Dear Stata Members
I have a cross country dataset that has a country-wise measure of policy uncertainty index for each year. There are 22 countries and for each year, each country will have a value which I call the "index_value". Now the issue is that, the U.S due to its large size and other influence on trade/monetary policies, it can have a cascading impact on other countries. For instance, when the U.S increases say its policy rates, not only does its "index_value"changes but other countries index_value also react to it. I would like to disentage the impact of the effect of index_value of U.S from other countries. One way in the literature is to "orthogonalize the index_value of each country in the sample with respect to that of the U.S. by regressing the "index_value" of each country on the "index_value" of the U.S. Having been purged of any potential confounding effect of U.S. index_value, the residuals of this regression (index_value_resid), by construction, represent a cleaner measure of policy uncertainty in each country".
My question is that what is the logic of orthogonality in the above circumstance? I tried the below code and got the following output
.
Is the above model a correct one? Should I go for reg or xtreg (I thought as it is a panel, I used xtreg and controlled for country level fixed effects (8), and clusters standard errors though clusters are 8 in this, I have 22 in real ). I haven't put year dummies as one dummy is constantly being omitted because of multicollinearity (could be case of US index).
Am I doing the correct thing? How do we know our measure Index_res, is orthogonal to us_index_value?
Any thoughts/remarks are highly welcome as I am experimenting with this
I have a cross country dataset that has a country-wise measure of policy uncertainty index for each year. There are 22 countries and for each year, each country will have a value which I call the "index_value". Now the issue is that, the U.S due to its large size and other influence on trade/monetary policies, it can have a cascading impact on other countries. For instance, when the U.S increases say its policy rates, not only does its "index_value"changes but other countries index_value also react to it. I would like to disentage the impact of the effect of index_value of U.S from other countries. One way in the literature is to "orthogonalize the index_value of each country in the sample with respect to that of the U.S. by regressing the "index_value" of each country on the "index_value" of the U.S. Having been purged of any potential confounding effect of U.S. index_value, the residuals of this regression (index_value_resid), by construction, represent a cleaner measure of policy uncertainty in each country".
My question is that what is the logic of orthogonality in the above circumstance? I tried the below code and got the following output
Code:
* Example generated by -dataex-. For more info, type help dataex clear input int year str24 countryofexchange byte country_code float(index_value us_index_value) 2000 "Australia" 1 4.28037 4.5701 2001 "Australia" 1 4.7955 5.0251 2002 "Australia" 1 4.43311 4.85707 2003 "Australia" 1 4.67781 4.85087 2000 "Brazil" 2 4.51194 4.5701 2001 "Brazil" 2 4.66751 5.0251 2002 "Brazil" 2 4.81762 4.85707 2003 "Brazil" 2 4.68208 4.85087 2000 "Canada" 3 3.97718 4.5701 2001 "Canada" 3 4.78865 5.0251 2002 "Canada" 3 4.66665 4.85707 2003 "Canada" 3 4.70914 4.85087 2000 "Chile" 4 4.78905 4.5701 2001 "Chile" 4 5.01483 5.0251 2002 "Chile" 4 4.94795 4.85707 2003 "Chile" 4 4.71154 4.85087 2000 "China" 5 3.5714 4.5701 2001 "China" 5 3.77717 5.0251 2002 "China" 5 3.97991 4.85707 2003 "China" 5 4.09675 4.85087 2000 "Colombia" 6 4.8058 4.5701 2001 "Colombia" 6 4.76195 5.0251 2002 "Colombia" 6 4.73215 4.85707 2003 "Colombia" 6 4.57414 4.85087 2000 "United Kingdom" 21 3.86795 4.5701 2001 "United Kingdom" 21 4.51501 5.0251 2002 "United Kingdom" 21 4.53173 4.85707 2003 "United Kingdom" 21 4.90331 4.85087 2000 "United States of America" 22 4.5701 4.5701 2001 "United States of America" 22 5.0251 5.0251 2002 "United States of America" 22 4.85707 4.85707 2003 "United States of America" 22 4.85087 4.85087 end
Code:
xtset country_code year
Panel variable: country_code (strongly balanced)
Time variable: year, 2000 to 2003
Delta: 1 unit
. xtreg us_index_value index_value , fe vce(r)
Fixed-effects (within) regression Number of obs = 32
Group variable: country_code Number of groups = 8
R-squared: Obs per group:
Within = 0.4204 min = 4
Between = . avg = 4.0
Overall = 0.1483 max = 4
F(1,7) = 31.29
corr(u_i, Xb) = -0.8045 Prob > F = 0.0008
(Std. err. adjusted for 8 clusters in country_code)
------------------------------------------------------------------------------
| Robust
us_index_v~e | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
index_value | .4820206 .0861737 5.59 0.001 .2782522 .6857889
_cons | 2.628203 .3928748 6.69 0.000 1.699202 3.557204
-------------+----------------------------------------------------------------
sigma_u | .15334544
sigma_e | .1466756
rho | .52222026 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. predict Index_res, residuals
. univar Index_res
-------------- Quantiles --------------
Variable n Mean S.D. Min .25 Mdn .75 Max
-------------------------------------------------------------------------------
Index_res 32 0.00 0.19 -0.37 -0.11 -0.02 0.09 0.58
-------------------------------------------------------------------------------
Is the above model a correct one? Should I go for reg or xtreg (I thought as it is a panel, I used xtreg and controlled for country level fixed effects (8), and clusters standard errors though clusters are 8 in this, I have 22 in real ). I haven't put year dummies as one dummy is constantly being omitted because of multicollinearity (could be case of US index).
Am I doing the correct thing? How do we know our measure Index_res, is orthogonal to us_index_value?
Any thoughts/remarks are highly welcome as I am experimenting with this
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