Qualitative and quantitative economics
andrea.parisi | Published: 1 Jun 2024, 6:45 p.m.
The terms "qualitative" and "quantitative" in research have different meanings depending on whether you work in soft or hard sciences. As Economics is a social science that tries to use methods of hard sciences, the use of these terms can be (and often is) misleading.
The term 'qualitative research' is used for research methodologies across various disciplines, including social sciences, humanities, and health sciences. Qualitative research is characterized by an emphasis on exploring and understanding complex phenomena through non-numerical data, often gathered through methods such as interviews, observations, and content analysis.
Generally speaking, use of mathematical and statistical methods on numerical data in soft sciences is classified as quantitative, as it permits to establish relationships between quantifiable entities. These relationship, though, are not exact, but they are sufficient to provide an understanding of existing relationships between measurable quantities.
In hard sciences, the term 'qualitative' has typically a different meaning with respect to soft sciences: 'qualitative' in hard sciences is similar to 'quantitative' in soft sciences. In Physics, qualitative refers to a the study of a phenomenon focussing on understanding the fundamental principles, concepts, and behaviors without relying heavily on specific numerical values. It involves qualitative analysis of a physical system, including conceptual models, visual and mathematical representations, and qualitative reasoning about physical phenomena which may not match exactly reality, but are still able to capture general features of the phenomena under study. In this case, a mathematical description is still present, but the comparison is less specific and limited to general properties.
Unfortunately, the term is often misused in Physics and Engineering, which adds to the confusion. The typical portrait of a qualitative physical model is the elastic spring. The motion of the tip of an elastic spring where the other end of the spring is fixed (for instance, fastened to a wall), is described by a simple mathematical differential equation where the position of the tip moves according to: \begin{equation} \ddot{x} = -k\,(x-x_0) \label{eq:spring} \end{equation} where $x_0$ is the rest length of the spring (its length when no force is applied), and $k$ is a constant that depend on the spring material. The above equation is an approximation to the true motion which is rather more complex, but works very well for small deformations. The above equation is often described as a qualitative description as long as $k$ does not correspond to a specific material: it becomes a true description of a specific material as soon as we put the correct value of $k$ for that material.
In reality, referring to the above as a qualitative description is quite misleading. The equation that describes springs, including springs of specific materials, is equation \eqref{eq:spring}: it is an exact equation (as long as deformations are small). For any given value of $k$ we can provide, the solution to the equation will be exact. That is: if we find (or engineer) a material that has that specific $k$, then we already know how a spring of that material will behave. There is nothing qualitative here: this is, rather, a general description, because it describes the relationship between measurable quantities without relying on specific values. This is not what a qualitative description entails. A more appropriate (and rarely used) example is the relationship between material density and tensile strength.
Suppose we take a bar of some material and we place it under a press: as we increase the force on the press, at some point the bar will break. We can build bars of different materials but with the same size and shape, and put them under the same press. If we press strong enough, any of these bars will break at some point, although the force required to break the bar will differ depending on the material. We may wish to find a relationship between the force required to break the bar, and some property of the material: its colour, its density, its reflectiveness. Reflectiveness might be a good candidate, as many metals are reflective and also quite hard to break: then come composite materials, and the reflectiveness does not seem to fit in properly. Material density is a better indicator of the breaking threshold (or tensile strength as it is known in engineering and metallurgy). As we look at the relationship between these two quantities, we may find a model that relates tensile strength $T$ and material density $\rho$. We may find that there is a good relationship of the kind \begin{equation} T \simeq A \rho^{\alpha} \label{eq:tensile} \end{equation} with $A$ and $\alpha$ parameters to be determined, which gives a qualitative description of this relationship. The description is qualitative, because once you determine by proper fitting the values of $A$ and $\alpha$, if you are interested in knowing precisely what the tensile strength of an iron bar is, the answer would likely be wrong, even by orders of magnitude. Yet the relationship will likely be able to reflect the fact that light materials break easily, while denser materials are much stronger. So on the right path, but not exactly so. That is a qualitative result. A quantitative comparison instead means that we are interested in knowing the exact threshold for a given material. We would like to be able to explain, for instance, why the tensile strength of diamond is larger than that of cast iron, despite the density of diamond being lower. This would require much more than knowing what the density is: it would require understanding how the atoms of the materials are arranged microscopically, how they interact and so on... The qualitative description above is very similar to the quantitative descriptions used in soft sciences.
This leads to the following three interdisciplinary definitions: (a) a fully-qualitative theory is a theory which is derived by a qualitative methodology in the sense of soft sciences (thus verbal, non-numerical data); (b) a hard-qualitative theory is a theory which is described mathematically by relationship between measurable quantities, but cannot provide exact results or forecasts due to its limitations; both quantitative theories in soft sciences and qualitative theories in hard sciences fall in this category; (c) a fully-quantitative theory is a mathematical relationship between measurable quantities that can be used to provide exact forecasts due to its ability to be tuned to specific cases.
As one may easily suspect, economic theories are hard-qualitative. Most economists do not appreciate this fact, which is why you will never see economic theories tagged as qualitative. In economics. as in most sciences, qualitative research in considered a research that uses qualitative arguments – not mathematics – to reach a set of conclusions. From this point of view, a lot of economic reasoning is qualitative. However, once you put maths in, you are supposedly moving into the domain of quantitative research. This however is only partially true, because the use of mathematics does not necessarily make a theory quantitative in the sense of hard sciences: it does make it hard-qualitative. This is quite important, because a forecast based on a hard-qualitative theory will likely have large estimate errors, which is what commonly occurs in the forecasts provided by the major economic institution: governments, central banks, investment banks.
The 'quantitative' analysis that economists use is based on continuous re-parametrization of economic equations to data. This is similar to tuning the equation \eqref{eq:tensile} as more materials are added to the list of data points: we would still be unable to make precise predictions for specific materials. In addition, any hard-qualitative theory can be limited to a set of data points that are as specific as possible to the set we wish to forecast on: this procedure can be used to make short range forecasts, that will give reasonable outcomes most of the time, not necessarily correct, as long as the equation parameters are tuned to reproduce a set of data, and forecasted points are close to this set of data. Hence it is not surprising that economists may produce reasonable forecast that are often proved incorrect.
