عدم اطمینان و شفافیت در بانک مرکزی : یک رویکرد غیر بیزین

We use a non-Bayesian approach to uncertainty, where “ambiguity” is taken into account, in order to analyze the issue of central bank transparency, and we underline that the use of such an approach may greatly change the results. We reconsider a specific argument against transparency found in the literature. We show that, in the presence of ambiguity, the argument can become a case in favor of transparency, which seems more in accordance with some stylized facts. Reduced Knightian uncertainty associated with increased transparency can contribute to making transparency beneficial.

In the past two decades, there has been a widespread move of central banks toward more transparency. Such a move has in part been due to the trend toward more central bank (CB) independence. Being more independent, CBs had to be more accountable and, for that, had to be more transparent about the way they conducted their monetary policies. But there are also economic reasons for CBs to be more transparent. By providing additional information on the underlying factors affecting monetary policy (objectives of the CB, economic data and forecasts made by the CB, procedures involved in the decision process, etc.), transparency can help the private sector to make better decisions. As a consequence, there has been a large development of both the theoretical and the empirical literature on the economic effects and possible usefulness of increased CB transparency.1 Theoretical studies have mixed conclusions. Although some results are favorable to transparency, there are also several types of arguments pointing to the possible deficiencies of increased transparency. Thus, the results obtained in the literature depend on the model considered and on the specific assumptions made. In this paper, we will develop the argument that the results obtained in the literature may also depend on the approach to uncertainty which is taken. The theoretical literature on CB transparency usually adopts a Bayesian expected utility criterion.2 However, Knight (1921) already argued that a distinction should be made between a situation of “risk”, where there is some known objective probability distribution, and a situation of “(Knightian) uncertainty”, where this is not the case. Furthermore, some insufficiencies of the Bayesian approach (where uncertainty is represented by a subjective probability distribution) in describing behavior have been pointed out. Thus, the Ellsberg’s paradox (Ellsberg, 1961) has underlined the existence of some “aversion to ambiguity ”. Therefore, in the past two or three decades, new approaches to uncertainty, where such an aversion to ambiguity is introduced, and which encompass the Bayesian approach as a special case, have been developed.3 Such a non-Bayesian approach has been applied to some number of issues in economics. This has actually helped us understand some rather puzzling phenomena.4 It would therefore seem worthwhile to try to apply this approach to the issue of CB transparency. Here, we will see that, by using of a non-Bayesian approach, some theoretical argument found in the literature on CB transparency could be made more in accordance with some existing stylized facts on CB transparency. In the literature on CB transparency, there seems to be some discrepancy between the results found in the theoretical literature and those found in the empirical literature. While, as we have just mentioned, the theoretical literature leads to mixed conclusions, the empirical literature is largely in favor of CB transparency. This especially concerns the effect of “political transparency” of the CB, which includes transparency on the CB’s objectives. Depending on the model used, the existing theoretical arguments may be either favorable or unfavorable to such transparency. But empirical studies seem more in favor of political transparency of the CB. Empirical results tend to show that higher political transparency of the CB leads to a better performance in terms of macroeconomic variables and, in particular, reduces inflation.5 In this paper, we will reconsider some rather simple specific theoretical argument against political transparency of the CB which is found in the literature. We will show that the argument can actually become a case for transparency when we depart from the Bayesian case. By using a non-Bayesian approach, the results we obtain are therefore more in accordance with the existing empirical finding that political transparency of the CB tends to improve macroeconomic performance. The specific argument of the literature that we will consider, underlines that reduced uncertainty on the CB’s preferences may be harmful through its unfavorable effect on the level of the nominal wage (Grüner, 2002 and Sorensen, 1991). The argument relies on the analysis of a game between a monopoly labor union and a CB. The labor union sets the nominal wage before the CB chooses its monetary policy. As the weight the CB attaches to its inflation objective relatively to its unemployment objective is not known to the labor union, this creates some uncertainty on how the CB reacts to the nominal wage. It is then shown that less uncertainty increases the level of the nominal wage chosen by the labor union. As a consequence, this may worsen macroeconomic performance defined in terms of unemployment and inflation, and therefore may be harmful.6 In this analysis of the literature, uncertainty is represented by a probability distribution, and a standard expected utility criterion is used. Less uncertainty is associated with a smaller variance of the probability distribution. In Sorensen (1991), the source of the uncertainty is assumed to be some political factors, and the implication of the result is that political uncertainty, which creates variability in the weight between the CB’s objectives, may be beneficial. In Grüner (2002), this result is rather interpreted as an argument against too much transparency, where more transparency is assumed to imply a lower variance of the probability distribution. As we have indicated, in the present paper, we will revaluate this argument by using a non-Bayesian approach, where the decision maker has some aversion to ambiguity. Such a framework will allow us to introduce Knightian uncertainty into the analysis. As we want to compare situations which are more or less uncertain in some sense, we need to consider the effects of changes in the information available to the decision maker. Therefore, we will consider a non-Bayesian approach which makes explicit the information available to the decision maker.7 We will use the approach of Gajdos et al. (2004), which introduces some aversion to ambiguity under the form of an “aversion to the imprecision of information ”. Under this approach, the information available to the decision maker consists in two things: a “central probability distribution”; and a set of possible probability distributions around this central probability distribution, which represents Knightian uncertainty around this central distribution. We will assume that political factors can create fluctuations in the CB’s preferences which follow some given probability distribution. This probability distribution is only imperfectly known to the private sector. In the information available to the private sector, the central probability distribution is an estimate of this probability distribution obtained under some central prior, while Knightian uncertainty around this central distribution represents the sensitivity of the estimates to other priors. Increased CB transparency reduces both the variance of the central distribution and the amount of Knightian uncertainty. The presence of Knightian uncertainty and of some aversion to ambiguity will lead to results which are different, and often opposite to those obtained in the literature under a Bayesian approach. First, we will find that a decrease in the variance of the central distribution, which may be due to less variable political factors or to more CB transparency, does not affect the nominal wage when we are far enough from the Bayesian case. Consequently, in this case, this smaller variance can never be harmful and is in general beneficial. Second, we will find that the nominal wage is never raised but, on the contrary, is often lowered by a decrease in Knightian uncertainty. As a consequence, less Knightian uncertainty is, in general, always beneficial. These results tend to make more political uncertainty harmful, and more CB transparency beneficial. This is opposite to what was underlined in the literature under the Bayesian approach. The model of Grüner (2002) that we have used does not have any stochastic shock affecting employment. However, the stabilization motive of responding to shocks is certainly an important aspect of monetary policy. Therefore, we have also examined if and how the conclusions may change when such a stabilization motive is introduced into the analysis. As we will see, the results become less clear-cut when such a motive is introduced. Our framework of analysis is presented in Section 2. In Section 3, the equilibrium nominal wage is determined. The effects on the nominal wage of changes in the variance of the central distribution, or of the amount of Knightian uncertainty, is considered. The welfare effects are examined in Section 4. Section 5 considers the extension of the model obtained by adding a stochastic shock to the unemployment equation. Section 6 concludes.

The literature on central bank transparency mainly uses an expected utility Bayesian approach to uncertainty. Here, we have underlined that the results obtained may be very different when we depart from this Bayesian approach and use a non-Bayesian approach to uncertainty, which contains the Bayesian approach as a special case, but which, more generally, introduces an aversion to ambiguity and Knightian uncertainty. We have considered a specific argument which appears in the literature. This argument shows that more uncertainty on central bank (CB) preferences could be beneficial because, in a game between the CB and a monopoly labor union (LU), this would lead the LU to lower the nominal wage. Such a result has been interpreted as an argument showing that political uncertainty, which creates fluctuations of CB objectives, may be beneficial; and also as an argument against CB transparency, because more CB transparency would tend to reduce the uncertainty that the private sector has on CB preferences. We have tried to extend and revaluate this argument (obtained under the standard Bayesian expected utility approach in the literature) by using a non-Bayesian framework. In our framework, as in the literature, political factors can create fluctuations of the CB’s preferences which follow some probability distribution. This distribution is only imperfectly known to the private sector. Under the non-Bayesian approach we have considered, the information available to the LU has two parts. First, there is a “central probability distribution” which reflects the estimate of this distribution under some central prior held by the private sector (the LU) on this distribution. More political risk, which leads to more fluctuations of CB preferences, increases the variance of this central distribution. And more CB transparency, which increases the accuracy of the estimates, reduces this variance. Second, in addition to this central distribution, the information available to the private sector also takes the form of some Knightian uncertainty around this central probability distribution. Such an uncertainty results from the lack of confidence that the private sector has on its priors when it tries to estimate the probability distribution which governs the CB’s preferences. More CB transparency, which increases the amount and quality of data, reduces this Knightian uncertainty by diminishing the importance of priors relatively to data in the resulting estimates. We have considered the effects of the corresponding two parameters which are affected by CB transparency: the variance of the central distribution, on the one hand; and a parameter which is an index of the amount of Knightian uncertainty, on the other hand. When we consider the effect of a change in the variance of the central distribution, the level of “ambiguity” has been shown to play a crucial role. “Ambiguity” is a mix of two parameters of the model: the “aversion to the imprecision of information” of the decision maker, on the one hand; and a parameter which is an index of the amount of Knightian uncertainty, on the other hand. This ambiguity parameter can be considered as an index measuring the distance from the Bayesian case. When ambiguity is lower than some threshold value, then a smaller variance of the central distribution raises the nominal wage and, consequently, can be harmful for some values of the parameters. As a consequence, greater fluctuations of the CB’s preferences, due to more political risk, can be beneficial; and, as more CB transparency decreases the variance of the central distribution, this also gives an argument against CB transparency. This result can be seen as a generalization of the result obtained in the literature in the Bayesian case of no ambiguity, to the non-Bayesian case, where ambiguity is not zero, but still not too large. However, when ambiguity becomes larger than the threshold value, a smaller variance of the central distribution does not affect the nominal wage (which stays equal to the nominal wage under certainty), and, consequently, can never be harmful (and is in general beneficial). This means that the result obtained in the literature under the Bayesian approach, does not hold when ambiguity is large enough: in this case, more political risk is in general harmful; and the effect of CB transparency which goes through a reduced variance of the central distribution, becomes favorable. As long as ambiguity is not equal to zero, i.e. as soon as we depart from the Bayesian case, less Knightian uncertainty is never harmful. In general, it is beneficial. There are two reasons for that. First, the nominal wage is never raised (and is even lowered when ambiguity is not too large), and, second, for a given nominal wage, reduced Knightian uncertainty tends to increase welfare. This favorable effect on welfare of reduced Knightian uncertainty is an other argument in favor of CB transparency which was not taken into account in the literature. When ambiguity is not too large, the favorable effect going through reduced Knightian uncertainty dampens, or may even dominate, the possible unfavorable effect due to a reduced variance of the central distribution that more CB transparency may imply. And, when ambiguity is large enough, as the two effects go into the same direction, the favorable effect of reduced Knightian uncertainty further contributes to make CB transparency beneficial. As an illustration, we have considered the extreme case where a change in CB transparency would imply a move from complete ignorance to complete knowledge of the underlying probability distribution followed by the CB’s preferences. In the Bayesian case, such a move can be harmful. However, when the aversion to the imprecision of information is large enough, then, because of the favorable effect due to the elimination of Knightian uncertainty, such a move has been shown to be always beneficial. Therefore, in the presence of ambiguity, the specific theoretical argument that we have considered (which, in the literature, was developed under a Bayesian approach) may become an argument for transparency rather than against transparency. As underlined in the Introduction, this may help bridge the gap between the theoretical and the empirical results which can be found in the literature on CB transparency. The results we obtain are more in accordance with the empirical finding that greater “political transparency” of the CB (which includes transparency on CB preferences) has beneficial effects and, in particular, leads to lower inflation. However, we should be cautious and not draw too general conclusions from these results. In particular, the presence of ambiguity may not always be in favor of transparency. The reason is that the effect of ambiguity goes through what is the worst case for the decision maker. But the worst case may depend on the model. And this could lead to different implications for CB transparency. This clearly appears if we introduce a stabilization motive into our model, by adding a shock to the unemployment equation. This could actually change the worst case for the LU, and, as we have seen, might lead to effects on the nominal wage which are less favorable to transparency. This could lead to different results. Nonetheless, the analysis of this extended model, which adds a stochastic shock, confirms the general point that the results on CB transparency found in the literature, under a Bayesian approach, may greatly change if we use a more general non-Bayesian approach to uncertainty. The certainty equivalence property, which holds under the Bayesian approach, is not valid anymore: in the presence of ambiguity, the stochastic shock in the unemployment equation could affect the nominal wage by changing the worst case for the LU. As a consequence, the effect that a stabilization motive has on the issue of CB transparency could differ from what was obtained in the literature under a Bayesian approach.