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Aim
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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 so-called fractional regression
models and some simple code for
computing the main alternative estimators and specification tests.
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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), 619-32.
- 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), 19-68.
- Endogeneity and neglected
heterogeneity:
Ramalho,
E.A. and J.J.S. Ramalho, "Moment-based estimation of nonlinear
regression models with boundary outcomes and endogeneity, with
applications to non-negative 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 fractional-response fixed-effects 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), 239-255.
[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),
515-552.
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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
two-part 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) one-part models
(ii) the binary component of two-part models
(iii) the fractional component of two-part models
(iv) two-part models |
| frm.reset |
frm_reset |
RESET test for the
link specification in:
(i) one-part models
(ii) the binary component of two-part models
(iii) the fractional component of two-part models |
| frm.ggoff |
frm_ggoff |
GGOFF,
GOFF1 and GOFF2 tests for the link specification in:
(i) one-part models
(ii) the binary component of two-part models
(iii) the fractional component of two-part models |
| frm.ptest |
frm_ptest |
P test for
assessing, against each other:
(i) two alternative specifications for the link function in one-part
models
(ii) two alternative specifications for the link function in the binary
component of two-part models
(iii) two alternative specifications for the link function in the
fractional component of two-part models
(iv) two alternative specifications for two-part models
(v) a one-part model versus a two-part model
(vi) two models based on the same link specifiction(s) but using sets of
non-nested 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 |
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