Table 2 Multivariate analysis using cross-validation lasso

Models predicting TFC
Lasso path for model A			Estimated coefficients
λ	(A)dded, (R)emoved	CV MPSE		Model A	Model B
0.711	GDP(A)	0.703	GDP	0.494	0.572
0.371	BL_cap(A)	0.319	DENS	−0.017	−0.039
0.161	HDD(A), RWD_tot(A)	0.179	UPOP
0.121	RD_urb-rur(A)	0.166	HDD	0.021	0.051
0.111	PGAS(A)	0.161	PGAS	−0.352	−0.288
0.101	RD_urb(A)	0.155	BL_cap	0.184
0.076	RWD_urb(A)	0.135	BL_mono	−0.017
0.063	RWD_tot(R)	0.125	RD_urb	−0.392
0.048	DENS(A)	0.115	RL_urb-rur	−0.024
0.030	BL_mono(R)	0.108	RD_urb-rur	−0.074
0.027	RL_urb-rur(A)	0.107	RWD_urb	0.045
0.017*	(Unchanged)	0.105	Intercept	3.457	2.542
0.016	RWD_urb-rur(A)	0.105
0.013	BL_comp(A)	0.105	Measures of in-and-out-of-sample fit
0.011	(Unchanged)	0.106	BIC	84.17	100.32
			r²	0.900	0.851
			oSr²	0.865	0.833

Models predicting CO₂
λ	(A)dded, (R)emoved	CV MPSE	variable	Model A	Model B
0.867	GDP(A)	1.278	GDP	0.449	0.582
0.544	BL_cap(A)	0.801	DENS	−0.061	0.023
0.496	UPOP(A)	0.738	UPOP	0.466	0.558
0.452	RWD_tot(A)	0.683	HDD	0.055	0.109
0.312	HDD(A)	0.530	PGAS	−0.680	−0.688
0.215	PGAS(A)	0.446	BL_fract	0.201
0.135	RD_urb-rur(A)	0.338	BL_cap	0.176
0.123	BL_fract(A)	0.323	BL_comp	0.489
0.085	RWL_urb-rur(A)	0.289	RD_urb	−0.201
0.070	BL_fract(R)	0.280	RWD_urb	0.130
0.048	BL_comp(A)	0.269	RWD_rur	0.017
0.044	RD_urb(A)	0.266	Intercept	−2.723	−4.294
0.037	RWD_urb(A)	0.262
0.025	BL_fract (A)	0.256	Measures of in-and-out-of-sample fit
0.023	DENS(A)	0.255	BIC	178.44	190.82
0.021	RWL_urb-rur(R)	0.254	r²	0.873	0.812
0.016	RWD_rur(A)	0.251	oSr²	0.817	0.785
0.016	RD_urb-rur(R)	0.251
0.014	RWD_tot(R)	0.250
0.012*	(Unchanged)	0.249
0.006	(Unchanged)	0.250

The leftmost three columns show the lasso path for predicting cross-country patterns of TFC (above) and CO₂ (below) using all variables. In the first column, the λ value marked with an asterisk denotes the optimal model (Model A) emerging from the cross-validation. CV MSPE is the cross-validated mean-square prediction error evaluated with tenfolds (for detail, see Methods section). For Model B, only conventional factors are selected. The same folds are used for the assessment of all models. BIC is the Bayesian Information Criterion for model selection. r² is the goodness of fit within the sample of countries, and oSr² refers to the (cross-validated) out-of-sample goodness of fit.

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