*4.2. Hypothesis 2*

The second hypothesis refers to the ability of survey's respondents to distinguish between current and prospective uncertainty and between general and personal uncertainty. Since the CIS barometers include current, retrospective and prospective assessments of the economic situation in Spain, we have compared the corresponding levels of Shannon's and quadratic uncertainty, represented in Figures 3 and 4. As it can be seen, according to both entropy measures current uncertainty is found to be higher than prospective uncertainty, which generally exceeds past uncertainty. However, some exceptions are found, corresponding to years 2012 and 2013 when the present uncertainty reaches its minimum values and is exceeded by prospective uncertainty.

**Figure 3.** Shannon's uncertainty for current, retrospective and prospective economic situation in Spain.

**Figure 4.** Quadratic uncertainty for current, retrospective and prospective economic situation in Spain.

As we have seen in the previous figures, Shannon's and quadratic entropy mostly agree in the quantification of uncertainty. No matter if we consider the general or the personal situation or if uncertainty refers to present, past or future periods, the correlation coefficients always exceed 90% as summarized in Table 3.

**Table 3.** Correlation coefficients between Shannon's and quadratic Uncertainty.


In order to analyze to which extent survey's respondents can properly distinguish between general and personal uncertainty we have also studied the perceptions about their personal economic situation. Although these series, represented in Figure 5 were quite short (they are only available since 2010) and therefore should be considered cautiously, the results show that until 2015 the level of uncertainty was higher when it refers to the personal situation. However, the perception of personal uncertainty seems to be more stable than that referred to the general economic situation and both measures are negatively correlated (−0.73 and −0.6 for Shannon and quadratic uncertainty respectively).

It is also interesting to mention that this situation changes when we focus on uncertainty about the future. In this case, we find no significant correlation between personal and general uncertainties, measured either with Shannon or quadratic entropy.

**Figure 5.** Shannon's (**left**) and quadratic (**right**) uncertainty for personal and Spanish economic situation.

Regarding the relationship between current and prospective uncertainty, the findings differ from personal to country's uncertainty (Table 4). It is interesting to remark that—independently of the measure of entropy used—when we pay attention to the personal situation there is a strong relationship between current and prospective uncertainty while this correlation does not exist when we focus on the assessment of the general economic situation. These findings confirm that the respondents were able to properly distinguish the perceptions related to their own economic situation and prospects from those referred to the country as a whole.


**Table 4.** Correlation coefficients between current and prospective uncertainty.

With regard to the industrial trend surveys, the experts' answers referred to future prospects (whose alternative options are to increase, to stay and to decrease) allow the estimation of future uncertainty, leading to similar results for Shannon's and quadratic entropy (the correlation coefficient amounted to 0.99). As in the previous application, the obtained results show that the respondents clearly distinguished between present and prospective uncertainty. In fact, regardless of the entropy measure considered, uncertainty referred to the present industrial output is found to be higher and more stable than uncertainty referred to the future industrial production.

These findings, represented in Figure 6 for the quadratic entropy, have been corroborated through paired difference tests, leading to the conclusion that the expected current uncertainty significantly exceeds prospective uncertainty.

**Figure 6.** Evolution of quadratic uncertainty associated to current and prospective industrial production in Asturias.
