plm包固定效应回归：ID索引顺序影响的技术咨询

The core reason for the differences in your regression results lies in what the index parameter in plm actually controls when using a one-way within model. Let's break this down step by step:

1. How plm interprets the index parameter for one-way fixed effects #

When you set model="within" without specifying effect="twoways", plm defaults to a one-way fixed effect model—it only controls for fixed effects of the first variable in your index vector:

• For index=c("Year","Company"): The model treats Year as the "individual" dimension, so it estimates and removes year-specific fixed effects (absorbing unobserved heterogeneity that's constant across all firms in a given year).
• For index=c("Company","Year"): The model treats Company as the "individual" dimension, so it estimates and removes firm-specific fixed effects (absorbing unobserved heterogeneity that's constant for a given firm across all years).

These are two entirely distinct models, so divergent results are expected.

2. Matching output details to this explanation #

Let's cross-reference your regression outputs to confirm this logic:

Panel structure differences #

• MV_Year output shows n = 17 (number of "individuals" = 17 years) and T = 557-4280 (number of firms per year).
• MV_Company output shows n = 5911 (number of "individuals" = 5911 firms) and T = 1-17 (number of years per firm).

This directly confirms which dimension is being used for fixed effects.

Coefficient estimates #

Differences in coefficients (e.g., LEV shifts from -1.95 to -1.88, RDlog from 0.131 to 0.139) occur because each fixed effect absorbs different sources of omitted variable bias:

• Year fixed effects account for economy-wide shocks that hit all firms in a year (e.g., macroeconomic trends, annual policy changes).
• Firm fixed effects account for time-invariant firm traits (e.g., corporate culture, inherent business model differences).

Each adjustment reshapes the remaining variation in your dependent variable that can be explained by the covariates.

R-squared and residual statistics #

• Total Sum of Squares: For one-way within models, this is the sum of squares after de-meaning the data by the individual dimension. De-meaning by firms (which have smaller cross-sectional variation over time) results in a smaller total sum of squares (58168 vs 102610) compared to de-meaning by years.
• Adjusted R-squared: The larger drop in adjusted R² for MV_Company (0.726 vs 0.828) stems from the far larger number of fixed effects being estimated (5911 firm effects vs 17 year effects)—this reduces degrees of freedom more drastically, leading to a lower adjusted value.
• F-statistic degrees of freedom: The residual DF for MV_Year is 29890 - 17 (year effects) - 4 (covariates) = 29869, while for MV_Company it's 29890 - 5911 (firm effects) - 4 = 23975—exactly matching your outputs.

3. How to run a two-way fixed effect model #

If you want to control for both firm and year fixed effects (the standard approach in many panel data analyses), explicitly set effect="twoways" in your plm call:

MV_Twoway <- plm(MVlog ~ LEV + Size + DY + RDlog, 
                 data=Values, 
                 model="within", 
                 index=c("Company", "Year"), 
                 effect="twoways")

This model will absorb both time-invariant firm characteristics and year-specific shocks, producing results distinct from either of your one-way models.

内容的提问来源于stack exchange，提问作者Aria T