19.04.2014 Views

Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

Appendix A: Estimation strategy<br />

Estimating CPI biases<br />

Following Costa (2001) the estimation strategy starts formally form the following<br />

equation:<br />

( PFjt<br />

− ln PNjt<br />

) + β ( lnYijt<br />

− ln PGjt<br />

) + θ<br />

x<br />

X<br />

ijt ijt<br />

w<br />

ijt<br />

= φ + γ ln ∑ + µ , (1)<br />

where w<br />

ijt<br />

is the ratio of food to nonfood of household i, in region j at time t ;<br />

P<br />

Fjt<br />

is the true unobservable price of food in region j at time t ;<br />

P<br />

Njt<br />

is the true <strong>and</strong> unobservable price of non food in region j at time t ;<br />

Y<br />

ijt<br />

is nominal income for household i, in region j at time t ;<br />

PGjt<br />

is the true <strong>and</strong> unobservable general price level in region j at time t;<br />

X<br />

ijt<br />

is a set of control variables for household i, in region j at time t ;<br />

µ<br />

ijt<br />

is a r<strong>and</strong>om term;<br />

φ ,γ , β , <strong>and</strong> the different θ<br />

x<br />

are parameters.<br />

If we call<br />

∏<br />

Gjt<br />

the cumulative percentage growth of the observable CPI in region j, since time 0<br />

<strong>and</strong> time t ;<br />

∏<br />

Fjt<br />

the cumulative percentage growth of the price of food, in region j, between time 0<br />

<strong>and</strong> time t ;<br />

∏<br />

Njt<br />

the cumulative percentage growth of the price of nonfood, in region j, between<br />

time 0 <strong>and</strong> time t ;<br />

E<br />

Gjt<br />

the cumulative percentage increase in the measurement error in the CPI in region j,<br />

between time 0 <strong>and</strong> time t ;<br />

E<br />

Fjt<br />

the cumulative percentage increase in the measurement error in the price of food,<br />

in region j, between time 0 <strong>and</strong> time t ;<br />

E<br />

Njt<br />

the cumulative percentage increase in the measurement error in the price of<br />

nonfood, in region j, between time 0 <strong>and</strong> time t ;<br />

we can rewrite (1) as:<br />

w<br />

ijt<br />

[ ln( 1+ ∏Fjt<br />

) − ln( 1+ ∏<br />

Njt<br />

)] + β[ lnYijt<br />

− ln( + ∏Gjt<br />

)]<br />

[ ln PFj0 − ln PNj0] − β ln PGj0<br />

[ ln( 1+<br />

E ) − ln( 1+<br />

E )] − β ln( + E )<br />

= φ + γ<br />

1<br />

+ γ<br />

+ γ<br />

1<br />

x<br />

Fjt<br />

x<br />

X<br />

ijt<br />

µ<br />

ijt<br />

Njt<br />

+ ∑ θ + . (2)<br />

If we assume that the mismeasurement does not change across regions, we can rewrite<br />

(2) as:<br />

x<br />

Gjt

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!