Granger Is Not Causal: What Directed Links Between SDGs Can and Cannot Tell Us

A directed edge in a Granger network means “changes here help predict later changes there.” It does not mean “push here and that moves.”

Development policy has a recurring hope: that some Sustainable Development Goals are “accelerators”. Invest in one, and progress spreads to the others. It is an attractive idea for anyone allocating a limited budget, and it has encouraged a literature of SDG networks and rankings of which goals are most influential.

I spent a large part of the last year building one of these networks. The most useful thing I learned was how little the network can support the claim people most want from it.

What we estimated#

The data were a balanced panel of 114 countries observed every year from 2000 to 2024, using the goal scores from the Sustainable Development Report (SDR). Countries with complete data on all 17 goals for all 25 years made it in. That selection is based on data completeness, and the panel still covers 89% of the world’s population.

Goal scores are persistent and trending. A panel unit-root test could not reject a unit root for 11 of the 17 goals in levels, while all 17 were stationary after first differencing. So we worked with year-over-year changes, and for each of the 272 directed goal pairs we ran a Dumitrescu-Hurlin panel Granger non-causality test at lag 2, with false-discovery control across all pairs.

After correction, 84 directed linkages remained: 40 synergies and 44 trade-offs.

Separately, for 31 indicator pairs chosen in advance from the literature, we estimated panel local projections with country and year fixed effects and Driscoll-Kraay standard errors. These trace how a one-point change in one indicator relates to another over the next ten years.

Four levels of evidence#

The word “interlinkage” gets used for very different things. It helped me to separate them explicitly.

Co-movement. Two outcomes move together. Correlation networks and expert coding live here. No temporal order.
Directed predictability. A lagged change in one measure improves prediction of a later change in another, after conditioning on persistence and common components. Panel Granger tests and local projections live here.
Mechanism consistency. The same relationship appears in independent indicator data, not only in the composite scores.
Intervention effect. A feasible policy changes the outcome through the claimed mechanism.

Our study reaches level 2 across the network and level 3 for one pathway. It does not reach level 4, and nothing in the design could. So in the paper we call the edges “Granger-causal linkages”, the local projections “dynamic responses”, and the independent-data check “mechanism consistency”. None of them is described as an intervention effect.

Why a Granger edge is not a causal effect#

The distinction is easy to state and easy to forget when writing the discussion section, so I will be specific about what could produce an edge without any causal link.

Omitted common drivers. If income growth improves both sanitation and child survival, but sanitation’s improvements show up in the data a year earlier, sanitation will “Granger-cause” child survival even if building latrines did nothing.
Shared shocks. Countries move together through commodity cycles, pandemics and global financing. We checked this two ways. Under the common correlated effects estimator, which lets each country respond differently to shared factors, 72 of the 84 edges survived and the goal ranking correlated at 0.81 with the primary one. But simply removing the common year effect left only 44 edges, and the ranking then correlated at just 0.32. The network is not an artifact of shared shocks, but its details depend on how you model them.
Measurement timing. Composite scores are built from indicators collected on different schedules and sometimes smoothed or interpolated. An edge can reflect when things are measured rather than when they happen.
Reverse feedback. Direction in a Granger test is about which series leads. Both directions can be true at once.

No universal accelerator#

If accelerators existed in the strong sense, some goals should rank consistently as drivers. They did not.

Rankings were fragile to choices that should not matter much. Per-country information criteria mostly preferred a lag of 1 over the lag of 2 we used as primary. Only about half the edges survived at lag 1, and the correlation of goal-level net influence with the primary ranking was 0.03 at lag 1 and 0.18 at lag 3. A 500-resample country bootstrap of each goal’s net influence separated only two roles from noise: peace and strong institutions as a net receiver, and poverty reduction as an effect-size-weighted driver.

What was stable was the density of the network and its mix of synergies and trade-offs. Which specific goals sat at the top moved around.

The two pathways that held up#

Of the 31 prespecified local-projection linkages, two were supported at the five-year horizon after false-discovery control. Both lead to child survival.

A one-point improvement in sanitation access was followed by about a 1.2-point rise in the under-five mortality score over five years.
Poverty reduction was followed by lower under-five mortality over the same horizon.

Both built up over four to five years rather than appearing immediately. That is itself informative: a cross-sectional or single-lag analysis would understate them.

The diagnostics complicated both, and I think that is where the real content is.

The poverty pathway also runs backwards. Improvements in child survival also predict later poverty reduction (five-year coefficient +0.34, p = 0.008). That looks like a reinforcing loop, not a lever you pull at one end.

The sanitation pathway has no reverse effect. But when next year’s change in sanitation (a lead term) and the current change compete in one model, the lead wins. Because these indicators move slowly, some lead signal is expected. A lead that beats the current change points to smoothing or timing misalignment in how the indicator is measured. We read it as a robust predictive association whose precise timing annual data cannot resolve.

For the education to child health link we also went outside the composite scores. In World Development Indicators data for 183 countries and 2,861 country-years, a lagged rise in secondary enrollment predicted a later fall in under-five mortality: about 0.44 fewer deaths per 1,000 live births per 10-percentage-point enrollment increase (95% interval -0.66 to -0.21), robust to health and education spending, GDP per capita and fertility. That is level 3 evidence. It is still not level 4.

What a causal design would need#

If I wanted to claim that improving sanitation causes lower child mortality at the national level, I would need something that breaks the link to confounders. For example:

a policy change with plausibly exogenous timing, such as a national sanitation programme rolled out in phases across districts, analysed as a staggered difference-in-differences with modern estimators;
an instrument that shifts sanitation investment without affecting child health through other channels, which is hard to find and harder to defend;
or, at smaller scale, randomised evaluations, several of which exist for sanitation and whose mixed results are a useful warning against reading national aggregates too literally.

A Granger network can suggest where to look for such designs. It cannot replace them.

Limits#

Predictive, not structural. Stated above, and worth repeating as the first limitation.
Selection. The most data-sparse countries, often fragile states, are missing. Conclusions for them are extrapolation.
Short and annual. Twenty-five annual observations limit what dynamics are visible, and structural breaks remain possible.
First differences only. This answers a short-to-medium-run question. Long-run equilibrium relationships in levels are a separate question the design does not address.
Averages hide countries. Each edge’s sign summarises heterogeneous country coefficients. Some countries move against the average.

The policy reading#

None of this argues against integrated SDG planning. It argues against fixed global accelerator rankings. A more defensible approach is a portfolio built around the few linkages that survive multiple checks, treated as hypotheses to monitor through their constituent indicators, and revised as the data change.

The paper is on arXiv, and there is a summary on the publication page.