# A Further Reply to David Andolfatto

David Andolfatto has written a response to my recent post on nominal GDP targeting. My initial response was largely a broader explanation of why a nominal GDP target might be optimal given a spectrum of posts that David and others have written on nominal GDP targeting. The post got so long-winded that I failed to respond in detail to David’s OLG model. Thus, in David’s recent post he summarizes the main conclusions from his OLG model and poses the following questions:

What is missing in my model? Are frictions other than nominal debt required? I have a hard time seeing how the presence of sticky nominal wages or prices are going to alter my conclusion here. But who knows, maybe someone can tell me?

I would like to take this time to answer these questions. I will do so first by discussing my view regarding nominal GDP targeting and why this element is missing from David’s model. Second, I will discuss minor issues with David’s model.

Liquidity

The main question to answer is what is missing from David’s model and why it might be important. I will answer this in a roundabout fashion. As I have previously noted, my own personal advocacy of nominal GDP targeting is due to the connection between liquidity and transaction assets. To illustrate why (I believe) this is important, consider a non-technical summary of a project that I have been working on — hopefully I will be able to post on the technical features in the very near future.

Suppose that individuals have three assets that they can use in transactions: fiat currency, government bonds, and claims to some private asset. One interpretation of this latter asset is a repurchase agreement. One question is why individuals would choose to hold all three assets. The argument that I make is that these assets have different liquidity properties, and I assume that these properties are exogenous (more on that assumption later). Government bonds differ from fiat money because they can only be used in a fraction of transactions. The same is true of the liquid assets, but in the case of liquid assets the degree of liquidity is stochastic.

Within the framework individuals are matched pairwise. Once they are matched, the liquidity shock is realized. As such, if the liquidity shock is negative, then the buyer in the pairwise meeting becomes liquidity constrained and must reduce their purchases relative to their original intentions. The result is a reduction in nominal spending and a corresponding reduction in real economic output (there is no mechanism to adjust the price level to raise the real value of the assets).

Within this type of framework, individuals gain utility from consumption. As such, the reduction in liquidity is welfare reducing. This is a characteristic to most all models in which liquidity is important. For example, Li, Rocheteau, and Weill have a paper in which the liquidity of assets is endogenous. The conclusion is the same. A reduction in aggregate liquidity results in a welfare-reducing decline in consumption.

Given the welfare properties of the model, an optimal monetary policy can come in one of two forms. The first, which I will call a first best policy is one that maximizes welfare in the steady-state. In models where money is important, this is almost always a money growth rule. In particular, optimal monetary policy is often the Friedman rule where money growth is equal to minus the rate of time preference. The second type of optimal monetary policy is one that minimizes deviations of consumption from its steady-state. In that type of framework a nominal GDP target can be shown to be consistent with that goal. (It is important to note that nominal GDP is not special in these models. Rather nominal GDP is a signal of a liquidity shock.)

What is missing from David’s model is the importance of the interaction between liquidity and transaction assets. In other words, liquid assets (i.e. money, broadly defined) are a medium of exchange. Reductions in the supply of liquid assets therefore lead to welfare-reducing declines in spending. This is absent from David’s model because money does not serve the role as a medium of exchange. Money is only a store of value. There are no liquidity shocks. A news shock could potentially take on the role of a liquidity shock as it seems to exhibit similar properties. However, the OLG framework gives different results in this context than a monetary search model would because in a search model individuals are meeting pairwise to trade.

David makes the claim in his post that nominal GDP is suboptimal because of the responsiveness to bad news shocks when the news shock turns out to be fundamentally true. In particular, he claims in his follow-up post:

So, if the news is bad, the government should increase the supply of money to accommodate the increase in demand for money (via the asset substitution induced by bad news over the expected return to investment). But if the news truly is fundamentally bad, the future real GDP should decline, and along with it, the NGDP should decline as well (it’s decline is stemmed in part by maintaining the price level target). Stabilizing the NGDP in this context would mean increasing the price-level so high as to create a transfer of wealth from creditors to debtors (instead of debtors to creditors) — something these agents would have wanted to prevent ex ante if nominal debt could have been indexed to the price-level.

I have added the boldface because this is the sentence that I want to focus on. I don’t believe that the model is unambiguous with regards to this matter.

Suppose that there is a bad news shock. Proposition (1) in David’s model implies that $q_t = M_t / p_t$ declines. Holding the money supply constant, this implies that the price level must rise. David implies above that both real economic activity should decline and that nominal GDP should also decline. It is not clear what happens to nominal GDP. Suppose that the shock is truly fundamental (i.e. productivity, $z_t$, declines). In this case, David is correct that real GDP should decline. However, since the price level rises, the extent to which this effects nominal GDP is therefore dependent on how much the price level changes relative real GDP. If the change is directly proportional, then nominal GDP remains unchanged and the monetary authority would do nothing. If I have understood his model correctly, and we assume that the marginal product of capital is constant, then this is indeed the case.

[Note: As David points out in an email, a bad news shock would increase q rather than reduce q. Thus, this criticism is incorrect as nominal GDP does unequivocally decline if the news is fundamentally bad.]

### 2 responses to “A Further Reply to David Andolfatto”

1. Josh: You might want to take a look at this paper here, where I embed “liquidity shocks” into an OLG model.

http://research.stlouisfed.org/publications/review/12/05/187-196Andolfatto.pdf

Off the top of my head, I’m not sure what this implies for NGDP targeting. However, let’s assume that it implies a positive role for the practice. Then the question becomes this: How can we distinguish empirically between a “bad news shock” and a “liquidity shock”? I think they might have very similar effects, qualitatively, in the model. And yet, they may deliver very different policy implications — although I’m not sure about this yet.

2. David,

That type of model is more consistent with what I am referencing. Nonetheless, I still see two issues of separation in our thinking.

1. The difference between OLG models and Lagos-Wright search models seems important. In the LW model, money serves as a medium of exchange. As such with multiple transaction assets, it is the total stock of liquidity that matters. In the OLG model, the liquidity shock results in a credit crisis. This is different from the liquidity shock in the LW model and the reason is because money and other assets are stores of value in the OLG model and not media of exchange. This distinction is important as it suggests that in the LW model stabilizing the supply of liquidity is welfare-increasing. A second-best policy (as defined in the post above) is one that stabilizes nominal GDP. A first-best policy is one of constant money growth — the Friedman rule or a positive rate of growth if there are distributional effects. It is not clear that this is true in the OLG model for the reason mentioned above.

2. You suggest that it might be hard to distinguish between a bad news shock and a liquidity shock. This is certainly true of these two models. However, the empirical evidence on news shocks seems to be at odds with your model. For example, in your model, a good news shock causes an decrease in real money demand. Holding the money supply constant, this implies that price level should rise. However, empirical evidence on news shocks seem to suggest that the price level falls following a good news shock. See for example, Barsky and Sims:

http://www.nd.edu/~esims1/news_combined_final.pdf