Thinking

Causal Channels in Global Polarization: The evidence from anthropometry

International differences in mean height and weight contain significant economic information about global polarization. This is true of height because the heritable component gets averaged away when we take national means. And BMI contains very significant information about nutritional standards.

Waaler_surface.png

The simplicity of Waaler surfaces allows us to capture all the evidence from anthropometry with a simple actuarially fair measure. We posit that anthropometric status is linear in height and quadratic in BMI. We use OLS to regress life expectancy on this specification and use the fitted values as our estimate of anthropometric status. In effect, we allow the Waaler surface to pick the weights we use to combine height and BMI. The weights can be read as reflecting the trade-off in mortality risk between height and BMI. We recenter and rescale the estimates to match the mean and variance of contemporary stature in centimeters. We call this representation Effective Stature.

Effective stature is roughly equivalent to Kim (1996)’s Waaler Index. The difference is that while the method proposed in Kim (1996) required survival tables by height and weight, we have developed a new method that allows us to estimate Waaler surfaces from panel data. The time-variation in the panel allows us to stochastically detrend national means of life expectancy, height and BMI, and thus more efficiently extract information from the cross-sectional variation. See explainer.

Waaler_stature.png

Explainer: Waaler Index and Effective Stature.

In what follows, “Disease” refers to natural log of Years Lost to Infectious Disease estimated by the World Health Organization; “Temperature” refers to mean winter highs; “Nutrition” refers to the linear combination of food balances in vegetal calories, animal calories, vegetal protein, and animal protein that best tracks life expectancy. We begin with the correlation structure.

Correlation Coefficients
Nutrition Disease Effective stature
Temperature -0.72 0.67 -0.75
Nutrition -0.55 0.86
Disease -0.49

The strongest raw correlate of effective stature is Nutrition. Temperature is also a very strong correlate of effective stature. Disease is somewhat less so. Note also that Temperature and nutrition are strongly correlated. So too are Disease and Nutrition although not as strongly. What explains this correlation structure?

The standardized slope coefficients naturally contain the same information. Although already some clarity begins to emerge. It seems plausible that there are causal pathways that run from Temperature to Nutrition and Disease, from Nutrition to Disease, and from one or all three to Effective Stature.

Standardized Slope Coefficients
Columns are dependent variables Nutrition Disease Effective Stature
Temperature -0.78 0.71 -0.76
Nutrition -0.49 0.79
Disease -0.43

Unpacking the causal structure underlying these correlations is the key to understanding global polarization. Causal inference from linear models requires an identification strategy. This is not always possible. But if one is interested in testing the Heliocentric theory, things become considerably easier because we know a priori that causal vectors point out from Temperature and not towards it. This dramatically reduces the number of possible path coefficients. Simply put, the plausible direct effects are Temperature on Nutrition, Disease, and Effective Stature; Nutrition on Disease and Effective Stature; Disease on Nutrition; and Nutrition and Disease on Effective Stature. We can test these from the following “wholesale” regression table.

Global Polarization in human stature, weight and mortality
Dependent variable is Effective Stature. Estimates significant at the 1 percent level are in bold. All variables have been standardized to have mean 0 and variance 1.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
Constant -0.24 -0.04 -0.07 -0.18 -0.25 -0.04 -0.18
0.00 0.36 0.30 0.00 0.00 0.35 0.00
Temperature 0.76 -0.30 -0.79 -0.35
0.00 0.00 0.00 0.00
Nutrition 0.79 0.63 0.75 0.65
0.00 0.00 0.00 0.00
Disease -0.43 0.04 -0.10 0.09
0.00 0.58 0.09 0.17
R^2 0.50 0.63 0.19 0.77 0.50 0.65 0.78
adj-R^2 0.50 0.63 0.18 0.77 0.49 0.65 0.77
N 114 172 180 105 112 163 103
Source: NCD-RisC, WHO, FAO, author’s computations.

To begin with, since there are no causal channels from Nutrition, Disease and Effective Stature to Temperature, we can expect the total effect of Temperature on Effective Stature to be identified by Model 1. Our estimate is statistically significant. A one standard deviation difference in Temperature implies a –0.76 standard deviation change in Effective Stature. All on its own, Temperature explains half the cross-sectional variation in Effective Stature.

What portion of this total effect is mediated by Disease and Nutrition? And what if any is the direct effect of Temperature on Effective Stature? In order to identify that we have to first identify the path coefficients “downstream.” The direct effect of Nutrition on Effective Stature is identified once we control for Disease (Model 6). Our estimated path coefficient is a highly significant 0.75. This is nearly as large as the total effect 0.79 of Nutrition on Effective Stature (Model 2). The direct effect of Disease is also identified once we control for Nutrition (Model 6 again). To our considerable surprise, this path coefficient turns out to be entirely insignificant. We can thus rule out causal channels that run through Disease.

The direct effect of Temperature on Effective Stature can now be identified by controlling for Nutrition (Model 4). Our estimate for the path coefficient is a statistically significant -0.30. That is an extremely large effect after controlling for Nutrition. Note also that if we control for both Nutrition and Disease the estimated path coefficient becomes slightly larger (Model 7). The indirect effect of Temperature on Effective Stature  mediated by Nutrition corresponds to the product of the path coefficients, 0.59 (-0.78*0.75). The total effect of Temperature on Effective Stature implied by the path coefficients is thus -0.89 (-0.3-0.59). This is significantly larger than the univariate estimate of -0.76 (Model 1). Is this because the two models are estimated from different samples? We refit all models with the same (slightly smaller) sample.

Restricted Sample Estimates
Dependent variable is Effective Stature. Estimates significant at the 1 percent level are in bold. All variables have been standardized to have mean 0 and variance 1.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
Constant 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.00 1.00 1.00 1.00 1.00 1.00 1.00
Temperature -0.75 -0.28 -0.76 -0.33
0.00 0.00 0.00 0.00
Nutrition 0.86 0.66 0.84 0.67
0.00 0.00 0.00 0.00
Disease -0.49 0.01 -0.04 0.09
0.00 0.88 0.54 0.17
R^2 0.56 0.73 0.24 0.77 0.56 0.74 0.78
adj-R^2 0.56 0.73 0.24 0.77 0.56 0.73 0.77
N 103 103 103 103 103 103 103

 

We see that coefficient estimates are very stable. No coefficients change sign or significance. The total effect of Temperature on Effective Stature from Model 1 is -0.75, while the direct effect from Model 4 is -0.28. The direct effect of Temperature on Nutrition with this sample is -0.78 (Model not shown above) while the path coefficient of the direct effect on Nutrition on Effective Stature is 0.84, yielding an indirect effect of Temperature on Effective Temperature mediated through Nutrition of -0.66 (-0.78*0.84) and thus a total effect of -0.93 (-0.28-0.66).

Recall also that we have standardized all variables to have mean 0 and variance 1. So the fact that the intercept vanishes in the restricted sample suggests that the estimates in the last table are more reliable than the estimates in the penultimate table. Moreover, the model fit is much better with three-fourths of the variation in more than a hundred countries explained by Nutrition alone. We can thus be fairly confident that we have identification. We estimate that the total causal effect of Temperature on Effective Stature is between -0.75 and -0.93, of which less than –0.3 is the direct effect of Temperature on Effective Stature and the rest is mediated through Nutrition. We posit that since thermal burdens suppress productivity the direct effect of Temperature on Effective Stature is mediated through productivity and hence income. We’ll leave that question open for future study. What is clear is that the Heliocentric theory is very hard to reject.

Nutrition emerges from this analysis as both the principal mediator between Temperature and Effective Stature and the most important causal influence on Effective Stature in its own right. We estimate the direct effect of Nutrition on Effective Stature to be 0.84, close to the total effect implied by the univariate coefficient, 0.86. It is quite simply the single best predictor of living standards as captured by Effective Stature. The strength of the relationship between nutrition and our purely anthropocentric measure suggests that we were not remiss in thinking of effective stature as a good measure of underlying nutritional status.

The empirical evidence from anthropometry suggests that the main causal channel from latitude to global polarization in living standards runs through Nutrition.

Advertisements
Standard

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s