چرا سیاست های پولی مهم است؟مطالعه تجربی از پس انداز و نرخ تورم در مدل نسل های متداخل

The following is an examination of experiments using an overlapping generations model, where inflation is determined by the monetary policy and by the amount of average saving within each period. A new experimental setup is used that allows us to observe more details in the process of expectation forming and to separate this process from the actual saving process. In contrast to experimental findings by Lim, Prescott, Sunder; Marimon, Spear, Sunder; and Marimon, Sunder we have found that (1) agents do not form first-order adaptive expectations; (2) subjects ‘over-save’ for precautionary reasons; and as a result (3) the so-called Friedman conjecture holds, i.e. monetary policies which are equivalent in static equilibrium exhibit different levels and different volatility with regard to inflation in the experiment. This may generate important policy trade-offs between monetary regimes. We then discuss our findings and relate them to current research on adaptive learning and the role it may have in ranking alternative monetary policies

The inflationary impact of monetary policy is a classic theme in macroeconomics, which has long been investigated through theory and econometric studies. More recently it has also been the focus of an interesting series of experiments. Following the resurgence of interest by macroeconomists in theories of adaptive learning (see Evans and Honkapohja, 1999, for a thorough review), Lim et al. (1994), Marimon and Sunder 1993, Marimon and Sunder 1994 and Marimon and Sunder 1995 and Marimon et al. (1993), all ran experiments to investigate whether the inflationary processes in overlapping generation economies (OLG) with multiple equilibria would be better explained by adaptive expectations or by the rational expectations hypothesis. In the setting underlying the experiments, which closely mimics an OLG model studied theoretically by Sargent and Wallace (1987), Marcet and Sargent (1989), Bruno and Fisher (1990), monetary policy is public knowledge and subjects use money as a unique asset to transfer wealth across two periods. The model displays a well-known indeterminacy problem:1 under any monetary policy, the economy has two stationary rational expectation solutions – a low (classical) inflation stationary state (ISS) and a high ISS – and a continuum of non-stationary rational expectations equilibria which reach the high ISS in the long run. On the other hand, the stability of the ‘adaptive dynamics’ implies convergence towards the low ISS under a large class of adaptive learning rules and for a large set of initial conditions. The inflation paths observed in the first wave of experiments (e.g. Marimon and Sunder 1993 and Marimon and Sunder 1994) documented a broad convergence towards the stationary equilibrium with low inflation, giving substantial support to adaptive learning as a valuable theory of equilibrium selection. Later, Marimon and Sunder (1995) in the same experimental setting compared the inflationary impacts of two classical monetary regimes. Under the first regime, which Marimon and Sunder call the ‘real deficit rule’, the government fixes a constant level of real deficit and finances it through seigniorage (though government expenditure does not enter into agents’ utilities). Such a rule may yield high inflation in some periods and low inflation in others. Under the second regime, called the ‘money growth rule’, the government fixes the rate of growth of the money supply and adjusts the level of seigniorage to satisfy its money growth rule. This rule may lead to a high government deficit in some periods and to a small one in others. Although the two regimes correspond to different fiscal environments, in Marimon and Sunder's (1995) experiment the two rules were fixed so as to share the same steady-state equilibrium and also to yield, in equilibrium, the same government revenue. The goal of the investigation was to test a classical conjecture, first suggested by Friedman 1948 and Friedman 1960, where in order to stabilise inflation, a simple rule, such as constant growth of the money supply, may be better because it can more easily be learned, thus making it easier for agents to co-ordinate their behaviour. Marimon and Sunder (1995) found little supporting evidence for this conjecture: price volatility as observed in their experiments is better explained by the stability properties of the adaptive learning rules which subjects seemed to adopt than by differences in the monetary regimes. They specifically found support for first-order adaptive expectations and showed theoretically that first-order adaptive expectations imply equivalence of the volatility of inflation under the two rules. Here we submitted Friedman's conjecture to further scrutiny, using an experimental set-up that allows us to observe more details of the subjects’ behaviour and to study the process of expectation formation independently of that of the actual saving decisions. We further tried to make sure that subjects easily understand what is going on in their economy. Our findings indicate that the two monetary rules are no longer equivalent, but differ significantly in terms of both the level and the volatility of inflation. Since we can observe more details of the subjects’ decision-making process, we can relate the changes in the macroeconomic properties to changes in microeconomic behaviour. Different approaches to modelling an OLG economy in an experiment are reported in the literature. Marimon et al. (1993) introduced a very straightforward procedure to assist subjects in making their optimal saving decisions. This procedure was later also used by Marimon and Sunder (1995): subjects are asked to make one inflation forecast for one period ahead (knowing past realised inflation), and then the computer software, given that unique forecast and treating it as if it were certain, automatically computes and implements the subjects’ optimal saving.2 Individuals, however, may have reasons for deviating from this ‘certainty equivalent’ behaviour and, more generally, from strict optimisation. Firstly, there is the possibility that agents do not hold point expectations and therefore react to the volatility of inflation with precautionary saving. Secondly, rather than proceeding to individual maximisation, agents may to some extent copy others believed to be better equipped to make good decisions. Thirdly, various other factors such as inertia, small transactions costs (also interpreted in psychological terms), rules of thumb, may generate small deviations from optimality.3 We therefore made a few changes in designing our experimental set-up which we considered important for understanding better the forces which may drive the inflationary processes of the two monetary rules. Let us emphasise three of these changes. Firstly, in our network economy subjects make both forecasts, receiving from the computer a suggestion for optimal saving, but then making their actual saving decisions. In this way, we can analyse whether and how actual decisions differ from optimal ones. Second, we do not restrict our subjects to holding quasi-point forecasts: our subjects can check the implication of many forecasts for various periods ahead before making a final saving decision. This allows us to distinguish subjects whose forecasts in a given period vary little from others whose forecasts vary more and may perhaps generate higher savings. Third, in a further attempt to make our experimental environment descriptively richer, we introduced labels for monetary policies and make participants vote for monetary policies. We alternately placed the ‘real deficit rule’ and the ‘money growth rule’ under two different labels: our subjects were presented with the experimental market as a market operating in the European Monetary Union, the two rules being implemented either by the Bundesbank or by the EU Commission. Besides making the experimental environment more interesting, and hence actualising the attention of the participants, our hypothesis was that labels could themselves affect the subjects’ expectations and the volatility of the inflation under the two rules. We conjectured that the ‘Bundesbank label’ might generate less inflation volatility than the ‘EU Commission label’, but found little to support this notion in the end.4 Anticipating briefly our results, regardless of the effect of labels, we first of all noted that, like our precursors, we found convergence to the low ISS in most of our experimental economies. The actual transition dynamics, however, around the low ISS equilibria are much more complex under both regimes and for all of our experimental economies than can be approximated by a first order or by any other simple adaptive scheme. In particular, the inflation rates under the real deficit regime are, on average, lower than the inflation equilibrium levels and also than the average inflation rates observed under the revenue equivalent money growth rule; in support of Friedman's conjecture, the price to be paid a greater inflation volatility under the real deficit regime than under the money growth rule. This can be explained by the characteristics of the saving decision processes which our subjects seem to follow. First of all, actual saving rates differ significantly from the optimal saving decisions implied by individual forecasts: the latter enter into the explanatory mechanism of the former, together with past average saving rates, in a convex combination which explains our findings rather well. Most importantly, we also found a significant amount of over-saving at individual and aggregate level, probably due to a form of precautionary saving: since the payoff functions given to our subjects imply that savings should increase to a mean preserving spread in the expected rate of inflation, and since with our setup we can measure the variance of individual forecasts, we found that uncertainty about the future (shown by forecasts with greater variance) explains over-saving as precautionary saving. Over-saving is important because it is at the root of the trade-off between the two regimes implied by our findings. In particular, we will show that only under the real deficit regime will increasing average saving rates yield decreasing inflation rates; but we will also show that stability of adaptive learning near the low ISS is negatively related to the inflation rates. While from one perspective our findings seem to support Friedman's conjecture on the comparison between the two regimes, it must however be noted that from a different perspective they contrast with another hypothesis also advanced by Friedman in his Nobel lecture (Friedman, 1977). There he suggested that a positive relation exists between the level of inflation and its volatility. Despite the fact that this second conjecture was formulated in a context of the uncertainty of monetary regimes, rather than the comparison of regimes, the policy trade-off is quite interesting. We will later discuss this issue, commenting upon the results. The rest of the paper is organised as follows. In Section 2 we briefly review the theoretical OLG model which we are investigating. In Section 3, we specify the changes introduced in our experimental setup from previous studies and will give reasons for them. Details of the experiments we have run in Florence (Italy), Mannheim (Germany) and Pavia (Italy) are given in Section 4; the results and their implications in 5 and 6. A brief final section (Section 7) relates our findings to current research on models of adaptive learning and the role the latter may in general have in ranking monetary policies.

7. Concluding remarks on the literature of adaptive learning The last observation of the previous section allows us to consider an ultimate, more general question underlying our experimental investigation and concerning the extent to which, as in some current research (see the comprehensive survey in Evans and Honkapohja, 1999), different monetary policies can be studied and possibly ranked according to the stability properties of their adaptive dynamics. The answer provided by our evidence is not simple. On the one hand, from an ex ante position, considering that the theoretical stability properties of the two monetary rules we study imply equivalence of the two regimes, we should reject stability analysis because it is inconsistent with our observations. From an ex post position, however, after rejecting the equivalence hypothesis on empirical grounds, we have used stability analysis – in the light of the observed deviations from optimal saving decisions – to explain the different inflationary impacts of the rules. Should the ex ante- or the ex post-perspective be preferred? The answer depends on the aims of the analysis. If the purpose of the analysis is to understand and to describe what one observes in the data, our experiments clearly confirm that the theory of adaptive learning may be quite fruitful. If instead one wishes to derive policy recommendations simply by the theoretical stability properties of alternative policy options, much more caution should be used. Attention must in particular be paid to the possible effects of the large number of issues which, unavoidably, a theoretical model must abstract from; but which, if taken into account, may affect the conclusion of stability analysis substantially. This seems an obvious consideration, valid for any of the theoretically based policy recommendation. But in the present case, it assumes a special importance. We would emphasise that the question we are addressing is not the reliability of the theory of adaptive learning in its final implications for equilibrium selection, but the extent to which adaptive learning can also be useful in an ex ante perspective, in order to anticipate fully the dynamic transitional aspects out of an equilibrium. It is this much more subtle issue which is causing much debate among macroeconomists (e.g. Sargent, 1993; Honkapohja, 1995; Farmer, 1996). The problem seems to be that ‘the environments into which we have cast our adaptive agents seem much more stable and hospitable than the real-life situations for which we would want transition dynamics’ (Sargent, 1993, p. 169). An important specific difficulty seems to be that the environments in which adaptive agents are normally embedded typically refer to general equilibrium economies where there is no uncertainty. While this assumption could perhaps be justified in models of rational expectations (since, by definition, in such models the economy is always in equilibrium), a characteristic of the models of adaptive learning is precisely that the actual law of motion of the forecasted variables differ, during the transitional process, from the perceived law of motion, thus giving rise to an obvious source of endogenous uncertainty. In this respect, we would conclude by noting that among the different factors one may have to consider in future research to increase the robustness of monetary policy recommendations based on stability analysis, special efforts should be made to check how robust the recommendations are in view of the effect that endogenous inflation uncertainty may have on agents’ behaviour.