Does wealth buy health? The standard way to ask is the Preston Curve, the famous log-linear relationship between national income and longevity. This guide explains how to analyze GDP per capita against life expectancy with country-level panel data: what to plot, how to transform the variables, how to find countries that over- or under-perform their income, and what the method cannot tell you.
The question for anyone analyzing global development is: if the gains from income flatten out at higher levels, what else explains health? And how do you identify which countries are overperforming or underperforming relative to their economic resources? The Gapminder dataset, the data Hans Rosling used in his talks, is a common public starting point for practising this analysis.
The Experimental Standard
Before we dive in: this is observational analysis, not experimental. Correlation between GDP and life expectancy across countries cannot support causal claims without randomized experiments. Countries differ in countless ways beyond income: healthcare systems, culture, geography, governance. The Preston Curve shows association, not causation. To claim "increasing GDP causes longer life," you'd need a randomized controlled design, which is impractical at the country level. What you can do is identify which nations outperform their income predictions and investigate what policies they share.
Does Your Development Data Tell the Full Story?
Most global development analyses stop at calculating correlation coefficients or running a single regression. That approach can miss three dimensions:
First, the relationship is non-linear. The Preston Curve is concave: a country moving from $1,000 to $2,000 GDP per capita is expected to gain far more life expectancy than one moving from $30,000 to $31,000. Linear models overestimate health gains for wealthy countries and underestimate them for poor ones. The Preston Curve uses a logarithmic transformation of GDP to capture this diminishing return, but you still need to visualize the scatter to see where specific countries fall.
Second, continental differences matter more than global averages. A continental mean can hide a wide spread between the healthiest and least healthy countries in that continent. That within-group inequality tells you more about healthcare system quality and governance than the mean ever could. You need distribution analysis, box plots rather than bar charts, to surface these patterns.
Third, trajectories reveal more than snapshots. Time series analysis by continent shows which regions are catching up, which have stagnated, and where specific historical events caused reversals. A region that starts high will naturally show smaller gains because of diminishing returns, which is not the same as failing.
A single correlation coefficient does not tell you which countries are outliers, which continents are converging, or whether the relationship has strengthened or weakened over time.
What This Analysis Measures
GDP per capita and life expectancy analysis uses panel data, meaning multiple countries observed over multiple time periods, to examine both cross-sectional patterns (how countries differ at a given moment) and longitudinal trends (how individual countries evolve over time).
A typical analysis produces four complementary views:
The Preston Curve scatter plot shows the relationship between GDP per capita (x-axis, logarithmic scale) and life expectancy (y-axis, linear scale) for a chosen year. Each point represents a country. The logarithmic transformation is critical: it compresses the right tail of the income distribution, making the relationship approximately linear and allowing you to see patterns across the full range of incomes. Countries far above the fitted line are health over-performers (living longer than their income predicts); countries far below are under-performers.
The time series by continent tracks how average life expectancy within each continental region has evolved over time. This reveals convergence (regions growing more similar) or divergence (growing gaps), plus historical inflection points where specific regions accelerated, stagnated, or reversed.
The bar chart of GDP by continent shows the economic ranking for a chosen year. This anchors the life expectancy analysis: you need to know which regions are rich versus poor to interpret health outcomes.
The box plot distribution within continents reveals health inequality that continental averages hide. The box spans the 25th to 75th percentile (the middle 50% of countries), the line inside marks the median, and whiskers extend to the min/max (or 1.5x IQR for outliers). Wide boxes indicate high within-group inequality; tight boxes indicate uniform outcomes.
Together these views address the core research question: To what extent does national income predict population health, and where do policy and institutions override pure economic determinism?
Why the Preston Curve Needs a Logarithmic Axis
From a methodological standpoint, the logarithmic x-axis is non-negotiable. On a linear scale, the entire low-income cluster compresses into the left margin, making it impossible to see variation among poor countries. The log transformation gives equal visual weight to a country moving from $1,000 to $2,000 (a doubling) and one moving from $20,000 to $40,000 (also a doubling). This matches the logic of diminishing returns: basic gains such as clean water, vaccination and maternal care scale with income at low levels, while at high levels further health gains require systemic improvements that do not automatically scale with GDP.
Why Box Plots Beat Bar Charts for Distribution Analysis
Bar charts showing group averages hide how widely countries are spread inside each group. Box plots surface the spread, the median (which is robust to outliers), and the outliers themselves. When analyzing panel data with geographic groupings, always check distributions: averages lie when variance is high.
How to Interpret Your Own Global Development Data
If you're analyzing country-level health and economic indicators, here's an analytical workflow:
Step 1: Transform GDP to logarithmic scale before any modeling. The Preston Curve is fundamentally non-linear. If you run a linear regression of life expectancy on raw GDP, you'll typically get poorer model fit and misleading predictions. The log transformation linearizes the relationship and matches the logic of diminishing returns. Compare the R-squared of both specifications on your own data.
Step 2: Fit the Preston Curve, then analyze residuals. The fitted line shows the expected life expectancy for a given income level. Countries with large positive residuals (observed life expectancy far above the line) are over-performers worth studying. What policies do they share? Strong primary care systems? Universal coverage? Low inequality? Conversely, large negative residuals indicate under-performers, which may reflect weak governance, conflict, or healthcare system failures. The residuals are where the interesting research questions emerge.
Step 3: Stratify by continent or region before calculating summary statistics. Global averages obscure regional patterns. Stratification reveals which regions are catching up, which are stagnating, and whether global health inequality is shrinking. Always plot time series by group; don't average across groups first.
Step 4: Use box plots to check within-group inequality before trusting group means. The median (the line inside the box) is often more representative than the mean when distributions are skewed. If the box is wide (large IQR), the mean doesn't describe a typical member of the group. Report the full distribution, not just the central tendency.
Step 5: Look for temporal inflection points that explain deviations. A stagnation that is invisible in a single-year cross-section can jump out in the time series. Historical events such as epidemics, wars, and policy reforms leave signatures in trend lines. If a region's trajectory suddenly changes slope, investigate what happened in that period. These inflection points can suggest mechanisms that cross-sectional analysis misses.
What the Preston Curve Can't Tell You (And What It Can)
The Preston Curve analysis reveals association, not causation. Countries with higher GDP tend to have higher life expectancy, but that does not show that raising GDP causes longer lives. Countless confounding variables differ between rich and poor countries: education systems, infrastructure, governance quality, culture, climate, historical factors. Any of these could explain part or all of the correlation.
To make causal claims, you'd need a randomized experiment, which is impossible at the country level. The next-best approach is a natural experiment or quasi-experimental design: finding cases where income changed for reasons unrelated to health policy, then examining whether life expectancy followed.
Here's what the Preston Curve can tell you:
First, it quantifies the income-health gradient. The fitted curve describes the empirical relationship between income and life expectancy, which is useful for benchmarking and prediction even without a causal interpretation. If your country sits well below the curve for its income level, you know you're underperforming relative to similar-income nations and should investigate why.
Second, it identifies outliers worth studying. Countries far above the curve are existence proofs: it is possible to achieve strong health outcomes without high income. Researchers can study these outliers to identify common factors. The Preston Curve doesn't prove those factors are causal, but it generates hypotheses for further investigation.
Third, it tracks progress over time. If a country's position moves upward relative to the curve (gaining life expectancy faster than income growth would predict), that suggests improving health systems or public health interventions. If it moves downward, investigate conflict, epidemics, or healthcare system collapse. The curve provides a reference frame for evaluating whether a country's health trajectory is on track.
What it cannot do: tell you whether investing in healthcare, education, or infrastructure will improve health outcomes. Those are causal questions requiring experimental or quasi-experimental evidence.
When to Run This Analysis (And When to Skip It)
GDP per capita and life expectancy analysis is most valuable in three scenarios:
1. Country health benchmarking. If you're a policymaker or global health researcher asking "Is our country's health system performing well relative to our income level?", the Preston Curve gives you a reference point. Countries far below the fitted line may be underperforming and should investigate healthcare access, quality, or social determinants. Countries far above can serve as case studies.
2. Regional development tracking. If you're monitoring progress toward global health goals, the time series by region shows which regions are catching up and which are falling behind. This informs resource allocation: if one region is stagnating, it may need targeted intervention.
3. Resource allocation and prioritization. If you're a global health funder deciding where to invest, the shape of the curve suggests where additional income is associated with the largest health gains: the steep part of the curve at low income levels. Treat this as a prioritization hint, not a causal estimate.
Skip this analysis if:
You need causal estimates. If your question is "Will increasing GDP by $1,000 improve life expectancy, and by how much?", you need instrumental variables, difference-in-differences, or regression discontinuity designs, not a cross-sectional Preston Curve.
You're analyzing within-country variation. The Preston Curve works at the country level, where GDP per capita and healthcare systems vary dramatically. Within a single country, income inequality affects health, but the relationship is weaker and more complex. Use different methods (like Gini coefficient analysis or small-area estimation) for sub-national health equity studies.
You need real-time monitoring. Life expectancy data lags (it requires complete mortality records and age-specific death rates). If you need current indicators, use leading metrics like infant mortality or vaccination coverage, which are reported more often.
Your turn
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Frequently Asked Questions
What is the Preston Curve and how do you read it?
The Preston Curve describes the log-linear relationship between GDP per capita and life expectancy, first documented by Samuel Preston in 1975. Because the relationship is concave, a given gain in income is associated with a larger gain in life expectancy at low income levels than at high ones, which is why GDP is plotted on a logarithmic scale. It shows association, not causation.
Why do some countries have much higher life expectancy than their GDP predicts?
Fit the Preston Curve and look at the residuals: countries far above the line live longer than their income predicts, and countries far below live shorter. The curve does not explain why. Candidate explanations to investigate include access to primary care, public health infrastructure, inequality, conflict and disease burden, but the curve only generates these hypotheses and cannot prove them.
Why plot GDP per capita on a logarithmic scale?
Income is heavily right-skewed, and the health benefit of additional income diminishes as income rises. A logarithmic scale gives equal visual weight to every doubling of income and makes the relationship approximately linear, which improves model fit and makes variation among poorer countries visible.
Can a Preston Curve analysis show that raising GDP causes longer lives?
No. A cross-country analysis is observational. Countries differ in many ways beyond income, including healthcare systems, governance, culture and geography. Causal questions need designs such as natural experiments, instrumental variables or difference-in-differences.
Start Your Own Development Analysis
If you're working with country-level health and economic data, whether tracking progress toward development goals, benchmarking national health systems, or identifying resource allocation priorities, this analytical framework applies. You need to see where your countries fall on the Preston Curve (over-performing or under-performing?), how regional trends have evolved over time (catching up or falling behind?), and whether within-region inequality is widening or narrowing.
Prepare a table with country, year, GDP per capita, and life expectancy columns, and work through the four views described above.