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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.
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 1 / 22
Modelling Status Quo Decisions in Monetary Policy
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 2 / 22
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
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 3 / 22
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”
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 4 / 22
Two-part zero-in‡ated models
The two latent decisions
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 5 / 22
"Ask not what you can do to the data but
rather what the data can do for you."
–Zvi Griliches
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 6 / 22
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
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 7 / 22
Policy rate of the BoE
Policy easing (E), maintaining (M) and tightening (T) periods
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 8 / 22
Policy rate of the ECB
Policy easing (E), maintaining (M) and tightening (T) periods
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 9 / 22
Policy rate of the NBP
Policy easing (E), maintaining (M) and tightening (T) periods
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 10 / 22
Policy rate decisions
in response to changes in in‡ation and economic situation
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 11 / 22
Policy rate decisions
in response to changes in in‡ation and economic situation
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 12 / 22
Policy rate decisions
in response to changes in in‡ation and economic situation
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 13 / 22
Policy decisions
in response to changes in in‡ation and economic situation
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 14 / 22
Policy decisions
in response to changes in in‡ation and economic situation
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 15 / 22
Cross-Nested Ordered Probit Model
Three latent regimes with endogenous switching
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 16 / 22
Cross-Nested Ordered Probit Model
A generalization of the NOP, MIOP and ACH models
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 17 / 22
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.
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 18 / 22
Comparison of competing models
CNOP model provides the more reasonable estimates of choice probabilities
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 19 / 22
Estimated probabilities of three policy regimes
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 20 / 22
Probabilities of latent regimes in di¤erent policy periods
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 21 / 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.
Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 22 / 22

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Presentation sirchenko

  • 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. Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 1 / 22
  • 2. Modelling Status Quo Decisions in Monetary Policy Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 2 / 22
  • 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 Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 3 / 22
  • 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” Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 4 / 22
  • 5. Two-part zero-in‡ated models The two latent decisions Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 5 / 22
  • 6. "Ask not what you can do to the data but rather what the data can do for you." –Zvi Griliches Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 6 / 22
  • 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 Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 7 / 22
  • 8. Policy rate of the BoE Policy easing (E), maintaining (M) and tightening (T) periods Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 8 / 22
  • 9. Policy rate of the ECB Policy easing (E), maintaining (M) and tightening (T) periods Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 9 / 22
  • 10. Policy rate of the NBP Policy easing (E), maintaining (M) and tightening (T) periods Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 10 / 22
  • 11. Policy rate decisions in response to changes in in‡ation and economic situation Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 11 / 22
  • 12. Policy rate decisions in response to changes in in‡ation and economic situation Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 12 / 22
  • 13. Policy rate decisions in response to changes in in‡ation and economic situation Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 13 / 22
  • 14. Policy decisions in response to changes in in‡ation and economic situation Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 14 / 22
  • 15. Policy decisions in response to changes in in‡ation and economic situation Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 15 / 22
  • 16. Cross-Nested Ordered Probit Model Three latent regimes with endogenous switching Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 16 / 22
  • 17. Cross-Nested Ordered Probit Model A generalization of the NOP, MIOP and ACH models Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 17 / 22
  • 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. Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 18 / 22
  • 19. Comparison of competing models CNOP model provides the more reasonable estimates of choice probabilities Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 19 / 22
  • 20. Estimated probabilities of three policy regimes Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 20 / 22
  • 21. Probabilities of latent regimes in di¤erent policy periods Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 21 / 22
  • 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. Andrei Sirchenko (HSE) 40th EERC workshop May 21, 2016 22 / 22