The Irish Potato Famine - Analysis

Begin the analysis by stating the purpose of the study. In this case we want to model the population of Ireland in the years before and after the potato famine. Some historians believe that emigration caused by the famine ended in 1854. We will use our model to see if that belief is consistent with actual population data. If it is not, we will then use the model to find an average rate of emigration that is consistent with the actual data.

To begin an analysis "brainstorm" and make a list of all variables which might be included in the system. In this case, we have a written system description (you will not have one in the "real world.") so begin by reading it and listing all the variables you can identify.

Variables from Initial Reading:

Deaths during famine from starvation
Deaths during famine from epidemics

Potato production
Land productivity

Population

Emigration

Now add any variables to the list that are not explicitly mentioned in the text but are, nevertheless, a part of the system.

Added Variables:

Normal Death Rate
Normal Deaths
Birth Rate
Births
Now indentify the one or more primary behaviors of interest. These will be associated with either stocks or flows in the system.

Primary Behaviors of Interest:

Population over time
Emigration over time
When we build a model to analyze a system, we abstract and simplify by excluding from consideration components that have minor influence and components that are not needed to study the behaviors of interest. The structure of the model is also influenced by the data that is available to us.

Simplification:

Deaths from starvation and epidemics are logically different but we do not have data for them individually. Only the total deaths caused by the famine are needed for the purpose of this model so they can be combined into one.

We will not model land productivity and potato production. While we know that poor land and failed crops led to the famine, we do not need to model this relationship mathematically. That is the number of deaths from famine conditions is known (1.5 million) and thus does not have to be computed from food supply.

Likewise, we will not model epidemic conditions. While we know that poor nutrition leads to illness which leads to the spreading of disease and to increased deaths, we do not need to model this relationship mathematically. That is the number of deaths from famine conditions-starvation and disease-is known (1.5 million) and thus does not have to be computed.

Exogenous Variables:

Deaths from Famine
Emigration
Normal Death Rate
Birth Rate
Endogenous Variables:
Population
Births
Normal deaths
Next, let's begin defining the stock and flow structure of the model. The behaviors of interest are "population over time" and "emigration over time." Population is a stock and emigration is a component of the outflow (along with deaths) from the population.

So we have:

    Stock -
      Population
    Flows (out) -
      Emigration
      Deaths
Deaths come from the usual causes and, in 1846, from the famine. So we can add:
    Deaths -
      Normal deaths
      Deaths from famine
The only inflow in the model is from births. The structure can thus be summarized as:
    Stock -
      Population
    Flows (out) -
      Emigration
      Deaths -
        Normal deaths
        Deaths from famine
    Flow (In) -
      Births
The endogenous variables are Population, Births, and Normal deaths. The Population is a stock so it will be calculated with an initial value plus the accumulated net flows in and out of the stock. Births and Normal deaths will be computed using the corresponding birth and death rates.