regife (Bai 2009)

The command regife estimates models with interactive fixed effects following Bai (2009). (Note: to estimate model with interacted fixed effects, use reghdfe.)

For an observation i, denote (jλ(i), jf(i)) the associated pair (id x time). The command estimates models of the form

The model is estimated by least square, i.e. by finding the coefficients β, of factors (f1, .., fr) and of loadings (λ1, ..., λr) that minimize

The command is slow. A much faster algorithm is available in Julia

Syntax

regife requires a formula and the option factors, that specifies the id variable, the time variable, and the dimension:

insheet "data/cigar.csv", clear
regife sales price, ife(state year, 3)

Absorb

You can impose id and/or time fixed effect by estimating models of the form

Just use the option absorb along with the option factors:

regife sales price, ife(state year, 2)  a(state year)

Unbalanced Panel

The command handles unbalanced panels (ie missing observation for a given id, time) as described in the appendix of Bai 2009.

Weights

Weights are supported but should be constant within id

Save factors

Save loadings and/or factors by specifying new variable names at the left hand side of =

regife sales price, a(fe_state=state) ife(ife_state=state ife_year=year, 2) 

To save residuals, use the option residuals

regife sales price, ife(state year, 2) residuals(newres)

FAQ

When should one use interactive fixed effects models?

Some litterature using this estimation procedure::

• Eberhardt, Helmers, Strauss (2013) Do spillovers matter when estimating private returns to R&D?
• Hagedorn, Karahan, Movskii (2015) Unemployment Benefits and Unemployment in the Great Recession: The Role of Macro Effects
• Hagedorn, Karahan, Movskii (2015) The impact of unemployment benefit extensions on employment: the 2014 employment miracle?
• Totty (2015) The Effect of Minimum Wages on Employment: A Factor Model Approach

How are standard errors computed?

Errors are obtained by regressing y on x and covariates of the form i.id#c.year and i.year#c.id. This way of computing standard errors is hinted in section 6 of of Bai (2009).

Does this command implement the bias correction term in Bai (2009)?

In presence of cross or time correlation beyond the factor structure, the estimate for beta is consistent but biased (see Theorem 3 in Bai 2009, which derives the correction term in special cases). However, this package does not implement any correction. You may want to check that your residuals are approximately i.i.d.

References

• Bai, Jushan. Panel data models with interactive fixed effects. (2009) Econometrica
• Ilin, Alexander, and Tapani Raiko. Practical approaches to principal component analysis in the presence of missing values. (2010) The Journal of Machine Learning Research 11
• Koren, Yehuda. Factorization meets the neighborhood: a multifaceted collaborative filtering model. (2008) Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining.
• Raiko, Tapani, Alexander Ilin, and Juha Karhunen. Principal component analysis for sparse high-dimensional data. (2008) Neural Information Processing.
• Srebro, Nathan, and Tommi Jaakkola. Weighted low-rank approximations (2010) The Journal of Machine Learning Research 11
• Nocedal, Jorge and Stephen Wright An Inexact Levenberg-Marquardt method for Large Sparse Nonlinear Least Squares (1985) The Journal of the Australian Mathematical Society

Installation

regife is now available on ssc. It requires reghdfe

ssc install reghdfe
ssc install regife

To install the latest version on Github

• with Stata13+

   net install regife, from("https://raw.githubusercontent.com/matthieugomez/regife/master/")
  

• with Stata 12 or older, download the zipfiles of the repositories and run in Stata the following commands:

   net install regife, from("SomeFolderRegife")
  

Cite

You can cite the package as

Matthieu Gomez, 2015. REGIFE: Stata module to estimate linear models with interactive fixed effect. Statistical Software Components s457874, Boston College Department of Economics. https://ideas.repec.org/c/boc/bocode/s458042.html