# Table 1 Expectations quantification methods

Probabilistic methods Regression methods
Author(s) Theil (1952);Carlson and Parkin (1975) Anderson (1952); Pesaran (1984)
Idea Individual percentages of respondents are expressed in terms of the probabilities of future inflation being in certain intervals. Additionally, sensitivity intervals are applied for (1) respondents declaring that prices will be stable (they do not necessarily mean that future inflation will be exactly equal to zero) and for (2) respondents reporting that prices will increase at the same rate (they do not necessarily mean that future inflation will be exactly equal to zero). Solving a set of equations returns the expected inflation rate, its standard deviation, and sensitivity intervals It is assumed that the same relationship holds between respondents’ qualitative opinions concerning future price changes and expected inflation. Thus, inflation perception is a yardstick for the quantification of respondents’ expectations. Coefficients derived from Q5 answers are used together with Q6 answers to reveal expected inflation
Assumptions The original Carlson and Parkin approach assumes the unbiasedness of inflation expectations and their normal distribution. Extensions remove the former and allow for the modifications of the latter. There is a need for an assumption about the scaling factor to which respondents refer while answering the survey’s questions Unbiasedness of inflation perception. Additional assumptions differ across the models applied. No assumption about distribution needed
Versions Regarding the scaling factor: objectified (actual inflation rate serves as a scaling factor) and subjectified (perceived inflation). Regarding the distribution: uniform, logistic, t-distributions, triangular distribution The primary version of the procedure was presented by Anderson (1952). Coefficients of Anderson’s model do not change over time even if the inflation dynamic changes. This is the most important objection towards the simplest method
Extensions The most commonly applied extension is that of Batchelor and Orr (1988). It adjusts the probabilistic method to polychotomous (five-question) surveys, which are currently a standard tool for examining expectations, broadly expanding the literature regarding the method and aiming at limiting method’s shortcomings and adjusting it to modern economic conditions Models by Pesaran (1984), Smith and McAleer (1995) allowed for different solutions regarding general price level changes. Pesaran introduced asymmetrical relation of perceived inflation and expected price change. Smith and McAleer presented a model with time-varying parameters. Simmons and Weiserbs (1992) model was designed to work for the polychotomous survey
Critique Unrealistic assumptions and difficulties regarding the empirical application of the method; empirical distributions do not mimic theoretical distributions of variables; accuracy of quantified expectations Problems related to models’ estimations including standard econometric problems as the choice of estimator. Designed mostly for use in three-question surveys. Modern surveys of expectations are extended to five questions