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I'm reading this book on macroeconomics.

When determining the nominal interest rate, the Central Bank has in mind its real interest rate goal. By the Fisher Equation: $i_t=r_t+\pi^{E_{CB}}_{t+1}$, since at time $t$, I would need to know the price level at time $t+1$ to know inflation for next period, we use an expected value for inflation. I put the superscript $^{E_{CB}}$ to denote that the expectancy is formed by the central bank.

In the usual Philips Curve, we have $\pi_{t+1}=\pi^{E_{SS}}_{t+1}+\alpha(y_{t+1}-y_e)$ I put the superscript $^{E_{SS}}$ to denote that the expectancy is formed by the Supply Side (wage and price setters, i.e., with all available public information).

Recently, from a talk with someone who worked at a central bank, I learned that there's some difference in amount/quality of information that it's publicly available to wage and price setters, and that which is available to the Central Bank.

In the book I'm reading, the authors state one possible way of escaping a deflation trap, even if in practice it will not always work, is that to have higher expectations so that the minimum threshold for the real interest rate is lower enough to increase output until equilibrium.

Now I was wondering if it was not possible for, in some situation, the CB publicly divulged information lead to workers and firms have higher expected inflation, while the CB would know those expectations to be a bit too optimistic, such that in reality that period real interest rate would be much lower to be enough to get out of deflation trap?

I think I must be making some errors in this reasoning.

Any help would be appreciated

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    $\begingroup$ It is my impression that you have installed a tap in my brain. Differentiated information sets and strategic use of information from "opinion makers" and whether it can successfully manipulate the public's expectations (at least in the short run) is the next step in the research I have started in my PhD! $\endgroup$ – Alecos Papadopoulos Nov 22 '15 at 16:44
  • $\begingroup$ In my opinion, strategies where information sets are used strategically could work in a static sense. However, in a case where interactions are dynamic , misrepresentation of information should lead to decreases in credibility. Put differently, if the monetary authorities divulged exactly the opposite of the information which would lead to individuals making large errors in prediction, perhaps the optimal strategy of individuals next period should be to completely discount the information given out/ or act opposite to what they would have done if information was credible. $\endgroup$ – ChinG Nov 22 '15 at 18:38
  • $\begingroup$ I guess a model of the form where information sets are mispresented should take into account the costs of this misrepresentation as well...I can imagine models where the monetary authorities have to optimize with regards to amount of information to misrepresent, with a cost of loss of credibility for future amounts of information. $\endgroup$ – ChinG Nov 22 '15 at 18:41
  • $\begingroup$ @AlecosPapadopoulos =D It's a great compliment you give me to be able to have an idea with some semblance to one of yours. ;) $\endgroup$ – An old man in the sea. Nov 22 '15 at 23:47
  • $\begingroup$ @ChinG Yes, there would be a cost in the reputation, only if the public were aware of this possibility and the CB had no way in the near future to return to the true values without making the reversion public knowledge. Intuitively, at least. $\endgroup$ – An old man in the sea. Nov 22 '15 at 23:51
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It is certainly possible for a central bank to move the economy away from liquidity trap or deflation trap by proper signals. Signals and targets are undoubtedly effective, as this NBER paper discusses http://www.nber.org/papers/w13932. I read an article, which I cannot find now, saying that signalling and targeting by central banks are sometimes more effective than actual policy changes. The problem is that the economy and financial markets have a huge amount of different players with different interests and goals so it is hard to predict with certainty the effect of the CB revealing certain information.

One thing I have to disagree with is that signalling higher expectations would reduce real interest rates and move the economy away from deflation trap. The equation it=rtt+1 would be more accurate as it+1=rt+1t+1. If you write it like that, then you can see that signalling higher inflation expectations would also signal an incoming interest rate hike, given that any central bank has the policy to keep inflation low and stable. When markets expect a rate hike, they reduce their equity and commodity positions (sell stocks, oil, gold etc.) and move into bonds and other cash positions. This sucks the money out of economy and creates more deflation. So if the CB wants to reduce deflation, the ideal strategy would be the opposite: signal sluggish growth and prolonged low interest rates. This is just what Fed has been doing for several years now and, arguably, it has worked.

I can also add, as @ChingG noted in comments, the CB has to maintain credibility and not lie. On top of hurting its reputation, the central bank board members are also liable to the government for saying the truth. For example, if the Fed Chairwoman lied to Congress, she would be breaking the law. It makes more sense for the CB disclose the true data and to interpret the information the way the CB sees fit and give the signals and targets it deems necessary, but not "hide" information.

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Regarding specifically whether a CB may divulge information that leads to workers and firms have higher expected inflation, (despite the fact that the CB knows those expectations would be a bit too optimistic), there is evidence of something related (CBs have incentives to misrepresent information in order to manipulate inflation expectations) in this article: https://ideas.repec.org/a/bla/coecpo/v32y2014i4p802-810.html

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