Hello all,
I am looking at the relationship between terms of trade and GDP growth:
- where delta y_{it} is the log difference of real GDP, and delta tot_{it} is the log difference of the terms of trade index.
The sample contains N=120 developing countries that are not major oil exporters, with T=45 (1974-2019).
Simply running OLS with fixed effects would be inconsistent as the lagged dep variable would likely be correlated with the error term by construction due to its differenced nature, as I understand it. Thus, I would like to use an Anderson-Hsiao IV instrument - either the second-lagged log difference or the second-lagged log level of GDP.
My coefficient of interest is the effect of the terms of trade change, but I thought it would be appropriate to include the lagged dependent variable due to the correlation between GDP growth across consecutive periods.
Simply running OLS with fixed effects would be inconsistent as the lagged dep variable would likely be correlated with the error term by construction due to its differenced nature, as I understand it. Thus, I would like to use an Anderson-Hsiao IV instrument - either the second-lagged log difference or the second-lagged log level of GDP. I do not run the equation in log GDP and TOT levels due to the stationarity/persistence of GDP.
These are my results using the second-lagged log difference as an instrument (I remove the country and year dummies for ease of reading).
I split the time periods into 1974-2019, 1974-2004, and 2004-2019 in columns (1), (2) and (3) respectively.
The lack of significance on the post-2004 lagged dep variable coefficient worries me - does that indicate a weak instrument if we use a lag as the IV?
However, the weak instrument test statistic is high enough to reject the null hypothesis that the instrument is weak. Is the instrument fine to use, in that case, even if the coefficient on the lagged dep variable is insignificant?
Alternatively, I could use the log level
However, here, the coefficient on the lagged dep variable is higher than 1 - this does not make sense, does it? It would imply a 1% higher log real GDP growth at t-1 would be associated with a 1.3% higher log real GDP growth at t.
For reference, these are my results if I run OLS.
What instrument do you recommend using? And can anyone tell why the coefficient using the lagged level instrument is so absurdly high?
Alternatively, if I used GMM, could I run it on the already-differenced estimators? This is because due to the nonstationarity of log GDP, using log GDP in the regression in difference GMM rather than log difference, would give coefficients of the lagged dep variable that are very close to 1 and an R2 of something like 0.9993.
Thank you!
I am looking at the relationship between terms of trade and GDP growth:
- where delta y_{it} is the log difference of real GDP, and delta tot_{it} is the log difference of the terms of trade index.
The sample contains N=120 developing countries that are not major oil exporters, with T=45 (1974-2019).
Simply running OLS with fixed effects would be inconsistent as the lagged dep variable would likely be correlated with the error term by construction due to its differenced nature, as I understand it. Thus, I would like to use an Anderson-Hsiao IV instrument - either the second-lagged log difference or the second-lagged log level of GDP.
My coefficient of interest is the effect of the terms of trade change, but I thought it would be appropriate to include the lagged dependent variable due to the correlation between GDP growth across consecutive periods.
Simply running OLS with fixed effects would be inconsistent as the lagged dep variable would likely be correlated with the error term by construction due to its differenced nature, as I understand it. Thus, I would like to use an Anderson-Hsiao IV instrument - either the second-lagged log difference or the second-lagged log level of GDP. I do not run the equation in log GDP and TOT levels due to the stationarity/persistence of GDP.
These are my results using the second-lagged log difference as an instrument (I remove the country and year dummies for ease of reading).
I split the time periods into 1974-2019, 1974-2004, and 2004-2019 in columns (1), (2) and (3) respectively.
Code:
ivreg2 dcgdp dtot i.country i.year (L.dcgdp = L2.dcgdp) if oil==0, r
ivreg2 dcgdp dtot i.country i.year (L.dcgdp = L2.dcgdp) if(oil==0 & year<2004), r
ivreg2 dcgdp dtot i.country i.year (L.dcgdp = L2.dcgdp) if(oil==0 & year>2004), r
------------------------------------------------------------
(1) (2) (3)
dcgdp dcgdp dcgdp
------------------------------------------------------------
L.dcgdp 0.425*** 0.312* 0.185
(4.95) (2.15) (1.16)
dtot 0.107** 0.117* 0.112
(2.62) (2.40) (1.58)
However, the weak instrument test statistic is high enough to reject the null hypothesis that the instrument is weak. Is the instrument fine to use, in that case, even if the coefficient on the lagged dep variable is insignificant?
Code:
Weak identification test (Cragg-Donald Wald F statistic): 87.626
(Kleibergen-Paap rk Wald F statistic): 19.182
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
Alternatively, I could use the log level
Code:
ivreg2 dcgdp dtot i.country i.year (L.dcgdp = L2.lncgdp) if oil==0, r
ivreg2 dcgdp dtot i.country i.year (L.dcgdp = L2.lncgdp) if(oil==0 & year<2004), r
ivreg2 dcgdp dtot i.country i.year (L.dcgdp = L2.lncgdp) if(oil==0 & year>2004), r
----------------------------------------------------------
(1) (2) (3)
dcgdp dcgdp dcgdp
------------------------------------------------------------
L.dcgdp 1.259*** 1.093*** 1.491***
(7.23) (7.56) (4.71)
dtot 0.136** 0.136* 0.162
(2.72) (2.29) (1.95)
However, here, the coefficient on the lagged dep variable is higher than 1 - this does not make sense, does it? It would imply a 1% higher log real GDP growth at t-1 would be associated with a 1.3% higher log real GDP growth at t.
For reference, these are my results if I run OLS.
Code:
reg dcgdp L.dcgdp dtot i.country i.year if oil==0, r
reg dcgdp L.dcgdp dtot i.country i.year if(oil==0 & year<2004), r
reg dcgdp L.dcgdp dtot i.country i.year if(oil==0 & year>2004), r
------------------------------------------------------------
(1) (2) (3)
dcgdp dcgdp dcgdp
------------------------------------------------------------
L.dcgdp 0.259*** 0.207*** 0.229***
(6.43) (4.17) (4.13)
dtot 0.132** 0.166*** 0.114
(3.24) (3.64) (1.55)
What instrument do you recommend using? And can anyone tell why the coefficient using the lagged level instrument is so absurdly high?
Alternatively, if I used GMM, could I run it on the already-differenced estimators? This is because due to the nonstationarity of log GDP, using log GDP in the regression in difference GMM rather than log difference, would give coefficients of the lagged dep variable that are very close to 1 and an R2 of something like 0.9993.
Thank you!
