Inflation experiences and inflation expectations--论文代写范文精选

在大多数时期,通胀预期调查两个问题:一个对未来价格的预期方向变化,和一个预期价格变化的百分比。因为分析旨在进行定量预测,因此更关注预期的百分比。下面的essay代写范文进行阐述。

Abstract 
We estimate the learning-from-experience effects by fitting the estimating equation (6) and the underlying AR(1) model to data on inflation expectations from the Reuters/Michigan Survey of Consumers.

We measure inflation experiences using long-term historical data on the consumer price index (CPI) from Shiller (2005). In order to fully capture inflation experiences during the lifetimes of all individuals in the survey data, including the oldest respondents in the earliest survey wave, we need inflation data stretching back 74 years before the start of the survey data in 1953. We obtain the time series of inflation data since 1872 (until the end of 2009) from Robert Shiller’s website and calculate annualized quarterly log inflation rates. For illustration, Figure 3 shows annual inflation rates from this series. 

The inflation expectations microdata is from the Reuters/Michigan Survey of Consumers (MSC), conducted by the Survey Research Center at the University of Michigan. This survey has been administered since 1953, initially three times per year, then quarterly from 1960 through 1977, and monthly since 1978 (see Curtin (1982)). We obtain the surveys conducted from 1953 to 1977 from the Inter-university Consortium for Political and Social Research (ICP SR) at the University of Michigan. From 1959 to 1971, the questions of the winter- 15 quarter Survey of Consumer Attitudes were administered as part of the Survey of Consumer Finances (SCF), also available at the ICP SR. The data from 1978 to 2009 is available from the University of Michigan Survey Research Center. Appendix B provides more detail on the data. 

In most periods, the survey asks two questions about expected inflation: one about the expected direction of future price changes (“up,” “same,” or “down”), and one about the expected percentage of price changes. Since our analysis aims to make quantitative predictions, we focus on the percentage expectations. However, for quarters in which the survey asks only the categorical questions about the expected direction, we are able to impute percentage responses from the distribution of the categorical responses. The imputation procedure is described in Appendix C. Figure 1 in the introduction highlights the periods in which we have percentage expectations data in light grey, and the quarters in which the survey asks only the categorical questions in dark grey. 

Since the learning-from-experience hypothesis predicts that inflation expectations are heterogeneous across different age groups, we aggregate the data at the cohort level, i.e., by birth year. For each survey month and each cohort, we compute the mean inflation expectations of all members of the cohort. In the computation of this mean, we apply the sample weights provided by the MSC. If multiple monthly surveys are administered within the same quarter, we average the monthly means within each quarter to make the survey data compatible with our quarterly inflation rate series. We restrict the sample to respondents aged 25 to 74. This means that for each cohort we obtain a quarterly series of inflation expectations that covers the time during which members of this cohort are from 25 to 74 years old. Figure 1 provides some sense of the variation in the data. 

As mentioned in the introduction, the figure plots the average inflation expectations of young individuals (averaging, for the figure only, across all cohorts below 40 years of age), middle-aged individuals (ages 40 to 60), and older individuals (ages above 60), expressed as deviations from the cross-sectional mean expectation each period. To better illustrate lower-frequency variation, we plot the data as four-quarter moving averages. The dispersion across age groups widens to almost 3 percentage points (pp) during the high-inflation years of the 1970s and early 1980s. The fact that young individuals at the time expected higher inflation is consistent with the learningfrom-experience hypothesis: The experience of young individuals around 1980 was dominated by high and persistent inflation in recent years, while the experience of older individuals also included the modest and less persistent inflation rates of earlier decades. For younger individuals, these recent observations exert a stronger influence on their expectations since their experience set contains a smaller number of data points.

Baseline results 
To check whether the imputation of percentage responses from categorical responses affects our results, we re-run the estimation using only those time periods in which percentage responses are directly available. As can be seen in column (ii), not using the imputed data has little effect on the results. We estimate a similar gain parameter, θ = 3.144 (s.e. 0.257), 18 and a similar sensitivity paramenter β = 0.675 (s.e. 0.079). Figure 4 illustrates the extent to which learning-from-experience effects explain crosssectional differences in inflation expectations. 

The figure shows both the raw survey data and fitted values based on the estimates in column (i) of Table 1. For the purpose of these plots, we average inflation expectations and the fitted values within the same categories of the young (age < 40), middle-aged (age between 40 and 60) and old (age > 60) that we used earlier in Figure 1. Since our baseline estimation with time dummies focuses on cross-sectional differences, we plot all time series as deviations from the respective population means, i.e., after subtracting their cross-sectional mean each period. To eliminate high-frequency variation, we show four-quarter moving averages for both actual and fitted values. Fitted values are drawn as lines, raw inflation expectations are shown as diamonds (young), triangles (middleaged) or filled circles (old). 

The plot shows that the learning-from-experience model does a good job of explaining the age-related heterogeneity in inflation expectations. In particular, it accounts, to a large extent, for the large difference in expectations between young and old in the late 1970s and early 1980s, including the double-spike. It also captures all of the low-frequency reversals in the expectations gap between older and younger individuals. The presence of the time dummies in these regressions is important to rule out that the estimates pick up time-specific effects unrelated to learning from experience. If individual expectations were unaffected by heterogeneity in inflation experiences—for example, if all individuals learned from the same historical data applying the same forecasting rules—then β would be zero. The effect of historical inflation rates, including “experienced” inflation rates, on current forecasts would be picked up by the time dummies. The fact that β is significantly different zero is direct evidence that differences in experienced-inflation histories are correlated with differences in expectations. 

The significant β-estimate also implies that recent observations exert a stronger influence on expectations of the young since the set of historical inflation rates experienced by the young that enters into the construction of the learning-from-experience forecast comprises only relatively few observations. We now fit the estimating equation (6) and the underlying AR(1) model using nonlinear least squares on the cohort-level aggregate data. We relate the inflation forecasts in the MSC to learning-from-experience forecasts. We assume that the data available to individuals who are surveyed (at various points) during quarter t are quarterly inflation rates until the end of quarter t − 1. Since the survey elicits expectations about the inflation rate over the course of the next year, but the (annualized) inflation rates that serve as input to the learning-fromexperience algorithm are measured at quarterly frequency, we require multi-period forecasts from the learning-from-experience model. We obtain these multi-period forecasts by iterating on the perceived AR(1) law of motion (1) at each cohort’s quarter-t estimates of the AR(1) parameters α and φ (which are based on inflation data up to the end of quarter t − 1). Hence, the one-year forecast that we relate to survey expectations is the average of the AR(1) forecasts of quarter t + 1 to quarter t + 4 annualized inflation rates. To account for possible serial correlation of residuals within cohorts and correlation between cohorts within the same time period, we report standard errors that are robust to two-way clustering by cohort and calendar quarter.（essay代写)

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