To quantify qualitative survey data, the Carlson-Parkin method assumes normality, a time-invariant symmetric indifference interval, and long-run unbiased expectations. Interval-coded data do not require these assumptions. Since April 2004, the Monthly Consumer Confidence Survey in Japan asks households their price expectations a year ahead in seven categories with partially known boundaries; thus one can identify up to six parameters including an indifference interval each month. This paper compares normal, skew normal, and skew t distributions, and finds that the skew t distribution fits the best throughout the period studied. The results help to understand the dynamics of heterogeneous expectations.
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| Abstract ------------------------------------------------ |
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| 1. INTRODUCTION ----------------------------------------- |
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| 2. SKEW NORMAL AND SKEW t DISTRI-BUTIONS -------------- |
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| 2.1. Skew Normal Distribution ------------------------------ |
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| 2.2. Skew t Distribution ----------------------------------- |
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| 3. Skew t Distribution --------------------------------------- |
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| 4. INTERVAL REGRESSION ---------------------------------- |
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| 5. APPLICATION ------------------------------------------- |
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| 5.1. Data ------------------------------------------- |
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| 5.2. Parameter Estimates ---------------------------------- |
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| 5.3. Model Selection -------------------------------------- |
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| 5.4. Inflation Expectations ----------------------------------- |
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| 6. DISCUSSION --------------------------------------------- |
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| ACKNOWLEDGMENTS --------------------------------------- |
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| References ------------------------------------------------- |
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