Tests to check the model specifications

Usage

checkSpecif(obj1, obj2, level = 0.05)

Arguments

obj1

If obj2 is left unspecified the specification test proposed by Kneip, Sickles, and Song (2012) is computed. In this case obj1 can be an object of class 'KSS' or 'Eup'. The given KSS- or Eup-model needs unspecified factor dimensions (factor.dim=NULL). See also the Details.
If obj2 is specified by an object of class 'Eup' the Hausman-type test proposed by Bai (2009) is computed, which compares the model in obj1 with the model in obj2. The Hausman-type test of Bai applies to 'Eup'-objects only. See also the Details.

obj2

An object of class 'Eup'. If obj2 is left unspecified the test proposed by Kneip, Sickles, and Song (2012) is computed.

level

The significance level.

Details

This function is equipped with two types of specification-tests:

The first specification-tests is the Hausman-type test proposed by Bai (2009), which is computed if obj1 as well as obj2 are specified by 'Eup'-objects. In this case the model given to the arguments obj1 and obj2 are compared with each other. Note that this test assumes that the (unobserved) true factor dimension is lower or equal to 2; see Section 9 in Bai (2009) for more details. Given the assumption that there is only one unobserved common factor:
- Null-Hypothesis: 'The unobserved common factor is a classical individual or time effect'.
- Alternative-Hypothesis: 'The unobserved common factor is an arbitrary process'.
Given the assumption that there are two unobserved common factors:
- Null-Hypothesis: 'The two unobserved common factors are classical twoways effects'.
- Alternative-Hypothesis: 'The two unobserved common factors are arbitrary processes'.
The second specification-test tests the existence of an additional factor structure beyond a classical additive effects model; as suggested in Kneip, Sickles, and Song (2012), which is applied if only obj1 is specified and obj2 is left unspecified. This test can be used for 'Eup'-objects as well as for 'KSS'-objects.
- Null-Hypothesis: 'There are no unobserved common factors beyond the classical individual, time, or twoways effects'.
- Alternative-Hypothesis: 'There are additional unobserved common factors'.

References

Bai, J., 2009 “Panel data models with interactive fixed effects”, Econometrica
Kneip, A., Sickles, R. C., Song, W., 2012 “A New Panel Data Treatment for Heterogeneity in Time Trends”, Econometric Theory

Author

Oualid Bada, Dominik Liebl

Examples

## See the example in 'help(Cigar)' in order to take a look at the
## data set 'Cigar'

##########
## DATA ##
##########

data(Cigar)
## Panel-Dimensions:
N <- 46
T <- 30
## Dependent variable:
  ## Cigarette-Sales per Capita
  l.Consumption      <- log(matrix(Cigar$sales, T,N))
  d.l.Consumption    <- diff(l.Consumption)
## Independent variables:
  ## Consumer Price Index
  cpi           <- matrix(Cigar$cpi, T,N)
  ## Real Price per Pack of Cigarettes 
  l.Price       <- log(matrix(Cigar$price, T,N)/cpi)
  d.l.Price     <- diff(l.Price)
  ## Real Disposable Income per Capita  
  l.Income      <- log(matrix(Cigar$ndi,   T,N)/cpi)
  d.l.Income    <- diff(l.Income)

#####################################################################
## Testing the Sufficiency of a classical 'twoways' effects model: ##
## Hausman-type Test of Bai (2009)                                 ##
#####################################################################

## Model under the null Hypothesis:
twoways.obj <- Eup(d.l.Consumption ~ -1 + d.l.Price + d.l.Income,
  factor.dim = 0, additive.effects = "twoways")

## Model under the alternative Hypothesis:
not.twoways.obj <- Eup(d.l.Consumption ~ -1 + d.l.Price + d.l.Income,
  factor.dim = 2, additive.effects = "none")

###########
## Test: ##
###########

## (This test returns an error message, since the (unobserved) true
## factor dimension is probably greater than 2.)
if (FALSE) {
checkSpecif(obj1 = twoways.obj, obj2 = not.twoways.obj, level = 0.01)
}

#####################################################################
## Testing the Existence of additional (unobserved) common Factors ##
## Specification Test of Kneip, Sickles, and Song (2012)           ##
#####################################################################

## For the model of Bai (2009):
Eup.obj <- Eup(d.l.Consumption ~ -1 + d.l.Price + d.l.Income,
     additive.effects = "twoways")

## Test:
checkSpecif(Eup.obj, level = 0.01)
#> ----------------------------------------------
#> Testing the Presence of Interactive Effects
#> Test of Kneip, Sickles, and Song (2012)
#> ----------------------------------------------
#> H0: The factor dimension is equal to 0.
#> 
#> Test-Statistic        p-value    crit.-value     sig.-level 
#>          13.29           0.00           2.33           0.01 

## For the model of Kneip, Sickles, and Song (2012):
KSS.obj <- KSS(l.Consumption ~ -1 + l.Price + l.Income,
     additive.effects = "twoways")

## Test:
checkSpecif(KSS.obj, level = 0.01)
#> ----------------------------------------------
#> Testing the Presence of Interactive Effects
#> Test of Kneip, Sickles, and Song (2012)
#> ----------------------------------------------
#> H0: The factor dimension is equal to 0.
#> 
#> Test-Statistic        p-value    crit.-value     sig.-level 
#>      104229.55           0.00           2.33           0.01