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It is the changes individuals experience in life that motivate us to use a fixed effects approach. However, these decisions are typically under the control of the individual. People change jobs; they get married; they earn more money; they change their political affiliation; they move; they have children; they become unionized; they join the military; they drop out of school. In practice, we wish to understand how this change in people's lives (treatment/exposure) affects the change in another variable (outcome). For example, does more education reduce infant mortality? Does one's union status affect wages? But, when changes in treatment/exposure status are under the control of the individual units we observe over time, then concerns about unobserved factors that are correlated with changes in treatment/exposure status remain.

I hope this gave you a better understanding of why DD is a special case of fixed effects. As for establishing causality, fixed effects doesn’t always cut it. It is up to you show that the policy/treatment change is plausibly unconfounded.

It is the changes individuals experience in life that motivate us to use a fixed effects approach. However, these decisions are typically under the control of the individual. People change jobs; they get married; they earn more money; they change their political affiliation; they move; they have children; they become unionized; they join the military; they drop out of school; they get arrested. In practice, we wish to understand how this change in people's lives (treatment/exposure) affects the change in another variable (outcome). For example, does more education reduce infant mortality? Does one's union status affect wages? But, when changes in treatment/exposure status are under the control of the individual units we observe over time, then concerns about unobserved factors that are correlated with changes in treatment/exposure status remain.

I hope this gave you a better understanding of why DD is a special case of fixed effects. As for establishing causality, fixed effects doesn’t always cut it. It’s up to you to show that the policy/treatment change is plausibly unconfounded.

where $\alpha_{i}$ represents a fixed parameter. We can define this fixed effect as the individual heterogeneity that is different across individuals but stable over time. Some of these time-invariant variables may be observed and known to a researcher (e.g., sex, race, ethnicity, etc.); some may be unobserved yet still known to be a source of individual heterogeneity (e.g., innate ability, stable personality characteristics, temperament, etc.); and, well, some of the other stable factors be unobserved and unbeknownst to a researcher. In a fixed effects specification, demeaning removes (i.e., ‘sweeps out’) the fixed effect, $\alpha_{i}$. The average of a time-invariant variable is the time-invariant variable, and so demeaning 'wipes out' (subtracts out) the stable characteristics of individuals that differ across individuals but are stable over time.

where $\alpha_{i}$ represents a fixed parameter. We can define this fixed effect as the individual heterogeneity that is different across individuals but stable over time. Some of these time-invariant variables may be observed and known to a researcher (e.g., sex, race, ethnicity, etc.); some may be unobserved yet still known to be a source of individual heterogeneity (e.g., innate ability, stable personality characteristics, temperament, etc.); and, well, some of the other stable factors may be unobserved and unbeknownst to a researcher. In a fixed effects specification, demeaning removes (i.e., ‘sweeps out’) the fixed effect, $\alpha_{i}$. The average of a time-invariant variable is the time-invariant variable, and so demeaning 'wipes out' (subtracts out) the stable characteristics of individuals that differ across individuals but are stable over time.

Enter the DD model. Under a DD specification, we are measuring the before-and-after change in the outcome of the treatment group relative to the before-and-after change in the outcome of the control group. It is important to note a subtle distinct here. In DD settings, the change in treatment exposure is typically determined outside of the unit of observation. For example, a policy/law may be introduced at the county/state level and affect a particular group of individuals/entities within that state. Often times, these policies/laws don't go into effect everywhere. Thus, these 'non-adopters' can serve as a suitable counterfactual. This is one of the attractive features of DD models; you can exploit this source of variation.

Enter the DD model. Under a DD specification, we are measuring the before-and-after change in the outcome of the treatment group relative to the before-and-after change in the outcome of the control group. It is important to note a subtle distinction here. In DD settings, the change in treatment exposure is typically determined outside of the unit of observation. For example, a policy/law may be introduced at the county/state level and affect a particular group of individuals/entities within that state. Often times, these policies/laws don't go into effect everywhere. Thus, these 'non-adopters' can serve as a suitable counterfactual. This is one of the attractive features of DD models; you can exploit this source of variation.