CBR’s inflation expectations estimates: introduction (1/2)

Inflation expectations at some point have become the corner stone of CBR’s monetary policy. Changes in their level are cited in each and every monetary policy press release. The most recent reference is as follows:

“… In addition, inflation expectations of households escalated in November, although projected to decrease.”

In order to identify these expectations CBR regularly orders “Public opinion” fund to conduct countrywide surveys. These surveys ask a variety of question on topics ranging from preferred savings vehicles to consumer confidence. Additionally two types of questions on inflation expectations are asked:

  1. open question about numerical estimate of inflation 12mo ahead;
  2. multiple-choice question on prices 12mo ahead.

By averaging (or taking a median of) responses to the type 1 question one can obtain a so called direct estimate of inflation expectations. Its ease of calculation has a certain downside attached. Direct estimate has a known upside bias possibly explained by availability hypothesis, i.e. respondents reporting more recently observed or sizable price growth as inflation expectations (these are almost invariably related to food inflation), while less impressive price trends (i.e. stagnating rent) are left unacknowledged. Current CBR’s direct report provides a median of the numerical responses of 15.0% YoY and it has rarely been under 11.0% since 2010.

An alternative method helps partly alleviate the problem by simplifying the problem for the surveyed and asking them where relatively to current inflation would future trends lay.  This method is called probabilistic estimate and relies on responses to type 2 question.

Because it will be the focus of what follows let me cite the text of the question here:

“Do you believe prices in the next 12 months will:

  • will be growing faster than now
  • will be growing at the same pace as now
  • will be growing at the same pace as now
  • will not change
  • will decrease”

Results are presented in the report (Russian only) as a chart:


Source: CBR.

So with a short introduction to why we do this and where the data come from let’s proceed with identification methodology.

Methodology [1]

In order to recover expected inflation with probabilistic method we should make two additional assumptions:

  •  F(*) family of the probability distributions of inflation expectations;
  •  \pi_0 the reference inflation rate to which the surveyed do benchmark their expectations, i.e. “inflation now”.

Next we assume that when answering questions people do have some confidence intervals, i.e. regions within which inflation is assumed to be qualitatively equal. That is if I think that inflation might be -0.5 – 0.5% in the next 12mo I would likely choose “prices will remain constant” option.

Fist let’s denote the shares of the answers as follows:

  • \beta_1 is the share of surveyed reporting inflation will accelerate;
  • \beta_2 is the share of surveyed reporting inflation to remain stable;
  • \beta_3 is the share of surveyed reporting inflation to decelerate;
  • \beta_4 is the share of surveyed reporting inflation to be zero;
  • \beta_5 is the share of surveyed reporting inflation to be negative;
  • \beta_6 is the share of the surveyed that had failed to respond.

Next we will get rid of those who find it too difficult forming 12mo ahead inflation expectations, making sure the remaining shares do sum to unity:

 \alpha_n=\frac{\beta_n}{(1-\beta_6)} for n=1..5

Graphically the whole picture might look as follows if we assume normal distribution:


At this point we might write the following system of equations :

 \begin{cases} \alpha_1=1-F(\pi_o+s,\theta)\\ \alpha_2= F(\pi_o+s,\theta)-F(\pi_o-s,\theta)\\ \alpha_3=F(\pi_o-s,\theta) - F(l,\theta)\\ \alpha_4=F(l,\theta)-F(-l,\theta)\\ \alpha_5=F(-l,\theta) \end{cases}

where $\theta[/latex] is a vector of two parameters of the distribution of inflation expectations, s and l are sensitivities.

This system has four unknowns: s, $l[/latex], 2 for $\theta[/latex] which makes the last equation redundant.

The last step would be to solve the system for parameters of the F(\theta) and calculate the expected value implied by the estimated distribution.

Example: Verify November estimates

We now can try and verify CBR reported estimates of inflation expectations for the Nov-15 wave of the survey, which put it at 15.0%. As the chart above from this report shows:

  • \beta_1 is .19;
  • \beta_2 is .52;
  • \beta_3 is 15
  • \beta_4 is .0;
  • \beta_5 is .0;
  • \beta_6 is .15.

Because of the rounding effects these numbers do sum up to 1.01, so I divide them through by \sum{beta_n}.

After that we can get rid of the ‘do not know’ answers dividing through by $(1-\beta_6)[/latex], so we have:

  • \alpha_1 is .22;
  • \alpha_2 is .60;
  • \alpha_3 is .17
  • \alpha_4 is .0;
  • \alpha_5 is .0;

For simplicity we make the uniform probability distribution assumption:

F(x)= \begin{cases} 0 & \text{for }x < a \\[8pt] \frac{x-a}{b-a} & \text{for }a \le x \le b \\[8pt] 1 & \text{for }x > b \end{cases}

Now we can solve the whole thing numerically. I use Mathematica, which is matter of personal preference, but a suitable routine can be developed even in Excel. I assume \pi_0=14.8 which is the YoY inflation rate during the week when the report has been published















The result is {s -> 3.00759, l -> 1., a -> 10.0573, b -> 20.0054}. Expected value of the uniform distribution is \frac{a+b}{2}, so our estimate of inflation expectations is 15.0 exactly in line with the CBR.

Alternative, we can use Mathematica to calculate expected value of the distribution: [wlcode]Expectation[x, x \[Distributed] pd /. sol][/wlcode].

The results might vary due to the difference in the choice of the \pi_0 so full transparency would require the CBR reporting its choice of the ‘current inflation rate’ or the \pi_{0} in the inflation expectation reports.


In the next post, we are going to decompose changes in inflation expectations into the change in the survey results and change in the \pi_0.

Recommended reading:

  1. We discuss a simplified methodology. Actual one is outlined in Khazanov, Alexey (2015),  Inflation expectations quantification by the Bank of Russia (pdf), Money and credit
  2. CBR (2014), Guide to inflation expectations (pdf)
CBR’s inflation expectations estimates: introduction (1/2)

Afanasyev et. al: Budget and the fiscal system

Coming from a monetary policy background I still find it buffing how much more complex is fiscal policy. There’s a substantial number of levers that central bank can use. Still you might call the key rate The Instrument.
When it comes to fiscal policy volume of revenue and spending, their structure and a universe of related issues come into play so that bottom line deficit/surplus alone is far from being an indicator of fiscal policy stance. This not even looking at issues of budget federalism or politics of the budget process.
I gather, this complexity of the topic does not lend it to clear exposition.
The result is, there’s still no decent book on fiscal policy in Russia. I went through a couple of textbooks which were not substantial enough to mention here, before deciding to give a closer look at ‘Budget and fiscal system’  by Mstislav Afanasyev.
The book had a promising feature of being authorised by Alexey Kudrin who was behind many of the current features of the fiscal system including the Reserve fund and NWF, medium term budget planning, fiscal rule etc.
Having spent a fair amount of time with this book I’ve come to the conclusion that it might be one of the better books on fiscal policy in Russia. But this resulted not because of high quality of the text but because the bar is set at quite a low level.
Some of its more visible shortcomings below.
Extensive quotes from the Budget code, weak on economics 
The book is basically an introduction into the fiscal law, but it does lack any analysis of the fiscal system from the economics view point. Even such basics as cross country comparative tax burden analysis, efficiency of spending, tax collection efficiency are avoided.
Weak on case studies, examples
The text is close to sterile when it comes to the intersection of law and its application. There’re exactly zero information on problems of fiscal federalism, fiscal discipline on regional and municipal levels and politics seem to be absent from the budget process.

The text needs editing: extensive repetitions

The text is written in the this variety of language which you might expect to find in legal papers, but which seems much less appropriate for the textbook. Many paragraphs are word by word repetition of text in the preceding paragraph with the difference being that the same idea applies for example to two levels of the budget system. I think a more thorough editing would allow to cut up to a forth of the text.

The rediculous pie 3d charts
The 3D pie charts (authors favorite type of chart) occupy up to half of the page to show the relationship between two numbers.
Stub chapters: sovereign external lending
The chapter on external lending of the country is basically a plan to write a chapter. In the chapter explicitly devoted to external debt there’s no single example of external lending of any country, not to say discussion of the terms or a purpose of such a loan.
The philosophical chapter fetish 
For some reason the book devotes a whole complete chapter on the philosophy of the fiscal system which goes as far as discussing the nature of the state. It tries to cover everything from Thomas Aquinas to Mikhail Bakunin. The reason for this escapes me.

My personal preference would be for more detailed presentation of the core material.

All in all, it is hard to recommend this  this book. Text obviously needs work: more cases, examples, less repetitions etc.

To add a constructive touch, here’s a list of sources on fiscal issues which are highly readable: i) Economic Expert Group’s publications, ii) NIFI’s Financial journal is a good source but I usually only look at the articles authored by NIFI’s own researchers and skip everything else.
Afanasyev et. al: Budget and the fiscal system

HSE Seminar: Signal and structural models at the service of monetary policy

Back a good couple of years ago when I was working on my diploma on monetary policy I stumbled upon an interesting paper by the CBR’s economists. It was about some model they’ve used for macro forecasting. The thing that struck me was that it seemed to be only published nowhere expect for some conference proceedings on the site of the National Bank of Belarus. That is not exactly where you would expect to see it. No Russian journals, nor presentations.

Now time to make up for it. One of the coauthors and my current colleague Alexander Borodin presents the CBR’s model at HSE banking seminar ‘Empirical methods in banking sector analysis‘.

Here’s Alex’s presentation:

I’ve also presented my article that was published in Russian ‘Applied econometrics’


HSE Seminar: Signal and structural models at the service of monetary policy

Fioramonti: Gross Domestic Problem

The other day finished Fioramonti’s  “Gross Domestic Problem: The Politics Behind the World’s Most Powerful Number” [1] and here’s what I learned.

In the first part the author provides light introduction into history of attempts to measure level of economic activity.  Before GDP emerged as a dominant standard there were some alternatives including social accounts system that was in use in USSR.  Overall this background chapter is also the most powerful one.  One key take away is the notion of recency of creation of the GDP framework.  Today you compare one government to another on their performance in terms of economic expansion until the 1930s there was no systematic approach to measure it.

The second chapter is devoted to shortcomings of the GDP as a measure of growth of the economy. Here Fioramonti plunges into the usual kvetching: how does GDP change if the worker is happy or not, how is quality of life represented in the GDP growth number. Apparently the author implies that the decent indicator of economic activity would show externalizes of economic activity: degradation of environment and lower wildlife population. For reason that escapes me he’s not happy with having all those indicators but wants to incorporate ecology into GDP.

Another critic, which is somewhat more of a methodological issue is the fact that GDP does not record activity of some of the  sectors, that are deemed outright illegal… in some periods, but might someday admitted into the formal economy. This however again is a minor issue. This part of the book is considerably weaker than the fitst, but…

…the weakest part comes last. It’s the collection of proposals for reform. For one, Fioramonti promotes the idea of ‘local money’, the money which can be earned and spent within some predefined geographical coordinates. This, in my view, does solve no problem, but in extreme scenario makes the owner of such money essentially chained to the place where his savings worth something.

Other statements are too emotional:  “There’s little doubt, indeed, that the popularity of national income accounts has given the upper hand to all industries that pollute and deplete, since GDP portrays these acts as economic progress.”

This is a rather naive way of thinking of the forces behind ‘pollution and depletion’.

The whole proposals chapter reminds me of the good old Hugh Laurie scetch:

Overall the first chapter might worth a read, but the book is quite unfocused and short on original ideas.

Fioramonti: Gross Domestic Problem