Malthusian Crisis in Ethiopia?

 

Wasn't Malthus Wrong?

The PBS NewsHour is reporting (here) that "millions ... [in Ethiopia] ... still face the risk of starvation as a result of drought conditions", even though the Civil War ended in November, 2022. The last time Ethiopia faced famine was in 1984. Last March, the World Food Program and the USAID suspended food deliveries because grain was being stolen, sold on the black market and not getting to those in need.

Why should I even bother trying to apply a Malthusian model to Ethiopia (ETH) when Nobel Laureate William Nordhaus and most of the Economics profession argue that a Neoclassical General Equilibrium model (the DICE model) apples to every region of the World-System and, supposedly, to every country in the World-System. Critics will argue that I am just trying to push the conventional Malthusian policy conclusion: Ignore the poor and hungry because feeding them will just increase their birth rate and further increase population pressure.

World-Systems Theory (WST) has an answer to the question of what is the appropriate model to apply to a particular country: It depends on the country's place in the hierarchical structure of the World-System. Is it a Core, Semi-peripheral or Peripheral country? Core countries are mostly Capitalist, Semi-peripheral countries are Mixed with some elements of Capitalism and Peripheral countries are, I would argue, Malthusian-agricultural economies living on the edge of repeated food crisis and domination by core and semi-peripheral countries.* Most readers will understand what a Capitalist or Mixed economy is because they live in one. But what is a Malthusian economy?

Thomas Robert Malthus (1766-1834) was an English economist, cleric and scholar (political economy and demography). He predicted, controversially, that if population growth exceeded the productive capacity (carrying capacity) of the economy, a Malthusian Crisis would result, where "positive checks" such as famine, war, drought, immigration, etc. would reduce population pressure. Only "preventive checks" (birth control, delayed marriage, etc.) would prevent these catastrophes because population growth would, if uncontrolled, always exceed the productive capacity of the economy.

Famines have occurred periodically in the history of Ethiopia according to records dating to the 9th Century. To say why these famines happened and that they are definitely not the result of population pressure would be amazingly arrogant. And, to say that Neoclassical Economic Theory applies to all countries and to all recorded history would be equally arrogant. In fact, none of the modern models can be tested on Ethiopia because, aside from sparse World Bank data after WWII (the WDI or World Development Indicators), data is very weak for Ethiopia (although there is more data for regions in Africa but still not enough to test the regional DICE model).

Still, Karl Marx (1818-1883) called Malthus' population principle a "libel on the human race" and Malthus himself the "reverend scribbler." Indeed, "every schoolboy knows that Malthus was wrong" (Benjamin Higgins, 1968). Julian Simon (1932-1998) has argued that the World's carrying capacity is essentially unlimited. On the other hand, Jared Diamond has documented that the Rwanda Genocide was the result of population pressure. Why is Malthusian Theory so controversial and requires current analysts to keep writing Why Malthus Is Still Wrong. The continuing confusion involves failing to differentiate between the "Malthusian Model," the evidence supporting it, the "Malthusian Policy Recommendations" and the World-System. This particular Model-Evidence-Policy-System confusion, however, is true of every mental or formal model and is worth understanding for the well-documented and simple Malthusian Model.

The Malthusian Model (MM) is the model on which all other models are implicitly based (see Table I). Usually population growth is taken as exogenous because Capitalist economies can accommodate the demands of an expanding population. The original MM was simply two equations: a linear one for production growth, Q, and a geometric one for population growth, N. The equations didn't interact as a system** and when growth in N exceed Q, a Malthusian crisis was triggered. Kenneth Boulding put (Q,N) together in a system, with no assumptions about functional forms, and we have the modern version. The MM System model uses the state of the system S=(Q-N) as an Error-Correcting Controller (ECC); when (Q>N) population can expand (a feedback effect) and when (Q<N) population will contract through "positive checks".

Measuring Crisis

The MM Systems Model can be estimated for Ethiopia after WWII using the WDI to determine the state of the Malthusian Crisis. The first step is to estimate a measurement model using data we have from the WDI. N and Q are the most complete series and, luckily, form the basic Malthusian model.

 Measurement Matrix 

      N     Q

[1,]  0.707 0.707

[2,] -0.707 0.707

 Fraction of Variance 

[1] 0.958 1.000

The Measurement matrix can be estimated using Principal Components Analysis (PCA). The components will be used to form the approximate state variables of the Malthusian System. When estimated, the first component is overall growth (ETH1 = 0.707 N + 0.707 Q) and the second component, the Error Correcting Growth Controller (ETH2 = 0.707 Q - 0.707 N). Growth explains 96% of the variance and the ECC explains 4%.

The Figure above shows ETH1 (Growth) and ETH2 (The Malthusian ECC) plotted over time. ETH2 enters negative Malthusian-Criss territory around 1990 and starts recovering after 2010 (the 1983-1985 Famine was the worst in a Century and started the downward slide in the Malthusian Crisis). Overall growth (ETH1) although wiggling a little over time was not permanently affected.

Typically, commenting on historical time plots is as far as historical analysis gets, Malthusian or not. But I want to estimate a system model and try to understand how trends are causally related. 

Modeling Results

Modeling forces the question of "What is the System?" World Systems Theory (WST) provides a framework for answering the question. Ethiopia (ETH) is a country embedded with in a system of other countries. 

Discussion

NOTES

* My identification of Ethiopia as a Peripheral Country is a little casual and can be debated (see Babones, 2005). In studying the WDI, one indicator of Peripheral status is simply the lack of information in the data set. Semi-Peripheral and Core countries are fully populated with data.

** We might criticize Malthus for not inventing Systems Theory (a Twentieth Century discovery) and Marx came close recognizing that social systems are "over-determined" (Wolff and Resnick, 2006). You can read more Marx and Engels on the Population Bomb here. Unified Growth Theory puts all these various approaches together in one model starting with the MM at low levels of growth or stagnation (the Malthusian Trap) and ending with the Steady State Economy.

Appendix: ECC Models

Appendix: Systems Model

Models have a compact R-code in dse and can be run easily in Snippets. Note that the RUL20 model is only unstable in the feedback components $F[3,3] = 1.03$. If you stabilize the third feedback component (e.g.,$F[3,3] = 0.98$)  the entire system is stable. 

===========

merge.forecast <-

function (fx,n=1) {

#

# Merges a forecast with the output data

x <- splice(fx$pred,fx$forecast[[n]])

colnames(x) <- seriesNames(fx$data$output)

return(x)

}

#

#

# RUL20  Russia (1950-2000)

#

# Measurement Matrix 

#    EN.ATM.CO2E.KT EG.USE.COMM.KT.OE NY.GDP.MKTP.KD SL.TLF.TOTL.IN SP.POP.TOTL

#[1,]        0.28209            0.4060         0.3336         0.4343      0.3721

#[2,]       -0.43993           -0.2199        -0.1359         0.1328      0.2266

#[3,]        0.06433           -0.1446         0.5944         0.0494     -0.3944

#     SL.UEM.TOTL.ZS     HDI      EF    KOF

#[1,]         0.1893 0.43400  0.2348 0.1948

#[2,]         0.4971 0.03409 -0.3950 0.5161

#[3,]        -0.3374 0.22538 -0.4878 0.2470

#

 #Fraction of Variance 

#[1] 0.5489 0.8484 0.9677 0.9814 0.9921 0.9975 0.9988 0.9995 1.0000

require(dse)

require(matlab)

AIC <- function(model) {informationTestsCalculations(model)[3]}

f <- matrix( c( 0.976658001, 0.02127754,  0.2249071, 0.161990376,

                     -0.008392259, 0.97543675, -0.2319674, 0.001666581,

                     -0.005587383, 0.09718186,  1.0312754, 0.035854885,

                      0.000000000, 0.00000000,  0.0000000, 1.000000000

),byrow=TRUE,nrow=4,ncol=4)

h <- eye(3,4)

k <- f[1:4,1:3,drop=FALSE]

RUL20 <- SS(F=f,H=h,K=k,

z0=c(0.161990376, 0.001666581, 0.035854885, 1.00000000),

              output.names=c("RU1","RU2","RU3"))

stability(RUL20)

#tfplot(simulate(RUL20,sampleT=20))

shockDecomposition(toSSChol(RUL20))

RUL20.data <- simulate(RUL20,sampleT=50,start=1950,noise=matrix(0,50,3))

m <- l(RUL20,RUL20.data)

#tfplot(m)

AIC(m)

tfplot(RUL20.f <- forecast(m,horizon=50))

RUL20.fx <- merge.forecast(RUL20.f)

#    Models have a compact R-code in dse and can be run easily in Snippets. 

#    The RU20 must be run first to provide input for #ETH20.

#

# W20 ETH (Ethiopia) Russia Input

#

# Measurement Matrix 

#       N  Q

#[1,]  0.707 0.707

#[2,] -0.707 0.707

#

#Fraction of Variance 

#[1] 0.958 1.000

#

require(dse)

require(matlab)

AIC <- function(model) {informationTestsCalculations(model)[3]}

f <- matrix( c(  1.04647269, -0.1059723, 0.10155553,

                        0.01918655,  0.9306230, 0.01335861,

                  0.000000000,  0.00000000,  1.00000000

),byrow=TRUE,nrow=3,ncol=3)

g <- matrix(c(-0.003819938, -0.01406381, 0.009235749,

                     -0.010773904, -0.01627134, 0.017135870,

                      0.000000000 , 0.00000000, 0.000000000

),byrow=TRUE,nrow=3,ncol=3)                      

h <- eye(2,3)

k <- f[1:3,1:2,drop=FALSE]

ETH20 <- SS(F=f,H=h,K=k,z0=c(0.11991149, 0.04457381, 1.00000000),

              output.names=c("Growth","(Q-N)"))

stability(ETH20)

shockDecomposition(toSSChol(ETH20))

ETH20.data <- simulate(ETH20,sampleT=50,start=1950,noise=matrix(0,50,2))

m <- l(ETH20,ETH20.data)

#tfplot(m)

AIC(m)

tfplot(forecast(m,horizon=50))

ETH20x <- SS(F=f,H=h,K=k,G=g,z0=c(0.11991149, 0.04457381, 1.00000000),

              output.names=c("Growth","(Q-N)"))

ETH20x

data <- TSdata(output=outputData(ETH20.data),input=RUL20.fx)

m <- l(ETH20x,data)

#tfplot(m)

AIC(m)

shockDecomposition(m)

tfplot(forecast(m,horizon=50,conditioning.inputs=RUL20.fx))