Working with the Tautology Model

Scott Sumner writes,

the NGDP approach is a very naive model that treats NGDP sort of like a big pot of money, which is shared out among workers with sticky wages. If some day the pot is smaller, then there’s less money to share, and some workers end up disappointed (unemployed.) It’s completely agnostic about the micro foundations…

Which is fine with me. Again, think of the mineshaft analogy, with real-world observations on the surface and the optimization-equilibrium paradigm buried below. To connect the two, you can try to start inside the mine and tunnel out, or you can start outside and tunnel in. My displeasure with much of macro the past thirty years is that it insists on the inside-out approach.

Consider the tautology model: hours worked = total wages divided by the hourly wage.

If the Fed were to target total wages, what could go wrong? Sumner cites the Lucas critique. In this context that would mean that the sticky nominal wages you observed in the past were due to the Fed not trying to mess with total wages. As soon as the Fed tries to mess with total wages, workers will catch on and start paying closer attention to real wages.

I believe that something else will go wrong. The Fed will not be able to hit its target for total wages! Suppose we write MV = W, where W is total wages and V is the velocity of money expressed in terms of total wages rather than nominal GDP. What I am inclined to believe is that moderate changes in M will lead to approximately equal and opposite changes in V.

Picture this as the Fed having a steering wheel, M, that is only loosely connected with the front axle, W. The Fed can turn the wheel quite hard while the axle barely wiggles. It may take extensive turning of the monetary steering wheel over a long period of time to obtain a response of total wages. In fact, the period over which wages are sticky may turn out to be shorter than the lag between shifts in monetary policy and changes in total nominal wages.

We have a complex, sophisticated monetary system, in which people’s ability to undertake transactions is not proportional to the amount of currency in circulation. We have a large financial system, in which the Fed is only one player. I keep trying to hold down people’s estimation of the power of the Fed.

4 thoughts on “Working with the Tautology Model

  1. For April Fools day I think you should write a post about why Scott (& macro generally) are totally right, you are wrong, and don’t forget to issue apologies to all the aggrieved parties. Scott should do the opposite and we agnostic readers will award the first Annual Test Match Cup.

  2. If moderate changes in M lead to approximately equal and opposite changes V, then what a bout slightly larger changes in M? At some point V starts to move in the same direction as M.

    I must assume then that your MV = W model implies that the Fed basically has two options – moderate changes in M that have no effect on W or large changes in M that cause rapid growth in W. What in your model results in this knife edge distinction between pushing on a string and hyperinflation?

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