers of a minimum length are eligible