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After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus be correlated with both independent and the dependent variables. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. With a fixed effect model, the hope is that all unobserved and time-invariant variables can be controlled by conditioning out across group (or across individual) variation. Indeed, the second model in my question is precisely a fixed effect model, and as such gives the estimate I expect.

I welcome comments that will further illuminate this circumstance. Thanks for your consideration.

After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus be correlated with both independent and the dependent variables. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. With a fixed effect model, the hope is that all unobserved and time-invariant variables can be controlled by conditioning out across group (or across individual) variation. Indeed, the second model in my question is precisely a fixed effect model, and as such gives the estimate I expect.

I welcome comments that will further illuminate this circumstance. Thanks for your consideration.

After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus be correlated with both independent and the dependent variables. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. With a fixed effect model, the hope is that all unobserved and time-invariant variables can be controlled by conditioning out across group (or across individual) variation. Indeed, the second model in my question is precisely a fixed effect model, and as such gives the estimate I expect.

I welcome comments that will further illuminate this circumstance.

3 added 181 characters in body
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After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus depend on some other variables other thanbe correlated with both independent and the dependent variablevariables. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. With a fixed effect model, the hope is that all unobserved and time-invariant variables can be controlled by conditioning out across group (or across individual) variation. Indeed, the second model in my question is precisely a fixed effect model, and as such gives the estimate I expect.

I welcome comments that will further illuminate this circumstance. Thanks for your consideration.

After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus depend on some other variables other than the dependent variable. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. Indeed, the second model in my question is precisely a fixed effect model and gives the estimate I expect.

I welcome comments that will further illuminate this circumstance. Thanks for your consideration.

After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus be correlated with both independent and the dependent variables. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. With a fixed effect model, the hope is that all unobserved and time-invariant variables can be controlled by conditioning out across group (or across individual) variation. Indeed, the second model in my question is precisely a fixed effect model, and as such gives the estimate I expect.

I welcome comments that will further illuminate this circumstance. Thanks for your consideration.

2 deleted 20 characters in body
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After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus depend on some other variables other than the dependent variable. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. Indeed, the second model in my question is precisely a fixed effect model and gives the estimate I expect.

I welcome comments that will further illuminate my understanding of this circumstance. Thanks for your consideration.

After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus depend on some other variables other than the dependent variable. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. Indeed, the second model in my question is precisely a fixed effect model and gives the estimate I expect.

I welcome comments that will further illuminate my understanding of this circumstance. Thanks for your consideration.

After considerable contemplation, I believe I have discovered my own answer. I believe an econometrician would define my independent variable to be endogenous and thus depend on some other variables other than the dependent variable. In this case, those variables are omitted or unobserved. However, I do observe the groupings between which the omitted variable ought to vary.

I believe the econometrician would suggest a fixed effect model. That is, a model that includes a dummy for every grouping level (or an equivalent specification that conditions the model such that many grouping dummies are not required) in this case. Indeed, the second model in my question is precisely a fixed effect model and gives the estimate I expect.

I welcome comments that will further illuminate this circumstance. Thanks for your consideration.

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