In this exercise, you are asked to reproduce some of the empirical results from Feenstra (1989).
To complete the exercise, the files “cars.csv, trucks.csv, cycon.csv, cyship.csv, cypool.csv” should be stored in the directory: first-edition/Chapter-7. Each of these can be used in STATA programs “cars.do, trucks.do, cycon.do, cyship.do, cypool.do” to create a dataset with the variables described in “Documentation_Chp7.doc.”
Data Description for Feenstra (1989)
There are five data sets in excel format: cars.csv, trucks.csv, cycon.csv, cypool.csv, cyship.csv. All of the variables in the data sets are fitted values from instrumental variables regression.
Variable
Description
iprice
Import price
usprice
US price
gprice
German price
tariff
Tariff rate
income
Expenditure on product class
lag0
First order polynomial lag on betas
lag1
Second order polynomial lag on betas
lag2
Third order polynomial lag on betas
y
Import price transformed, y = iprice – income
x1
US price transformed, usprice – income
x2
German price transformed, gprice – income
z0
First order polynomial lag transformed
z1
Second order polynomial lag transformed
z2
Third order polynomial lag transformed
Note: all the transformations are done to reflect their restrictions. So some are restricted to homogeneity, where others are restricted to symmetry and homogeneity.
Explanation of lag0, lag1 and lag2
With a second-order polynomial, \(\alpha_i = a + bi + ci^2\) it follows that
\[\begin{align}
\sum_{i=0}^4 \log(c_t^* s_{t-i}) \alpha_i &= \sum_{i=0}^4 \log(c_t^* s_{t-i}) (a + bi + ci^2) \\
&= a \sum_{i=0}^4 \log(c_t^* s_{t-i}) + b \sum_{i=0}^4 \log(c_t^* s_{t-i}) i + c \sum_{i=0}^4 \log(c_t^* s_{t-i}) i^2.
\end{align}\]
Letting \(\log(c_t^* s_{t-i}) = x_i\), we can define the three lags appeating in this formula as
When estimating the equation using lag0, lag1, and lag2, the coefficient estimates that you obtain are a, b, and c, respectively. Using this, you can recover the coefficient estimate and standard error for each individual exchange rate term reported in the Table 7.2. You can always do this by hand, but STATA does offer a command to calculate the linear combination of the estimated coefficients. The syntax for this is,
lincom lag0 + lag1 + lag2
This will calculate the coefficient estimates for the \(\log(c_t^* s_{t-1})\). This is much in a same way as the syntax for test. Lag0 in above command does not refer to the data, but the coefficient estimate associated with lag0.
Exercise 1
Replicate Table 7.2, i.e., run the specifications of (7.34) without imposing the tests of symmetry or homogeneity. Duplicate all of the coefficients that are reported in this table, except the Durbin-Watson statistics.
Feenstra’s code
Cars
clearcapturelogcloselogusing Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-7\cars.log, replaceinsheetusing Z:\home\pacha\github\advanced-international-trade\first-edition\Chapter-7\cars.csv* dropif time<=12regress iprice time timesq lag0 lag1 lag2 usprice gprice income*i=0lincom lag0*i=1lincom lag0+lag1+lag2*i=2lincom lag0+2*lag1+4*lag2*i=3lincom lag0+3*lag1+9*lag2*i=4lincom lag0+4*lag1+16*lag2*summation of betai'slincom 5*lag0+10*lag1+30*lag2*Impose the homogeneity constraintregressy time timesq z0 z1 z2 x1 x2*summation of betai'slincom 5*z0+10*z1+30*z2logcloseexit
Then replicate Feenstra’s Table 2 by imposing the tests of homogeneity and symmetry, shown in (7.35a) and (7.35b). Instead of conducting the Wald test, as done in Feenstra (1989), instead conduct the analogous F-test. Do you accept or reject the hypotheses of symmetry and homogeneity?