Description Usage Arguments Details Value Author(s) References See Also Examples
Estimation of Panel Data Models with Heterogeneous Time Trends
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formula 
An object of class 'formula'. 
additive.effects 
Type of Data Transformations:

consult.dim.crit 
logical.

d.max 
A maximal dimension needed for some
dimensionalitycriteria that are implemented in the function

sig2.hat 
Standard deviation of the errorterm. The default
( 
factor.dim 
Dimension of FactorStructure. The default
( 
level 
Significancelevel for DimensionalityCriterion of Kneip, Sickles & Song 2012. 
spar 
Smoothing parameter for spline smoothing of the
residuals. If ( 
CV 
logical. Selects the procedure for the determination of the
smoothing parameter

convergence 
Convergence criterion for the CVoptimization of
the smoothing parameter 
restrict.mode 
Type of Restriction on the FactorStructure:

... 
Additional arguments to be passed to the low level functions. 
'KSS' is a function to estimate panel data models with unobserved heterogeneous time trends v_i(t). The considered model in Kneip, Sickles & Song (2012) is given by Y_{it}=θ_{t}+∑_{j=1}^Pβ_{j} X_{itj}+v_i(t)+ε_{it}, i=1,...,n; t=1,...,T. Where the individual time trends, v_i(t), are assumed to come from a finite dimensional factor model v_i(t)=∑_{l=1}^dλ_{il}f_l(t), λ_{il}\in R, f_l\in L^2[0,T]. The unobserved functions v_i(t) can be interpreted as smooth functions of a continuous argument t, as well as stochastic processes for discrete argument t.
formula
Usual 'formula'object. If you wish to
estimate a model without an intercept use '1' in the
formulaspecification. Each Variable has to be given as a
TxNmatrix. Missing values are not allowed.
additive.effects
"none"
: The data is not transformed, except for an
eventually subtraction of the overall mean; if the model is
estimated with an intercept. The assumed model can be written as
Y_{it}=μ+∑_{j=1}^Pβ_{j}
X_{itj}+v_i(t)+ε_{it}, i=1,...,n; t=1,...,T.
The parameter 'mu' is set to zero if '1' is used in formula
.
"individual"
: This is the "within"model, which
assumes that there are timeconstant individual effects,
tau_i, besides the individual time trends v_i(t). The
model can be written as
Y_{it}=μ+∑_{j=1}^Pβ_{j}
X_{itj}+v_i(t)+α_{i}+ε_{it}, i=1,...,n; t=1,...,T.
The parameter 'mu' is set to zero if '1' is used in formula
.
"time"
: This is the "between"model, which assumes
that there is a common (for all individuals) time trend, beta_0(t). The
model can be written as
Y_{it}=μ+θ_{t}+∑_{j=1}^Pβ_{j}
X_{itj}+v_i(t)+ε_{it}, i=1,...,n; t=1,...,T.
The parameter 'mu' is set to zero if '1' is used in formula
.
"twoways"
: This is the "twoways"model ("within" &
"between"), which assumes that there are timeconstant
individual effects, tau_i, and a common time trend,
beta_0(t). The model can be written as
Y_{it}=μ+θ_{t}+∑_{j=1}^Pβ_{j}
X_{itj}+α_i+v_i(t)+ε_{it}, i=1,...,n; t=1,...,T.
The parameter 'mu' is set to zero if '1' is used in formula
.
'KSS' returns an object of 'class' '"KSS"'.
An object of class '"KSS"' is a list containing at least the following components:
dat.matrix
: Whole data set stored within a
(N*T)x(p+1)Matrix, where P is the number of independent
variables without the intercept.
dat.dim
: Vector of length 3: c(T,N,p)
slope.para
: Betaparameters
beta.V
: Covariance matrix of the betaparameters.
names
: Names of the dependent and independent variables.
is.intercept
: Used an intercept in the formula?: TRUE or FALSE
additive.effects
: Additive effect type. One of: "none","individual","time", "twoways".
Intercept
: Interceptparameter
Add.Ind.Eff
: Estimated values of additive individual effects.
Add.Tim.Eff
: Estimated values of additive time effects.
unob.factors
: Txdmatrix of estimated unobserved common
factors, where 'd' is the number of used factors.
ind.loadings
: Nxdmatrix of loadings parameters.
unob.fact.stru
: TxNmatrix of the estimated factor
structure. Each column represents an estimated individual unobserved time trend.
used.dim
: Used dimensionality of the factor structure.
optimal.dim
: List of proposed dimensionalities.
fitted.values
: Fitted values.
orig.Y
: Original values of the dependent variable.
residuals
: Residuals
sig2.hat
: Estimated variance of the error term.
degrees.of.freedom
: Degrees of freedom of the residuals.
call
Dominik Liebl
Kneip, A., Sickles, R. C., Song, W., 2012 “A New Panel Data Treatment for Heterogeneity in Time Trends”, Econometric Theory
Eup
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  ## See the example in 'help(Cigar)' in order to take a look at the
## data set Cigar
##########
## DATA ##
##########
data(Cigar)
## PanelDimensions:
N < 46
T < 30
## Dependent variable:
## CigaretteSales per Capita
l.Consumption < log(matrix(Cigar$sales, T,N))
## Independent variables:
## Consumer Price Index
cpi < matrix(Cigar$cpi, T,N)
## Real Price per Pack of Cigarettes
l.Price < log(matrix(Cigar$price, T,N)/cpi)
## Real Disposable Income per Capita
l.Income < log(matrix(Cigar$ndi, T,N)/cpi)
## Estimation:
KSS.fit < KSS(l.Consumption~l.Price+l.Income, CV=TRUE)
(KSS.fit.sum < summary(KSS.fit))
plot(KSS.fit.sum)

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