Hi,
I'm estimating a fertilizer demand model for Brazil, and to do so, I'm utilizing a panel dataset comprising 27 states over a span of 10 years.
Here's what I've gathered:
Now, the issues/considerations:
- I understand that for models that include the lagged dependent variable, opting for the Dynamic Panel approach is recommended. However, GMM performs poorly under a small N panel like mine. Also, with N being only 27, my options are limited when including instruments as they easily surpass the number of groups, resulting in highly inefficient estimates. The bias for using a lagged dependent variable in a FE model tends to zero as T grows, but I'm uncertain if my T is sufficiently large (which it probably isn't).
- I conducted a Wooldridge correlation test (using a simpler specification, as the -xtserial- command has issues in dealing with lag operators and factor variables) and confirmed that this model is serially correlated. In a previous thread addressing a similar issue, I saw Prof. Wooldridge mention that a FE model with Driscoll-Kraay errors might resolve this, as it accounts for serial correlation. However, as I intend to use this model for one-year-ahead forecasts the -xtscc- imposes a few challenges: i) the command is not compatible with various post-estimation commands, such as 'predict ln_fert_est, xbu', ii) it appears to disregard any 'if' statements I include, iii) creates colinearity problems in specifications that run perfectly under the xtreg command, and iv) is incompatible with iterations like '##'. These complications make the updating/forecasting process far more challenging than it should be and somewhat manual.
- The estimated coefficients derived from the FE model align with empirical observations and are quite comprehensible. Demand estimates are fairly accurate as well. Forecasts aren't as precise, but I suspect there might be one or two missing variables that are being captured by the year dummies.
Any recommendations? Should I stick to the FE model, or would you suggest an alternative approach?
I'm estimating a fertilizer demand model for Brazil, and to do so, I'm utilizing a panel dataset comprising 27 states over a span of 10 years.
Here's what I've gathered:
HTML Code:
. xtreg l(0/1).ln_fert ln_sb_barter i.big_farms#c.ln_sb_barter ln_wc_barter ln_area ln_credit i.big_farms#c.ln_credit i.year if year>=2013 & year<=2022, fe robust
note: 2021.year omitted because of collinearity
note: 2022.year omitted because of collinearity
Fixed-effects (within) regression Number of obs = 270
Group variable: id Number of groups = 27
R-sq: Obs per group:
within = 0.5992 min = 10
between = 0.6859 avg = 10.0
overall = 0.6849 max = 10
F(14,26) = 118.64
corr(u_i, Xb) = -0.4599 Prob > F = 0.0000
(Std. Err. adjusted for 27 clusters in id)
------------------------------------------------------------------------------------------
| Robust
ln_fert | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
ln_fert |
L1. | .3984597 .0548065 7.27 0.000 .2858034 .5111161
|
ln_sb_barter | -.5074911 .0833269 -6.09 0.000 -.6787721 -.3362101
|
big_farms#c.ln_sb_barter |
1 | .1151301 .0627154 1.84 0.078 -.0137831 .2440434
|
ln_wc_barter | -.2719184 .0614063 -4.43 0.000 -.3981409 -.1456959
ln_area | .2986246 .0778739 3.83 0.001 .1385526 .4586966
ln_credit | .075654 .0220205 3.44 0.002 .0303903 .1209177
|
big_farms#c.ln_credit |
1 | .1360088 .0536807 2.53 0.018 .0256666 .2463511
|
year |
2014 | -.1036127 .0257664 -4.02 0.000 -.1565763 -.0506491
2015 | -.190189 .0383895 -4.95 0.000 -.2690997 -.1112783
2016 | -.2760926 .0390131 -7.08 0.000 -.3562852 -.1959
2017 | -.2534009 .0482792 -5.25 0.000 -.3526401 -.1541616
2018 | -.1051378 .0281969 -3.73 0.001 -.1630972 -.0471783
2019 | -.1708704 .0382155 -4.47 0.000 -.2494235 -.0923172
2020 | -.2324278 .0281857 -8.25 0.000 -.2903643 -.1744913
2021 | 0 (omitted)
2022 | 0 (omitted)
|
_cons | 3.746749 1.025084 3.66 0.001 1.639659 5.853839
-------------------------+----------------------------------------------------------------
sigma_u | 1.3831548
sigma_e | .13176596
rho | .99100624 (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
- I understand that for models that include the lagged dependent variable, opting for the Dynamic Panel approach is recommended. However, GMM performs poorly under a small N panel like mine. Also, with N being only 27, my options are limited when including instruments as they easily surpass the number of groups, resulting in highly inefficient estimates. The bias for using a lagged dependent variable in a FE model tends to zero as T grows, but I'm uncertain if my T is sufficiently large (which it probably isn't).
- I conducted a Wooldridge correlation test (using a simpler specification, as the -xtserial- command has issues in dealing with lag operators and factor variables) and confirmed that this model is serially correlated. In a previous thread addressing a similar issue, I saw Prof. Wooldridge mention that a FE model with Driscoll-Kraay errors might resolve this, as it accounts for serial correlation. However, as I intend to use this model for one-year-ahead forecasts the -xtscc- imposes a few challenges: i) the command is not compatible with various post-estimation commands, such as 'predict ln_fert_est, xbu', ii) it appears to disregard any 'if' statements I include, iii) creates colinearity problems in specifications that run perfectly under the xtreg command, and iv) is incompatible with iterations like '##'. These complications make the updating/forecasting process far more challenging than it should be and somewhat manual.
- The estimated coefficients derived from the FE model align with empirical observations and are quite comprehensible. Demand estimates are fairly accurate as well. Forecasts aren't as precise, but I suspect there might be one or two missing variables that are being captured by the year dummies.
Any recommendations? Should I stick to the FE model, or would you suggest an alternative approach?
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