Which panel data model to choose?

[cind du bois]

Dear community,
For my study I'm analysing defense expenditures for all NATO countries over a period of 23 years. The Hausmann-test clearly indicates I should use a fixed effects model. When testing for time effects, heterogeinty and serial correlation and adjusting my model, the results do not seem very robust. How do I know whether I have a good model and which one to choose?

Variable name % to personnel	Random effects model	Fixed effects model	Fixed effects model with time effects	Fixed effects model with time effects and robust standard errors	Linear dynamic panel model
Ideology variables
MoD left dummy	1.512441* (0.9328862)	1.680197* (0.9126713)	0.4122638 (0.9346421)	0.4122638 (1.993553)	1.950547** (0.8087553)
MoD right dummy	1.135277 (0.921039)	1.649345* (0.9059467)	0.7.71812 (0.9093065)	0.7071812 (1.473121)	1.4195 (0.8745139)
Control variables
GDP	-0.0008396 (0.0005681)	0.0005658 (0.0008544)	0.0012762 (0.0008648)	0.0012762 (0.0008444)	-0.0007733* (0.0004283)
Unemployment rate	0.6657644*** (0.1027658)	0.6452617*** (0.1009946)	0.3464043** (0.1121592)	0.3464043* (0.1788313)	0.6465263*** (0.0979289)
Armed forces in % of labour force	-1.252134 (0.9430639)	-2.397579** (0.9749935)	-3.044518** (1.135696)	-3.044518 (2.392644)	2.022514** (0.9780823)
WGIscore	0.0081857** (0.0035284)	0.0115299*** (0.0036109)	0.0063384* (0.0039227)	0.0063384 (0.0061555)	-0.0013217 (0.0034632)
Distance to Moscow	0.000933 (0.0012788)	/
Lag % personnel spending	/	/			0.4943256*** (0.0406795)
Constant	46.36936*** (3.527201)	47.28703 (2.323946)***		51.98476*** (6.100107)	20.50039*** (2.395178)
Number of observations	546	546	546	546	517
Number of groups	28	28	28	28	28
R² within	0.0909	0.1003	0.1866	0.1866
R² between	0.1197	0.0973	0.1644	0.1644
R² overall	0.1177	0.0076	0.0336	0.0336
F		9.51***	4.52***	285.2***
Wald chi	54.94***				422.66***

[Andrew Musau]

When testing for time effects, heterogeinty and serial correlation and adjusting my model, the results do not seem very robust.

By "not robust," I understand this to mean that the results change from one specification to the next. In \(N>T\) panels where you are dealing with non-experimental data (no random assignment of units to treatment), the most robust model is the two-way fixed effects model with cluster-robust standard errors (no pun intended!). You have 28 clusters which is on the low side, but you can get away with clustering. Therefore, you should not compare this specification to the rest, except for pedagogic reasons.

GDP

-0.0008396 (0.0005681)

0.0005658 (0.0008544)

0.0012762 (0.0008648)

0.0012762 (0.0008444)

WGIscore

0.0081857** (0.0035284)

0.0115299*** (0.0036109)

0.0063384* (0.0039227)

0.0063384 (0.0061555)

Also, you will want to rescale your GDP and WGIscore variables so that their coefficients are readable.

[cind du bois]

Dear Andrew,

Thank you very much for your answer. So, you mean that the 'best' model for my data is the fixed effects model with time effects and robust standard errors (column 4 in my table)?


Thanks also for the tip of rescaling!

C

[Andrew Musau]

Correct. Do not report the constant for the FE models. It is meaningless.