Dear all,
I'm estimating a fixed effects model using reghdfe to identify credit supply shocks at the bank level. The specification I am working with is the following:
ΔLf,b,t=αILS,t+βb,t+εf,b,t\Delta L_{f,b,t} = \alpha_{ILS,t} + \beta_{b,t} + \varepsilon_{f,b,t}ΔLf,b,t=αILS,t+βb,t+εf,b,t
In this specification, ΔLf,b,t=Lf,b,t−Lf,b,t−1Lf,b,t−1\Delta L_{f,b,t} = \frac{L_{f,b,t} - L_{f,b,t-1}}{L_{f,b,t-1}}ΔLf,b,t=Lf,b,t−1Lf,b,t−Lf,b,t−1 denotes the annual growth rate of credit from bank b to firm f at time t. The term αILS,t\alpha_{ILS,t}αILS,t captures fixed effects at the industry, location, and size level for each time period (ILST fixed effects), while βb,t\beta_{b,t}βb,t is the parameter of interest, representing the bank-time fixed effect associated with the credit supply shock—commonly referred to as the bank credit channel.
I estimate this model using the following Stata code:
The goal is to recover the bank-time fixed effects β^bt\hat{\beta}_{bt}β^bt and then center them by time to obtain β~bt\tilde{\beta}_{bt}β~bt, which represents the time-demeaned bank credit supply shocks.
I would appreciate any clarification on the following three points:
Best regards,
José Marcelo
I'm estimating a fixed effects model using reghdfe to identify credit supply shocks at the bank level. The specification I am working with is the following:
ΔLf,b,t=αILS,t+βb,t+εf,b,t\Delta L_{f,b,t} = \alpha_{ILS,t} + \beta_{b,t} + \varepsilon_{f,b,t}ΔLf,b,t=αILS,t+βb,t+εf,b,t
In this specification, ΔLf,b,t=Lf,b,t−Lf,b,t−1Lf,b,t−1\Delta L_{f,b,t} = \frac{L_{f,b,t} - L_{f,b,t-1}}{L_{f,b,t-1}}ΔLf,b,t=Lf,b,t−1Lf,b,t−Lf,b,t−1 denotes the annual growth rate of credit from bank b to firm f at time t. The term αILS,t\alpha_{ILS,t}αILS,t captures fixed effects at the industry, location, and size level for each time period (ILST fixed effects), while βb,t\beta_{b,t}βb,t is the parameter of interest, representing the bank-time fixed effect associated with the credit supply shock—commonly referred to as the bank credit channel.
I estimate this model using the following Stata code:
Code:
reghdfe delta_l, absorb(ilst beta_bt, savefe) nocons resid gen hat_ilst = __hdfe1 gen hat_beta_bt = __hdfe2 egen mean_hat_beta_bt = mean(hat_beta_bt), by(time) gen tilde_beta_bt = hat_beta_bt - mean_hat_beta_bt
The goal is to recover the bank-time fixed effects β^bt\hat{\beta}_{bt}β^bt and then center them by time to obtain β~bt\tilde{\beta}_{bt}β~bt, which represents the time-demeaned bank credit supply shocks.
I would appreciate any clarification on the following three points:
- Omitted category of fixed effects: Since I’m including two full sets of fixed effects (ILST and bank-time), do I need to explicitly omit one category from one of these sets to avoid perfect multicollinearity? Or does reghdfe handle this internally by applying some kind of normalization (e.g., sum-to-zero)? I want to ensure that the fixed effects I extract are properly identified and interpretable.
- Constant term and the nocons option: Even when using the nocons option, reghdfe still displays an estimated constant in the output. The documentation says nocons is mostly cosmetic and does not truly remove the constant. Why is that? Should I worry about this when estimating a model with two full sets of fixed effects? Could the presence of a constant affect my recovered fixed effects?
- Order of fixed effects and stability of estimates: I noticed that changing the order of variables inside absorb() (e.g., absorb(ilst beta_bt) vs. absorb(beta_bt ilst)) changes both which __hdfe# corresponds to which fixed effect and the actual numeric values of the fixed effects extracted. I understand that fixed effects are only identified up to a normalization, but does this affect interpretation? And more practically, which version of the estimates should I use when computing β~bt\tilde{\beta}_{bt}β~bt?
Best regards,
José Marcelo
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