First Difference Regression

[Ainun Nisa]

Hi,
I'm looking for the right command to run first difference regression and have found it. I found several way to run first difference regression:
1. reshape to wide and create new variable using

g new_var= old_var2-old_var1

. Then run the regression
2.

reg d.dependent_var d.independent, nocons

My data is two years panel data in 2007 and 2014. I have my independent variable in the dummy form and i tried the first way to run first difference regression. I use this command:

reshape wide variable, i(id) j(year)
g diff_dependent= dependent_variable2014 - dependent_variable2007
g diff_independent= independent_variable2014- dependent_variable2007

after changing the independent variable (in the form of dummy), I get results 0 and -1 (due to subtraction).
Am I taking the right steps? Can I run first difference regression with an independent variable in the form of dumny?

[Andrew Musau]

My data is two years panel data in 2007 and 2014. I have my independent variable in the dummy form and i tried the first way to run first difference regression. I use this command:

It does not matter that your regressor is a dummy as long as it varies for some panels between the two time periods. No need to take the differences yourself, just let Stata know that 1 time unit is equal to 7 years.

xtset id year, delta(7)
reg d.dependent_var d.independent, nocons

Note that in the case of T=2, FD regression is equivalent to fixed effects. To see this, write the differenced equation as

$$
\Delta y_{i} = \beta \Delta x_{i} + v_{i}
$$

With T=2,

$$
v_{i} = u_{i2} - u_{i1} = 2u_{i2} - (u_{i1} + u_{i2}) = 2(u_{i2} - \bar{u}_{i} )
$$

where

$$
\bar{u}_{i} = \frac{u_{i1} + u_{i2}}{2}
$$

xtset id year, delta(7)
reg d.dependent_var d.independent, nocons
xtreg dependent_var independent, fe

[Ainun Nisa]

Thank you for the answer. I tried it and it works.