Modeling interest rates Riksbank

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Table of contents

Introduction

1. Literature overview

2. The decision-making process of Riksbank: description and results of main researches

3. Econometric framework: cross-nested ordered probit

4. Data collection and construction the model specification

5. Estimation results

Conclusion

List of references

Appendixes

Introduction

In the majority of econometrics analysis the great number of zero observations prevails. It is the feature of many different fields of science. When labor economists and sociologists study the behavior of unemployed people - “zero job” - they should separate people, who search but cannot find a proper job, from those who do not search at all. Reasons of “zero children” are said to be the choice or the illness, reasons of fast recovery of patients - strong immune system or correct treatment. There are many such examples from sociology, medicine, natural sciences and, of course, economics.

My diploma paper is devoted to the study of zero but meaningful data in macroeconomics field. Zero change of interest rates made by many central banks worldwide is quite usual phenomena, however the nature of status quo decisions (zero responses) is not always taken into account due to the complexity of analysis. But such responses could occur in different economic conditions - in the periods of neutral, loose or tight policy regimes. These regimes are identified by the following algorithm: neutral policy - the rate was maintained in the previous periods and is not changed in the present, loose - the rate can be decreased or left unchanged, tight - the rate can be increased or also left unchanged. Zeros that are obtained while neutral regime is observed are named “always”, others - “not-always”.

I am going to analyze status quo responses of the central bank of Sweden - Riksbank. There are two main reasons that have motivated me to use the national bank of this country for the practical part of my work. First of all, by analyzing Riksbank's interest rates from 1999 to the present time a lot of zero changes are investigated. At the graph that is represented in the Appendix №1 it is clearly seen that these zeros are heterogeneous - they exist in the presence of different trends. And secondly, central bank of Sweden always publishes official report of the Monetary Policy Council (MPC) meetings from the every first session. On such meetings each MPC policymaker votes for the change in the interest rate. Sweden is one of the few countries that store information about every meeting in open access immediately after the session. Such kind of data gives an opportunity to build the panel data analysis - to analyze not only the whole committee but also each member in each period of time. It expands the amount of data collected and makes my practical part deeper and more accurate.

The main problem that arises when you discover this topic is how to analyze and which method to use because simple discrete methods fail due to the complexity - you should analyze not only zero responses but also zero responses in different conditions. In my graduation thesis I would use as the main tool the absolutely new model that was suggested by Andrei Sirchenko in “Modeling status quo decisions: a cross-nested ordered probit model” in 2015. This approach (CNOP) simultaneously estimates three different equations of three regimes that previously could be only separately estimated by ordinary probit model (OP) and its extensions. I am going to test the efficiency of the new model against the classical one using macroeconomic data of Sweden by different methods of comparison two models.

In Section 1 of my work I would make a short review of the main literature resources that made a base of my thesis. Section 2 will contain the theoretical discussion of the fundamentals of Monetary Policy Committee of the Riksbank and already existed researches on this topic. This information will help me to understand the decision-making process of individual members and the whole committee and to emphasize the significance and relevance of my paper. Section 3 will describe in details the model that was suggested for the analysis. This part is about the econometric framework of cross-nested ordered probit approach and its advantages in contrast of older models. In section 4 I am going to start to describe the practical part of the thesis - the specification and data that is collected. In section 5 I will continue it by reporting my main results. All results - theoretical and practical - will be pulled together and analyzed in the conclusion.

1. Literature overview

My graduation thesis is based on the paper of Andrei Sirchenko “Modeling status quo decisions: a cross-nested ordered probit model”. At this statement author emphasized the problem of studding abundant status quo decisions using probit models that had existed before. Cross-nested ordered approach was developed to overcome this problem. The paper describes how CNOP and correlated CNOP models were generated from older models for the first time. It contains all full information about the new approach and also the compassion of it with Ordered probit, Nested ordered probit, correlated Nested ordered probit and Middle inflated ordered probit. Andrei Sirchenko has used new flexible model to explain the process of making decisions of monetary policy committee of the National Bank of Poland.

In my paper I will test if CNOP model that was suggested by Sirchenko is efficient for modeling interest rates of Swedish central bank. My thesis is different from this paper mainly because mine is focused on practical use of cross-nested ordered probit approach for macroeconomics data and comparison it with ordinary OP rather than in the process of creating this model. “Modeling status quo decisions: a cross-nested ordered probit model” will help me to understand how to apply CNOP to my model specification.

One of the models that were used for this problem before is Middle inflated ordered probit that was created by Benjamin E. Bagozzi and Bumba Mukherjee in “A mixture model for middle category inflation in ordered survey responses”. In this paper authors introduced a problem of “face-saving” answers - answers that do not reflect real opinion of the respondents but were given rather because of non-acquaintance or anxiety of expressing real opinion. This model also studies zero responses but it divides it into two groups - those that really means “no change” and those that are “face-saving” ones and do have meaning. B.E. Bagozzi, B. Mukherjee “A mixture model for middle category inflation in ordered survey responses”, 2012, p.2.

Another important literature source is “Picking the Brains of MPC Members” by Mikael Apel, Carl Andreas Claussen and Petra Lennartdotten. The paper contains all needful information about the structure of the Executive Board of Riksbank: optimal size, decision-making process and the degree of transparency. It reports the results of the survey that was made using responses of all present and former members of Riksbank MPC. By using these responses it becomes clearer what motivates individual members to make the certain decision. It is quite important for generating the true specification - what explanatory variables to choose and why.

There are some papers that compare the effectiveness of the work of Executive Board of Swedish central bank with effectiveness of those of central banks of other countries. “Monetary policy committees: comparing theory and “Inside” information from MPC members” by Mikael Apel, Carl Andreas Claussen (representatives from Riksbank), Petra Lennartsdotten and Oisten Roisland (representatives from the central bank of Norway) compares MPC of two Scandinavian central banks. Authors have studied all features that should be examined while observing this topic: how each member of the committee formed his view, for what extent the role of the Governor was important, why they changed their minds during the session. One important for my thesis conclusion that was made by the authors is the foundation of “preferences for the status quo” in both banks. Apel M., Claussen C.A.,. Lennartsdotten P., Roisland O. “Monetary policy committees: comparing theory and “Inside” information from MPC members”, 2015, p 81. It means that the object of my work has real meaning that was emphasized by the authorities.

In this paper authors have referred for the idea of analyzing policymakers' decisions by applying individual loss function that was firstly suggested by Alessandro Riboni and Francisco J. Ruge-Murcia in “Preference heterogeneity in monetary policy committees”. They have used standard New Keynesian model as the framework to study the heterogeneity in preferences within the committee's members. They introduced the utility function of each individual and maximized expected utility of the whole committee, which was obtained by aggregation of individual utility functions, subject to aggregate supply and IS curve. Riboni A., Ruge-Murcia F.J., “Preference heterogeneity in monetary policy committees”, 2007, p. 217.

Another paper about the MPC work is “Policymakers' interest rate preferences: recent evidence for three monetary policy committee” by Alexander Jung from the European central bank. Author made econometric analysis of the Taylor rule - “monetary policy rule that stipulates how much the central bank should change the nominal interest rate in response to changes in inflation, output or other economic conditions” Taylor J.B., “Discretion versus Policy rules in practice”, 1993, p. 202. using information from FOMC, MPC of the Bank of England and of the Riksbank. The main conclusion of the paper also refers to the evidence of heterogeneity of preferences of the committee members. It confirms the hypothesis that detailed analysis of responses of each MPC member should be conducted. Jung A., “Policymakers' interest rate preferences: recent evidence for three monetary policy committee”, 2013, p.164. Thus, very different theoretical and practical approaches were used to explain the problem of studding the heterogeneity of individual decisions.

There are several papers that examine the effect of the introduction of monetary policy committee in Riksbank in 1999 on market conditions. For example, Malin Andersson, Hans Dillйn and Peter Sellin, authors of “Monetary Policy Signaling and Movements in the Swedish Term Structure of Interest Rates”, emphasized that some parts of the MPC meeting could act as a market signal. Meanwhile, Makram El-Shagi and Alexander Jung (“Has the Publication of Minutes Helped Markets to Predict the Monetary Policy Decisions of the Bank of England's MPC?”) examined the effect of minutes publishing on market using the example of the Bank of England. Econometric approach is based on probit model and Vuong test. Structurally the same but modified approach will be done in my thesis.

For my analysis it is extremely important to examine the time path of Swedish repo rate and to understand why the particular rate has existed at the particular period of time. It is very convenient to do this through special reviews that are made regularly by representatives of the central bank. Review for the last period from 2010 to 2015 that was made by Marvin Goodfriend and Mervyn King should be attended specially because this information is the newest.

“An Econometric Model of Monetary Policy Decision-Making with Applications to the United Kingdom and Sweden” by Henry W. Chappell Jr., Rob Roy McGregor and Todd A. Vermilyea is about the process of creating an efficient econometric model that will study the decision-making process. Authors have included to their model the following elements: a specification of each committee member's “true” monetary policy preference, a description of how individual's policy preferences are modified as the committee deliberates, a mapping of individual preferences to a committee decision and a description of formal voting. Chappell Jr. H.W., McGregor R.R., Vermilyea T.A., “An Econometric Model of Monetary Policy Decision-Making with Applications to the United Kingdom and Sweden”, 2009, p. 6. Authors have suggested that all these figures could be used to describe how individuals' preferences are mapped with those of the whole committee. This policy decision-making model is tested on the central banks of the United Kingdom and Sweden. I will also use these results of Riksbank to describe the theoretical aspect of my problem and try to understand how to use this information for modeling interest rates.

What about theoretical part of my work, a lot of researches have been conducted concerning the effectiveness, the reasons of introduction, the comparison with other central banks, the heterogeneity and status quo decision of Riksbank's Executive Board. I will use the main of them to examine the decision-making process in the Section 2 of my work. For my practical part I will mainly focus on the work of Sirchenko about creating cross-nested ordered probit model and I will also lean on the papers in which other probit models were created in order to compare CNOP with other existed models.

2. The decision-making process of Riksbank: description and results of main researches

Apel, Claussen and Lennartsdotter have given some simple description of the functionality of the Riksbank. It has started to adopt inflation and interest rate targeting in 1993 but first meetings of Executive Board appeared only in January 1999. Data from the first meeting until those that exist in present times is collected for my future analysis. Moreover, in 1999 Executive board that always contains of 6 members was established. Executive Board is responsible both for Bank's budget and monetary policy. Apel M., Claussen C.A., Lennartsdotten P., “Picking the Brains of MPC Members”, 2010 p. 2. However, for my thesis only monetary policy sessions are important.

The instrument rate of Swedish Bank is repo rate at which commercial banks lend and deposit money for a period of one week. It is obtained by voting of each member at the special committee sessions that since 2008 normally have taken place 6 times a year. The whole decision-making process is quite complicated and usually takes about 6 weeks to get the final result. At the beginning of the process the Monetary Policy Department represents its forecast that should be discussed by MPC members altogether. These meetings are obligatory only for committee members but some people like representatives from the Monetary Policy Department and the Communications Secretariat and some outside advisors can also take part. Finally, MPC members non-anonymously vote and the decision is made by a majority vote. If the tie occurs the main power is owned by the special Governor. The next day after the last day of the session the official report is made and information about new interest rate becomes available for the public. Apel M., Claussen C.A., Lennartsdotten P., “Picking the Brains of MPC Members”, 2010 p. 3.

Special attention is paid to the role of Governor also known as Chairman. It is always a question if he has real influence on other committee members and for what extent this power can change individual decision. Research made in “Picking the Brains of MPC members” has showed that in the majority of views the opinion of the Chairman did not press the opinion of others - members decided how they would vote far before the final meeting. Especially it has become more obvious after the reform in 2007 when repo rates forecasts have been introduced. Since 2007 the influence of the Governor has been declining more and more. It is reasonable to consider that the Executive Board of Riksbank is very individualistic committee. Apel M., Claussen C.A., Lennartsdotten P., “Picking the Brains of MPC Members”, 2010 p. 2. It means that each member expresses his own opinion and does not try to adjust his answer to that of someone else. So the idea to study not just the whole committee but also every member is quite legitimate.

These results were obtained by the questionnaire of all 18 existed MPC members made by Apel, Claussen and Lennartsdotter. However, an econometric research that was described by Chappell, McGregor and Vermilyea has suggested an opposite conclusion: members have been heavily influenced by the Governor and the Executive board of Riksbank has been very collegial committee. An econometric methodology was the following. In order to estimate a complex and nonlinear function of such parameters as reaction function parameters, weighted parameters and error term variances maximum simulated likelihood estimation has been applied. The main result of Sweden is that the estimated coefficient и, the weight of the Governor's answer, occurred to be large, positive and significantly different from zero. Chappell Jr. H.W., McGregor R.R., Vermilyea T.A., “An Econometric Model of Monetary Policy Decision-Making with Applications to the United Kingdom and Sweden”, 2009, p. 9,2 5. This opposition of results of different researches makes the problem of analyzing decisions of Executive Board more interesting at it has not been examined to the last yet.

Another feature that may influences results of voting is Riksbank's forecasts. For every meeting the data of such macroeconomic variables as inflation, employment and production is collected and forecasts of further economic performance are made based on this data. Riksbank's forecasts are mainly based on CPI inflation, GDP growth and unemployment. I will also include these variables to my model. At the “Review of the Riksbank's Monetary policy for 2010-2015” Marvin Goodfriend and Mervyn King emphasized two main problems of forecasting. Nevertheless central bank has certain power to judge the future macroeconomic performance, forecasts for the chosen period were “too optimistic about the euro area from the spring of 2010” and “it uses a far from obvious assumption about interest rates overseas”. Goodfriend M,, King M., “Review of the Riksbank's Monetary policy for 2010-2015”, 2015, p. 83. The question of completely trusting forecasts during Executive Board's meeting is still not obvious. As for any forecast it is hard to investigate the proper model that will always be optimal and efficient. Therefore, it is more reliable to lean on present macroeconomic variables rather than on their forecasts.

The main advantage of Riksbank among many other central banks is its transparency. From the first meeting it was decided to publish the minutes of MPC sessions and press releases explaining the reasons of such decision. Moreover, each member makes speeches, writes articles and takes part in interviews to demonstrate that his decision is reliable and individual. During the whole period of its existence Executive Board is developing new mechanisms to become even more transparent. Since May 2009 results of voting have became available without any lags - immediately after the meeting. So nowadays Riksbank is one of the world's most transparent central banks. Apel M., Claussen C.A., Lennartsdotten P., “Picking the Brains of MPC Members”, 2010 p. 4 Therefore, it is very convenient to work with repo rates of Sweden - you can find all necessary data from the first meeting until the present ones.

One important reason why we should study Executive board's meetings is that it may become a monetary policy signal that affects term structure of interest rate as it was defined in “Monetary Policy Signaling and Movements in the Swedish Term Structure of Interest Rates” by Malin Andersson, Hans Dillйn and Peter Sellin. They found out such signals as repo rates changes, inflation reports, speeches of monetary policy committee and final minutes, so all the parts of MPC session. Authors have illustrated the whole process of the meeting by the following scheme assumed that the first step - forecasting and representation of economic news - always appears at t0.

Scheme 1. The policy process at the Riksbank. Resource: “Monetary Policy Signaling and Movements in the Swedish Term Structure of Interest Rates”

How the whole cycle or its separate parts can affect the term structure of interest rates? Andersson, Dillen and Sellin emphasized that if one central bank always followed the same policy rule there could not be any signaling at all because market participants would adjust their expectations according to the known for them rule so nothing unanticipated would occur and term structure of interest rate would not be affected. However, the following the same rule in each session does not occur in the reality. One of the important signals is “interpretation of new economic information made by decision makers during their speeches”. It was noticed that central banks that have good system of signaling their policy changes usually had small term structure effects due to changes in their main rate. Andersson M., Dillen H., Sellin P., “Monetary Policy Signaling and Movements in the Swedish Term Structure of Interest Rates”, 2001, p. 270-271.

The main argue of the paper is about the effectiveness of signals before and after Riksbank's reform in January 1999 when the committee of 6 people replaced the single Governor. It is reasonable to consider that when the only one Chairman took part in decision-making process of the new repo rate it was easier to forecasts his decision. But when several members started to take part in voting it has becomes quite harder: nobody could predict by certain the vote of each MPC member, even members themselves. However, on the other hand, if policymakers are replaced very seldom it is more likely that their decision are made by long run intensions so the time path of monetary policy for long horizon becomes more predictable. Thus, at this point of view, the efficiency of the work of Executive board is the question that is not still answered yet for some aspects.

For the whole period that will be analyzed Swedish repo rates and monetary policy stances have passed all stages. If we look at repo rates for the recent period from 2010 to 2015 we can observe that there was a whole cycle of repo rates. Firstly, they were close to zero, then after recovery positive rates were seen and they started to decline and now reach negative rates. In “Review of the Riksbank's monetary policy” authors of the paper have distinguished six main conclusion of the monetary policy for the chosen period:

1. Sharp increase of repo rate from 0,25% to 2% between June 2010 and July 2011 was accepted by all six MPC members as efficient and rapid recovery of Sweden after the global financial crisis. The tendency of recovery was being kept during 2010 and 2011. However, the answers of the committee voting have become to be more individual. Differences of views were explained as “reasonable differences of judgments about the outlook for the economy and for the inflation”. But dissenters from the majority of views chose repo rate that were only slightly different from the one that was finally adopted. So there is not any evidence that some individual members wanted to make absolutely different repo rate.

2. In late 2011 and 2012 the situation started to change dramatically. Significant problems of euro area occurred. Thus, forecasts that were built based on overoptimistic judgments about economic growth in euro area failed because usually central banks' forecasts gave high weights to the forecasts that were made overseas. Moreover, there was a significant divergence between market forecast of repo rate and repo rate that was decided by the Executive Board - the gap reached even 4%. Goodfriend and King have recommended committee to carefully explain in the minutes why they diverge from the market forecasts.

3. Since 2007 Riksbank has published its own forecast of the future policy path as it was recommended in the review of Giavazzi and Mishkin: Swedish central bank “should base its forecasts on its own assesment of the policy part”. Giavazzi F., Mishkin F.S., “An evaluation of Swedich Monetary policy between 1995 and 2005”, 2006, p.48. After it has been made, in spite of the fact that a lot of individuals desagreed about the chosen policy regime they all were highly satisfied that such publication were started to be done.

4. Forecasting models created by Riksbank are based on strong assumptions. For example, one of the big failes of such models - too restrict assumption of complete credidibility of the willininness and ability to keep 2% inflation target.

5. There was strong disruption among members of the Executive Board in 2012 and 2013. Disputes were so significant that members could not reach an agreement not only about the level of interest rate but also about the objectives of policy at all. The apogee was reached in April 2013. The reasons of the dispute betweeen the majority and the minority were quite obvious. The major part of Executive Board's members was concerned about the affects from the rising prices of assets. They felt that their mission was to reestablish financial stability of the national economy by making right decision of the repo rate. What about dissenters of the committee, they had a lit bit narrower view on the economic stability. They considered that the main aim of the monetary policy of that time was to set such interest rates that would be consistent with the idea of inflation targeting for two yeas based on some particular forecasted models of inflation. The main weakness of such models was that they were based on past correlations but in the reality were not able to say anything about “how and why crisis came about”. The problem of determing which factors were more responsible for monetrary policy decisions occurred. So it is highly recommended for the governers of the Riksbank to declare clearly the framework of all forecasting models.

6. The atmosphere which presents in the MPC meetings is one of the key factors that determine the effectiveness of their work. It is extremely important that members respect each other's views and are able to make decisions collectively. Debates are necessary in any team-working process but it is more necessary to reach the consensus after such debates. Minutes should contain all viewpoints but they should be more focused about why and how the final solution was reached. Goodfriend M,, King M., “Review of the Riksbank's Monetary policy for 2010-2015”, 2015, p. 86-95.

While studding the key points of Swedish monetary policy for the period of last five years it can be concluded that the main problems were connected with conducting efficient forecasts that consist of significant economic factors and also publishing all topics and information that was discussed at each meeting. Riksbank tries to overcome theses problems by creating new more efficient forecasting models and especially to improve the quality of its publications to become even more transparent. In general, the governance of the central bank follows the recommendations of the responsible authorities and adequately reacts to the criticism.

One of the interesting for analysis features is that Sweden has negative key interest rates in the end of 2015 and in the present year as Bloomberg has outlined. It means that now Riksbank is not paying interest for the deposits to commercial institutions, but rather it is claiming a fee for “safeguarding” cash. Such banks as central banks of Switzerland and Denmark and the European Central Bank also follow this policy. Monetary authorities of Sweden have decreased interest rate in order not to allow krona to appreciate. Households stop saving and put their money in consumption and investment instead. Riksbank is buying government bonds in order to increase the supply of money in the economy and thus weaken the national currency. Expansionary monetary policy was needed to keep inflation rate low and at the same time not to deviate from forecasted exchange rate. Negative repo rates are also included into my dataset.

After the analysis and comparison of some existing papers about the decision-making process of monetary policy committee of Swedish national bank it has appeared that this topic is not so simple. Some researches have come to the very different conclusion. Therefore, the idea of analyzing MPC is very actual and there is a considerable work that may be done on this topic. However, the main theme of these articles is the influence of particular objects and subjects on decision-making process. But in my thesis I will analyze why particular decisions are made, especially status quo decisions and how estimate them more efficiently. I found it more interesting and practically needful to try to make the work that has not been done before with the dataset of Sweden.

3. Econometric framework: cross-nested ordered probit

If to try to characterize CNOP model by the simple words it is “new a mixture model with overlapping latent regimes that was made by combining three ordered probit equations”. Sirchenko A., “Modeling status-quo decisions: cross-nested ordered probit approach”, 2015, p. 31. In this section I am going to describe this model in details and explain why it is proper to use it for the problem that I have chosen for my thesis.

First of all, it is reasonable to talk about the nature of CNOP model - ordered probit model. OP model has arisen from the simple probit model, but if in probit dependent variable can take only two values ordered probit is its generalization that allows dependent variable to take more than two outcomes. So if you want to estimate the relation of variable that is more complex than just “yes or no” answers you should use ordered probit. It is often used in rating systems and opinion surveys that always suggest more than two answers like strong disagree and strong agree, but also have some options of middle category. In finance ordered probit is widely used while examine bonds' ratings. In medicine when researcher studies drug's efficiency he uses OP to discrete conditions of patient: from strong recovery to death. Especially it is popular in sociological surveys. Like simple probit, ordered probit is not linear function so cannot be estimated by ordinary least squares and maximum likelihood should be applied for the estimation.

When analyzing monetary policy committee's answers OP model has also been used. Answers are not continuous variables because voters cannot come up with any interest rate that he wants. It is always allowed to choose rate only with some step. In Sweden the usual step is 0,25 percentage points, seldom 0,1 and 0,15 percentage points are also used. So monetary policy decision is discrete function with more than two outcomes. From this point of view, ordered probit is efficient model for this problem. However, it does not account for the phenomena that discrete answers may arise in different conditions. It is the reason why OP fails and more complex approach should be introduced.

Some extensions of ordered probit have been developed aimed to analyze the middle category of responses that is zero answers in my dataset. The most famous one is the Middle inflated ordered probit (MIOP) that was created by Benjamin E. Bagozzi and Bumba Mukherjee in “A mixture model for middle category inflation in ordered survey responses”. Authors have proved the disadvantage of ordered probit and suggested the model that accounts for “face saving” answers that inflate the middle category. These types of responses may occur due to being uniformed respondent, not because it is his real opinion. Ordered probit will account these answers as “no change” ones and, thus, will be inefficient. MIOP allows zero answers to appear in both “change” and “no change” categories, in my case in “neutral” and “no neutral” regimes. Bagozzi and Mukherjee used their model to estimate the level of desire of becoming the member of European Union of citizens of EU-candidate countries. Bagozzi E., Mukherjee B.,“A mixture model for middle category inflation in ordered survey responses”, 2012, p.2.

CNOP model is based on the same idea as MIOP, however it assumes the usage of 3-part structure (neutral/loose/tight regimes) versus 2-part structure of MIOP (change/no change). Generally, “CNOP is cross-nested generalization of a two-level nested ordered probit (NOP) model with three nests”. Sirchenko A., “Modeling status-quo decisions: cross-nested ordered probit approach”, 2015, p. 6. The main distinction of CNOP against NOP is that it suggests that zero responses are included into each regime simultaneously while in NOP zeros are only no change responses. Therefore, it can be concluded that cross-nested ordered probit collects the ideas of different probit extension:

1) dependent variable is a discrete function of more than two variables from ordinary ordered probit;

2) responses can be belonged to three different nests - nested ordered probit;

3) zero responses not always mean no change solution - middle inflated ordered probit.

For visibility I attach the schemes of work of there different probit models: NOP, MIOP and CNOP to the Appendix №2.

In CNOP there are two stages of estimation. All information about methodology of cross-nested ordered probit I have taken from the paper of Sirchenko.

Stage 1. Choosing regime equation - is a degree the i member's policy inclination:

,

where is the row t from the matrix , is the number of observation that is used by the individual i, в is a vector of coefficients and - independent identically distributed disturbance term.

On the basis of regime decision is chosen as a discrete variable: 1 for tight policy regime, -1 for loose and 0 for neutral. The relation of these two variables is set by the conditions - inequalities with specified threshold () that should be estimated.

Probabilities of each outcome are calculated though cumulative density function of some distribution F of disturbance term:

Stage 2. Three latent regimes already exist

At the neutral regime interest rate always remains unchanged:

And conditional probabilities of the outcome j in the case of neutral policy:

What about loose and tight regimes the picture begins to be more complicated. The sign of loose regime is ““, of tight “+” and “for either one. Amount equation is introduced:

,

where - vector of coefficients, belongs to the row t of matrix ( and is IID disturbance term with CDF .

The rule of discrete change of is determined by:

,

where

and - 2J unknown thresholds that should be estimated. In my model j can have only three values so only 2 thresholds will be estimate: one for loose and one for tight.

If we make the assumption that disturbance terms and are IID then full probabilities then full probabilities can be calculated as:

For the simplicity Sirchenko also assumed that distributions of all disturbance terms ( are standard normal and calculated all probabilities using this fact. Another assumption was also made: zero intercepts - and . Because of the nonlinearity all three OP equations of CNOP are estimated through partial pooled ML estimator.

where is a indicator that is equal to 1 if = j or 0 otherwise. is aggregation of all parameters that should be estimated. N is number of policymakers, T - number of observations for each policymaker, J - number of thresholds.

Some problems that may arise while estimating CNOP:

1) The model requires the usage of simultaneous equations that create the multicolinearity and weak identification problems. It always comes into existence when matrixes and have a lot of terms in common. Sirchenko suggests “exclusion restrictions” as the solution of this problem. It means that it is not necessary to include all variables into all three equations. Alternatively, it is accurate to make restrictions of some variables either in tight or loose regimes.

2) Invalid standard errors and thus test-statistics may occur while estimating by pooled ML. Validity can be achieved only in the case of no serial correlation among disturbance terms. No autocorrelation is the main assumption that should be made to work with CNOP model. Sirchenko A., “Modeling status-quo decisions: cross-nested ordered probit approach”, 2015, p. 9-11.

What about the choice of testing extensions of probit models it depends on whether the models are nested in each other. For example, NOP is nested in the CNOP model. For testing the efficiency of one of these models against each other tests for nested hypothesis should be used. Simple likelihood ratio test is a proper test in this case.

But OP, MIOP and CNOP are not nested models, so this type of test cannot be used. Special test for non-nested hypothesis is Vuong test. “Vuong test for Non-Nested models” was created by Vuong in 1989. It suspects that under null hypothesis two non-nested models fit equally well. Also under log-likelihood ratio statistics is normal. When I test which model fits better CNOP or OP I will use Vuong test.

Testing procedure of Vuong test concerning two non-nested probit extensions is described in Online Appendix C of “Modeling status quo decision: cross-nested ordered probit approach”. At the first step we should check if two models are not equivalent. It is made by usual F-test, namely we need to “check whether the parameters of interest violate the overlapping constraints”. Sirchenko A., “Modeling status-quo decisions: cross-nested ordered probit approach Online Appendix C”, 2015, p. 7. Then directly Vuong test is conducted. It has simple test statistics that is computed as average difference of two individual likelihoods divided by the standard error of this difference. As I have also mentioned test statistics of Vuong test is standard normally distributed under null hypothesis, so it should be compared with Z statistics. If we test CNOP model versus another model, the equivalence of two models is not rejected at 5% significance level if test statistics is less than 1,96 in absolute value. If it is higher than 1,96 OP model should be chosen, if it is lower than -1,96 CNOP model should be chosen.

Another method that should be used for comparison of models is information criteria. The most commonly used are Akaike (AIC) and Bayesian (BIC) information criteria.

where is maximized log likelihood function, is number of explanatory variables and is number of observations. It is known that for models that are estimated by the maximum likelihood it is better to have higher log likelihood function and lower number of estimated parameters. So if information criteria are calculated we should choose that model that has lower both Akaike and Bayesian ones or in special cases we can compare models by using only one information criteria.

By analyzing methodologies of different probit models it becomes obvious that new generalization of some older ordered probit - cross-nested ordered probit - suits the best for the modeling interest rates by studding status quo decisions of monetary policy committee. To check this hypothesis I am going to apply OP and CNOP models to the dataset of Swedish central bank and check if CNOP really fits better for this problem.

4. Data collection and construction the model specification

I am going to model the official interest rate of Riksbank, repo rate, by applying cross-nested ordered probit approach to investigate what factors really influence Swedish MPC decisions. The period of my research is from January 1999 - the day when monetary policy committee was created in Sweden - to December 2015 - the time when I have started to collect data. All time series of my data was checked for stationarity at 1% significance level by Augmented Dickey Fuller test.

There are some stages of data collection. Two types of data were collected: Executive board's decisions and macroeconomic indicators. The next step was to generate required variables that would be significant for my analysis. It should be noticed that not every variable was included into the final specification but I found it reasonable to describe every data and every explanatory factor that I have tried.

Repo rate decisions were downloaded from the official Riksbank's databases that include information about each member's decision from each committee's session. There have been six sessions a year from 2009 - in February, April, July, September, October and December. Before 2009 on average seven or eight meetings had taken place. Totally the number of my observations on time is 124. For the whole period there were 18 members of committee but no one of them have worked for the whole observed period so a lot of observations are omitted. Therefore, my panel table consists of 680 observations where individual dimension is generated by the number of voters and time dimension - by the number of meetings.

My dependent variable is constructed from the individuals' decisions and has discrete values. If member i at time t decided to increase repo rate -

CHANGE_RATE it > 0 - then , if he decided to decrease rate

CHANGE_RATE it < 0 - then, if he had status quo decision

CHANGE_RATE it = 0 - then

From all 680 observations policymakers preferred status quo decisions - 383 zero decisions (56%). They decided to decrease repo rate 177 times (26%). The least popular decision was to increase interest rate - only 120 times (18%). The diagram of all policymakers' decisions is represented in appendix №4.

From the dataset of individual decisions some explanatory variables have also been generated. One of such variable is DISSit - dissent of member i from the final decision of the committee at time t. It was calculated as the change of rate that was chosen by the individual minus the change of rate the committee has chosen. Dissent takes discrete values: 1 if the difference is positive (individual preferred the rate that is higher than the final decision of the whole committee); -1 if difference is negative (he preferred lower rate) and 0 if the level of dissent is zero and the decision of the member i coincided with the final decision. Only lags of dissent may influence the voting because of the 100% correlation with dependent variable so I have generated three lags of this variable and tried to include into my specification DISSit-1, DISSit-2 and DISSit-3.

Other variables are lags of individual repo rate decisions RATEit-1 and RATEit-2. Since in the official report only individual increments (the change of rate) are published I generate individual repo rate decision by the following rule:

RATE it = RATE t-1 + CHANGE_RATE it.

Another type of data that was collected for my thesis is macroeconomic data that is always taken into account during the meetings. I have found such real sector indicators as consumer price index, unemployment, production price index and national accounts. All data was found at Special Data Dissemination Standard Plus Swedish section.

Data on CPI plays special role for monetary policy committee. As CPI measures changes in price level the annual percentage change in a CPI is considered as a good measure of inflation. So I will also use such measure. I have collected monthly data of the annual percentage change in a CPI and approved it with the time of each meeting. To understand which level of the macro indicator was known for the committee during every session a reasonable assumption should be made. If the final decision was made after the 20^th date of the month I assume that the committee has already known CPI for the previous month. If the meeting was hold before 20^th day of the month then the committee can use information only for the month that was previous from the last. For example, if the meeting was at 21^st of March then data for February is already available, but if it was at 15^th of March committee could use data only for January. I use the same approach for every macroeconomic data.

If we look at the graph of the annual percentage in a CPI that is represented in the appendix №5 and compare it with the graph of repo rate that I have discussed in the introduction we can observe that there is positive relationship between these two variables. So I expect the positive sign of the coefficient of this indicator. Whereas my dependent variable is the change of repo rate relatively to the previous meeting I will also take the change in CPI - .

Other important macroeconomic variables that I have also tried to include into my final specification are annual percentage change in GDP that was taken quarterly - CHANGEGDPi, monthly unemployment that was also included as increment from the last meeting - UNEMPLOYMENT, and the gain of monthly percentage level of production index -PRODINDEX. Unemployment appeared as insignificant variable while data of production index was not full so I have excluded these two variables from my final specification.

And my last variable is SPREADt - the spread between short-term and long-term market interest rates. As short-term interest rate I have taken one month treasury bill (SE 1M) while as long-term - two years Swedish government bond (SE GVB 2Y). So the spread of mine was generated by the formula: SPREADt = SE_GBB_2Yt - SE_1Mt. Andrei Sirchenko described the meaning of this variable as “a low-dimension market-based aggregator of publically available information on inflationary expectations that are not reflected in the current inflation rate”. Sirchenko A., “Modeling status-quo decisions: cross-nested ordered probit approach”, 2015, p. 19.

Cross-nested ordered probit model can be estimated only in Gauss10. The main part of my work was to find the best specification with significant coefficients with signs that have economic sense. Because CNOP model is three parts model that contains of three equations: for neutral - policy regime equation, loose and tight regimes - amount equations, I had to try different combinations for each of the three equations. I have found out that variables UNEMPLOYMENT and two lags of dissents (DISSit-2 and DISSit-3) are insignificant variables in any specification so they were excluded. All other variables were tried in different specification and the most efficient was found. I included the table of mnemonics - description of every variable - into appendix №6.

In policy regime equation individual decisions are determined by CHANGEGDPi, RATEit-1 and RATEit-2. In both amount equations explanatory variables are DISSit-1, RATEit-1, RATEit-2 and SPREADt.

5. Estimation results

The whole analysis starts with calculating covariance for all explanatory variables to make sure that there is no multicolinearity. Covariances were calculated by Invert of computed Hessian. High correlation (more than 0.9) was found only between variables RATEit-1 and RATEit-2. Since these two variables are lags of the same variable, the presence of high correlation between them is not surprising and does not harm the estimation. All other sample descriptive statistics (mean, standard deviation, variance, minimum and maximum) of all explanatory variables is represented in the table in the appendix №7.

Firstly, I would like to analyze estimated coefficients of CNOP model that are represented in the table below with their t-statics in the brackets. All coefficients are significant at 1% significance level (Z-critical = 2.6 as the sample is large enough). It is more important to look at signs of coefficients, not on their values. Positive signs of such macroeconomic variables as CHANGEGDPi and SPREADt have real economic meaning so CNOP model has given significant and adequate estimated coefficient for my specification. CNOP also predicts that the discrete level of policymaker's dissent at the previous meeting positively affects his decision at the present meeting in the case of both loose and tight regimes. In amount equations first lag of the repo rate chosen by the particular policymaker has positive sign and the second lag of the same variable - negative sign. Quite the opposite situation connected with these two lags was estimated for the policy regime equation. Thresholds that were mentioned in the econometric framework section have also been estimated; one of them has appeared insignificant.

Table 1

Coefficients and t-statistics estimated by CNOP model

Nevertheless my specification appears efficient when it has been estimated by cross-nested ordered probit I have also estimated it by ordinary ordered probit in order to compare these two models and to approve that the creation of CNOP does really have value for the datasets with large fraction of zeros. OP calculates coefficients for one ordinary equation. Such variables as CHANGEGDPi and SPREADt also have positive coefficients. However, coefficients of three variables (CHANGEGDPi, RATEit-1 and RATEit-2) are insignificant at 1% level: coefficient of RATEit-1 is significant at 5% level (Z-critical = 1,96), coefficient of RATEit-2 is significant only at 10% level (Z-critical = 1,62), while coefficient of CHANGEGDPi is not significant even at 10% level. The coefficient of first threshold also appears insignificant. So OP model does not efficiently account for the specification that includes such important variable as annual percentage change in GDP while CNOP accounts this variable in policy regime equation.