# A Flawed Assumption in the IS-LM Model

In this article I am going to argue what I believe is wrong with the current understanding of the IS-LM model. This model is taught in general macroeconomics and used to create and understand the implications of economic policy. Therefore it is important that a model of such importance reflects reality accurately to some certain extent. Of course I am not trying to argue that we can develop a model that is completely accurate because the world is far too complicated for that, but the assumption I am going to be discussing is so far from the truth that I think imposing it is incredibly wrong to do. However, modern thought is insistent on the success of the IS-LM model and as a result seems blind to its shortfalls.

The ordinary IS-LM model is characterized by the following two equations where the first is the IS curve and the second is the LM curve:

The equilibrium is found at the crossing of these two curves where Y=M/P. This equality comes from the quantity equation MV=PY where velocity V is taken to be constant and presumably absorbed into Y when the equation is written as M/P=Y/V. However, making this assumption is incredibly wrong to do. This is obvious if we take a look at M2 velocity data:

One thing to note from this chart is that M2 velocity seemed to be contained to a narrow range from the late 1950s to the early 1990s. In fact, the slope of a regression line constructed though this period would find a slope indistinguishable from zero utilizing a typical t-test. Thus, it might have been reasonable to make a constant velocity assumption argument during this period. However, since the late 1990s something has clearly changed. I found that a sup-wald test confirms this by finding a break in the data in 1992. So then the next natural question to ask might be: why did this change occur? After some thought I’ve pieced together a working theory. First, I argue that we can interpret the magnitude of variation in the velocity as a measure of people’s wiliness or ability to take part in transactions. Since the period from the 1950s through the 1990s saw a velocity that was contained to a narrow range I would argue this reflects consumers and firms had some “baseline” level of willingness to consume, invest, and otherwise participate in economic transactions. However, since the 1990s I think we could interpret the increased volatility in velocity to indicate that consumers and firms have lessened their willingness or have less ability to participate in additional spending. This interpretation originates from looking at a chart of total debt minus government debt as a percentage of GDP:

I present this debt chart excluding government liabilities because doing so provides a conservative look at debt levels. You’ll notice that the late 1980s/early 1990s is the point in time when this level of debt eclipsed 100% of GDP for the first time. Since then debt has ascended even higher. Debt as a percentage of GDP reached an all-time high prior to the financial crisis and has since come down to around 130%. However, 130% is nonetheless still well above levels seen prior to the late 1980s. With this consideration in mind I hypothesis that at some point firms and households reached some level of debt that is unmanageable– possibly in the late 1980s/early 1990s when debt reached a level north of 100%. Households and firms are no longer as able to take on more debt to continue increasing their spending in a manageable, responsible manner like was once the case. As a result, we see this fundamental change broadcast itself in the form of large swings in money velocity.

So bringing our conversation back to the IS-LM model, if we do indeed drop this assumption of constant velocity we can alter the IS equation slightly to find an interesting result. David Romer derives the “New” Keynesian IS Curve in his *Advanced Macroeconomics *book from microeconomics foundations. He begins with the following equation:

Next he argues that we can set C=Y since consumption is assumed to be the only component of GDP in this derivation. However, if we drop the constant velocity assumption then C=Y/V instead. Thus substitution into the above equation yields:

Romer approximates the natural log of (1+r) to be equal to r and suppresses the natural log of beta. So if we do this and simplify then we end up with the following equation:

The only way this differs from Romer’s IS derivation is that it contains the natural log term with money velocity. However, we can see that Romer’s equation is just a special instance of the derivation above because if we assume velocity to be constant then the velocity term drops out since the natural log of one is zero. But if velocity changes from one period to the next then the velocity term is always negative. So think about what this means. When the Fed wants to act to stimulate the economy they will shift the LM curve right in order to move the IS-LM model into a higher equilibrium Y. Although, if money velocity changes from one period to the next then this stimulus effort turns out to be pointless. This is because the negative drag of money velocity can partially or completely offset the effort of expansionary policy. This concept highlights a topic that is paramount to our discussion of economics in the world today. The Fed and everyone else that believes monetary policy works as it has been taught in schools for years fail to see that we are living in a new era. I would make the claim that we are living in an era where the last few recessions and weak growth rates witnessed since the financial crisis are not an “Aggreate Demand” problem. Instead, our economy is structurally broken. Households and businesses don’t want or can’t handle more debt shoved down their throats. You would think this would be unbelievably clear since we’ve experienced a slow, very lackluster recovery since the financial crisis compared with prior recoveries even despite the extraordinary monetary policies put into place since then. But instead all that these policies have done is stolen demand from the future to the here and now. Thus, in order for the United States to see truly great times again we must address the causes of these structural problems rather than masking them with policies that just kick the can down the road.