1) The document presents a model for analyzing ordinal data with many zero observations, known as status quo decisions. It specifically focuses on modeling central bank interest rate decisions. 2) It introduces the Cross-Nested Ordered Probit model, which allows for three latent regimes with endogenous switching to better model the preponderance of no-change decisions in interest rate policy. 3) The model is estimated using data on interest rate decisions of the Fed, ECB, BoE, and NBP. It provides more reasonable estimates of the choice probabilities compared to competing models and allows examining how the probabilities of the different regimes vary across policy periods.

1. Modelling Ordinal Data with Abundant and
Heterogeneous Zero (Status Quo) Observations
Andrei Sirchenko1
National Research University – Higher School of Economics
Moscow, Russia
May 21, 2016
1This paper is partially based on the research supported by a grant from the National Bank of Poland and a grant from the
EERC.
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2. Modelling Status Quo Decisions in Monetary Policy
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3. A phenomenon of zero in‡ation
The preponderance of zero observations is observed in many …elds
visits to a doctor
tobacco consumption
disease lesions on plants
manufacturing defects
recreational demand
sexual behavior
fertility
insurance claims
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4. Heterogeneity of zero observations
Numerous studies make a distinction between the di¤erent types of zeros
no medical appointments due to chance, doctor avoidance, lack of
insurance, or medical costs
no children due to infertility or choice
no illness due to strong resistance or lack of infection
a “genuine nonuser” versus a “potential user”
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5. Two-part zero-in‡ated models
The two latent decisions
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6. "Ask not what you can do to the data but
rather what the data can do for you."
–Zvi Griliches
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7. Changes to policy interest rates
The preponderance of no-change decisions
larger
cut
25 bp
cut
no
change
25 bp
hike
larger
hike
Fed 10/1982 - 10/2012 9% 11% 63% 13% 3%
ECB 01/1999 - 10/2012 6% 4% 79% 10% 1%
BoE 06/1997 - 10/2012 5% 9% 76% 10% 0%
NBP 03/1998 - 10/2012 14% 9% 66% 11% 0%
Change to policy rate
Central
bank
Period
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8. Policy rate of the BoE
Policy easing (E), maintaining (M) and tightening (T) periods
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9. Policy rate of the ECB
Policy easing (E), maintaining (M) and tightening (T) periods
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10. Policy rate of the NBP
Policy easing (E), maintaining (M) and tightening (T) periods
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11. Policy rate decisions
in response to changes in in‡ation and economic situation
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12. Policy rate decisions
in response to changes in in‡ation and economic situation
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13. Policy rate decisions
in response to changes in in‡ation and economic situation
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14. Policy decisions
in response to changes in in‡ation and economic situation
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15. Policy decisions
in response to changes in in‡ation and economic situation
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16. Cross-Nested Ordered Probit Model
Three latent regimes with endogenous switching
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17. Cross-Nested Ordered Probit Model
A generalization of the NOP, MIOP and ACH models
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18. Allowing for endogenous explanatory variables
Simple mimicing of the two-stage least squares estimation of linear
models (i.e. inserting the …tted values from the reduced form in place
of the endogenous regressors in the structural equation) does not
generally work for nonlinear models and often makes the endogeneity
bias worse (Bhattacharya et al. 2006).
To accommodate continuous endogenous regressors in the CNOP
framework I implement the control function approach (Smith and
Blundell 1986, Rivers and Vuong 1988), which introduces residuals
from the reduced form for the endogenous regressors into the
structural equation as controls for endogeneity.
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19. Comparison of competing models
CNOP model provides the more reasonable estimates of choice probabilities
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20. Estimated probabilities of three policy regimes
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21. Probabilities of latent regimes in di¤erent policy periods
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22. Concluding remarks
"The model is often smarter than you are." –Paul Krugman
The proposed cross-nested ordered probit model is applicable in many
situations and can be applied to a variety of ordinal data sets
(changes to consumption, prices, rankings, etc.) and survey responses
(when the respondents are asked to indicate the negative, neutral or
positive attitude).
The model can be extended by relaxing the iid assumption among the
error terms.
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