Including News II: STAR

low, we would interpret the result as such that households slowly change their reaction to professional forecasters’ expectations if the media increase the amount of news coverage on inflation. In the extreme case γ = 0, we are back to the linear model. Note that both the shape and the threshold are determined endogenously during the estimation process.

Applied to the epidemiology model, we expect that households react more strongly to an upward revision of expert predictions in periods of high news coverage of inflation, while at the same time relying less on their own belief formed in the previous period. Therefore, we should getβ₁ >0, andβ₂ <0. In addition, households might also react differently to the inflation rate depending on how prominently prices are discussed in the media. Therefore, we also include the inflation rate (and a constant) in the nonlinear part of the model and test whether this increases the fit of the model.

Before estimating the model, we check whether the relationship between households’ and experts’ expectations is indeed nonlinear, and whether the nonlinearity depends on the number of news reports. For that purpose, we apply the nonlinearity test proposed by Teräsvirta (2004), which approximates the nonlinear function G with its first-order Taylor expansion aroundγ = 0.³⁷ The test regression is given by

y_t=θ⁰₀x_t+

3

X

j=1

θ⁰_jx˜_tq_t^j+u^∗_t, (2.12) wherey_tis the dependent variable,x_ta vector of explanatory variables,q_tthe transition vari-able and the error termu^∗_t =u_t+RwithRas the remainder of the Taylor expansion. In this regression, the null hypothesis of linearity isH₀ : θ₁ = θ₂ = θ₃ = 0, since the coefficientsθ_j are a function ofβ_j andc. We test both for nonlinearity stemming from the number of news reports M EDIA_tand from variation over time including a time trend. Finally, the smooth transition model is estimated with conditional maximum likelihood after performing a grid search on various values ofγ andc.³⁸ As it is emphasized byTeräsvirta(2004), ifγis found to be large meaning that the model is close to a regime-switching model, numerical prob-lems can often affect the estimated standard deviation of γ, which becomes equally large.

However, given the nonexistence of the null hypothesis of the standard t-test of statistical significance ofγ, these numerical problems should not lead to the conclusion that the model is in fact linear.

Table (2.11) shows the results for the full sample, separating households according to whether they have heard news about inflation. Starting with the linearity tests, we clearly reject the null hypothesis of linearity for all households and for households who have heard some news, only marginally missing the critical value for households who have heard news about inflation. By contrast, we cannot reject the null hypothesis for households who state to have

37Using the Taylor approximation is necessary given the fact that the linearity test is not defined under the null hypothesisH₀:γ= 0. See for detailsTeräsvirta(2004).

38Note that it is also possible to allow for more than one threshold or, likewise, more than two regimes.

heard good or bad news on inflation.

Table 2.11: STAR - Full Sample - Different Information Sets

all news news news news

households heard inflation good bad

linear part

cons 0.62*** 0.57*** 1.71*** 0.57** 2.09***

(0.11) (0.10) (0.31) (0.25) (0.36)

π_t^exp,prof 0.14*** 0.08** -0.21 0.52*** 0.42***

(0.04) (0.03) (0.22) (0.08) (0.15)

π_t−1^{exp,N EW S} 0.71*** 0.74*** 0.47*** 0.20*** 0.21***

(0.05) (0.04) (0.09) (0.05) (0.05)

π_t−1 0.04 0.04 0.29*** 0.14*

(0.03) (0.03) (0.07) (0.08)

nonlinear part

consG - - - 75.29***

-(24.72)

π_t^exp,profG 0.52** 2.61**** 0.40** -8.86*** 0.35*

(0.22) (0.91) (0.17) (2.91) (0.20)

π_t−1^{exp,N EW S}G -0.89*** -2.60*** -0.27*** 0.24 -0.34**

(0.26) (0.91) (0.10) (0.38) (0.16)

π_t−1G 0.35*** - - -

-(0.11)

γ 2.13* 13.56* 35.60 590.96 1004.50

(1.24) (8.18) (42.91) (3.10E+08) (2.63E+05)

c1 0.60*** 0.90*** 0.28*** 0.89 0.46***

(0.09) (0.01) (0.01) (4.46E+03) (0.03)

AIC -1.42 -1.39 0.76 1.31 1.38

SBIC -1.33 -1.31 0.85 1.39 1.46

HQ -1.39 -1.36 0.80 1.35 1.41

R²adj. 0.91 0.88 0.46 0.32 0.29

Linearity Test

w.r.t.N EW St 0.000 0.000 0.177 0.924 0.618

w.r.t.T IM E 0.000 0.000 0.000 0.329 0.000

Note: Standard errors in brackets. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively. Values of linearity tests are p-values derived from the F-statistic.

Looking at the linear part of the STAR model which corresponds to the epidemiology model without news coverage, we get positive and significant coefficients of both experts’ and households’ expectations. Moreover, for all households except those who have heard good or bad news about inflation, the degree of updating is found to be relatively low. Next, looking at the nonlinear part of the model, we find evidence supporting the epidemiol-ogy model. The coefficient of experts’ expectations is positive and statistically significant,

whereas lagged household expectations have a negative impact. Hence, it seems that more news coverage increases the impact of professional forecasters’ predictions on households’

expectation formation, and lowers the degree of expectation stickiness. This holds true for all households except those who have heard good news on inflation. Interestingly, we find that the media also increases the degree of adaptive expectation formation. A rising number of articles increases the impact of the lagged inflation rate.

The STAR model allows us to endogenously determine how exactly the nonlinear media effect influences households’ expectation formation. For that purpose, we plot the estimated transition functions in Figure (2.3) which have been calculated according to equation (2.11).

Figure 2.3: Estimated Transition Functions

0 .2 .4 .6 .8 1

0 .2 .4 .6 .8 1

ALL NH NINFL NGOOD NBAD

Note: The graph shows the estimated transition functions that are computed using equation (2.11). ALLis the transition function of all households with threshold 0.6, N Hthe function for households who have heard about economic news in general with threshold 0.9,N IN F Lis the function for households who have heard news about in-flation with threshold 0.3, andN GOODandN BADshow the functions of those who have heard good and bad news on inflation, with thresholds 0.9 and 0.5. Note that there are also some observations in the nonlinear regime ofN GOOD, but these are covered by the other graphs.

Looking at the estimated thresholdsc₁of the transition functions, we observe that the strength of the media effect differs according to whether households follow the news or not. For all households, the threshold is found to be at 0.6, i.e. at an average amount of coverage.

Households who claim to follow news on economic issues have a much larger threshold at 0.9, whereas households who have heard news about inflation already react to media

re-ports if news coverage exceeds a value of 0.3. Moreover, the transition from the linear to the nonlinear regime differs remarkably. The full sample of survey participants adjusts very smoothly to rising amounts of newspaper articles on inflation, whereas having heard news in general and in particular news on inflation leads to a much quicker adjustment. Hav-ing heard any news on inflation, or bad news on inflation does not make a large difference.

The threshold is lower compared to the full household sample, and the adjustment is much quicker. Finally, the STAR model does not perform well for households who have heard good news on inflation. The null hypothesis of linearity cannot be rejected and for the good news group, the estimated transition function while being very steep results in the fact that most of the estimated reactions belong to the linear regime. And as regards the estimated coefficients, the model suggests that households reactlessstrongly to experts if newspapers write more about inflation.

Note that the linearity test with respect to the time trend suggests a structural break in the full sample for all households groups except for those who have heard good news on in-flation. Hence, in the appendix, we also show the estimated STAR models for the different subperiods that have been identified earlier keeping in mind that the relatively low num-ber of observations in some periods might affect the results. Overall, our general results also hold if we split the sample into different periods. Taking the full set of households (Table (A.11)), the media thresholds are considerably lower since 1993:01 and the transition functions get steeper throughout. If we estimate the STAR model for different households groups, no matter if households have heard some news, good, or bad news on inflation, the results are fairly similar with the exception of the time span 2003:08-2006:12 (Tables (A.12)-(A.15)). In this period, we find that more news coverage makes households react less to experts and stick more to their own forecast from the previous period. Finally, during the financial crisis period 2007:01-2011:11, households who have heard bad news on inflation adjust less to experts in response to rising news coverage. This latter result might be due to the fact that households have a different interpretation of “bad news on inflation” than professional forecasters. While the actual inflation rate dropped below zero in 2009, house-holds seemed to think that the financial turmoil would result in higher inflation. By contrast, experts’ expectations remained rather constant at an inflation rate of about 2% (see Figure 2.1)