Toni Whited and Luke Taylor discuss structural estimation (e.g. GMM) of economic models: these models include parameters which are shared by all firms/agents. They suggest to reduce firm heterogeneity by ''eliminating fixed effects,'' see here in Taylor's slides (slide 36):

My question: I'm not quite sure what they mean with this statement and how to implement it.

My aim is to use portfolio returns to calculate the moment conditions. Let $R_{i,t}$ denote monthly returns. Following wikipedia, I can

• use the fixed effects estimator (essentially demean the returns within firms/months)
• subtract lagged values in a first-difference way

Does this mean I compute the GMM moment conditions from the either the demeaned returns or the first differenced returns?

When discussing GMM estimation, Toni Whited and Luke Taylor suggest to reduce heterogeneity by ''eliminating fixed effects,'' see here on Taylor's slides (slide 36):

My question: I'm not quite sure what they mean with this statement and how to implement it.

My aim is to use portfolio returns to calculate the moment conditions. Let $R_{i,t}$ denote monthly returns. Following wikipedia, I can

• use the fixed effects estimator (essentially demean the returns within firms/months)

In this case, I do not only subtract the means $\frac{1}{T}\sum\limits_t R_{i,t}$ and $\frac{1}{N}\sum\limits_i R_{i,t}$ but also the cross-term $\frac{1}{T}\frac{1}{N}\sum_\limits{i}\sum\limits_t R_{i,t}$?

• subtract lagged values in a first-difference way

In this case, I can consider $\Delta R_{i,t}=R_{i,t}-R_{i,t-1}$ but what would be the cross-sectional lag term? $R_{i,t}-R_{i-1,t}$ does not make sense, does it?

In the end, I compute the GMM moment conditions from either the (properly) demeaned returns or the (somehow?) first differenced returns?

Toni Whited and Luke Taylor discuss structural estimation (e.g. GMM) of economic models: these models include parameters which are shared by all firms/agents. They suggest to reduce firm heterogeneity by eliminating fixed effects, see here in Taylor's slides (slide 36):

My question: I'm not quite sure what they mean with this statement and how to implement it.

My aim is to use portfolio returns to calculate the moment conditions. Let $R_{i,t}^e$ denote monthly excess returns. Do I first run the panel regression

$$R_{i,t}^e=\alpha_i+\beta_t+\varepsilon_{i,t}$$

and compute the GMM moment conditions from the residuals, $\hat{\varepsilon}_{i,t}$ (essentially demeaned returns)?

Toni Whited and Luke Taylor discuss structural estimation (e.g. GMM) of economic models: these models include parameters which are shared by all firms/agents. They suggest to reduce firm heterogeneity by ''eliminating fixed effects,'' see here in Taylor's slides (slide 36):

My question: I'm not quite sure what they mean with this statement and how to implement it.

My aim is to use portfolio returns to calculate the moment conditions. Let $R_{i,t}$ denote monthly returns. Following wikipedia, I can

• use the fixed effects estimator (essentially demean the returns within firms/months)
• subtract lagged values in a first-difference way

Does this mean I compute the GMM moment conditions from the either the demeaned returns or the first differenced returns?

Toni Whited and Luke Taylor discuss structural estimation (e.g. GMM) of economic models: these models include a hand full of parameters which are shared by all firms/agents. They suggest to reduce firm heterogeneity by eliminating firm and time fixed effects, see here in Taylor's slides (slide 36):

My question: I'm not quite sure what they mean with this statement and how to implement it.

My aim is to use portfolio returns to calculate moment conditions. Let $R_{i,t}^e$ denote monthly excess returns. Do I first run the panel regression

$$R_{i,t}^e=\alpha_i+\beta_t+\varepsilon_{i,t}$$

and compute the GMM moment conditions from the residuals, $\hat{\varepsilon}_{i,t}$ (essentially demeaned returns)?

Toni Whited and Luke Taylor discuss structural estimation (e.g. GMM) of economic models: these models include parameters which are shared by all firms/agents. They suggest to reduce firm heterogeneity by eliminating fixed effects, see here in Taylor's slides (slide 36):

My question: I'm not quite sure what they mean with this statement and how to implement it.

My aim is to use portfolio returns to calculate the moment conditions. Let $R_{i,t}^e$ denote monthly excess returns. Do I first run the panel regression

$$R_{i,t}^e=\alpha_i+\beta_t+\varepsilon_{i,t}$$

and compute the GMM moment conditions from the residuals, $\hat{\varepsilon}_{i,t}$ (essentially demeaned returns)?