*4.3. Hypothesis 3*

According to the third hypothesis, which we consider especially interesting, uncertainty negatively affects economic growth. In order to analyze this assumption we first focus on the CIS barometer, considering the estimated Shannon's and quadratic entropy together with two additional quarterly series: the annual GDP growth rate and a synthetic indicator.

Denoting by *Xt* the quarterly GDP, the related annualized growth rate is given by the expression *g* = *Xt Xt*−<sup>4</sup>− 1.

Furthermore, following a widely extended practice in this kind of surveys, a synthetic index can be computed in order to summarize the answers. Focusing on the assessment of the current economic situation in Spain, this indicator can be easily obtained as follows: *SI* = <sup>2</sup>*pvery*\_*goo<sup>d</sup>* + *pgood* − *pbad* − <sup>2</sup>*pvery*\_*bad*, where *pvery*\_*good*, *pgood*, *pbad*, *pvery*\_*bad* represent the probabilities assigned to each of the considered categories, estimated through the corresponding relative frequencies.

Once this indicator has been computed we can analyze the relationship between the perceived economic situation and the corresponding level of uncertainty. Although these quarterly series appear to be contemporaneously uncorrelated, the scatter diagram represented in Figure 7 provides some interesting hints about the parabolic pattern of uncertainty regarding the synthetic index.

As it can be seen in this graph, low uncertainty with low dispersion is associated with very negative perceptions of the economic situation, whilst as perceptions of economic situation increase, so too do measures of uncertainty with associated increasing dispersion.

With the aim of examining how uncertainty impacts on economic activity, a more detailed analysis has been developed through VAR models. More specifically, we propose VAR models involving the economic growth, the synthetic index and the uncertainty measure, and we run two versions by using either Shannon's entropy or quadratic entropy as the measure of uncertainty. We estimated both VAR models on quarterly data from 1996 to 2018 (T = 89) and, following the commonly used information criteria (Akaike, Schwartz and Hannah–Quinn), we considered two lags (*p* = 2). Tables A1 and A2 in the Appendix A collect the VAR estimation results.

It is interesting to notice that the Granger causality test (whose null hypothesis is "no Granger causality") leads to the p-values collected in Tables 5 and 6, showing that variations in GDP are explained by both the synthetic index and the level of uncertainty, regardless of the entropy measure used. Moreover, uncertainty was found to Granger cause the synthetic index at the 10% level.

**Figure 7.** Shannon's and quadratic uncertainty versus synthetic index.

**Table 5.** *p*-values for the Granger causality tests (F-test of zero restrictions) in vector autoregresive (VAR) 1.



**Table 6.** *p*-values for the Granger causality tests (F-test of zero restrictions) in VAR 2.

Since uncertainty causes economic growth, we have also analyzed the impulse responses for GDP growth and the synthetic index to a one standard deviation shock in the uncertainty level, measured both by Shannon and quadratic entropy. The results are plot in Figures 8 and 9, showing that the effects of one standard deviation shock to the uncertainty in economic growth are mostly negative with their largest impacts around 12–15 months.

According to the impulse-response analysis, the behavior is quite robust with regard both to the economic indicator (GDP growth and synthetic index) and the uncertainty measure (Shannon's and quadratic entropy).

Regarding the impact of the synthetic index on GDP growth, Figure 10 represents the impulse-response analysis for one standard deviation shock in the synthetic index. As expected, the response in this case is positive and faster, with its largest impact taking place around five months.

Following the same method we examine the relationship between uncertainty and industrial production. As in the previous analysis we estimate two VAR models including, in this case, four monthly series, corresponding to the regional IPI, the ICI, the synthetic index (SI) and the level of uncertainty.

**Figure 8.** Impulse responses of GDP growth to a shock in Shannon's uncertainty (**left**, VAR 1) and quadratic uncertainty (**right**, VAR 2).

**Figure 9.** Impulse responses of the synthetic index to a shock in Shannon's uncertainty (**left**, VAR 1) and quadratic uncertainty (**right**, VAR 2).

**Figure 10.** Impulse response of GDP growth to a shock in the synthetic index according to VAR 1 (**left**) and VAR2 (**right**).

These series have been obtained from SADEI [21], the regional statistical office of Asturias which provides monthly information about the industrial production index (currently referred to year 2010) and the ICI, a leading indicator of economic activity [16] computed as an arithmetic mean of the balances of the portfolio orders, the production expectations and—with the opposite sign—the level of stocks. Regarding the Synthetic Index, it has been computed as in the previous subsection from the balance of positive and negative answers referred to industrial output, using the estimated frequency probabilities.

Finally, with regard to the level of uncertainty, two VAR models have been estimated, using Shannon's entropy in the first one and quadratic entropy in the second. Since Shannon's index cannot be computed for some months with null probability in any of the categories we have restricted the sample size in both models (T = 124) in order to provide fully homogeneous results.

It is interesting to remark that, taking into account the series analyzed, VAR specification includes in this case constant, trend and seasonality. Following the information criteria, only one lag was considered.

The estimation results are collected in the Appendix A (Tables A3 and A4) and the conclusions show outstanding similarities for the two uncertainty measures, as it can be seen in Figure 11. As expected, the impulse responses of the regional industrial production index to a one standard deviation shock to the uncertainty level are negative with their largest impacts during the first two periods and a quick recovery in the medium run.

**Figure 11.** Impulse response of industrial production index (IPI) to a shock in Shannon's (**left**) and quadratic uncertainty (**right**).

## **5. Discussion and Concluding Remarks**

Our empirical results show that qualitative surveys can be successfully used to approach both the economic situation and the surrounding uncertainty, thus agreeing with the first proposed hypothesis. More specifically, the information provided by the respondents to the CIS barometer and the industrial trend survey confirms the usefulness of both sources and the adequacy of entropy-based measures to approach uncertainty. In addition, we find that—as indicated by previous works [2]—the level of expertise does not affect the adequacy of respondents' answers.

According to the two empirical applications, based in confidence barometers and industrial trend surveys, Shannon's and quadratic entropy mostly agree in the quantification of uncertainty, no matter if we consider the Spanish or the personal economic situation or if uncertainty refers to present, past or future periods.

Regarding the second hypothesis, the available information suggests that surveys respondents can properly distinguish between current and prospective uncertainty and between general and personal uncertainty. According to the CIS barometer and the Industrial Trend Survey, current uncertainty is higher than prospective uncertainty, regardless of the measure used. Furthermore, the CIS barometer provides significant evidence about the capability of survey's respondents to distinguish between personal and national uncertainty: first, the perception of personal uncertainty seems to be more stable than that referred to the Spanish economic situation and second, a strong positive correlation is found between current and prospective uncertainty referred to the personal situation, unlike what happens when we focus on the economic situation of the country. Finally, our empirical applications show that uncertainty negatively affects economic growth, providing evidence about the responses of economic growth and industrial production to a shock in the uncertainty measures.

The estimation of VAR models leads to some interesting findings that broadly match with previous works as [26–28]. More specifically, the adverse impacts of uncertainty shocks on economic activity have been documented among others in [26,27] while [28] provides significant evidence about the fall of industrial production as a response to a volatility shock.

Our results based on the CIS barometer are quite robust, since they confirm that uncertainty shocks, regardless of the entropy measure used, have a negative impact on economic activity, whether measured through GDP growth or the synthetic index. According to the impulse-response analysis, the largest impacts take place around 12–15 months, followed by a slow recovery. Similarly, when we focus on the industrial trend survey, we find that one standard deviation shock to the uncertainty level (measured either by Shannon's or quadratic entropy) leads to sharp reductions in the regional industrial production, with a quick recovery in the medium run.

Despite their limitations, these interesting findings confirm the potential of qualitative surveys in the assessment of economic uncertainty also suggesting the need of further research in this field.

**Author Contributions:** Both authors contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.

**Funding:** This research was funded by Consejería de Hacienda y Sector Público (Treasury and Public Sector Counseling, Government of the Principalty of Asturias, Spain), Grant SV-PA-18-03.

**Acknowledgments:** The authors would like to thank two anonymous referees for very helpful comments. We would also like to acknowledge the financial support of the Government of the Principalty of Asturias.

**Conflicts of Interest:** The authors declare no conflict of interest.
