Modeling interest rates Riksbank

riksbank zero interest rate

Table 2

Coefficients and t-statistics estimated by OP model

I have compared these two models by Vuong test and two main information criteria. The maximum of the log-likelihood function is -495.5 for CNOP and -487.19. As we know model is better if it has higher maximum of log-likelihood function so by this feature CNOP beats OP. CNOP AIC = 954.99, OP AIC = 990.39, by Akaike information criteria CNOP model is also preferable. However, Bayesian info criteria has showed the opposite results: CNOP BIC = 1036.39, OP BIC = 1026.57.

Because CNOP and OP are non-nested models Vuong Non-Nested test of CNOP was conducted versus OP model. The test-statics of Vuong test = -2.443. So by the rejection rule that was described earlier I reject (2 models fit equally well) at 5% significance level so I can conclude that there is evidence that CNOP fits better.

Another statistical index that should be taken into account while comparing two models is the hit rate - the probability of correctly predicted dependent variables ( The total hit rate is calculated as the sum of probabilities of correctly predicted = 1, = 0 and -1. For CNOP hit rate is 69.1%, for OP it is lower - 67.7%. So by this index CNOP model also wins. However, what about hit rate only for zero observations then OP gives slightly better results - 87%, while CNOP - 85,9%. CNOP model predicts less zeros than OP (329 versus 335) while actual number of zeros is 383.

Table 3

Comparison of two models

By the estimated Hit and Miss table I have also calculated adjusted noise-to-signal ratios that were suggested by Graciela Kaminsky, Saul Lizondo and Carmen M. Reinhart in “Leading indicators of Currency Crises” in which system of warning signals which noticed that crisis would occur within the following 24 month was created. Adjusted noise-to-signal ratio gives the information of “the indicator's ability to issue good signals and to avoid bad signals - it measures the level of noisiness”. Kaminsky G., Lizondo S., Reinhart M., “Leading indicators of Currency Crises”, 1998, p. 19. This ratio is calculated as the proportion of bad signals divided by the proportion of good:

where for my model A is equal to number of events that the decision was predicted and occurred; B - events that were predicted but not occurred; C - events that were not predicted but occurred: D - events that were not predicted and did not occur. Other things being equal, the less is the ratio the better is the indicator.

This indicator shows that CNOP model is less noisy while accounting no change observations - 61.1% against 65.8% of OP. But for decreasing and increasing outcomes OP model appeared to be less noisy - 13.6% against 20.9% for hikes and the slight difference for cuts - 10.2% against 11.6%.

Table 4

Comparison of two models: continue

It is not quite right to compare OP and CNOP models only by the estimated coefficients because these two models have different number of parameters, different structure and depend on different assumptions. The main results of such empirical research could be obtained by calculating probabilities of each discrete outcome and partial effects of covariates of these probabilities. Marginal effects for discrete variables are computed differently than for continuous. “The partial effect (PE) of a continuous covariate on the probability of each discrete choice is computed as the partial derivative with respect to this covariate, holding all other covariates fixed”. A. Sirchenko “Modeling status-quo decisions: cross-nested ordered probit approach”, p. 13.

I have constructed table of partial effects by which I can compare marginal effects of CNOP and OP model in the case of different outcomes of dependent variable . The estimated coefficient of the partial effect of each explanatory variable means that if this variable increases by 1 unit the probability that = j for j = 0, 1 or -1 will increase by the , where is estimated marginal effect coefficient. It is important to calculate t-statics of each coefficient to understand if this variable is significant for measuring partial effects and judge the value and sign of each significant coefficient.

For OP model the marginal effects of CHANGEGDPi and RATEit-2 become insignificant at 5% level for all types of probabilities (cut, no change and hike). For P( = “no change”) RATEit-1 also appears as insignificant. For CNOP model there are only three insignificant coefficients for any probabilities: RATEit-1 and RATEit-2 for probability of rate decreasing and -1 for the probability that repo rate would be unchanged. Therefore, 7 insignificant coefficients that were estimated by OP against only 3 ones that CNOP has estimated.

What about signs of significant marginal effects is that they have appeared quite expected. Such comprehensible variables as CHANGEGDPi and SPREADt also give comprehensible results. Their marginal effects are negative for the probability of cuts and positive for the probabilities of no changes and hikes. It means that if one of these variables increases by 1 unit the probability that policymaker i would choose to decrease repo rate will decrease by the value of marginal effect, to increase or remain unchanged - conversely will increase. Positive economic conditions make policymaker to change his mind in the direction of unchanged or higher rates.

Table 5

Coefficients of marginal effects of two models. T-statistics in brackets.

Conclusion

Studding decision-making process of the monetary policy committee is the topic of many recent researches, however, it is still unobserved why policymakers make particular decisions - what factors should be taken into consideration. Status quo decisions of MPC have a special place in this question. Older econometrical models like OP and NOP suggest that this type of decisions could appear only in the case of neutral policy regime. While real date shows that zero answers exist in all types of policy. Cross-nested ordered probit is the new model that is suggested to be proper one to estimate this hypothesis. The model has two stages where at the first stage the policy regime is detected while at the second the decision of interest rate is made.

Riksbank is the good example to check this model because Swedish central bank is one of the most transparent central banks and status quo are the most popular decisions for its whole dataset. I have applied CNOP approach to model key interest rates of Riksbank and to compare this approach with ordinary ordered probit.

I have got results that I have expected at the begging of my work. CNOP has given more significant coefficients. Only one threshold has appeared insignificant in CNOP while OP has estimated three insignificant coefficients. The main test for comparison two non-nested models, Vuong test, has rejected the hypothesis that two models fitted equally well and has provided evidence that CNOP model is better. However, two information criteria have given opposite results: AIC in favor of CNOP, BIC in favor of OP. By analyzing hit rates and adjusted noise-to-signal ratios obvious decision could not be made, however, the overall hit rate is higher and the level of noise of zero responses is lower for CNOP model. The number of significant coefficients of partial effects is also higher for CNOP: 7 insignificant ones were estimated by OP against only 3 ones of CNOP.

For the dataset of Sweden CNOP model has really appeared more efficient and more accurate to estimate interest rate decisions. My analysis could be expanded by adding more macroeconomic variables of Sweden or comparison cross-nested ordered probit with other probit extensions like MIOP and NOP.

List of references

1. Andersson M., Dillйn H., Sellin P., “Monetary Policy Signaling and Movements in the Swedish Term Structure of Interest Rates”, Stockholm, 2001, Svergies Riksbank working paper series.

2. Apel M., Claussen C.A., Lennartdotten P., Roisland O., “Monetary policy committees: comparing theory and “Inside” information from MPC members”, San Francisco, 2015, International Journal of Central Banking.

3. Apel. M., Claussen C.A., Lennartdotten P., “Picking the Brains of MPC Members”, 2010, Stockholm, Svergies Riksbank working paper series.

4. Bagozzi B.E., Mukherjee B., “A mixture model for middle category inflation in ordered survey responses”, Oxford, 2012, Political Analysis.

5. Chappell Jr. H.W., McGregor R.R., Vermilyea T.D., “An Econometric Model of Monetary Policy Decision-Making with Applications to the United Kingdom and Sweden”, 2009, Mimeo.

6. Giavazzi F., Mishkin F.S., “An evaluation of Swedish Monetary policy between 1995 and 2005”, Stockholm, 2006.

7. Goodfriend M,, King M., “Review of the Riksbank's Monetary policy for 2010-2015”, Stockholm, 2015.

8. Jung A., El-Shagi M., “Has the Publication of Minutes Helped Markets to Predict the Monetary Policy Decisions of the Bank of England's MPC?”

9. Jung A., “Policymakers' interest rate preferences: recent evidence for three monetary policy committee”, San Francisco, 2013, International Journal of Central Banking.

10. Kaminsky G., Lizondo S., Reinhart M.C., “Leading indicators of Currency Crises”, Munich, 1998, IMF Staff Papers.

11. Riboni A,. Ruge-Murci F.G., “Preference heterogeneity in monetary policy committees”, San Francisco, 2007, International Journal of Central Banking.

12. Sirchenko A., “Modeling status quo decisions: a cross-nested ordered probit model”, Moscow, 2015.

13. Taylor J.B., “Discretion versus Policy rules in practice”, New York, 1993, Carnegie-Rochester Conference Series on Public Policy.

14. Vuong Q., “Likelihood ratio tests for model selection and non-nested hypotheses”, 1989, Econometrica.

15. Bloomberg.com

16. Riksbank.se

17. Scb.se

Appendix 1

Repo rates and decisions of MPC committee

Repo rate and the decision of committee of Riksbank from January 1999 to December 2015

Red line - repo rate, blue dots - the decision of the committee. By analyzing trends of repo rate regimes were identified (arrow that is top-down - loose regime, down-up - tight regime, from left to right - neutral regime). Resource: official database of the Riksbank and author's calculations.

Appendix 2

CNOP as generalization of NOP and MIOP

Сross-Nested Ordered Probit model

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Nested Ordered Probit model

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Middle Inflated Ordered Probit model

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Resource: A. Sirchenko “Modeling status-quo decisions: cross-nested ordered probit approach”

Appendix 3

Testing for stationarity

Calculated by Eviews

Appendix 4

The distribution of decisions of all policymakers from January 1999 to December 2015

Resource: Riksbank's official database and author's calculations

Appendix 5

Annual percentage change in CPI from January 1999 to December 2015 - monthly data

Resource: Special Data Dissemination Standard Plus Swedish section and author's calculations

Appendix 6

Definitions of variables

Resource: Special Data Dissemination Standard Plus Swedish section, Riksbank's official databases and author's calculations

Appendix 7

Sample descriptive statistics

Calculated by Gauss 10

Appendix 8

Hit and Miss tables

OP

HIT and MISS TABLE

% Correctly Predicted = 0.67794118

CNOP

HIT and MISS TABLE

% Correctly Predicted =0.69117647

Number of observations: 680.00000

Calculated by Gauss10.

Appendix 9

Comparison of 2 models: partial effects

Coefficients of marginal effects and t-statistics in brackets of two models

Calculated by Gauss10

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