FIRST DIFFERENCE REGRESSION

[Guy Salgado]

Hi,

I have run the regression as a fixed effects model xtreg log_Individual_Consumption log_Individual_Income c.log_Village_average_Consumption##c.EFL, fe

But would also like to run the same regression using the first difference approach. I know that FE and FD are essentially the same, but I have read that there are differences in their efficiency so I would like to compare both results. My data is organised two rows for each household observation as I have two years. For example:

Unique_id	Year	individual consumption	village average
1	2002	8	9
1	2005	12	15
2	2002	5	10
2	2005	9	12

I have searched through the internet but couldnt find any clear commands, any ideas on how I could do this?

many thanks

[Carlo Lazzaro]

Guy:
what follows can do the trick.

xtset unique_id year
xtreg individualconsumption villageaverage, fe
reshape wide individualconsumption villageaverage , i( unique_id ) j(year)
g diff_individualconsumption= individualconsumption2005- individualconsumption2002
g diff_villageaverage= villageaverage2005 - villageaverage2002
reg diff_individualconsumption diff_villageaverage, nocons

As an aside FE and FD estimators give back the same results when T=2.
When T>2, things get more cumbersome (and FD is side-tracked in favour of FE).

Two textbooks may be interesting about this topic, as both of them provide the reader with comprehensive theoretical coverage along with Stata codes:
- Allison PD. Fixed effect regression models. Thousand Oaks, CA: Sage, 2009.
- Hans-Jürgen Andreß, Katrin Golsch, and Alexander W. Schmidt. Applied panel data analysis for economic and social surveys. Berlin Heidelberg: Springer, 2013.

I hope this helps.

Kind regards,
Carlo

[George Hoffman]

would this work more simply?

xtset unique_id year
xtreg individualconsumption villageaverage, fe
xtreg d.individualcomsumption d.villageaverage

[Carlo Lazzaro]

George's solution is smarter than mine, but has two drawbacks:
-d.- will not work for Guy's dataset, in that there are gaps between 2002 and 2005. This drawback can be easily worked around via:

replace year=1 if year==2002

replace year=2 if year==2005 
  
       
  xtset unique_id year

- given the previous remark, the last line of George's code should be amended as follows:

reg d.individualconsumption d.villageaverage, nocons

or, in a more compact way:

reg D.( individualconsumption villageaverage), nocons

Kind regards,
Carlo

[Nick Cox]

xtset with delta(3) avoids later fixes.

[Carlo Lazzaro]

Thanks Nick for this (for me unknown) further clarification.

Kind regards,
Carlo

[Konstantin Stamm]

Do I have to put every variable into first difference or is it also possible to just change the DV?

[Nick Cox]

Konstantin: I guess that your question is too vague and general to allow good answers. Depends on what you want to do. Add more detail to get better answers.

[Lucrecia Lei]

George's solution is smarter than mine, but has two drawbacks:
-d.- will not work for Guy's dataset, in that there are gaps between 2002 and 2005. This drawback can be easily worked around via:

replace year=1 if year==2002

replace year=2 if year==2005


xtset unique_id year

- given the previous remark, the last line of George's code should be amended as follows:

reg d.individualconsumption d.villageaverage, nocons

or, in a more compact way:

reg D.( individualconsumption villageaverage), nocons

Kind regards,
Carlo

Hi! Find this super old post. Does anyone know why here need to add no constant option? Is it because here is perfect collinearity problem, if so where is it? Maybe caused by having only one observation, so the value of this observation and constant will have multicollinearity, if there are more observation it will be fine?

Thanks a lot!

[Carlo Lazzaro]

Lucrecia:
the -nocons- option was added because the OLS considered two observations only.
See the following toy-example that replicates the issue on a different dataset:

. sysuse auto.dta
(1978 automobile data)

. reg price mpg if _n<=2

      Source |       SS           df       MS      Number of obs   =         2
-------------+----------------------------------   F(1, 0)         =         .
       Model |      211250         1      211250   Prob > F        =         .
    Residual |           0         0           .   R-squared       =    1.0000
-------------+----------------------------------   Adj R-squared   =         .
       Total |      211250         1      211250   Root MSE        =         0

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |       -130          .        .       .            .           .
       _cons |       6959          .        .       .            .           .
------------------------------------------------------------------------------

. reg price mpg if _n<=2, nocons

      Source |       SS           df       MS      Number of obs   =         2
-------------+----------------------------------   F(1, 1)         =     24.13
       Model |  37788576.9         1  37788576.9   Prob > F        =    0.1279
    Residual |  1566225.13         1  1566225.13   R-squared       =    0.9602
-------------+----------------------------------   Adj R-squared   =    0.9204
       Total |    39354802         2    19677401   Root MSE        =    1251.5

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |   221.1009   45.01294     4.91   0.128    -350.8427    793.0445
------------------------------------------------------------------------------

.

[Andrew Musau]

Does anyone know why here need to add no constant option?

Also, the intercept is eliminated after differencing, so there is no need to have the software attempt to estimate one if there is none present.

[Lucrecia Lei]

To Professor Lazzaro and Musau: It is clear, thanks a lot!