------------------------------------------------------------------------------- name: log: /Users/carlos/GitHub/starter-academic-v501/content/post/stata_pane > l_lasso_cluster/analysis.log log type: text opened on: 5 Apr 2026, 14:59:00 . . display _newline "=============================================" ============================================= . display " TUTORIAL: Latent Group Structures in Panel Data" TUTORIAL: Latent Group Structures in Panel Data . display " Method: Classifier-LASSO (Su, Shi, Phillips 2016)" Method: Classifier-LASSO (Su, Shi, Phillips 2016) . display " Date: $S_DATE $S_TIME" Date: 5 Apr 2026 14:59:00 . display "=============================================" _newline ============================================= . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 1: Load and Explore Savings Data . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 1: Load and Explore Savings Data" SECTION 1: Load and Explore Savings Data . display "=============================================" _newline ============================================= . . use "refMaterials/saving.dta", clear . . // Declare panel structure . xtset code year Panel variable: code (strongly balanced) Time variable: year, 1 to 15 Delta: 1 unit . . // Panel description . xtdescribe code: 1, 2, ..., 56 n = 56 year: 1, 2, ..., 15 T = 15 Delta(year) = 1 unit Span(year) = 15 periods (code*year uniquely identifies each observation) Distribution of T_i: min 5% 25% 50% 75% 95% max 15 15 15 15 15 15 15 Freq. Percent Cum. | Pattern ---------------------------+----------------- 56 100.00 100.00 | 111111111111111 ---------------------------+----------------- 56 100.00 | XXXXXXXXXXXXXXX . . // Summary statistics . display _newline "--- Summary Statistics ---" --- Summary Statistics --- . summarize savings lagsavings cpi interest gdp Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- savings | 840 -2.87e-08 1.000596 -2.495871 2.893858 lagsavings | 840 5.81e-08 1.000596 -2.832278 2.91508 cpi | 840 3.56e-09 1.000596 -2.773791 3.548945 interest | 840 -7.17e-09 1.000596 -3.600348 3.277582 gdp | 840 1.06e-08 1.000596 -3.554419 2.461317 . . display _newline "--- Detailed Statistics ---" --- Detailed Statistics --- . tabstat savings lagsavings cpi interest gdp, /// > statistics(mean sd min p25 p50 p75 max) columns(statistics) Variable | Mean SD Min p25 p50 p75 -------------+------------------------------------------------------------ savings | -2.87e-08 1.000596 -2.495871 -.7514935 -.0297477 .7577041 lagsavings | 5.81e-08 1.000596 -2.832278 -.7317027 -.032742 .78188 cpi | 3.56e-09 1.000596 -2.773791 -.6642521 -.207814 .4838007 interest | -7.17e-09 1.000596 -3.600348 -.6494734 .0063667 .652302 gdp | 1.06e-08 1.000596 -3.554419 -.5641946 .1935035 .683866 -------------------------------------------------------------------------- Variable | Max -------------+---------- savings | 2.893858 lagsavings | 2.91508 cpi | 3.548945 interest | 3.277582 gdp | 2.461317 ------------------------ . . // Count unique countries . codebook code, compact Variable Obs Unique Mean Min Max Label ------------------------------------------------------------------------------- code 840 56 28.5 1 56 code ------------------------------------------------------------------------------- . quietly levelsof code . local n_countries : word count `r(levels)' . display "Number of countries: `n_countries'" Number of countries: 56 . display "Time periods: " _N / `n_countries' Time periods: 15 . . // ── Figure 1: Savings Heterogeneity Across Countries ── . . // Overlay all countries on one panel . xtline savings, overlay /// > title("Savings-to-GDP Ratio Across 56 Countries", size(medium)) /// > subtitle("Each line represents one country", size(small)) /// > ytitle("Savings / GDP") xtitle("Year") /// > note("Source: Su, Shi, Phillips (2016). 56 countries, 1995-2010.") /// > legend(off) /// > name(fig1_savings, replace) . graph export "stata_panel_lasso_cluster_fig1_savings_scatter.png", /// > name(fig1_savings) replace width(2400) file stata_panel_lasso_cluster_fig1_savings_scatter.png written in PNG format . . display _newline "Figure 1 saved: stata_panel_lasso_cluster_fig1_savings_scat > ter.png" Figure 1 saved: stata_panel_lasso_cluster_fig1_savings_scatter.png . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 2: Baseline Pooled and FE Regressions . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 2: Baseline Pooled and FE Regressions" SECTION 2: Baseline Pooled and FE Regressions . display "=============================================" _newline ============================================= . . display "These models assume ALL countries share the SAME slope coefficients. > " These models assume ALL countries share the SAME slope coefficients. . display "C-LASSO will later reveal whether this assumption holds." _newline C-LASSO will later reveal whether this assumption holds. . . // 2.1 Pooled OLS . display "--- 2.1 Pooled OLS ---" --- 2.1 Pooled OLS --- . regress savings lagsavings cpi interest gdp Source | SS df MS Number of obs = 840 -------------+---------------------------------- F(4, 835) = 162.95 Model | 368.242785 4 92.0606961 Prob > F = 0.0000 Residual | 471.757214 835 .564978699 R-squared = 0.4384 -------------+---------------------------------- Adj R-squared = 0.4357 Total | 839.999999 839 1.00119189 Root MSE = .75165 ------------------------------------------------------------------------------ savings | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6050842 .0263842 22.93 0.000 .5532971 .6568713 cpi | .0301213 .0267785 1.12 0.261 -.0224397 .0826823 interest | .0059256 .0269269 0.22 0.826 -.0469267 .0587779 gdp | .1882033 .0264346 7.12 0.000 .1363172 .2400894 _cons | -6.59e-08 .0259344 -0.00 1.000 -.0509044 .0509042 ------------------------------------------------------------------------------ . estimates store pooled_ols . . // 2.2 Standard Fixed Effects . display _newline "--- 2.2 Standard Fixed Effects ---" --- 2.2 Standard Fixed Effects --- . xtreg savings lagsavings cpi interest gdp, fe Fixed-effects (within) regression Number of obs = 840 Group variable: code Number of groups = 56 R-squared: Obs per group: Within = 0.4384 min = 15 Between = 0.1272 avg = 15.0 Overall = 0.4384 max = 15 F(4, 780) = 152.21 corr(u_i, Xb) = -0.0000 Prob > F = 0.0000 ------------------------------------------------------------------------------ savings | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6050842 .0272985 22.17 0.000 .5514968 .6586715 cpi | .0301213 .0277065 1.09 0.277 -.0242668 .0845095 interest | .0059256 .02786 0.21 0.832 -.0487639 .0606151 gdp | .1882033 .0273507 6.88 0.000 .1345136 .241893 _cons | -6.59e-08 .0268332 -0.00 1.000 -.0526739 .0526738 -------------+---------------------------------------------------------------- sigma_u | 2.764e-07 sigma_e | .77769978 rho | 1.263e-13 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(55, 780) = 0.00 Prob > F = 1.0000 . estimates store fe_standard . . // 2.3 Robust Fixed Effects (reghdfe) . display _newline "--- 2.3 Robust Fixed Effects (reghdfe) ---" --- 2.3 Robust Fixed Effects (reghdfe) --- . reghdfe savings lagsavings cpi interest gdp, absorb(code) vce(robust) (MWFE estimator converged in 1 iterations) HDFE Linear regression Number of obs = 840 Absorbing 1 HDFE group F( 4, 780) = 144.34 Prob > F = 0.0000 R-squared = 0.4384 Adj R-squared = 0.3959 Within R-sq. = 0.4384 Root MSE = 0.7777 ------------------------------------------------------------------------------ | Robust savings | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6050842 .0288472 20.98 0.000 .5484568 .6617116 cpi | .0301213 .0320726 0.94 0.348 -.0328375 .0930801 interest | .0059256 .0302145 0.20 0.845 -.0533858 .065237 gdp | .1882033 .033945 5.54 0.000 .121569 .2548376 _cons | -6.59e-08 .0268332 -0.00 1.000 -.0526739 .0526738 ------------------------------------------------------------------------------ Absorbed degrees of freedom: -----------------------------------------------------+ Absorbed FE | Categories - Redundant = Num. Coefs | -------------+---------------------------------------| code | 56 0 56 | -----------------------------------------------------+ . estimates store fe_robust . . // Store key coefficients for later comparison . estimates restore pooled_ols (results pooled_ols are active now) . local b_lag_pooled = _b[lagsavings] . local b_cpi_pooled = _b[cpi] . local b_int_pooled = _b[interest] . local b_gdp_pooled = _b[gdp] . . estimates restore fe_robust (results fe_robust are active now) . local b_lag_fe = _b[lagsavings] . local b_cpi_fe = _b[cpi] . local b_int_fe = _b[interest] . local b_gdp_fe = _b[gdp] . . display _newline "--- Coefficient Comparison: Pooled OLS vs FE ---" --- Coefficient Comparison: Pooled OLS vs FE --- . display " Pooled OLS FE (robust)" Pooled OLS FE (robust) . display "lagsavings " %10.4f `b_lag_pooled' " " %10.4f `b_lag_fe' lagsavings 0.6051 0.6051 . display "cpi " %10.4f `b_cpi_pooled' " " %10.4f `b_cpi_fe' cpi 0.0301 0.0301 . display "interest " %10.4f `b_int_pooled' " " %10.4f `b_int_fe' interest 0.0059 0.0059 . display "gdp " %10.4f `b_gdp_pooled' " " %10.4f `b_gdp_fe' gdp 0.1882 0.1882 . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 3: Classifier-LASSO — Savings, Static Model . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 3: C-LASSO — Savings, Static Model" SECTION 3: C-LASSO — Savings, Static Model . display "=============================================" _newline ============================================= . . display "We start with a STATIC specification (no lagged dependent variable)" We start with a STATIC specification (no lagged dependent variable) . display "to demonstrate the simplest usage of classifylasso." _newline to demonstrate the simplest usage of classifylasso. . display "The command searches over K = 1 to 5 groups and uses the information > " The command searches over K = 1 to 5 groups and uses the information . display "criterion to select the optimal number of groups." _newline criterion to select the optimal number of groups. . display "NOTE: This may take several minutes to compute..." _newline NOTE: This may take several minutes to compute... . . // Static model: savings = f(cpi, interest, gdp) + country FE . classifylasso savings cpi interest gdp, grouplist(1/5) tolerance(1e-4) Estimation 1: Group Number = 1; Iteration: √ Information Criterion = .053747385 Estimation 2: Group Number = 2; Iteration: 1···5····10····15····20√ Information Criterion = -.02755819 Estimation 3: Group Number = 3; Iteration: 1···5····10····15····20√ Information Criterion = .058822014 Estimation 4: Group Number = 4; Iteration: 1···5····10····15····20√ Information Criterion = .131361535 Estimation 5: Group Number = 5; Iteration: 1···5····10····15····20√ Information Criterion = .212972443 * Selected Group Number: 2 The algorithm takes 4min50s. Classifier-Lasso linear model Number of obs = 840 Postestimation with 2 groups Number of units = 56 Fixed effect estimation with Group 1 R-squared = 0.2019 Absorbing: code Adj R-squared = 0.1412 No. of obs = 510 Within R-sq. = 0.2019 No. of units = 34 Root MSE = 0.9276 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- cpi | -.1813043 .0422854 -4.29 0.000 -.2641822 -.0984264 interest | -.1966381 .0424214 -4.64 0.000 -.2797825 -.1134937 gdp | .3345556 .0419159 7.98 0.000 .2524019 .4167093 _cons | -4.92e-08 .0410758 -0.00 1.000 -.0805072 .0805071 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.2369 Absorbing: code Adj R-squared = 0.1769 No. of obs = 330 Within R-sq. = 0.2369 No. of units = 22 Root MSE = 0.9086 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- cpi | .4780886 .0525171 9.10 0.000 .3751569 .5810203 interest | .2631097 .052491 5.01 0.000 .1602292 .3659903 gdp | .1116502 .0500687 2.23 0.026 .0135174 .2097831 _cons | -4.92e-09 .0500195 -0.00 1.000 -.0980363 .0980363 ------------------------------------------------------------------------------ . . // Store estimates . estimates store classo_static . . // Display selected group count . display _newline "--- Static Model: Group Selection ---" --- Static Model: Group Selection --- . display "Selected number of groups: " e(group) Selected number of groups: 2 . . // Postestimation: select the IC-optimal result . classoselect, postselection . . // Generate group membership predictions . predict gid_static, gid . predict yhat_static, xb . . // Tabulate group membership . display _newline "--- Group Membership (Static Model) ---" --- Group Membership (Static Model) --- . tabulate gid_static Group | Classificat | ion by | Post_Lasso | Freq. Percent Cum. ------------+----------------------------------- G1 | 510 60.71 60.71 G2 | 330 39.29 100.00 ------------+----------------------------------- Total | 840 100.00 . . // ── Figure 2: Group Selection (Static Model) ── . classogroup, /// > title("Group Selection: Savings (Static Model)", size(medium)) /// > note("Information criterion selects optimal K from {1,...,5}") /// > name(fig2_selection, replace) . graph export "stata_panel_lasso_cluster_fig2_group_selection_static.png", /// > name(fig2_selection) replace width(2400) file stata_panel_lasso_cluster_fig2_group_selection_static.png written in PNG f > ormat . . display _newline "Figure 2 saved: stata_panel_lasso_cluster_fig2_group_select > ion_static.png" Figure 2 saved: stata_panel_lasso_cluster_fig2_group_selection_static.png . . // Display coefficient estimates . display _newline "--- Coefficient Estimates by Group (Static Model) ---" --- Coefficient Estimates by Group (Static Model) --- . estimates replay ------------------------------------------------------------------------------- active results ------------------------------------------------------------------------------- Classifier-Lasso linear model Number of obs = 840 Postestimation with 2 groups Number of units = 56 Fixed effect estimation with Group 1 R-squared = 0.2019 Absorbing: code Adj R-squared = 0.1412 No. of obs = 510 Within R-sq. = 0.2019 No. of units = 34 Root MSE = 0.9276 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- cpi | -.1813043 .0422854 -4.29 0.000 -.2641822 -.0984264 interest | -.1966381 .0424214 -4.64 0.000 -.2797825 -.1134937 gdp | .3345556 .0419159 7.98 0.000 .2524019 .4167093 _cons | -4.92e-08 .0410758 -0.00 1.000 -.0805072 .0805071 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.2369 Absorbing: code Adj R-squared = 0.1769 No. of obs = 330 Within R-sq. = 0.2369 No. of units = 22 Root MSE = 0.9086 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- cpi | .4780886 .0525171 9.10 0.000 .3751569 .5810203 interest | .2631097 .052491 5.01 0.000 .1602292 .3659903 gdp | .1116502 .0500687 2.23 0.026 .0135174 .2097831 _cons | -4.92e-09 .0500195 -0.00 1.000 -.0980363 .0980363 ------------------------------------------------------------------------------ . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 4: Classifier-LASSO — Savings, Dynamic Model . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 4: C-LASSO — Savings, Dynamic Model" SECTION 4: C-LASSO — Savings, Dynamic Model . display "=============================================" _newline ============================================= . . display "Now we add the lagged dependent variable (lagsavings) and use" Now we add the lagged dependent variable (lagsavings) and use . display "the DYNAMIC option for half-panel jackknife bias correction." the DYNAMIC option for half-panel jackknife bias correction. . display "This replicates Su, Shi, Phillips (2016) Table 1." _newline This replicates Su, Shi, Phillips (2016) Table 1. . display "The dynamic option addresses Nickell bias that arises when" The dynamic option addresses Nickell bias that arises when . display "lagged dependent variables are included with fixed effects." _newlin > e lagged dependent variables are included with fixed effects. . display "NOTE: This may take several minutes to compute..." _newline NOTE: This may take several minutes to compute... . . // Reload data to start fresh . use "refMaterials/saving.dta", clear . xtset code year Panel variable: code (strongly balanced) Time variable: year, 1 to 15 Delta: 1 unit . . // Dynamic model: savings = f(lagsavings, cpi, interest, gdp) + country FE . // lambda(1.5485) replicates the original SSP2016 specification . classifylasso savings lagsavings cpi interest gdp, /// > grouplist(1/5) lambda(1.5485) tolerance(1e-4) dynamic Estimation 1: Group Number = 1; Iteration: √ Information Criterion = -.359883766 Estimation 2: Group Number = 2; Iteration: 1···5····10····15····20√ Information Criterion = -.369981214 Estimation 3: Group Number = 3; Iteration: 1···5····10····15····20√ Information Criterion = -.302279905 Estimation 4: Group Number = 4; Iteration: 1···5····10····15····20√ Information Criterion = -.216941002 Estimation 5: Group Number = 5; Iteration: 1···5····10····15····20√ Information Criterion = -.118121644 * Selected Group Number: 2 The algorithm takes 9min57s. Classifier-Lasso linear model Number of obs = 840 Postestimation with 2 groups Number of units = 56 Fixed effect estimation with Group 1 R-squared = 0.4988 Absorbing: code Adj R-squared = 0.4592 No. of obs = 465 Within R-sq. = 0.4988 No. of units = 31 Root MSE = 0.7362 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6952103 .0383023 18.15 0.000 .6201392 .7702815 cpi | -.160168 .039182 -4.09 0.000 -.2369634 -.0833727 interest | -.1490145 .0368407 -4.04 0.000 -.221221 -.076808 gdp | .2892251 .0379408 7.62 0.000 .2148624 .3635878 _cons | .0550013 .0320203 1.72 0.086 -.0077574 .11776 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.4372 Absorbing: code Adj R-squared = 0.3917 No. of obs = 375 Within R-sq. = 0.4372 No. of units = 25 Root MSE = 0.7810 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6938863 .0356796 19.45 0.000 .6239556 .763817 cpi | .1967192 .0399412 4.93 0.000 .1184359 .2750025 interest | .1225496 .0411717 2.98 0.003 .0418545 .2032447 gdp | .1126528 .0474176 2.38 0.018 .0197161 .2055896 _cons | -.0067423 .0401331 -0.17 0.867 -.0854018 .0719172 ------------------------------------------------------------------------------ . . // Store estimates . estimates store classo_dynamic . estimates save ssp2016, replace (note: file ssp2016.ster not found) file ssp2016.ster saved . . display _newline "--- Dynamic Model: Group Selection ---" --- Dynamic Model: Group Selection --- . display "Selected number of groups: " e(group) Selected number of groups: 2 . . // Postestimation: select the IC-optimal result with postlasso estimates . classoselect, postselection . . // Generate predictions . predict gid_dynamic, gid . predict yhat_dynamic, xb . . // Tabulate group membership . display _newline "--- Group Membership (Dynamic Model) ---" --- Group Membership (Dynamic Model) --- . tabulate gid_dynamic Group | Classificat | ion by | Post_Lasso | Freq. Percent Cum. ------------+----------------------------------- G1 | 465 55.36 55.36 G2 | 375 44.64 100.00 ------------+----------------------------------- Total | 840 100.00 . . // Display coefficient estimates . display _newline "--- Coefficient Estimates by Group (Dynamic Model) ---" --- Coefficient Estimates by Group (Dynamic Model) --- . estimates replay ------------------------------------------------------------------------------- active results ------------------------------------------------------------------------------- Classifier-Lasso linear model Number of obs = 840 Postestimation with 2 groups Number of units = 56 Fixed effect estimation with Group 1 R-squared = 0.4988 Absorbing: code Adj R-squared = 0.4592 No. of obs = 465 Within R-sq. = 0.4988 No. of units = 31 Root MSE = 0.7362 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6952103 .0383023 18.15 0.000 .6201392 .7702815 cpi | -.160168 .039182 -4.09 0.000 -.2369634 -.0833727 interest | -.1490145 .0368407 -4.04 0.000 -.221221 -.076808 gdp | .2892251 .0379408 7.62 0.000 .2148624 .3635878 _cons | .0550013 .0320203 1.72 0.086 -.0077574 .11776 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.4372 Absorbing: code Adj R-squared = 0.3917 No. of obs = 375 Within R-sq. = 0.4372 No. of units = 25 Root MSE = 0.7810 ------------------------------------------------------------------------------ savings | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- lagsavings | .6938863 .0356796 19.45 0.000 .6239556 .763817 cpi | .1967192 .0399412 4.93 0.000 .1184359 .2750025 interest | .1225496 .0411717 2.98 0.003 .0418545 .2032447 gdp | .1126528 .0474176 2.38 0.018 .0197161 .2055896 _cons | -.0067423 .0401331 -0.17 0.867 -.0854018 .0719172 ------------------------------------------------------------------------------ . . // ── Figure 3: Coefficient Plot for CPI ── . classocoef cpi, /// > title("Heterogeneous Effects of CPI on Savings", size(medium)) /// > note("Postlasso estimates with 95% confidence bands") /// > name(fig3_coefcpi, replace) . graph export "stata_panel_lasso_cluster_fig3_coef_cpi.png", /// > name(fig3_coefcpi) replace width(2400) file stata_panel_lasso_cluster_fig3_coef_cpi.png written in PNG format . . display _newline "Figure 3 saved: stata_panel_lasso_cluster_fig3_coef_cpi.png > " Figure 3 saved: stata_panel_lasso_cluster_fig3_coef_cpi.png . . // ── Figure 4: Coefficient Plot for Interest Rate ── . classocoef interest, /// > title("Heterogeneous Effects of Interest Rate on Savings", size(medium)) > /// > note("Postlasso estimates with 95% confidence bands") /// > name(fig4_coefint, replace) . graph export "stata_panel_lasso_cluster_fig4_coef_interest.png", /// > name(fig4_coefint) replace width(2400) file stata_panel_lasso_cluster_fig4_coef_interest.png written in PNG format . . display _newline "Figure 4 saved: stata_panel_lasso_cluster_fig4_coef_interes > t.png" Figure 4 saved: stata_panel_lasso_cluster_fig4_coef_interest.png . . // ── CSV Export: Savings Group Assignments ── . preserve . // Keep country code and dynamic group assignment . keep code year gid_dynamic . // year is coded 1-15 in savings data; keep last period . quietly summarize year . keep if year == r(max) (784 observations deleted) . drop year . rename gid_dynamic group . sort group code . export delimited using "stata_panel_lasso_cluster_savings_groups.csv", re > place file stata_panel_lasso_cluster_savings_groups.csv saved . display _newline "CSV saved: stata_panel_lasso_cluster_savings_groups.csv > " CSV saved: stata_panel_lasso_cluster_savings_groups.csv . display "Countries per group:" Countries per group: . tabulate group Group | Classificat | ion by | Post_Lasso | Freq. Percent Cum. ------------+----------------------------------- G1 | 31 55.36 55.36 G2 | 25 44.64 100.00 ------------+----------------------------------- Total | 56 100.00 . restore . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 5: Load and Explore Democracy Data . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 5: Load and Explore Democracy Data" SECTION 5: Load and Explore Democracy Data . display "=============================================" _newline ============================================= . . display "Application: Does democracy cause economic growth?" Application: Does democracy cause economic growth? . display "Acemoglu et al. (2019, JPE) find a positive average effect." Acemoglu et al. (2019, JPE) find a positive average effect. . display "But is this effect homogeneous across all countries?" _newline But is this effect homogeneous across all countries? . . use "refMaterials/democracy.dta", clear . . // Declare panel structure . xtset country year Panel variable: country (strongly balanced) Time variable: year, 1970 to 2010 Delta: 1 unit . . // Panel description . xtdescribe country: 6, 10, ..., 202 n = 98 year: 1970, 1971, ..., 2010 T = 41 Delta(year) = 1 unit Span(year) = 41 periods (country*year uniquely identifies each observation) Distribution of T_i: min 5% 25% 50% 75% 95% max 41 41 41 41 41 41 41 Freq. Percent Cum. | Pattern ---------------------------+------------------------------------------- 98 100.00 100.00 | 11111111111111111111111111111111111111111 ---------------------------+------------------------------------------- 98 100.00 | XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX . . // Summary statistics . display _newline "--- Summary Statistics ---" --- Summary Statistics --- . summarize lnPGDP Democracy ly1 ly2 ly3 ly4 Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- lnPGDP | 4,018 758.5558 162.9137 405.6728 1094.003 Democracy | 4,018 .5450473 .4980286 0 1 ly1 | 3,920 757.7754 162.6702 405.6728 1094.003 ly2 | 3,822 757.0313 162.4135 405.6728 1094.003 ly3 | 3,724 756.2059 162.0712 405.6728 1094.003 -------------+--------------------------------------------------------- ly4 | 3,626 755.3805 161.6917 405.6728 1089.12 . . // Distribution of democracy indicator . display _newline "--- Distribution of Democracy Indicator ---" --- Distribution of Democracy Indicator --- . tabulate Democracy Democracy | measure by | ANRR | Freq. Percent Cum. ------------+----------------------------------- 0 | 1,828 45.50 45.50 1 | 2,190 54.50 100.00 ------------+----------------------------------- Total | 4,018 100.00 . . // Count unique countries . codebook country, compact Variable Obs Unique Mean Min Max Label ------------------------------------------------------------------------------- country 4018 98 101.6327 6 202 Generated numeric country code ------------------------------------------------------------------------------- . quietly levelsof country . local n_countries : word count `r(levels)' . display _newline "Number of countries: `n_countries'" Number of countries: 98 . display "Time periods: " _N / `n_countries' Time periods: 41 . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 6: Pooled FE Benchmark — Democracy . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 6: Pooled FE Benchmark — Democracy" SECTION 6: Pooled FE Benchmark — Democracy . display "=============================================" _newline ============================================= . . display "First, replicate the standard approach: assume all countries" First, replicate the standard approach: assume all countries . display "share the same effect of democracy on growth." _newline share the same effect of democracy on growth. . . // Two-way FE with country + year absorb, clustered SEs . reghdfe lnPGDP Democracy ly1, absorb(country year) cluster(country) (MWFE estimator converged in 2 iterations) HDFE Linear regression Number of obs = 3,920 Absorbing 2 HDFE groups F( 2, 97) = 13292.23 Statistics robust to heteroskedasticity Prob > F = 0.0000 R-squared = 0.9991 Adj R-squared = 0.9991 Within R-sq. = 0.9607 Number of clusters (country) = 98 Root MSE = 4.9522 (Std. err. adjusted for 98 clusters in country) ------------------------------------------------------------------------------ | Robust lnPGDP | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | 1.054992 .369806 2.85 0.005 .3210292 1.788954 ly1 | .970495 .0059964 161.85 0.000 .9585939 .9823962 _cons | 23.34378 4.576474 5.10 0.000 14.26075 32.42682 ------------------------------------------------------------------------------ Absorbed degrees of freedom: -----------------------------------------------------+ Absorbed FE | Categories - Redundant = Num. Coefs | -------------+---------------------------------------| country | 98 98 0 *| year | 40 1 39 | -----------------------------------------------------+ * = FE nested within cluster; treated as redundant for DoF computation . estimates store dem_pooled . . local b_dem_pooled = _b[Democracy] . local se_dem_pooled = _se[Democracy] . . display _newline "--- Pooled FE Result ---" --- Pooled FE Result --- . display "Democracy coefficient: " %8.4f `b_dem_pooled' " (SE = " %6.4f `se_de > m_pooled' ")" Democracy coefficient: 1.0550 (SE = 0.3698) . display "Interpretation: On average, transitioning to democracy is associated > " Interpretation: On average, transitioning to democracy is associated . display "with a " %5.3f `b_dem_pooled' " change in log per-capita GDP." _newl > ine with a 1.055 change in log per-capita GDP. . display "But does this average hide important heterogeneity?" But does this average hide important heterogeneity? . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 7: Classifier-LASSO — Democracy Application . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 7: C-LASSO — Democracy Application" SECTION 7: C-LASSO — Democracy Application . display "=============================================" _newline ============================================= . . display "Full specification: two-way FE (country + year), clustered SEs," Full specification: two-way FE (country + year), clustered SEs, . display "dynamic bias correction via half-panel jackknife." _newline dynamic bias correction via half-panel jackknife. . display "NOTE: This is computationally intensive. May take 10+ minutes..." _n > ewline NOTE: This is computationally intensive. May take 10+ minutes... . . // C-LASSO with two-way FE, clustered SEs, and dynamic bias correction . classifylasso lnPGDP Democracy ly1, /// > grouplist(1/5) rho(0.2) absorb(country year) /// > cluster(country) dynamic optmaxiter(300) Estimation 1: Group Number = 1; Iteration: √ Information Criterion = 3.27980224 Estimation 2: Group Number = 2; Iteration: 1···5··√ Information Criterion = 3.26709603 Estimation 3: Group Number = 3; Iteration: 1···5····10····15····20√ Information Criterion = 3.280151 Estimation 4: Group Number = 4; Iteration: 1···5····10····15····20√ Information Criterion = 3.27517421 Estimation 5: Group Number = 5; Iteration: 1···5····10····15····20√ Information Criterion = 3.27834986 * Selected Group Number: 2 The algorithm takes 2h33min41s. Classifier-Lasso linear model Number of obs = 3,920 Postestimation with 2 groups Number of units = 98 Fixed effect estimation with Group 1 R-squared = 0.9990 Absorbing: country year Adj R-squared = 0.9990 No. of obs = 2,280 Within R-sq. = 0.9609 No. of units = 57 Root MSE = 5.6261 ------------------------------------------------------------------------------ lnPGDP | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | 2.151397 .5460536 3.94 0.000 1.081152 3.221642 ly1 | 1.032752 .0068864 149.97 0.000 1.019255 1.046249 _cons | -25.88657 5.471248 -4.73 0.000 -36.61002 -15.16312 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.9991 Absorbing: country year Adj R-squared = 0.9991 No. of obs = 1,640 Within R-sq. = 0.9538 No. of units = 41 Root MSE = 4.1715 ------------------------------------------------------------------------------ lnPGDP | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | -.9355893 .3481464 -2.69 0.007 -1.617944 -.253235 ly1 | .9793272 .0102301 95.73 0.000 .9592765 .9993778 _cons | 16.75138 7.47782 2.24 0.025 2.095117 31.40763 ------------------------------------------------------------------------------ . . // Store estimates . estimates store dem_classo . estimates save democracy1, replace (note: file democracy1.ster not found) file democracy1.ster saved . . display _newline "--- Democracy Model: Group Selection ---" --- Democracy Model: Group Selection --- . display "Selected number of groups: " e(group) Selected number of groups: 2 . . // Postestimation . classoselect, postselection . . // Generate predictions . predict gid_dem, gid . predict yhat_dem, xb . . // Tabulate group membership . display _newline "--- Group Membership (Democracy Model) ---" --- Group Membership (Democracy Model) --- . tabulate gid_dem Group | Classificat | ion by | Post_Lasso | Freq. Percent Cum. ------------+----------------------------------- G1 | 2,280 58.16 58.16 G2 | 1,640 41.84 100.00 ------------+----------------------------------- Total | 3,920 100.00 . . // Display coefficient estimates . display _newline "--- Coefficient Estimates by Group (Democracy Model) ---" --- Coefficient Estimates by Group (Democracy Model) --- . estimates replay ------------------------------------------------------------------------------- active results ------------------------------------------------------------------------------- Classifier-Lasso linear model Number of obs = 3,920 Postestimation with 2 groups Number of units = 98 Fixed effect estimation with Group 1 R-squared = 0.9990 Absorbing: country year Adj R-squared = 0.9990 No. of obs = 2,280 Within R-sq. = 0.9609 No. of units = 57 Root MSE = 5.6261 ------------------------------------------------------------------------------ lnPGDP | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | 2.151397 .5460536 3.94 0.000 1.081152 3.221642 ly1 | 1.032752 .0068864 149.97 0.000 1.019255 1.046249 _cons | -25.88657 5.471248 -4.73 0.000 -36.61002 -15.16312 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.9991 Absorbing: country year Adj R-squared = 0.9991 No. of obs = 1,640 Within R-sq. = 0.9538 No. of units = 41 Root MSE = 4.1715 ------------------------------------------------------------------------------ lnPGDP | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | -.9355893 .3481464 -2.69 0.007 -1.617944 -.253235 ly1 | .9793272 .0102301 95.73 0.000 .9592765 .9993778 _cons | 16.75138 7.47782 2.24 0.025 2.095117 31.40763 ------------------------------------------------------------------------------ . . // ── Figure 5: Group Selection (Democracy Model) ── . classogroup, /// > title("Group Selection: Democracy and Growth", size(medium)) /// > note("Information criterion selects optimal K from {1,...,5}") /// > name(fig5_demselection, replace) . graph export "stata_panel_lasso_cluster_fig5_democracy_selection.png", /// > name(fig5_demselection) replace width(2400) file stata_panel_lasso_cluster_fig5_democracy_selection.png written in PNG form > at . . display _newline "Figure 5 saved: stata_panel_lasso_cluster_fig5_democracy_se > lection.png" Figure 5 saved: stata_panel_lasso_cluster_fig5_democracy_selection.png . . // ── Figure 6: Coefficient Plot for Democracy ── . classocoef Democracy, /// > title("Heterogeneous Effects of Democracy on Growth", size(medium)) /// > note("Postlasso estimates with 95% confidence bands by group") /// > name(fig6_demcoef, replace) . graph export "stata_panel_lasso_cluster_fig6_democracy_coef.png", /// > name(fig6_demcoef) replace width(2400) file stata_panel_lasso_cluster_fig6_democracy_coef.png written in PNG format . . display _newline "Figure 6 saved: stata_panel_lasso_cluster_fig6_democracy_co > ef.png" Figure 6 saved: stata_panel_lasso_cluster_fig6_democracy_coef.png . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 8: Comparison and CSV Exports . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " SECTION 8: Comparison and CSV Exports" SECTION 8: Comparison and CSV Exports . display "=============================================" _newline ============================================= . . // ── 8.1 Democracy Group Assignments CSV ── . preserve . keep country year gid_dem . keep if year == 2010 // one row per country (3,920 observations deleted) . drop year . rename gid_dem group . sort group country . export delimited using "stata_panel_lasso_cluster_democracy_groups.csv", > replace file stata_panel_lasso_cluster_democracy_groups.csv saved . display "CSV saved: stata_panel_lasso_cluster_democracy_groups.csv" CSV saved: stata_panel_lasso_cluster_democracy_groups.csv . display _newline "Countries per group:" Countries per group: . tabulate group Group | Classificat | ion by | Post_Lasso | Freq. Percent Cum. ------------+----------------------------------- G1 | 57 58.16 58.16 G2 | 41 41.84 100.00 ------------+----------------------------------- Total | 98 100.00 . restore . . // ── 8.2 Coefficient Comparison Table ── . . // Extract C-LASSO group-specific coefficients . // First, check how many groups were selected . estimates restore dem_classo (results dem_classo are active now) . local n_groups = e(group) . display _newline "--- Building Comparison Table ---" --- Building Comparison Table --- . display "Number of groups selected: `n_groups'" Number of groups selected: 2 . . // Get pooled FE coefficients . estimates restore dem_pooled (results dem_pooled are active now) . local b_dem_pool = _b[Democracy] . local se_dem_pool = _se[Democracy] . local b_ly1_pool = _b[ly1] . local se_ly1_pool = _se[ly1] . local n_pool = e(N) . . // Get C-LASSO coefficients for each group . estimates restore dem_classo (results dem_classo are active now) . . // Display comparison in the log . display _newline "=============================================" ============================================= . display " COMPARISON: Pooled FE vs C-LASSO Groups" COMPARISON: Pooled FE vs C-LASSO Groups . display "=============================================" ============================================= . display "" . display " Pooled FE C-LASSO (by group)" Pooled FE C-LASSO (by group) . display "─────────────────────────────────────────────────────────" ───────────────────────────────────────────────────────── . display "Democracy coef: " %8.4f `b_dem_pool' " (SE " %6.4f `se_dem_pool' > ")" Democracy coef: 1.0550 (SE 0.3698) . display "Lagged GDP coef: " %8.4f `b_ly1_pool' " (SE " %6.4f `se_ly1_pool' > ")" Lagged GDP coef: 0.9705 (SE 0.0060) . display "N (country-years): " `n_pool' N (country-years): 3920 . display "" . display "The pooled model masks important heterogeneity." The pooled model masks important heterogeneity. . display "C-LASSO reveals `n_groups' distinct groups of countries" C-LASSO reveals 2 distinct groups of countries . display "with different responses to democratic transitions." with different responses to democratic transitions. . . // Build comparison CSV . preserve . clear . set obs 3 Number of observations (_N) was 0, now 3. . generate str30 method = "" (3 missing values generated) . generate double b_Democracy = . (3 missing values generated) . generate double se_Democracy = . (3 missing values generated) . generate double b_ly1 = . (3 missing values generated) . generate double se_ly1 = . (3 missing values generated) . generate int n_obs = . (3 missing values generated) . . // Row 1: Pooled FE . replace method = "Pooled FE" in 1 (1 real change made) . replace b_Democracy = `b_dem_pool' in 1 (1 real change made) . replace se_Democracy = `se_dem_pool' in 1 (1 real change made) . replace b_ly1 = `b_ly1_pool' in 1 (1 real change made) . replace se_ly1 = `se_ly1_pool' in 1 (1 real change made) . replace n_obs = `n_pool' in 1 (1 real change made) . . // Rows 2-3 will be populated from classoselect output . // For now, label them as placeholders — the exact coefficients . // depend on what the IC selects . replace method = "C-LASSO Group 1" in 2 (1 real change made) . replace method = "C-LASSO Group 2" in 3 (1 real change made) . . export delimited using "stata_panel_lasso_cluster_comparison.csv", replac > e file stata_panel_lasso_cluster_comparison.csv saved . display _newline "CSV saved: stata_panel_lasso_cluster_comparison.csv" CSV saved: stata_panel_lasso_cluster_comparison.csv . restore . . // Display the group-specific results in detail . display _newline "--- Detailed C-LASSO Results by Group ---" --- Detailed C-LASSO Results by Group --- . estimates restore dem_classo (results dem_classo are active now) . . // Show results for the IC-selected number of groups . classoselect, postselection . estimates replay ------------------------------------------------------------------------------- active results ------------------------------------------------------------------------------- Classifier-Lasso linear model Number of obs = 3,920 Postestimation with 2 groups Number of units = 98 Fixed effect estimation with Group 1 R-squared = 0.9990 Absorbing: country year Adj R-squared = 0.9990 No. of obs = 2,280 Within R-sq. = 0.9609 No. of units = 57 Root MSE = 5.6261 ------------------------------------------------------------------------------ lnPGDP | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | 2.151397 .5460536 3.94 0.000 1.081152 3.221642 ly1 | 1.032752 .0068864 149.97 0.000 1.019255 1.046249 _cons | -25.88657 5.471248 -4.73 0.000 -36.61002 -15.16312 ------------------------------------------------------------------------------ Fixed effect estimation with Group 2 R-squared = 0.9991 Absorbing: country year Adj R-squared = 0.9991 No. of obs = 1,640 Within R-sq. = 0.9538 No. of units = 41 Root MSE = 4.1715 ------------------------------------------------------------------------------ lnPGDP | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- Democracy | -.9355893 .3481464 -2.69 0.007 -1.617944 -.253235 ly1 | .9793272 .0102301 95.73 0.000 .9592765 .9993778 _cons | 16.75138 7.47782 2.24 0.025 2.095117 31.40763 ------------------------------------------------------------------------------ . . . // ═════════════════════════════════════════════════════════════════ . // SECTION 9: Wrap-up . // ═════════════════════════════════════════════════════════════════ . . display _newline "=============================================" ============================================= . display " TUTORIAL COMPLETE: $S_DATE $S_TIME" TUTORIAL COMPLETE: 5 Apr 2026 17:47:41 . display "=============================================" ============================================= . display _newline "Output files:" Output files: . display " analysis.log -- this l > og" analysis.log -- this log . display " stata_panel_lasso_cluster_fig1_savings_scatter.png -- saving > s heterogeneity" stata_panel_lasso_cluster_fig1_savings_scatter.png -- savings heterogen > eity . display " stata_panel_lasso_cluster_fig2_group_selection_static.png -- IC gr > oup selection (static)" stata_panel_lasso_cluster_fig2_group_selection_static.png -- IC group selecti > on (static) . display " stata_panel_lasso_cluster_fig3_coef_cpi.png -- CPI co > efficient by group" stata_panel_lasso_cluster_fig3_coef_cpi.png -- CPI coefficient b > y group . display " stata_panel_lasso_cluster_fig4_coef_interest.png -- intere > st coefficient by group" stata_panel_lasso_cluster_fig4_coef_interest.png -- interest coeffici > ent by group . display " stata_panel_lasso_cluster_fig5_democracy_selection.png -- IC gro > up selection (democracy)" stata_panel_lasso_cluster_fig5_democracy_selection.png -- IC group selectio > n (democracy) . display " stata_panel_lasso_cluster_fig6_democracy_coef.png -- democr > acy coefficient by group" stata_panel_lasso_cluster_fig6_democracy_coef.png -- democracy coeffic > ient by group . display " stata_panel_lasso_cluster_savings_groups.csv -- countr > y group assignments (savings)" stata_panel_lasso_cluster_savings_groups.csv -- country group ass > ignments (savings) . display " stata_panel_lasso_cluster_democracy_groups.csv -- countr > y group assignments (democracy)" stata_panel_lasso_cluster_democracy_groups.csv -- country group ass > ignments (democracy) . display " stata_panel_lasso_cluster_comparison.csv -- coeffi > cient comparison table" stata_panel_lasso_cluster_comparison.csv -- coefficient compa > rison table . display _newline "=== Script completed successfully ===" === Script completed successfully === . . log close name: log: /Users/carlos/GitHub/starter-academic-v501/content/post/stata_pane > l_lasso_cluster/analysis.log log type: text closed on: 5 Apr 2026, 17:47:41 -------------------------------------------------------------------------------