Aim

In
many regression models, the
variable of interest is a proportion or a fraction, i.e. it is defined
and observed only in the interval [0,1].
In Economics,
examples include pension plan participation rates, firm market share,
fraction of total weekly hours spent working, proportion of debt in the
financing mix of firms, fraction of land area allocated to agriculture,
and proportion of exports in total sales. The main aim of this page is
to provide some references for these socalled fractional regression
models and some simple code for
computing the main alternative estimators and specification tests.

Main references
 Seminal
paper:
Papke, L. and J.M. Wooldridge
(1996), "Econometric methods for fractional response variables with
an application to 401(K) plan participation rates", Journal of
Applied Econometrics, 11(6), 61932.
 Survey on models, estimation
methods and specification tests:
Ramalho,
E.A., J.J.S. Ramalho and J.M.R. Murteira (2011), "Alternative estimating and testing empirical
strategies for fractional regression models", Journal of
Economic Surveys, 25(1), 1968.
 Endogeneity and neglected
heterogeneity:
Ramalho,
E.A. and J.J.S. Ramalho, "Momentbased estimation of nonlinear
regression models with boundary outcomes and endogeneity, with
applications to nonnegative and fractional responses", Econometric
Reviews, forthcoming.[Dataset:
txt]
[Code: R]
 Panel data:
Ramalho,
E.A., J.J.S. Ramalho and L.M.S. Coelho, "Exponential
regression of fractionalresponse fixedeffects models with an
application to firm capital structure", Journal of Econometric
Methods, forthcoming.[Data
and code: zip]
 DEA
analyses:
Ramalho,
E.A., J.J.S. Ramalho and P.D. Henriques (2010), "Fractional
regression models for second stage DEA efficiency analyses",
Journal of Productivity
Analysis, 34(3), 239255.
[Dataset: dta txt]
[Code:
Stata R]
Murteira,
J.M.R., J.J.S. Ramalho (2016), "Regression analysis of multivariate
fractional data", Econometric Reviews, 35(4),
515552.

Code
 Packages:
Ramalho,
J.J.S. (2015), frmpd:
Regression Analysis of Panel Fractional Responses,
R package.
Ramalho,
J.J.S. (2014), frmhet:
Regression Analysis of Fractional Responses Under Heterogeneity,
R package.
Ramalho,
J.J.S. (2014), frm: Regression
Analysis of Fractional Responses, R package.
Ramalho,
J.J.S. (2013), FRM:
Stata Module to Estimate and Test Fractional Regression Models,
Statistical Software Components 457542, Boston College Department of
Economics.
R 
Stata 
Description 
frm 
frm 
Estimation of
one and
twopart fractional regression models. Available link
functions:
(i) logit
(ii) probit
(iii) cauchit
(iv) loglog
(v) cloglog 
frm.pe 
frm_pe 
Average and
conditional partial effects for:
(i) onepart models
(ii) the binary component of twopart models
(iii) the fractional component of twopart models
(iv) twopart models 
frm.reset 
frm_reset 
RESET test for the
link specification in:
(i) onepart models
(ii) the binary component of twopart models
(iii) the fractional component of twopart models 
frm.ggoff 
frm_ggoff 
GGOFF,
GOFF1 and GOFF2 tests for the link specification in:
(i) onepart models
(ii) the binary component of twopart models
(iii) the fractional component of twopart models 
frm.ptest 
frm_ptest 
P test for
assessing, against each other:
(i) two alternative specifications for the link function in onepart
models
(ii) two alternative specifications for the link function in the binary
component of twopart models
(iii) two alternative specifications for the link function in the
fractional component of twopart models
(iv) two alternative specifications for twopart models
(v) a onepart model versus a twopart model
(vi) two models based on the same link specifiction(s) but using sets of
nonnested regressors 
frmhet 
 
Estimation of
fractional regression models with neglected heterogeneity and/or
endogenous covariates. Available estimators:
(i) GMMx
(ii) GMMxv
(iii) GMMz
(iv) LINx
(v) LINxv
(vi) LINz
(vii) QMLxv 
frmhet.pe 
 
Average and
conditional partial effects for models estimated by the command frmhet 
frmhet.reset 
 
RESET test for
models estimated by GMMx or LINx 
frmpd 
 
Estimation of panel
data fractional regression models. Available estimators:
(i) GMMww
(ii) GMMc
(iii) GMMbgw
(iv) GMMpfe
(v) GMMcre
(vi) GMMpre
(vii) QMLcre 
