The land elasticities of Johnson and Vollrath (2020, hereafter JV) as published, and a re-estimation of them by double machine learning with Gaussian process first stages (DML-GP) and a story kernel. Every table downloads as a CSV file, and the last view holds every estimate in one file.
The sub-region estimates on a map of the districts. Every district takes the estimate of its sub-region and climate type, so a sub-region shows as patches of its temperate, tropical and mixed districts. The map does not estimate an elasticity for each district. Grey land holds no district of the estimation sample.
Thick lines mark the borders of sub-regions and thin lines those of countries. The districts come from GADM 2.8 on JV's grid of 5 arc-minutes, in the Equal Earth projection. Scroll or pinch to zoom, and drag to move the map (with two fingers on a touch screen); Lock keeps it where it is. Hover over or tap the map for a cell's values; the table under Sub-regions lists every cell.
JV's Figure 4 averages the residuals of log caloric yield and of the log labor/land ratio in 50 quantile bins for each region, and the slope of each region's fitted line is its land elasticity. Here JV's specification and the DML-GP re-estimation share one plot on fixed axes. Turn a study or a climate type off to compare the rest.
Each point averages one of 50 quantile bins of the labor/land residual within a region. JV's residuals partial state fixed effects and the linear controls out of the pooled temperate and tropical districts of the rebuilt data, as their programs do. The re-estimation's residuals are the cross-fitted residuals of the story kernel. Hover over or tap a point for its bin.
The slope of each line is the land elasticity of the region. JV's specification on the rebuilt data gives slopes within 0.005 of the published ones. The DML-GP lines pass through the origin, because the second stage regresses residual on residual without an intercept.
| Study | Climate | Slope (β) | SE | Intercept | Districts | Note |
|---|
JV estimate a land elasticity of — for districts suited only to temperate crops and — for districts suited only to tropical crops, from the variation in rural labor/land ratios across districts within states. The gap of — has a p-value of — and stays significant at the 5 percent level in all — specifications of their Tables 3 to 6.
Estimates with 95 percent intervals from Conley standard errors (500 km). Hover over or tap a row for its values.
OLS of log caloric yield on the log rural labor/land ratio with state fixed effects and controls for urbanization, night lights, population, roads, distance to a city and slope. Conley standard errors (500 km). R² without the fixed effects, except in Table 6. JV print p-values to three decimals.
| Specification | Col. | Region | β | SE | p, β = 0 | p, equal to temperate | Countries | Districts | R² |
|---|
Districts suited to crops of both groups. The p-values test equality with the temperate and with the tropical elasticity.
| Col. | Specification | β | SE | p, equal to temperate | p, equal to tropical | Countries | Districts | R² |
|---|
Each district takes the baseline elasticity of its region, — temperate, — tropical or — mixed, and the country average weights districts by their potential calories. The last column gives the group of the countries in Table 9.
Panel regressions on the low- and middle-income sample of Acemoglu and Johnson (2007), with country and year fixed effects and robust standard errors. Countries with an elasticity below 0.20 in Table 8 form the tropical group. The printed headers of columns (1), (3) and (5) read Temperate. However, these columns hold the — tropical countries, as JV's text and country counts show.
| Dependent variable | Countries | Col. | θ | SE | p, θ = 0 | p, equal to tropical | Number | Observations |
|---|
With DML-GP and the story kernel, the land elasticity is — for districts suited only to temperate crops and — for districts suited only to tropical crops, against — and — published. The gap of — has a p-value of — and is significant at the 5 percent level in — of the — specifications of JV's Tables 3 to 5 that use district data.
DML-GP partials the covariates and the spatial structure out of log caloric yield and out of the log labor/land ratio with Gaussian process (GP) regressions, and it estimates the land elasticity as the least squares slope of the yield residuals on the labor/land residuals. Each GP is fitted on four of five folds, balanced within states, and predicts the fifth. JV's controls other than distance and slope enter the mean of each GP. Standard errors are Conley (500 km), and each gap uses the joint Conley covariance of the two regions.
The story kernel gives each source of spatial variation in JV's labor demand condition its own term. I holds intercepts for states and countries, which stand for the state real wage and state productivity. T is a transport wedge, a surface in the distance to a city of 100,000 and in slope. R is a regional surface on location for the productivity that the potential-yield data miss, kept smooth over at least 150 km. Maximizing the marginal likelihood (ML-II) sets the hyperparameters of each term.
The forest residual check predicts what a conditioning set leaves in both residuals from a library of spatial features, and it turns the part that location predicts into the bias that it implies for the coefficient. The implied bias scores a conditioning set and does not correct its estimate. The re-estimation covers the specifications of JV's Tables 3, 4, 5 and 7 that use district data. It does not rebuild the census microdata of Table 4 or the household surveys of Table 6.
DML-GP estimates with 95 percent intervals from Conley standard errors (500 km), and JV's published estimates as open circles, on the same axis as the chart in the JV view. JV's census microdata (IPUMS) and household surveys (DHS) are not re-estimated. Hover over or tap a row for its values.
DML-GP with the story kernel. Conley standard errors (500 km), and the test of equal elasticities uses the joint Conley covariance of the two regions. The implied bias comes from the forest residual check. The samples keep the states that hold a single district, so they hold more districts and countries than JV's.
| Specification | Col. | Region | β | SE | p, β = 0 | p, equal to temperate | Countries | Districts | JV β | Implied bias |
|---|
Temperate minus tropical elasticity, on the same axis, with 95 percent intervals. The DML-GP interval uses the joint Conley covariance of the two regions. JV report only the p-value of the gap, so the interval of the published gap (dashed) combines the two regional standard errors as if they were independent. A hollow marker shows a DML-GP interval that includes zero.
Districts suited to crops of both groups. The p-values test equality with the temperate and with the tropical DML-GP elasticity of the same specification, using the joint Conley covariance of the two samples.
| Col. | Specification | β | SE | p, equal to temperate | p, equal to tropical | Countries | Districts | JV β |
|---|
Each district takes the DML-GP baseline elasticity of its region, — temperate, — tropical or — mixed, and the country average weights districts by their potential calories. The last column gives the group of the countries in Table 9.
Each dot is one of the — countries of JV's Table 8, and the dark dots are the — countries of Table 9. Countries below the cut-off of 0.20 form the tropical group, and the shaded areas hold countries that change group.
— countries change group. Of the — countries in JV's Table 9, — change group, so the regressions of Table 9 are the published ones. The standard deviation across countries falls from — to —.
With the DML-GP elasticities, — of the — countries in the sample of Table 9 change group, so its regressions are the published ones, shown here as JV print them. Panel regressions on the low- and middle-income sample of Acemoglu and Johnson (2007), with country and year fixed effects and robust standard errors.
| Dependent variable | Countries | Col. | θ | SE | p, θ = 0 | p, equal to tropical | Number | Observations |
|---|
DML-GP in the crop-suitability regions of JV's Table 3 with each candidate conditioning set. MSE is the squared implied bias plus the squared standard error, times 1,000, and † marks the smallest MSE in each region. The first row fits JV's conditioning set region by region, and it and T + R with state fixed effects drop the states that hold a single district.
| Conditioning set | Temperate | Tropical | Gap | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| β | SE | Implied bias | MSE | β | SE | Implied bias | MSE | Gap | SE | p | |
Estimates with 95 percent intervals, from Conley standard errors (500 km) for DML-GP and OLS and from the posterior for GP regression.
Hyperparameters tuned by ML-II on subsamples of 1,000 districts (the main estimates) or on whole training folds, or averaged over their posterior (Bayesian first stages). GP regression puts the labor/land ratio in the mean of a single GP regression and gives the posterior mean and standard deviation. Over the five cross-fitting splits the temperate estimate ranges from — to — and the tropical estimate from — to —.
| Estimator | Temperate | Tropical | Gap | ||||
|---|---|---|---|---|---|---|---|
| β | SE | β | SE | Gap | SE | p | |
JV estimate one land elasticity for each climate type. The same estimators work within any group of districts, so this view gives each sub-region its own elasticity, within each climate type and for all types pooled. Among temperate districts, the DML-GP elasticity runs from — in Oceania to — in Southern Europe, and among tropical districts from — in West, Middle and East Africa to — in South and Southeast Asia. Where both types occur in one sub-region, the temperate elasticity is the higher one: — against — in Latin America and the Caribbean, and — against — in West, Middle and East Africa.
The sub-regions are the ten that JV build from the UN's geographic regions, plus East Asia and Oceania, which their grouping leaves out. A sub-region gets an estimate for a climate type when it holds at least 100 districts of that type, and All types pools its temperate, tropical and mixed districts.
The re-estimation keeps the first stages of the paper, one GP per climate type fitted with cross-fitting on all of its districts, and runs the second stage on the cross-fitted residuals of each sub-region, so each sub-region's districts are adjusted by the same GP as every other district of their type. All types pools the residuals of the three types. JV's specification keeps their partialling of state fixed effects and the linear controls on the pooled sample (Table 3's for temperate and tropical districts, Table 7's for mixed districts and for all types) and fits a line with an intercept within each sub-region, as Figure 4 does for each climate type. JV do not estimate by sub-region.
A Conley kernel of 500 km covers much of a sub-region. When it covers all of it, the Conley variance is zero, because the residuals are orthogonal to the regressor, and with a uniform kernel it can turn negative. The intervals therefore use the larger of the Conley and the state-clustered standard error, and the CSV holds both.
Sub-regions ranked by the DML-GP estimate within each climate type, with 95 percent intervals from the larger of the Conley (500 km) and the state-clustered standard error. DML-GP estimates are dots with solid intervals, and JV's specification is diamonds with dashed intervals. Hover over or tap a row for its values.
Figure 4 for each sub-region. Each point averages a quantile bin of about 30 districts of the labor/land residual (at most 20 bins), and each line has the slope of the sub-region's estimate. All panels share their axes: the log labor/land ratio, residual, across and the log caloric yield, residual, up. JV's lines have an intercept, and the DML-GP lines pass through the origin. Hover over or tap a point for its bin.
β is the land elasticity and SE the larger of the Conley (500 km) and the state-clustered standard error. Change is the DML-GP estimate minus JV's. Districts and countries count the DML-GP sample, which keeps the states that hold a single district. The CSV adds both standard errors, the intervals, p-values, JV's sample sizes and the countries of each sub-region.
| Climate type | JV's specification | Re-estimation (DML-GP) | Change | Districts | Countries | Note | ||
|---|---|---|---|---|---|---|---|---|
| β | SE | β | SE | |||||
Every estimate on this dashboard in one long table of — rows. Filter or search it here, or download the whole file.
The file adds the parameter, the hypothesis behind each p-value, posterior intervals and ranges, the number of countries and a note on each row. JV print p-values to three decimals, so a p-value of 0 in their rows means below 0.0005.