Some clarifications to cool down the heat over economics-public health paper

Normally my work deals with topics that the general public would consider boring or put in the “Who cares?” section.

The poverty trap paper, however, generated quite a buzz on several sites — and their commenting section:

• Slashdot.org: Computer Model Reveals Escape Plan From Poverty’s Vicious Circle
• Medium.com: Poverty Escape Plan Revealed by Computer Model of Economic Vicious Cycles
• sophisticatedfinance.typepad.com: New Model to Address Healthcare and Poverty

In hindsight, it’s not too surprising for such a controversial topic as economics and health / development. Reading the comments showed me that Larry was right (again!) on his proposal for the future of publishing¹.

After reading those comments I think it’s necessary to re-iterate and clarify some points:

• First and foremost, this work is a proof of concept. We wanted to show that a dynamic, deterministic model of economy and health can lead to poverty traps if certain (idealized) steps are taken. And we did.
• This is a model. Thus as every model, it makes simplifying assumptions — and we make a lot of very extremely simplifying assumptions! Some people might consider some of these assumptions as unrealistic, while others are less problematic. But it is always under these assumptions that the conclusions of the model must be evaluated.
  If someone does not agree with the assumptions, then they don’t have to agree with the conclusions. That’s valid! – No harm done.
• The estimates we get out of our models, especially those related to costs and cost reduction, must not be taken literally. More than once have I read: ”This work shows that drugs only need to cost 50 cents and then poor countries can get out of poverty.” No, this is not what we –intend to– say. We say that in our very simplified model, with several assumptions and estimates serving as input, the simulations spit out 50 cents as the value for which poverty traps form. However, we did not put a lot of time and effort in this work to show that drugs should cost 50 cents, but that poverty traps are in principle possible.
• A commonly seen criticism / intended debunk of our work is Correlation is not causation:
• Of course we are aware of this misuse of observational data and statistical inference. However, our causal statements are made solely on the basis of a dynamic model of the economy and health state and how they evolve over time in an intertwined manner. The regression fits only parameterize the curves of sanitation and nutrition as a function of capital. I think most people agree that sanitation and nutrition increase with increase in capital (d / d K s(K) > 0 and d / d K n(K) > 0). We will not agree on how exactly they are related:
  • If you know the functional form, please let us know— we were desperately trying to be enlightened. No success.
  • Rather than rolling a die and using ad-hoc / random parameters, we used data from OECD and the UNO to get an estimate of a reasonable functional form. The fits have the agreed-upon property of monotonic increase as a function of capital — and that’s all we wanted (and we tried other curve shapes: results didn’t change)
  • If you disagree with the functional form we use, feel free to use your own and run our models (we put very detailed instructions in the paper; we might even publish our code once cleaned and commented well).
• Lots of development aid money does not reach the people in need. Correct. But for the point of the paper this does not make a difference. When we talk about cutting costs in half we are aware that it might need more money to put in the system so that the 50% cost reduction can be achieved. Just view the development aid as effective development aid (i.e., the part that’s not lost in bureaucracy/management of its infrastructure or lost in corruption).

We will include these points in an updated, reviewed version of this paper (it will be updated on arxiv, and also for the reviewing process.)

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set.seed(42)
yy <- lsarma11.sim(n = 1000, theta = c(0.5, -1), sigma = "constant")
layout(matrix(1:2, ncol = 2))
plot(yy)
acf(yy)

Box.test(yy, lag = 5, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  yy
## X-squared = 5.5603, df = 5, p-value = 0.3514

Box.test.ls(yy, lag = 5, K = 2, type = "Ljung-Box")

## 
##  LS Ljung-Box test; Number of windows = 2; non-overlapping window
##  size = 500
## 
## data:  yy
## X-squared = 47.813, df = 10, p-value = 6.715e-07

library(fracdiff)
library(data.table)
tree.ring <- ts(fread(file.path(data.path, "tree-rings.txt"))[, V1])
layout(matrix(1:4, ncol = 2))
plot(tree.ring)
acf(tree.ring)

mod.arfima <- fracdiff(tree.ring)
mod.arfimad)
plot(arfima.res)
acf(arfima.res)

Box.test(arfima.res, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  arfima.res
## X-squared = 1.8757, df = 1, p-value = 0.1708

Box.test.ls(arfima.res, K = 4, type = "Ljung-Box")

## 
##  LS Ljung-Box test; Number of windows = 4; non-overlapping window
##  size = 497
## 
## data:  arfima.res
## X-squared = 39.361, df = 4, p-value = 5.867e-08

lsarma11.sim

function (n, phi = 0, theta = 0, sigma = 1, rand.gen = rnorm, 
    innov = rand.gen(n)) 
{
    u.d <- seq_len(n)/n
    phi.u <- as.function(polynomial(phi))
    theta.u <- as.function(polynomial(theta))
    phi.t <- phi.u(u.d)
    theta.t <- theta.u(u.d)
    if (sigma == "constant") {
        var.arma11 <- (1 + theta.t^2 - 2 * theta.t * phi.t)/(1 - 
            phi.t^2)
        sigma.t <- sqrt(1/var.arma11)
    }
    else {
        sigma.u <- as.function(polynomial(sigma))
        sigma.t <- sigma.u(u.d)
    }
    xx <- innov
    for (ii in 2:n) {
        xx[ii] <- phi.t[ii] * xx[ii - 1] + sigma.t[ii] * innov[ii] + 
            theta.t[ii - 1] * sigma.t[ii - 1] * innov[ii - 1]
    }
    return(ts(xx))
}

Box.test.ls

function (x, lag = 1, type = c("Ljung-Box", "Box-Pierce"), fitdf = 0, 
    K = 1, plot = FALSE, ...) 
{
    stopifnot(is.numeric(x), K >= 1, K == round(K), is.logical(plot))
    type <- match.arg(type)
    if (K >= length(x)) {
        stop("Number of windows must be smaller than the length of the time series.")
    }
    N.k <- floor(length(x)/K)
    if (K == 1) {
        Box.test(x, type, lag = lag)
    }
    else {
        METHOD <- paste0("LS ", type, " test; \n Number of windows = ", 
            K, "; non-overlapping window size = ", N.k)
        stats.pvals <- rollapply(yy, width = N.k, by = N.k, FUN = function(x) {
            out <- Box.test(x, lag = lag, type)
            return(c(outp.value))
        }, fill = NA)
        stats.pvals <- stats.pvals[!is.na(stats.pvals[, 1]), 
            ]
        colnames(stats.pvals) <- c("statistic", "p-value")
        if (plot) {
            plot(stats.pvals[, "p-value"], ylim = c(0, max(stats.pvals[, 
                "p-value"])), type = "h", lwd = 2, ylab = "p-value", 
                xlab = "Window")
            abline(0.05, 0, col = 4, lty = 4)
            abline(0, 0, lty = 1, col = "gray")
        }
        STATISTIC <- sum(stats.pvals[, "statistic"])
        names(STATISTIC) <- "X-squared"
        df.total <- lag * K
        names(df.total) <- "df"
        PVAL <- 1 - pchisq(STATISTIC, df.total)
        return(structure(list(statistic = STATISTIC, parameter = df.total, 
            p.value = PVAL, method = METHOD, data.name = deparse(substitute(x))), 
            class = "htest"))
    }
}

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And if in the ‘student introduction’ session one student starts with “I am a PhD student in neuroscience and we study neural signal transmission in turtles after cutting off their head …” — I mean if that’s just the first day, how great will be the next 4 weeks 😉