feisr

The packages feisr provides a function to estimate fixed effects individual slope (FEIS) models in R. FEIS models constitute a more general version of the often used conventional fixed effects (FE) panel models. In contrast to conventional fixed effects models, data are not person ‘demeaned’, but ‘detrended’ by the predicted individual slope of each person, which relaxes the assumptions of parallel trends between treated and untreated groups. For more information see Bruederl and Ludwig (2015); Frees (2001); Polachek and Kim (1994); Wooldridge (2010).

Installation

You can install feisr from github with:

``````# install.packages("devtools")
devtools::install_github("ruettenauer/feisr")``````

Example

The following example investigates the ‘marriage wage premium’: we test whether marriage leads to an increase in the hourly wage for men. The packages provides the function feis to estimate fixed effects individual slope models, which control for the hypothesis that those men who marry earlier also have a steeper wage growth over time. Similar to the plm function, feis requires to indicate a unique person / group identifier. To include individual-specific slopes, feis uses two-part formulas (expr | slope_expr), where slope_expr gives the expression for modelling the individual slopes. In our example, we use work experience (exp) and squared work experience as the slope variables:

``````library(feisr)
data("mwp", package = "feisr")
feis.mod <- feis(lnw ~ marry + enrol + yeduc + as.factor(yeargr)
| exp + I(exp^2), data = mwp, id = "id")
summary(feis.mod)
#>
#>
#> Call:
#> feis(formula = lnw ~ marry + enrol + yeduc + as.factor(yeargr) |
#>     exp + I(exp^2), data = mwp, id = "id")
#>
#>
#> Residuals :
#>       Min.    1st Qu.     Median    3rd Qu.       Max.
#> -2.0790815 -0.1050450  0.0046876  0.1112708  1.9412090
#>
#> Coefficients :
#>                      Estimate Std. Error t-value  Pr(>|t|)
#> marry               0.0134582  0.0273006  0.4930    0.6221
#> enrol              -0.1181725  0.0234275 -5.0442 4.913e-07 ***
#> yeduc              -0.0020607  0.0137673 -0.1497    0.8810
#> as.factor(yeargr)2 -0.0464504  0.0352096 -1.3193    0.1872
#> as.factor(yeargr)3 -0.0189333  0.0510825 -0.3706    0.7109
#> as.factor(yeargr)4 -0.1361305  0.0616378 -2.2086    0.0273 *
#> as.factor(yeargr)5 -0.1868589  0.0769889 -2.4271    0.0153 *
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Normal standard errors
#> Slope parameters:  exp, I(exp^2)
#> Total Sum of Squares:    190.33
#> Residual Sum of Squares: 185.64
#> R-Squared:      0.024626

The package also comes with an artificial regression test, which performs a Hausman-like test comparing FEIS against FE, FEIS against random effects (RE), and FE against RE models. The option feistest can be used with cluster-robust standard errors:

``````ht <- feistest(feis.mod, robust = TRUE, type = "all")
summary(ht)
#>
#>
#> Call:
#> feis(formula = lnw ~ marry + enrol + yeduc + as.factor(yeargr) |
#>     exp + I(exp^2), data = mwp, id = "id")
#>
#> Robust Augmented Regression Test
#>
#> FEIS vs. FE:
#> ------------
#> H0: FEIS and FE estimates consistent
#> Alternative H1: FE inconsistent
#> Model constraints: marry_hat enrol_hat yeduc_hat as_factor_yeargr_2_hat
#> as_factor_yeargr_3_hat as_factor_yeargr_4_hat as_factor_yeargr_5_hat = 0
#>
#> Chi-squared test:
#> Chisq = 49.558, df = 7, P(> X2) = 1.7639e-08
#>
#>
#> FE vs. RE:
#> ------------
#> H0: FE and RE estimates consistent
#> Alternative H1: RE inconsistent
#> Model constraints: marry_mean enrol_mean yeduc_mean
#> as_factor_yeargr_2_mean as_factor_yeargr_3_mean as_factor_yeargr_4_mean
#> as_factor_yeargr_5_mean exp_mean exp_2_mean = 0
#>
#> Chi-squared test:
#> Chisq = 13.087, df = 9, P(> X2) = 0.15872
#>
#>
#> FEIS vs. RE:
#> ------------
#> H0: FEIS and RE estimates consistent
#> Alternative H1: RE inconsistent
#> Model constraints: marry_hat enrol_hat yeduc_hat as_factor_yeargr_2_hat
#> as_factor_yeargr_3_hat as_factor_yeargr_4_hat as_factor_yeargr_5_hat = 0
#>
#> Chi-squared test:
#> Chisq = 55.231, df = 7, P(> X2) = 1.342e-09``````

References

Bruederl J, Ludwig V (2015). “Fixed-Effects Panel Regression.” In H Best, C Wolf (eds.), The Sage Handbook of Regression Analysis and Causal Inference, pp. 327-357. Sage, Los Angeles. ISBN 1446252442.

Frees EW (2001). “Omitted Variables in Longitudinal Data Models.” Canadian Journal of Statistics, 29(4), 573-595. http://dx.doi.org/10.2307/3316008.

Polachek SW, Kim MK (1994). “Panel Estimates of the Gender Earnings Gap.” Journal of Econometrics, 61(1), 23-42. http://dx.doi.org/10.1016/0304-4076(94)90075-2.

Wooldridge JM (2010). Econometric Analysis of Cross Section and Panel Data}. MIT Press, Cambridge, Mass. ISBN 0262294354.