In defence of models

J.M Keynes once stated that ‘Economics is a science of thinking in terms of models joined to the art of choosing models which are relevant to the contemporary world.’

Unfortunately, the models encountered in economics are not the kind that strut down runways. No, the models encountered in economics are ways of representing real world phenomena in conceptual terms, through which they can be studied, understood and even predicted.

In this article I shall examine the strengths and weaknesses of IPCC climate change models, the capital asset pricing model (CAPM) and the Solow Growth Model. All of these models are well regarded within their fields but are often the subject of intense and sometimes unwarranted criticism.

IPCC Climate Change Models

Scientists have posited the correlation between Greenhouse Gas (GHG) emissions and rising global mean temperatures for some time now. Indeed, in a recent lecture at Melbourne Town Hall, Economist Jeffrey Sachs pointed out that this link was first hypothesised by French Physicist Joseph Fourier in 1824. Vast amounts of empirical data now evidence this relationship. Even a cursory look at any Intergovernmental Panel on Climate Change (IPCC) documents reveal graphs plotting the rise in global mean temperature since the Industrial Revolution against the proportionate rise in GHG emissions.

Where modelling intersects climate science is in testing causality. Do temperature rises cause increased GHG concentration or do increased GHG emissions cause temperature rises? The types of models scientists use to answer this question are known as simulation models. Scientists perform various computer simulations, which either include or omit the variable of GHG emissions and determine which simulations better match the actual data. The simulation models seen in the diagram below, show that anthropogenic forcings (e.g. GHG emissions) are required to explain the 20th Century warming. In other words, the rise in temperatures cannot be explained by natural forcings (variability in solar output, volcanic activity, etc) alone.

It is extremely difficult to seriously knock the robustness or intellectual rigour of this modelling which has been peer reviewed time and time again. Yet there are still those amongst us who refuse to accept the scientific consensus on climate change. My challenge to those who do not accept the science on climate change (or I suspect have not even looked at it) is ‘what do your models show?’ Can vehement deniers such as Senator Corry Bernardi or Andrew Bolt rise to this challenge and produce robust modelling explaining how global temperatures might increase without human activity? Until they can do this, their views will continue to be rejected.

The Capital Asset Pricing Model (CAPM)

Since its development by Harry Markowitz in the 1950s Modern Portfolio Theory (MPT) and CAPM have risen to prominence and now occupy a large part of a student’s financial education. Indeed it is almost impossible to undertake an introductory course in finance without encountering the CAPM model.

The CAPM essentially states that the return on an asset equals the return on a riskless asset plus the asset’s beta, all multiplied by the market-wide risk premium. Essentially, the model formalises the positive relationship between risk and return.

Many students (myself included) are quick to throw stones at CAPM. Students often point out that there is no such thing as the theoretical riskless asset, that CAPM ignores taxation and transaction costs, that CAPM falsely assumes informational efficiency, that investors are not rational, etc. In levelling these common criticisms, students are completely correct, and CAPM has been failing empirical tests since the 1970s[1]. It was for this reason Eugene Fama and Kenneth French developed their more empirically sound three-factor model.

These criticisms miss the point however. Undoubtedly, for a simple model like CAPM it is perhaps impossible to capture real-world asset returns perfectly. Despite this, Geltner wrote in his textbook ‘[w]hat CAPM loses as a result of its unrealistic assumptions, namely the ability to model the world completely, is more than made up for by what the model gains by these assumptions, namely, the ability to simplify the world so that we can understand it better.’[2] Perhaps the reason so many students are taught about CAPM is not because they should use it if they ever became portfolio managers but instead, like many other models, it is an invaluable educational tool which provides greater insights into the relationship between risk and return.

The Solow Growth Model

The Solow Growth Model attempts to explain long-run economic growth by focusing on capital accumulation, population growth and technology/productivity growth. The model posits that all economies should converge on a long-run equilibrium growth rate. It posits that in poorer economies the growth in capital per effective worker (capital deepening) should outpace depreciation or population growth (capital widening). The converse is true for richer economies. These forces cause economies to move towards a balanced growth path in the long-run.

If this model were ‘correct’ it would be wonderful! It would mean that economic growth is pre-determined! In time, poorer countries will catch-up via higher growth rates. Unfortunately, such a story is a fantasy. Empirical studies have shown that generalised convergence in growth rates is not a feature of the data. Convergence in growth rates conditional on a factor such as common geography seem to hold up, but the model’s predictions of all economies arriving at a balanced growth path appear unfounded.

Does that mean we should throw this growth model in the bin? Did the Nobel Committee make a mistake in awarding Solow the 1987 Nobel Prize for his work in economic growth theory? Of course not! Just like CAPM the Solow Growth Model is a brilliant educative tool, as it lets us consider the relationship between capital per effective worker and economic growth, and causes us to think about the forces influencing capital per effective worker. It has also been the starting point for more sophisticated and complete theories of economic growth which have been developed by economists since Solow. Moreover, it does not completely flunk empirical tests, as it explains the convergence in incomes across US States following the Civil War, and in European nations between the end of World War Two and the 1980s. It is remarkable that such a simplistic model with unrealistic assumptions can have this level of explanatory ability.

Drawing out some lessons

Through examining the three aforementioned models, we can learn two important lessons.

Firstly, checking whether a model achieves an A+ on an empirical test may be a narrow way to evaluate the model’s usefulness. By this yardstick, Newtonian physics is wrong, as it ignores developments in relativity and quantum physics and therefore does not perfectly represent the physical world. However, as Geltner, et al point out, ‘who can deny that we learn a lot that is quite useful from the Newtonian model, both at a practical level and at a deeper, more fundamental level.’ The lesson here is that models need not be perfect to be useful, and CAPM and the Solow Growth Model certainly fit into this category.

Secondly, there appears to be a trade-off between realism and comprehensibility. Because the real-world is so complex, models that are more empirically sound are by definition more difficult to understand. This can be seen in the IPCC’s climate change modelling, which is undoubtedly more empirically sound than the simple and attractive mathematical properties of CAPM and the Solow Growth Model. By the same token, the IPCC’s modelling is unlikely to convince a lot of climate-change deniers who perhaps do not possess the capability to understand it.

Essentially, Keynes was correct in describing modelling as part science, part art.



[1] Michael C. Jensen, Fischer Black and Myron S. Scholes ‘The Capital Asset Pricing Model: Some Empirical Tests’ in Michael C. Jensen (eds) Studies in The Theory of Capital Markets (Praeger Publishers Inc., 1972);

[2] David Geltner, et al, Commercial Real Estate: Analysis and Investments (On Course Learning, 2014) 559.