Forum: help

RE: Scaling of TotExp affects iterated (IL) estimation [ Reply ] By: Julien Mc Donald-Guimond on 2023-04-17 13:26	[forum:49640]
I understand now! Thank you very much for the quick turnaround M. Henningsen. Your package is very helpful to the community. All the best, Julien

RE: Scaling of TotExp affects iterated (IL) estimation [ Reply ]
By: Arne Henningsen on 2023-04-17 10:32

[forum:49639]

The 'full' AIDS model (e.g., estimated with the 'iterative linear' estimation method) is invariant to units of measurement of total expenditure only if alpha_0 adjusts to changes of the units of measurement. If you adjust alpha_0 manually, you get virtually the same results:

aidsResult.1b <- aidsEst(priceNames, shareNames, "xFood",data = BlanciX, method = "IL", alpha0 = log( 10 ))

all.equal( coef( aidsResult.0 )$alpha, coef( aidsResult.1b )$alpha )
# [1] "Mean relative difference: 1.913937e-07"

all.equal( coef( aidsResult.0 )$beta, coef( aidsResult.1b )$beta )
# [1] "Mean relative difference: 2.168397e-07"

all.equal( coef( aidsResult.0 )$gamma, coef( aidsResult.1b )$gamma )
# [1] "Mean relative difference: 6.879121e-07"

You can search for the 'optimal' values of alpha_0 (which can take some time) and then estimate the AIDS with these optimal values:

# optimal alpha_0 with unscaled xFood
a0.0 <- aidsBestA0(priceNames, shareNames, "xFood",data = Blanciforti86, stoprange = 0.02, stopiter = 50 )
# estimation with optimal alpha_0
aidsResult.0o <- aidsEst(priceNames, shareNames, "xFood",data = Blanciforti86, method = "IL", alpha0 = a0.0$alpha0 )

# optimal alpha_0 with scaled xFood
a0.1 <- aidsBestA0(priceNames, shareNames, "xFood",data = BlanciX, stoprange = 0.02, stopiter = 50 )
# estimation with optimal alpha_0
aidsResult.1o <- aidsEst(priceNames, shareNames, "xFood",data = BlanciX, method = "IL", alpha0 = a0.1$alpha0 )

# comparison
all.equal( coef( aidsResult.0o )$alpha, coef( aidsResult.1o )$alpha )
# [1] "Mean relative difference: 0.001127145"

all.equal( coef( aidsResult.0o )$beta, coef( aidsResult.1o )$beta )
# [1] "Mean relative difference: 6.353063e-05"

all.equal( coef( aidsResult.0o )$gamma, coef( aidsResult.1o )$gamma )
# "Mean relative difference: 0.0009082388"

Scaling of TotExp affects iterated (IL) estimation [ Reply ]
By: Julien Mc Donald-Guimond on 2023-04-14 22:12

[forum:49634]

I'm surprised to see that the scaling of total expenditures affects non-trivially the estimated coefficients. Not only alpha (which, being a constant, would change), but also beta and gamma.

Any guidance as to why and whether it is normal ?

Reproducible example below.

Thank you,
Julien

``` r
require(micEconAids)
data( "Blanciforti86" )
Blanciforti86 <- Blanciforti86[ 1:32, ]
priceNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
shareNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )

aidsResult.0 <- aidsEst(priceNames, shareNames, "xFood",data = Blanciforti86, method = "IL" )

BlanciX <- Blanciforti86
BlanciX$xFood <- BlanciX$xFood*10 ######## scaling #########
aidsResult.1 <- aidsEst(priceNames, shareNames, "xFood",data = BlanciX, method = "IL" )

all.equal( coef( aidsResult.0 )$alpha, coef( aidsResult.1 )$alpha )
#> [1] "Mean relative difference: 1.065724"
all.equal( coef( aidsResult.0 )$beta, coef( aidsResult.1 )$beta )
#> [1] "Mean relative difference: 0.04433987"
all.equal( coef( aidsResult.0 )$gamma, coef( aidsResult.1 )$gamma )
#> [1] "Mean relative difference: 0.8122552"
```

<sup>Created on 2023-04-14 by the [reprex package](https://reprex.tidyverse.org) (v2.0.1)</sup>