Hi,

I am trying to estimate the impact of climate variables on suicide rates. I am working with panel data of 10 years for each of 25 states.
As given below, srate denotes the annual suicide rate in a given state in a given year and yearlytemp refers to the annual temperature in a given state in a given year.

I am using this guide for reference: Panel Data Analysis Fixed and Random Effects using Stata (v. 4.2) https://www.princeton.edu/~otorres/Panel101.pdf

From what I have read so far on this forum as well as other sources, OLS results (although significant in terms of p-values) are invalid here because observations are almost never independent for panel data and that is a necessary requirement if one wants to use an OLS regression model.

I first tried a fixed effects model, followed by a random effects model.

I then do a Hausman test which gives me a Prob > chi2 value of 0.5043, i.e. greater than 0.05. This suggests that I follow a random effects model instead of a fixed effects model, and even I think that a random effects model is more suitable here since state fixed effects (like population, area etc) are not likely to affect the annual temperature of that state.

Now I also test for time-fixed effects as follows:
Code:
xtreg srate yearlytemp i.year, fe

Fixed-effects (within) regression               Number of obs      =       247
Group variable: state1                          Number of groups   =        25

R-sq:  within  = 0.1097                         Obs per group: min =         8
       between = 0.2039                                        avg =       9.9
       overall = 0.1075                                        max =        10

                                                F(10,212)          =      2.61
corr(u_i, Xb)  = -0.5011                        Prob > F           =    0.0052

------------------------------------------------------------------------------
       srate |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  yearlytemp |  -.5129098   .5935633    -0.86   0.388    -1.682952    .6571322
             |
        year |
       1991  |   .4169206    .633913     0.66   0.511    -.8326595    1.666501
       1992  |  -.0940757   .6223848    -0.15   0.880    -1.320931     1.13278
       1993  |   .2369076   .6330399     0.37   0.709    -1.010951    1.484767
       1994  |   .6744753   .6505162     1.04   0.301    -.6078333    1.956784
       1995  |   .8625228   .6680059     1.29   0.198    -.4542617    2.179307
       1996  |   1.483321   .6610198     2.24   0.026      .180308    2.786335
       1997  |   .7698841   .6239403     1.23   0.219    -.4600377    1.999806
       1998  |   1.803748   .7162068     2.52   0.013     .3919493    3.215547
       1999  |   2.583697    .726554     3.56   0.000     1.151501    4.015892
             |
       _cons |   21.12578   14.17553     1.49   0.138    -6.817256    49.06883
-------------+----------------------------------------------------------------
     sigma_u |  7.8994315
     sigma_e |  2.1997248
         rho |  .92803684   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(24, 212) =    84.20             Prob > F = 0.0000

. testparm i.year

 ( 1)  1991.year = 0
 ( 2)  1992.year = 0
 ( 3)  1993.year = 0
 ( 4)  1994.year = 0
 ( 5)  1995.year = 0
 ( 6)  1996.year = 0
 ( 7)  1997.year = 0
 ( 8)  1998.year = 0
 ( 9)  1999.year = 0

       F(  9,   212) =    2.45
            Prob > F =    0.0114
As you can see, the Prob > F value of the test shows that time-fixed effects are present, however including them in the regression model gives insignificant coefficients for each year.

So my questions are:
1. If time-fixed effects are present, why are they not significant in my (random effects) regression model?

2. The R-squared values without and with year dummies are as given below:
Code:
xtreg srate yearlytemp, re
R-sq:  within  = 0.0173                         Obs per group: min =         8
       between = 0.2141                                        avg =       9.9
       overall = 0.1959                                        max =        10

xtreg srate yearlytemp i.year, re
R-sq:  within  = 0.0977                         Obs per group: min =         8
       between = 0.2219                                        avg =       9.9
       overall = 0.1887                                        max =        10
So that means more variation in suicide rates is explained when year dummies are included - and they should be included as suggested by the test for time-fixed effects - but at the same time, they yield insignificant coefficients in the regression model.
How do I make sense of this?

3. What do we mean when we say that observations are not independent in panel data? I did a serial correlation test and obtained no serial correlation results. Does that not mean that one observation is not dependent (correlated) with the previous one?

Regards,
Sonal
(Stata/SE 13.0)