Regional growth, convergence, and spatial spillovers — a reproducible view from outer space
This article replicates and extends the analysis of “Regional growth, convergence, and spatial spillovers in India” (Mendez, Kabiraj & Li; building on Chanda & Kabiraj 2020, World Development): 520 Indian districts observed by radiance-calibrated DMSP-OLS nighttime lights between 1996 and 2010, used as a satellite proxy for economic activity.
Three questions organize everything:
520 districts x 6 years; 28 documented variablesTotal district luminosity, classified with Fisher-Jenks. The animation steps through all six satellite years with a pooled classification, so colors are comparable across frames:
The paper’s weights are 6 nearest neighbors (built, like the paper, on plain lon/lat centroids — pass crs=None; the geometrics default would project first):
Initial luminosity is strongly clustered — the paper reports Moran’s I = 0.73:
Moran's I (initial log luminosity pc): 0.73 (pseudo p = 0.001)
High-High districts: 169, Low-Low: 101And so is growth:
The paper’s dependent variable is the per-capita luminosity growth rate 1996-2010, shipped verbatim by load_india() (an honest per-capita panel is impossible — district population exists only for 1996 and 2001 — so the paper’s pre-computed columns are carried unchanged). To run the paper’s exact cross-section through the panel API, rebuild a two-period panel whose growth reproduces the paper’s dependent variable identically:
import numpy as np
import pandas as pd
HORIZON = 14 # 1996 -> 2010
base = df.query("year == 1996")[
["statedist", "state", "district", "ntl_pc_1996", "growth_ntl_pc_9610"]
]
paper_panel = pd.concat(
[
base.assign(year=1996, ntl_pc=base["ntl_pc_1996"]),
base.assign(
year=2010,
ntl_pc=base["ntl_pc_1996"]
* np.exp(HORIZON * base["growth_ntl_pc_9610"]),
),
],
ignore_index=True,
)
paper_panel = gm.set_panel(paper_panel, entity="statedist", time="year")Unconditional convergence, first ignoring space, then with the SDM (the paper’s Table 1, Model 1):
ols = gm.analyze_beta_convergence(paper_panel, "ntl_pc", model="ols")
sdm = gm.analyze_beta_convergence(
paper_panel, "ntl_pc", model="sdm", gdf=gdf, w=w, n_draws=5000
)
summary = pd.DataFrame(
{
"OLS": [ols.beta_total, np.nan, ols.beta_total, ols.speed, ols.half_life],
"SDM": [sdm.beta_direct, sdm.beta_indirect, sdm.beta_total,
sdm.speed, sdm.half_life],
},
index=["direct", "indirect", "total", "speed (per yr)", "half-life (yr)"],
).round(4)
summary| OLS | SDM | |
|---|---|---|
| direct | -0.0199 | -0.0212 |
| indirect | NaN | -0.0005 |
| total | -0.0199 | -0.0217 |
| speed (per yr) | 0.0233 | 0.0259 |
| half-life (yr) | 29.7493 | 26.7398 |
The headline finding: spatial spillovers raise the estimated speed of convergence. Part of every district’s catch-up arrives through its neighborhood — the indirect impact — which OLS attributes to nothing.
Across 520 units, the growth of **ntl_pc** over a 14-period window is associated with its initial log level with a total slope of **-0.0217** (SE 0.00611), statistically significant at the 1% level.
The slope is negative — the β-convergence pattern: units that started lower tended to grow faster, narrowing initial gaps.
That slope implies a convergence speed of λ = 0.0259 per period and a half-life of about 26.7 periods — the time for half of an initial gap to close at this pace.
The SDM decomposition splits the total into a direct component of -0.0212 (own initial level) and a spillover (indirect) component of -0.000534 operating through neighboring units, under the weights: 6-nearest-neighbor (geographic centroids), row-standardized, n=520.
The spatial-lag parameter ρ = 0.797 says each unit's growth moves together with its neighbors' growth, so part of the convergence pattern is shared across space rather than purely unit-by-unit.
_These are associations, not causal effects. A causal reading needs a research design — see `explain('correlation_vs_causation')`._error
At least one simple LM test rejects at alpha = 0.05, so the robust forms decide: robust LM error remains significant (statistic = 124.35, p = 7.06e-29) while robust LM lag does not (p = 0.298). The Anselin-Florax rule reads this as spatially correlated disturbances, pointing to the spatial error (SEM) model.| Spatial dependence diagnostics for NTL per capita growth (1996-2010) | |||
| OLS residual tests | W: 6-nearest-neighbor (geographic centroids), row-standardized, n=520 | |||
| Statistic | df | p-value | |
|---|---|---|---|
| Moran's I (residuals) | 0.5831 | -- | 0.0000 |
| LM lag | 452.2328 | 1 | 0.0000 |
| LM error | 575.4996 | 1 | 0.0000 |
| Robust LM lag | 1.0839 | 1 | 0.2978 |
| Robust LM error | 124.3508 | 1 | 0.0000 |
| LM SARMA | 576.5836 | 2 | 0.0000 |
| Anselin-Florax recommendation: error | |||
The paper re-estimates its preferred SDM under seven alternative weights (notebook c07). Here are four:
alt = {
"knn4": gm.make_weights(gdf, method="knn", k=4, crs=None),
"knn6": w,
"knn8": gm.make_weights(gdf, method="knn", k=8, crs=None),
"queen": gm.make_weights(gdf, method="queen"),
}
robust = gm.analyze_spatial_model_by_weights(
df.query("year == 1996"),
outcome="growth_ntl_pc_9610",
covariates=["log_ntl_pc_1996"],
gdf=gdf,
weights=alt,
baseline="knn6",
n_draws=2000,
)
robust.figIs the growth-initial association uniform across India? Geographically weighted regression maps the local convergence coefficient:
adaptive bandwidth: 46 neighbors; local R2 mean 0.40Beyond the regression slope: how does the whole distribution move? (One district records zero luminosity in some years; log-based and relative measures use the always-positive panel.)
bad = df.loc[df["ntl_total"] <= 0, "statedist"].unique()
pos = gm.set_labels(
df[~df["statedist"].isin(bad)].copy(), df_dict, set_panel=True
)
gdf_pos = gdf[~gdf["statedist"].isin(bad)].copy()
w_pos = gm.make_weights(gdf_pos, method="knn", k=6, crs=None)
gm.explore_distribution_over_time(pos, "ntl_total", relative=True).figQuintile-to-quintile mobility, then conditioned on the neighborhood:
Shorrocks mobility: 0.21 (diagonal persistence 0.83)Homogeneity LR test: 73.6 (p = 6.3e-07) — transition dynamics differ by neighborhoodThe spatial Markov chain splits **ntl_total**'s 4-state transition matrix by the neighbors' position (spatial lag under 6-nearest-neighbor (geographic centroids), row-standardized, n=519), giving one matrix per neighborhood class (4 classes); values were expressed relative to each period's mean first.
The unconditional matrix keeps regions in place with average probability 0.871.
Conditioning on context, regions surrounded by **low-value neighbors** stay in place with average probability 0.837, while regions surrounded by **high-value neighbors** do so with 0.896 — movement is more common in low-value neighborhoods.
The homogeneity tests (LR = 73.6, p = 6.26e-07; Q = 73.5, p = 6.3e-07; 24 degrees of freedom) are statistically significant at the 1% level: transition dynamics **differ across neighborhood contexts** — a region's mobility is associated with the state of its neighbors.
_These are associations, not causal effects. A causal reading needs a research design — see `explain('correlation_vs_causation')`._σ-convergence and the between/within split — how much of district inequality is between states?
The Theil index of **ntl_total** splits additively into inequality **between** the 28 state groups and inequality **within** them (between + within = total, exactly).
In the latest period (2010), the total Theil index is 0.504: about 59% of it lies between state groups and 41% within them — differences across state means are the dominant layer of inequality.
Over the window, the between-group share fell from 62% to 59% — group means are pulling closer together relative to the differences inside groups.
_These are associations, not causal effects. A causal reading needs a research design — see `explain('correlation_vs_causation')`._Finally, the Phillips-Sul log(t) machinery asks whether all districts share one steady-state path or sort into clubs: