presentation sirchenko

Modelling Ordinal Data with Abundant andHeterogeneous Zero (Status Quo) Observations

Andrei Sirchenko1

National Research University — Higher School of EconomicsMoscow, 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


A phenomenon of zero inflationThe preponderance of zero observations is observed in many fields

visits to a doctor

tobacco consumption

disease lesions on plants

manufacturing defects

recreational demand

sexual behavior

fertility

insurance claims


Heterogeneity of zero observationsNumerous studies make a distinction between the different types of zeros

no medical appointments due to chance, doctor avoidance, lack ofinsurance, 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”


Two-part zero-inflated modelsThe two latent decisions


"Ask not what you can do to the data butrather what the data can do for you."

—Zvi Griliches


Changes to policy interest ratesThe preponderance of no-change decisions

largercut

25 bpcut

nochange

25 bphike

largerhike

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 rateCentralbank

Period


Policy rate of the BoEPolicy easing (E), maintaining (M) and tightening (T) periods


Policy rate of the ECBPolicy easing (E), maintaining (M) and tightening (T) periods


Policy rate of the NBPPolicy easing (E), maintaining (M) and tightening (T) periods


Policy rate decisionsin response to changes in inflation and economic situation


Policy decisionsin response to changes in inflation and economic situation


Cross-Nested Ordered Probit ModelThree latent regimes with endogenous switching


Cross-Nested Ordered Probit ModelA generalization of the NOP, MIOP and ACH models


Allowing for endogenous explanatory variables

Simple mimicing of the two-stage least squares estimation of linearmodels (i.e. inserting the fitted values from the reduced form in placeof the endogenous regressors in the structural equation) does notgenerally work for nonlinear models and often makes the endogeneitybias worse (Bhattacharya et al. 2006).

To accommodate continuous endogenous regressors in the CNOPframework I implement the control function approach (Smith andBlundell 1986, Rivers and Vuong 1988), which introduces residualsfrom the reduced form for the endogenous regressors into thestructural equation as controls for endogeneity.


Comparison of competing modelsCNOP model provides the more reasonable estimates of choice probabilities


Estimated probabilities of three policy regimes


Probabilities of latent regimes in different policy periods


Concluding remarks

"The model is often smarter than you are." —Paul Krugman

The proposed cross-nested ordered probit model is applicable in manysituations 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 orpositive attitude).

The model can be extended by relaxing the iid assumption among theerror terms.


presentation sirchenko

Science