سیاست های پولی و قیمت سهام پویایی با مشارکت بازار سرمایه محدود

We study a New-Keynesian DSGE model subject to limited asset market participation (LAMP) and assess whether monetary policy should respond to stock prices for what concerns the determinacy and the learnability (E-stability) of the Rational Expectations Equilibrium (REE). We find that interest rate rules granting a positive response to stock prices facilitate both the determinacy and the E-stability of the fundamental REE when the degree of LAMP is sufficiently large to generate an inverted aggregate demand channel of monetary policy transmission. Moreover, according to our analysis, policy rules responding to stock prices appear to perform better than more standard rules responding to output with respect to both equilibrium determinacy and aggregate welfare.

Since the burst of the dot.com bubble in early 2000, a lively discussion started in the literature aimed at defining the appropriate response of monetary policy to large swings in asset prices. In particular, economists and policy-makers have been debating whether central banks should counteract sustained increases in stock prices by raising the short-term nominal interest rate, the monetary policy instrument.1 As stock prices presumably reflect market expectations on future profits and hence future aggregate activity, central banks targeting inflation might decide to adopt a “leaning against the wind” policy and raise the policy rate in response to higher stock prices to better shield the economy against anticipated inflationary pressure. Carlstrom and Fuerst (2007) challenge this view, showing that the introduction of an explicit response to stock prices in Taylor-type interest rate rules increases the scope for (local) equilibrium indeterminacy in a benchmark New-Keynesian model. By allowing endogenous variables to be driven by belief shocks, equilibrium indeterminacy introduces non-fundamental excess volatility in the model, thus lowering aggregate welfare. In their framework, higher inflation increases marginal costs, which in turn lower firm’s profits and stock prices. As a result, an interest rate rule augmented with an explicit positive response to stock prices implies an overall lower response to inflation, which might induce a decrease (rather than an increase) in the real interest rate. If that is the case, aggregate demand expands and an initial belief-driven increase in inflation can become self-fulfilling. The Taylor principle – i.e., the fact that the interest rate should respond more than proportionally to inflation (an active policy rule) – may then be insufficient to guarantee a unique Rational Expectations Equilibrium (REE) if the policy rule also responds to stock prices. As the authors show, determinacy requires instead a reinforced Taylor principle: the larger the explicit policy response to stock prices, the more active the policy rule should be towards inflation. This result leads them to conclude that, from the perspective of equilibrium determinacy, such augmented monetary policy rules should not be pursued. 2 In this paper, we assess the desirability of Taylor-type rules responding to stock prices in a New-Keynesian model subject to limited asset market participation (NK-LAMP). Namely, we assume that a fraction of agents in the economy has no access to financial markets such that consumption can only be financed through labor income. This assumption is supported by the extensive empirical literature on consumption behavior in the US showing that for a large fraction of the population individual consumption moves almost one-to-one with current income. In their seminal work, Campbell and Mankiw (1989) find this fraction to correspond, roughly, to 40–50% of the entire US population. Using PSID and SCF data, other studies document that, depending on the definition of wealth, about 20–70% of the US population can be classified as asset-poor.3 As shown by Gali et al., 2004 and Bilbiie, 2008, if the share of non-asset-holder is sufficiently large, the NK-LAMP economy features an inverted aggregate demand logic (IADL), in the sense that a decrease in the real interest rate determines a contraction (rather than an expansion) of current real activity. Under these circumstances, equilibrium determinacy requires the nominal interest rate to respond passively to inflation under a forward-looking Taylor rule ( Bilbiie, 2008), and either very actively or very passively under a contemporaneous Taylor rule ( Gali et al., 2004). Our main criteria of policy evaluation are (1) the (local) determinacy of REE, and (2) the stability under adaptive learning (or learnability) of the Minimum State Variable (MSV) representation of the fundamental REE (from now on, the MSV-REE). The determinacy analysis will allows us to directly compare our results to those obtained by Carlstrom and Fuerst (2007) for the case of a fully Ricardian New-Keynesian framework, and hence to evaluate the role played by LAMP for the (un)desirability of stock-price-augmented Taylor rules. The learnability analysis is instead motivated by the results of Evans and Honkapohja (2001), according to which there is no guarantee that the fundamental REE (even if determinate) can be attained if agents are not endowed with rational expectations at the outset, but instead make forecasts using simple adaptive rules, like least squares learning. As stated by McCallum (2009a), “… for any RE solution to be considered plausible, and thereby relevant for policy analysis, it should be learnable”, in the sense that, economic agents should be able to learn the quantitative relevance of all fundamental disturbances for the equilibrium dynamics.4 In particular, our learnability analysis focuses on the concept of E-stability defined in Evans and Honkapohja (2001): namely, a REE is said to be E-stable if the recursive least-squares forecasts of economic agents eventually converge to the true rational expectations solution.5 Making use of some results by Evans and McGough (2005), we also assess the E-stability of (Common Factor, CF, representations of) sunspot equilibria for parameterizations leading to equilibrium indeterminacy. Our main finding is the following. For an economy where the degree of LAMP is sufficiently large to imply a IADL, introducing an explicit positive response to stock prices in the policy rule enlarges the region where the equilibrium is locally determinate and its MSV representation is E-stable. In particular, it can restore the Taylor principle as good guidance for monetary policy design. This result – which holds true both under forward-looking and contemporaneous interest rate rules – can be explained as follows. Irrespective of the degree of LAMP, a permanent increase in inflation still implies a permanent drop in profits, and hence in stock prices, similar to Carlstrom and Fuerst (2007). This implies that, following an initial (sunspot-driven) increase in inflation, a rule that responds positively to stock prices is more likely to induce a decrease in the real interest rate, with respect to one which does not. However, this is exactly what is needed to induce equilibrium determinacy in a IADL economy. On the contrary, if, despite the presence of LAMP, the economy still features a SADL, the results by Carlstrom and Fuerst (2007) hold: a policy response to stock prices enhances the possibility of equilibrium indeterminacy. Moreover, such policy is also likely to make the MSV-REE not learnable. Interestingly, we also find that for both the case of SADL and of IADL there exists a significant range of policy parameterizations for which the (CF representation of) sunspot equilibria is E-stable. In the analysis, we also compare stock-price-augmented Taylor rules with more standard specifications, where the policy rate is set in response to fluctuations in output. For what concerns equilibrium determinacy, we find that, in a IADL economy, responding to output is likely to generate sunspot-driven fluctuations. In a SADL economy instead, the two specifications performs equally well with respect to equilibrium determinacy, but a stock-price-augmented rule appears to be superior with respect to aggregate welfare. Pfajfar and Santoro, 2011, Pfajfar and Santoro, forthcoming, Airaudo et al., 2011 and Airaudo et al., in press are additional examples of New-Keynesian frameworks where the introduction of an explicit response to stock prices in Taylor-type rules can improve equilibrium determinacy. Using the same model as Carlstrom and Fuerst, 2007 and Pfajfar and Santoro, 2011 show that if the policy rate includes a response to stock price growth (rather than the stock price level) a unique equilibrium always obtains if the Taylor principle is respected. Pfajfar and Santoro (forthcoming) extend the analysis to a New-Keynesian model with a cost channel of monetary policy. In this case, they find that responding to the stock price level can help ensure equilibrium determinacy. Airaudo et al., 2011 and Airaudo et al., in press study a framework where the presence of a constant turnover between new-comers and long-time traders in markets (due to a Blanchard-Yaari OLG structure) introduces an explicit structural linkage between stock price fluctuations and real activity. Both papers show that a systematic response of monetary policy to stock prices enlarges the equilibrium determinacy region. The rest of the paper is organized as follows. Section 2 presents the structure of the model. Section 3 describes the aggregate economy and the equilibrium. Section 4 defines and characterizes the steady state equilibrium. Section 5 presents the reduced-form linearized system describing the economy’s aggregate dynamics around the steady state. Section 6 presents our main results for both the determinacy and the stability under learning dynamics (E-stability) analysis. Section 7 discusses about the optimal monetary policy under discretion and its implementation. Section 8 concludes.

Whether policy-makers should or should not set the short-term interest rate in response to stock price fluctuations remains a very much debated issue in the macroeconomic literature. In principle, central banks targeting inflation may consider raising the policy rate in response to higher stock prices to better shield the economy against anticipated inflationary pressure, given that stock prices presumably reflect market expectations on future profits and hence future aggregate activity. However, as Carlstrom and Fuerst (2007) show, the introduction of such “leaning against the wind policy” in a benchmark New-Keynesian model – the workhorse of monetary policy analysis – can be a source of equilibrium indeterminacy and non-fundamental belief-driven fluctuations. In this paper, we have studied the desirability of Taylor-type rules responding to stock prices in a New-Keynesian model subject to limited asset market participation (NK-LAMP). We have found that such rules can facilitate both the determinacy and the learnability (E-stability) of the fundamental REE when the degree of LAMP is sufficiently large to generate an inverted aggregate demand logic of monetary policy transmission. On the contrary, if LAMP does not preclude a standard aggregate demand logic, then a positive response to stock prices is not desirable as it is likely to induce sunspot-driven fluctuations – as in the full-participation model studied by Carlstrom and Fuerst (2007) – and to make the fundamental REE unstable under learning dynamics. We have also found that there exists ranges of policy parameterizations for which (a Common Factor representation of) sunspot equilibria is learnable. We have compared these stock-price-augmented Taylor rules with more standard specifications where the policy rate responds instead to output. According to our analysis, the former outperform the latter both with respect to equilibrium determinacy and aggregate welfare.