Brazil’s trumpeted 2.40% Gross Domestic Product (GDP) growth forecast for 2020 is economically and mathematically unreasonable. A 1.20% is!
Every beginning of year comes about packed with great expectations. I suppose it’s all down to a sort of “renewal sentiment” with which mostly Westerners and the superstitious alike are used to start their new years. In Brazil that renewal sentiment has had government officials at the Ministério da Economia(Ministry of the Economy) announce, in early January, a Gross Domestic Product (GDP) growth expectation for 2020 of 2.40% in comparison to 2019’s somewhere at 0,89% (see picture above). Other notorious bodies like the International Monetary Fund (IMF), the World Bank and Fitch (a rating agency) all expect growth rates of at least 2% for Brazil in 2020: 2.20%, 2% and 2.34%, respectively. Is that reasonable? Let us talk basic economics … and some econometrics too!
In early September and December 2019 I jotted down a few words about GDP growth forecasts/expectations for the upcoming year (2020). So this is the third occasion I spare some time to reflect upon that subject (I also intend to revise this text at least quarterly so that I can track official GPD forecasts and stack them up against my own econometric forecast … and this for a purely educational purpose). Later on you’ll see that my forecast for 2020 is way more dismal than the official ones. As much as I would like my forecast to be accurate (that is, Brazil may grow way less than what is currently expected), I root for the official ones … after all, it’s the economy!
While on those September and December articles I restricted my analysis to a more qualitative approach, that is — a discussion of GDP forecasts for 2020 through a theoretical approach of the Real Business Cycle Theory (RBCT), the Production Possibilities Curve (PPC) and the overall importance of investments for the economy, in this third article I would like to expand on my analysis by introducing a more quantitative/mathematical approach, that is — my own 2020 GDP forecast/expectation through an econometric model I developed.
The meat and potatoes of my argument is this:
(i) considering that the Brazilian GDP has grown at a yearly average of 1.02% since 2017 (a year that brought in the first positive growth after the economy had hit rock bottom at -6.86% in the 2015–6 biennal) and (ii) considering how dismal and dim both the internal (politics) and external (covid-19, China slowdown, to mention a few) conditions currently present themselves, I believe that, unless overall conditions improve signifcantly, Brazil in 2020 will not witness the 2.40% GDP growth trumpeted because it far exceeds the 1.02% average we have had since 2017. How much should we then expect to grow? My econometric model (which I will discuss ahead) suggested a GDP growth for 2020 of 1.20%, which from a purely mathematical point of view seems to be more down to earth. (See graph and table below).
That said, I’ve decided to structure this text as follows.
Firstly, I am going to establish (1) a few preliminary remarks on econometrics. I’ll do that in order to lay out the needed technical foundation upon which I can then present my econometric model and properly explain why (2) mathematically speaking, growing 1.20% is more reasonable than growing 2.40%. Secondly, and finally, I am briefly going to put forth the qualitative/theoretical side of my argument. In this final portion of the article, the reader will be briefly** introduced the Real Business Cycle so that I can attempt to evince why (3) economically speaking, growing 1.20% is more reasonable than growing 2.40%
- A few preliminary remarks on econometrics
It can be argued that econometrics is the mathematical side of economics. The uninformed tend to place economics in the realm of hard sciences. Insofar as human behaviour towards choices is at the basis of an economy, economics, then, cannot be taken as hard science. It is a social one. Math and statistics — that is, econometrics — come in only as a way of measuring and predicting, or rather, trying to measure and predict, that which at its core is nearly unmeasurable and unpredictable: human behaviour. Sir Isaac Newton himself would back me up here. Contemporary to the early age of stock market, Newton lost a tidy sum in the game and ruefully recognised: “I can calculate the motion of heavenly bodies, but not the madness of people”.
Despite that, econometrics does play in invaluable role in economics. I suppose that most, if not all, forecasts are mostly quantitative (i.e. done through a level of econometrics). An econometric model draws heavily on linear regression to make forecasts. Nowadays there are a number of cutting-edge softwares that spare the practicioner of venturing in the Herculian task of “doing it all by hand”. For my 2020 Brazilian GDP forecast I’ve used Gretl.
How does an econometric model work? I want to forecast the Brazilian GDP. I will call it the dependent variable (Y). Economic rationale kicks in as I tried to think of all the other things that positively and/or negatively impact the performance of my response variable, the Brazilian GDP. Let us call “all the other things” the independent variables (X), regardless of how many those may be.
If I believe that only one independent variable explains the behaviour of my dependent variable, then, mathematically, I need a simple linear regression (because there’s a single independent variable) to predict the Brazilian GDP . On the other hand, if I’ve figured that two or more independent variables are responsible for how the dependent variable behaves, then I need a multiple linear regression (because there’s more than one independent variable) to predict the Brazilian GDP.
To come up with a reasonable forecast I needed a few independent variables (13, to be precise). That’s because GDP is too dynamic and complex to be represented by a single factor. Forecast models in general are a mere try at representing an observable reality. Much like a painter whose tools are ink and pencil brushes, the forecaster draws on economics, mathematics and statistics as he struggles to produce a representation that is as accurate and close to the observable object as possible. That implies a few things.
Firstly, because forecasts are mere representations of reality and that perfection is in all walks of life unattainable, it can be argued that every forecast is imprecise, but not useless. “All models are fundamentally wrong, but some are useful” is the motto¹. Secondly, as realistic as it may be and just like a painter’s work, a forecaster’s forecast is static. It assumes that the forecasted variable (the dependent variable) can only prove right if and only if all the other variables (the independent variables) remain constant. Because that is never the case (things change all the time), a forecast must then be revised as often as possible. That’s why I plan to revise mine and this accompanying text at least on a quarterly basis.
2. Mathematically speaking, growing 1.20% is more reasonable than growing 2.40%
Having laid out the basics of econometrics (no perfect model exists and constant revision is necessary), below is a description of all the variables (Y and Xs) I used in my econometric model on Gretl. On the left (name as found in model) is how each variable is read on the software and on the left is just a further description of each variable.
Whether you need a simple or a multiple linear regression in your model, you should know that a linear regression calculus assumes that there exists a somewhat mathematically linear correlation between the set of independent variables (Xs) and the dependent variable (Y). That correlation may be positive (Y increases when X increases) or negative (Y increases when X decreases or the other way round). If the variations in Y are not caused by variations in X, then we have a case of zero correlation (check picture below).
In an actual econometric model there is a handful of statistical tests that can be carried out to find out whether the relation between any given independent variable and the dependent variable is positively or negatively linear. Using the scatterplot is one of them (this is what you see on “Three types of Correlarion”, pictured above). On Gretl, once the model is built, the practicioner is taken to a window where a slew of statistical information is displayed. One of them are the coefficients. Each independent variables is multiplied by its coefficients.
Below are the coefficients for the twelve independent variables in my model. To make things simpler, what matters the most here is whether or not there exists an “alignment” between each independent variable and the dependent variable. A good model will have each of its independent variable aligned with Y both from an economic and econometric points of view. What does that mean? By alignment I mean that the independent variables — be it within the model or alone in relation to the dependent variable — must be reasonable econometrically (i.e. mathematically) and economically.
Let me clarify it with my model. For example: in Brazil the central bank offical interest rate is called Taxa SELIC (SELIC Rate). It’s a monetary policy tool that is manipulated by the Banco Central do Brasil (the Brazilian Central Bank) as it pursues the government’s economic policy in the monetary side of economics. From an economic point of view, when interest rates rise the economy is expected to slow down and inflation to decrease. That’s called a contractionary monetary policy and governments tend to implement this approach when statistics suggest that the economy is overheating and an inflationary gap may come about. Conversely, when monetary policy is expansionary, interest rates are decreased by the central bank in a bid to allow the economy to gather some steam. Governments pursue this type of policy when statistics suggest that the economy is underperforming.
In my model, this dynamics (expansionary vs contractionary monetary policies) is expressed through a negative coefficient for X5_SELIC. There is an economic and an econometric alignment between X5_SELIC and the Y_GDP. Why? Well, it is “economically reasonable” for X5_SELIC to have a negative coefficient because, as shown, when interest rates go up, the economy slows down and GPD tends to contract and when they go down the opposite tends to happen: the economy speeds up and GDP expands. In addition, it is “econometrically reasonable” for X5_SELIC to display a negative coefficient because that inverse relation between X5_SELIC and Y_GDP is mathmatically accurate. If, for instance, the model displayed the opposite dynamics (i.e. a positive coefficient for X5_SELIC), then it wouldd mean that GDP would increase as SELIC increased. And this would be contrary to the established economic thinking.
Having clarified what I mean by economic and econometric aligment, scroll up a little and take another look at the coefficients. Three of them are marked with red arrows pointing to a negative coefficient. X5_SELIC has a blue arrow of its own because, as shown, it is both economically and econometrically aligned. However, X8_STERI (Short-Term Economic Risk Index), X8***_USD_NGDP_USD (the USA GDP), X9_ARG_NGDP_USD (the Argentine GDP) present dynamics that seem to be questionable. *** I misnumbered the variables. Sorry!
The Short-Term Economic Risk Index (X8_STERI) is calculated by Fitch Solutions. The index comprises a number of other indicators. It ranges from 0 (zero) to 100. The closer a country’s STERI is to 100, the better, because it means there exists in the country a better economic environment. A similar reasoning must be applied to X7_STPRI (Short-Term Political Risk Index), with the only exception that it looks at the political environment rather than the economic one.
It follows, then, that a positive correlation should have been displayed by X8_STERI, meaning this: the closer to one hundred X8_STERI is, more of a positive impact on Y_GDP should have been expected. Why? As mentioned: because a greater X8_STERI means a better economic environment. Positive, correlations (rather than negative ones) should have also been observed for the USA Nominal GDP (X8*) and the Argentine Nominal GDP (X9). Both the United States and Argentina are among the top five trading partners for Brazil. Moreover, given the interconnectedness of economies, both at regional and global levels, the Brazilian GDP tends to be impacted by the performance of its most relevant trading partners.
Objectively, nontheless, does it all mean that my model is useless? Remember the motto: “all models are fundamentally wrong, but some are useful”. Although it can be rightly argued that the independent variables X8, X8* and X9 are not economically and econometrically aligned, they all remain invaluable imputs for the model, so much so that when I redid the model without them all the other statistical tests necessary to validate a model performed more poorly than they did when these models are kept.
3. Economically speaking, growing 1.20% is more reasonable than growin 2.40%
In this closing part of my article I would then like to briefly go through a paramount macroeconomic concept that should help us better understand the current economic stage of the Brazilian economy: the Real Business Cycle.
The Real Business Cycle (pictured below) depicts long-term economic growth and allows for a visual reading of an economy’s current stage within the business cycle. The Y and X axes account for Real GDP growth over the long-term (how long precisely is unkown and dependent on a country’s particuliarities).
The definitions of Potential GDP (P-GDP, blue, linear ascending line) and Effective GDP (E-GDP, green, wavy line) come in handy now. Take the difference between them as the difference between what a country could potentially be (P-GDP) and what it effectively is (E-GDP). Ideally, a country’s Real GDP would always be what it can potentially be, but what we have effectively seen historically are periods of (1) expansion/recovery, (2) peaks, (3) contraction/recession, and (4) troughs. The so-called four stages of the economic cycle.
What accounts for such fluctuations? A number of different factors (endogenous ones and exogenous ones) can lead to E-GDP fluctuations/deviations from its potential (P-GDP). Moreover, different schools of economic thought have vastly different stances on how to handle the economy when things go south. For instance, when the economy is underperforming (i.e. E-GDP < P-GDP), a Keynesian economist would likely call for a set of expansionary economic policies embedded in higher government spending to boost the economy. A more liberal economist, on the other end of the spectrum, would suggest less government meddling and that the economy be left to its own self-regulating devices.
Discussing which school of thought is right or wrong (if such can be said of non-hard sciences!) is not my goal in this article. What you, the reader, ought to take away from the Business Cycle is this: ideally and purely from an economic standpoint, a country’s policy-makers should aim at achieving sustainable potential GDP growth. This means a scenario in which E-GDP mirrors P-GDP, with as little deviations as possible (i.e. E-GDP = P-GDP). Why? Because it has historically been observed that when effective GDP distances itself too much upwards from potential GDP an inflationary gap comes about (i.e. E-GDP > P-GDP) and, conversely, when effective GDP distances itself too much downwards from potential GDP a recessionary gap ensues (i.e. E-GDP < P-GDP). That said, where is Brazil, currently?
Measuring E-GDP is easy. All you have to do is look for a Real GDP time-series (discounted for inflation, hence, real). The same can’t be said of P-GDP. To this day I still have not found a convincing way of measuring it, so my analysis basically rests upon yearly R-GDP averages. If you happen to know how to do it, please, contact me by leaving a comment on sending me an e-mail².
That said, mathematically speaking, after having reached the trough in 2015 with a nosedive of -3,55%, Brazil’s R-GDP growth on a yearly average, starting in 2017, hasn’t been above 1.10%. This average, as I’ve mentioned in the beginning, might be even lower, at 1.02%, if 2019’s R-GDP is confirmed at 0.89 (as the Central Bank has recently hinted) rather than 0.95% (we’ll know that by March). Whether we assume a 0.89 or 0.95 or even a 1% growth for 2019, it is hard to believe that 2020’s GDP will be anything above 1.5% (as I have been saying it since my September 2019 text). Mathematically speaking, a 2.40% growth this year would be a point way off the curve, unless overall conditions significantly improve.
Economically speaking, as I’ve mentioned in the opening of this article, both internal (endogenous) and external (exogenous) constraints remain dismal to believe that currentt overall conditions would allow for any growth that positively distances itself considerably from the 1.02/1.10% average. Taking all that into consideration, I still uphold my analysis that Brazil’s macroeconomic stage is clearly needs to be placed at the very beginning of an uphill ascending path with a forecasted R-GDP growth for 2020 of 1.20%, nothing close to 2% or above.
1— “ “All models are wrong” is a common aphorism in statistics; it is often expanded as “All models are wrong, but some are useful”. It is usually considered to be applicable to not only statistical models, but to scientific models generally. The aphorism is generally attributed to the statistician George Box, although the underlying concept predates Box’s writings”. (Wikipedia)
2 — my e-mail is: email@example.com