NOTE: This is a continuation to our previous post. Click “here“ to visit the first part of this article.
In the last post, we spent some time discussing an important reason behind the need for economic modelling. On that note, we talked a lot about DSGE, one of the popular models in contemporary economics. What I did not explain though is how a model is constructed. Understanding the process involved in modelling is essential if you want to be able to comprehend any economic model out there.
The amazing thing is that you only need to consider one simple model to have enough intuition to digest more complex models (within reason of course), their pros and cons, and why they do not work in certain scenarios.
DSGE is too complicated even for some economic professors out there. Just take a look at the picture attached with this post to have a taste of it (even that is still considered a basic framework). For our purpose, a simple and more intuitive model will do the trick.
Let’s give it a shot!
An example of a more complex economic model
2. First baby step into the realm of economic modelling
Consider a 2-period consumption model of a one-person economy. This model exists for only 2 periods (1 and 2). It has only 1 person (you!) in the economy who represents everyone else. This is called a representative agent economic model. Think of each period as consisting of 50 years, meaning you work and earn money in period 1 (the first 50 years of your life), and then retire and live off your saving the in period 2 (the second 50 years of your life).
Now, we introduce a set of assumptions:
– First, everybody else in the economy is just like you, so it is enough to study just one person.
– Second, you have no children (since the economy ends in period 2), and thus, you will leave no bequest (consume everything you earn).
– Third, there are no firms and no government in this economy (that is why it is called a consumption model).
– Fourth, you are a rational individual who maximize your well-being to the utmost extent.
– Fifth, your earning in period 1 will be either spent on immediate consumption or saved for future consumption in period 2.
– Sixth, the goods you consume generate only positive welfare for you, meaning no goods will cause pollution or other negative effects.
– Seventh, the satisfaction you gain from your consumption exactly equals to the amount in
*** QuickLaTeX cannot compile formula: that you consume (which is quite reasonable). - Eighth, your saving will generate interest for you (just to make it a tiny bit more realistic).</span> <span style="font-size:14px;">------------------------------------------------------------------------------- With this set of assumptions in mind, we begin building our simple economic model as below:</span> <span style="font-size:14px;">****2-PERIOD 1-PERSON CONSUMPTION MODEL****:</span> <span style="font-size:14px;">We maximize: U = C1 + C2</span> <span style="font-size:14px;">Subject to the following constraints: (1). C1 + S = W (2). C2 = S + R*S (3). C1>0; C2>0</span> <span style="font-size:14px;">Where U is the utility (satisfaction/welfare) you gain from consumption. C1 and C2 are consumption in period 1 and 2 respectively. S is saving in period 1. W is the total wage earned in period 1. R is the interest rate. </span> <span style="font-size:14px;">-------------------------------------------------------------------------------</span> <span style="font-size:14px;">Let me explain the model. </span> <span style="font-size:14px;">The main equation of the model simply says that your well-being will depend on your consumptions in both period, and this is all that matters to the economy because there are no firms, no government, and you represent all other people. If you are happier, so are they.</span> <span style="font-size:14px;">But, this is inadequate. In economic modelling, we have to present a set of constraints. Why? Because if there is no constraint, then you can just get infinite utility (U) since you can increase C1 and C2 as much as you like. In other words, with just the main equation U = C1 + C2, you have nothing to bind your consumption, so based on the equation alone, you can just get infinite amount of satisfaction (which is just stupid).</span> <span style="font-size:14px;">Thus, we create 3 constraints, each with its own purpose as below:</span> <span style="font-size:14px;">(1). You work and earn W amount of income. With this income earned in period 1, you spend some on consumption C1 and save whatever left (S). Note that W will be a finite number (say, W = 50 years * *** Error message: Missing $ inserted.
*** QuickLaTeX cannot compile formula: 100,000 total life income).</span> <span style="font-size:14px;">(2). Your consumption in period 2, C2, will equal to the amount you save in period 1 (S) plus the additional amount you earn from interest rate (R*S). This makes sense because: If you save *** Error message: Missing $ inserted.
100 and the interest rate is %20 for the 50 years, then the final amount of money you get in period 2 = 100*0.2 =
*** QuickLaTeX cannot compile formula: 120. This will bind your C2.</span> <span style="font-size:14px;">(3). Your consumptions from both periods have to be positive (the model allows for zero consumption, but we will assume otherwise). This also makes sense because you are maximizing your personal well-being, and since the consumption generates only positive payoff, choosing not to consume (choosing C1 = C2 = 0) would make you a very irrational person. But earlier, the model explicitly assumes you are rational (not stupid), so you will no doubt use your earning to consume. For this reasons, C1 and C2 have to be larger than 0.</span> <span style="font-size:14px;">Now, we have a nice and simple economic model to play with. Then what?</span> <strong><span style="font-size:16px;">3. WHAT IS THE POINT?</span></strong> <span style="font-size:14px;">The point is to simplify the economy by eliminating some elements and preserving some others to allow us to study the variables of our interest (in this case, consumption and saving). Okay, so what can our model tell us then?</span> <span style="font-size:14px;">Just from glancing this simple model, we can say that higher wage will lead to either higher period 1 saving or consumption or both. Higher interest rate R will allow us to consume more in period 2 if we save more. This might reduce C1 as you want to consume more in period 2. It is also easy to tell that any reduction in either period 1 or period 2 consumptions will make you worse off.</span> <span style="font-size:14px;">Is that it? No. This is just the main model. The goal is to perform some derivations of each of the variable of interest to see how they interact with other variables and parameters. Once we understand the relationship, we can introduce new values of our variables (like new values of C1, C2, S) into the model, and then use the model to predict the future economic performance, future saving or future consumption.</span> <span style="font-size:14px;">Our model is of course not realistic because I make it so simple that it does not even make sense once I manipulate it mathematically to find the optimal allocation of resources. It still generates some interesting results. With a bit of knowledge of calculus, anyone can derive the followings:</span> <ul> <li> <span style="font-size:14px;"> *** Error message: Missing $ inserted.
1 decrease in period 1 consumption will increase your well-being by whatever the value of R is. The optimal strategy for economic growth in this case is to consume as little as you can in period 1 and consume as much as you can in period 2. But, C1 cannot be 0 because the constraint said C1>0 (So that you do not starve to death in period 1).
A $1 increase in W (your income) will increase your well-being by (1+R).
You see, these are just two simple conclusions that we can get from a very barebone model (a model that far deviates from reality). Imagine a bigger and greater model with more variables and interactions coming into play. It will allow us to answer so many questions about our economy.
However, note that any model is only as good as its assumptions. Garbage in, garbage out. DSGE, though looking like an elegant model, back then did not include the financial sector into its equations. The result? A disaster. It failed to predict the global financial crisis which stemmed directly from the financial sector (obviously). Why did it not include financial sector from the beginning?? Because economists observed several prior recessions, and none was generated by financial fiasco. Big financial disasters before 2008, like the dot-com bubble, did not cause any severe crisis for the economy as a whole either. Economists like to observe the past to understand the present and the future, and as a result, they failed to consider the financial component of the economy in building their model. This is a huge miscalculation which shows the weakness of modern economics that relies too heavily on maths and statistical evidence than logical deduction. We however learned from such mistakes, and believe it or not, economic thinking has improved greatly resulting in a more stable economy we have now (economic volatility has decreased significantly compared to the past).
You might be tempted to think that it is not of relevance to you, but let me tell you that your life as it is now relies on the accuracy of such models. You may not know this, but many giant economies of the east and west employ economic models like DSGE to monitor and forecast their economies. This information is then used to set policies that affect you and your country. Remember, even in South-east Asia (which you might expect to be far removed from stupid decisions made in the US), millions of jobs were lost during the global financial crisis. This is just to show how powerful and dangerous an economic model can be. That is why economists can either save lives or kill indirectly… as history has unveiled so many times before.