سیاست های پولی و قیمت دارایی ها با نوسانات اعتقاد هدایت شده

We present a heterogeneous agents New-Keynesian model subject to a cost channel of monetary policy transmission. Constant turnover between long-time traders and newcomers in market activities, combined with restricted trading opportunities, introduces a feedback from the stock market to real activity, making stock prices non-redundant for the business cycle. We show that strict inflation targeting can lead to equilibrium indeterminacy, even if the policy rule satisfies the Taylor principle. A belief-driven shock to stock price generates relative volatilities of key financial variables which are very close to what is observed in U.S. data. This result hints to the possibility that the financial instability witnessed since the mid-to-late 1990s was the result of waves of (rational) exuberance and pessimism in financial markets. Our analysis suggests that a mild response to stock prices in the central bank's policy rule can restore equilibrium determinacy and therefore rule out non-fundamental volatility.

The global financial crisis of 2007–2009 has highlighted the interaction between financial variables and the aggregate economy. Although how to prevent a new crisis is likely to remain the subject of debates for quite some time, an emerging view calls for placing more emphasis on financial markets and banking in macroeconomic models to better grasp the underlying macro-financial linkages. Building on the previous contributions, the theoretical literature has identified three main channels accounting for the transmission of financial shocks to the real economy or the amplification of shocks coming from the real economy itself: (1) the borrower's balance sheet channel; (2) the bank lending channel; and (3) the bank liquidity channel.1 The first channel is based on the agency costs framework conceived by Bernanke and Gertler (1989) and Carlstrom and Fuerst (1997), and then further developed in the financial accelerator model of Bernanke et al. (1999). According to this view, because of a moral hazard problem due to lenders' imperfect monitoring of firms activities/risks and lack of enforcement in debt repayments, firms must provide a collateral in order to access external finance. By impacting the market value of the collateral, shocks to asset prices affect the tightness of firms' borrowing constraints, and hence real activity. At the same time, any shock to the real economy that eventually impacts firms' net worth is amplified relative to an economy where these credit frictions are absent. A similar mechanism applies to household borrowing, as financially constrained households pledge their home property to obtain mortgages from lenders. This channel has been successful at capturing the business cycle implications of structural linkages between the housing market and the real economy, as shown in Iacoviello (2005) and Iacoviello and Neri (2010). The second channel is related to the bank's balance sheet and capital requirements. On the one hand, as financial intermediaries, banks can exacerbate the contractionary effects of a monetary tightening via a reduction in the supply of loans to credit-constrained households and firms. On the other hand, similar to the financial accelerator framework, negative shocks to the bank's own capital are a threat to its solvency and can severely undermine its creditworthiness. To compensate for the resulting higher costs of external finance, the bank is likely to increase interest rates on loans, with a negative impact on economic activity.2 The third channel highlights the role of liquidity in banking, with a particular focus on the aggregate consequences of high leverage and maturity mismatches on banks' balance sheets. When banks rely on short-term debt to fund mortgages for the purchase of illiquid assets by households/firms, a negative shock to liquidity can force banks to undertake asset fire sales in order to meet debt obligations. The result is downward pressure on asset prices, which calls for further asset sales, generating a Fisherian deflationary spiral.3 Within the New Keynesian Dynamic Stochastic General Equilibrium (NK-DSGE) framework – the current workhorse of monetary policy analysis – the financial accelerator is indeed the most prominent of the three channels described above.4 However, while it constitutes a plausible description of the transmission/amplification of standard aggregate shocks (such as shocks to total factor productivity and to the policy instrument), the financial accelerator model fails to generate the large asset price volatility observed in the data. Starting with works by Shiller (1981) and LeRoy and Porter (1981), there is in fact no lack of empirical evidence supporting the idea that asset prices are much more volatile than what can be justified by the underlying fundamentals.5 In particular, both the late 1990s and the years preceding the 2007–2008 financial meltdown have been labeled as clear examples of bubble-driven fluctuations in stock or housing markets. In a context where central banks are strongly committed to price stability and stable growth, an important unsettled question is then whether they should take deliberate steps to prevent or deflate non-fundamental asset price fluctuations.6 On the one hand, given the direct impact of asset prices on both inflation and output, some economists have argued that central banks can improve macroeconomic performance by responding directly to movements in asset prices. For instance, based on simulations from a small-scale macroeconomic model, Cecchetti et al., 2000 and Cecchetti et al., 2002 argue that the short-term nominal interest rate (the central bank's policy variable) should be increased in response to temporary “bubble shocks”. On the other hand, because of the observational equivalence of fundamental and non-fundamental shocks hitting asset prices, and the fact that both types of shocks ultimately impact on aggregate variables, others have argued that central banks can do just as well by responding exclusively to output and inflation. Bernanke and Gertler, 1999 and Bernanke and Gertler, 2001 were among the first to promote this view.7 Despite the different conclusions, the models used by Cecchetti et al., 2000 and Cecchetti et al., 2002 and Bernanke and Gertler, 1999 and Bernanke and Gertler, 2001 share a common drawback: they assume that asset price bubbles are completely exogenous, i.e., bubbles randomly inflate and burst regardless of any policy intervention. Consequently, they cannot address the important question of whether policy-makers should take action to prevent bubbles from forming or to deflate a bubble once it has formed. Our paper contributes to this literature by investigating the quantitative importance of a non-fundamental shock with the following properties: (1) it is model-consistent and satisfies full rationality; (2) it originates from the stock market via a self-fulfilling belief-driven revision of agents' expectations; and (3) its existence depends on key structural features of the macroeconomy and on the policy rule followed by the central bank. The framework for our analysis is a heterogeneous agents NK-DSGE model where the macro-financial linkages arise due to intertemporally incomplete markets. In this sense, we highlight an additional channel through which financial shocks can be transmitted to the real economy. An advantage of our modeling framework with respect to the more common financial accelerator model is its small-scale reduced form. Once linearized around the unique non-stochastic steady state, the equilibrium dynamics are described by four equations: a IS curve, a New-Keynesian Phillips curve, an aggregate stock price equation and a monetary policy rule. This allows us to highlight the policy transmission mechanisms in a transparent way, and to provide a simple economic intuition for the propagation of the stock price belief shock to the rest of the economy. We use our framework to assess whether belief-driven shocks to the stock market can account for the excess volatility of financial variables (relative to GDP) observed in the U.S. over the last 20 years. We also consider whether an explicit response to stock prices in the central bank's policy rule can preclude non-fundamental fluctuations. Our model combines the discrete-time stochastic version of the Blanchard (1985) and Yaari (1965) perpetual-youth model with a cost channel of monetary policy transmission as developed by Ravenna and Walsh (2006). The market turnover between long-time traders (holding assets) and newcomers (entering the market with no assets) – due to the Blanchard–Yaari structure – implies a non-degenerate distribution both in financial wealth and consumption across agents. By breaking the identity between current and future traders in the economy, this heterogeneity makes financial markets intertemporally incomplete (as current traders cannot exchange assets with future traders), and hence weakens the typical consumption smoothing motive. The wedge between the current and the expected level of aggregate consumption is driven not only by the ex ante real interest rate – as in the standard representative agent model – but also by the stock of accumulated wealth, since the latter is responsible for the difference between the consumption levels of long-time traders and newcomers. Through this mechanism, stock price fluctuations feedback into real activity via their wealth effects on consumption and are therefore non-redundant for the business cycle. A sudden belief-driven boom in stock prices can then have sizable quantitative effects on real activity. We refer to this mechanism as the financial wealth channel. 8 To introduce endogenous credit spreads into the model, we modify the Ravenna–Walsh cost channel along the lines of Curdia and Woodford (2010). Namely, we assume that issuing loans to firms – whose equity shares are the main source of financial wealth for the households – is a costly activity for banks, in the sense that transforming deposits into loans involves resource costs. However, in contrast to Curdia and Woodford (2010), we model these costs in terms of labor rather than consumption units, as in Goodfriend and McCallum (2007) and Canzoneri et al. (2008). Within our framework, we show that a policy rule that exclusively responds to inflation and satisfies the Taylor principle can easily lead to equilibrium indeterminacy for reasonable parameter values. We show that a policy rule that responds mildly to stock prices can restore a unique rational expectations equilibrium. The stabilizing consequences of this policy rule are related both to the financial wealth channel and the cost channel, the two distinctive features of our model. The model economy is more prone to equilibrium indeterminacy the higher the turnover rate in markets, the larger the extent of the cost channel. Our results contrast with those of Carlstrom and Fuerst (2007) who find that responding to stock prices always enhances the possibility of indeterminacy in a benchmark New-Keynesian model. Our results are instead complementary to those of Pfajfar and Santoro, 2011 and Pfajfar and Santoro, forthcoming, Airaudo et al. (2009) and Airaudo (in press). Using the same model as Carlstrom and Fuerst (2007), 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 (in press) 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 (in press) shows instead that a positive response to stock prices can enlarge the determinacy area (and restore the Taylor principle) if the degree of limited asset market participation in the economy is sufficiently large.9 Using a simplified version of the model studied in this paper (which omits the cost channel), Airaudo et al. (2009) show that an explicit response to stock prices can enlarge the determinacy region. Given a policy rule that reflects the Fed's strong anti-inflationary stance during the 1990s, we show that belief-driven shocks originating from the stock market can help explain the volatility of some key U.S. financial variables (the price-dividend ratio, the credit spread, business loans) over the period 1990–2007. Our impulse response analysis is consistent with the observation by Christiano et al. (2011) that stock price booms are associated with low inflation and low policy rates, which further exacerbate financial instability. However, in our model, this is triggered by belief-driven shocks of the sunspot-type, while their analysis considers news shocks. Interestingly, the propagation mechanism of the belief shock is oscillatory and therefore resembles the boom-bust cycles observed in the data.10 The volatilities of endogenous variables in the model are considerably larger than those implied by fundamental shocks alone, and rather close to what is observed in the data. For instance, we find that our belief-shock model can explain about 75% of the observed volatility (relative to GDP) of the price-dividend ratio, while matching the relative volatilities of inflation, real loans and real dividends. The model can also capture the very large volatility of credit spreads, but this requires the introduction of a rather volatile shock to bank productivity. The quantitative performance of the model is very satisfactory irrespective of whether we assume that stock market belief-shocks hit the economy in every period or only over a restricted sample. In this sense, our model supports the idea that a short-lived wave of (rational) exuberance or pessimism in financial markets can exert considerable long-lasting effects on economic activity. The rest of the paper is organized as follows. Section 2 presents the model economy. Section 3 describes the equilibrium. Section 4 presents the log-linearized model characterizing the aggregate dynamics. Section 5 presents the equilibrium determinacy analysis. Section 6 analyzes the quantitative implications of a belief shock originating in the stock market. Section 7 concludes.

We have presented a heterogeneous agents New-Keynesian model where belief shocks that originate in the stock market are transmitted to the real economy. The feedback from the stock market to real activity (which we refer to as the financial wealth channel) arises because of a constant turnover between long-time traders and newcomers in financial markets. In this setting, market incompleteness results from the lack of trading opportunities between current and future generations of traders. This feature of the model implies a non-degenerate distribution of financial wealth across generations. As a result, swings in stock prices can affect agents differently, and thus influence the optimal path of aggregate consumption. To this framework, we append a simple cost channel of monetary policy transmission (à la Ravenna and Walsh, 2006), which allows for costly loan origination, thereby generating endogenous credit spreads. We show that a policy rule that satisfies the Taylor principle can still be conducive to equilibrium indeterminacy. This result implies that belief-driven revisions of expectations can become self-fulfilling in equilibrium, thereby generating non-fundamental aggregate volatility in the economy. We show that equilibrium indeterminacy is more likely when firm must finance a large fraction of their working capital with external loans (stronger cost channel) and when the turnover rate in markets is higher (stronger financial wealth channel). A unique equilibrium can be restored by a mild policy response to stock prices. More generally, the region of equilibrium determinacy expands as the magnitude of the response to stock prices increases. We assess the quantitative importance of belief-driven shocks originating in the stock market to explain the volatility of some key U.S. financial variables, including the price-dividend ratio, the credit spread, business loans and dividends. The impulse response functions show that belief-driven stock price booms are associated with low inflation and low policy rates, as in the data. The model's endogenous propagation mechanism delivers long-lasting and oscillatory responses to the shock which resemble the boom-bust cycles observed in the data. The relative volatilities of financial variables predicted by the full model with belief shocks are considerably larger than those implied by the model with fundamental shocks alone, and compare favorably to the volatilities observed in post-1990 U.S. data. Under indeterminacy, the full model generates a high relative volatility for the price-dividend ratio (capturing about 75% of what observed in the data), while nearly matching the relative volatilities of inflation, real loans, and real dividends. In this sense, our results suggest that U.S. financial market fluctuations witnessed since the mid-to-late 1090s could have been the result of waves of (rational) exuberance and pessimism among market participants. The analysis presented in this paper could be extended into several directions. One possibility is the study of optimized monetary policy rules. Along these lines, Nisticò (2011) shows that because of the turnover rate in markets and the resulting non-degenerate distribution of financial wealth across agents, the central bank's objective should include an explicit concern for stock price stabilization. We conjecture that a similar result would carry over to our environment, although, because of the cost channel and the real balances in utility, the relevant central bank's objective might also include a concern for interest rate smoothing and, possibly, a different definition of efficient output. Another possible extension is the assessment of the empirical potential of our model. Castelnuovo and Nisticò (2010), Castelnuovo (2013), and Castelnuovo (2012) estimate a NK-DSGE model with Blanchard–Yaari consumers using Bayesian methods. However, in their framework the cost channel is absent, essentially ruling out equilibrium indeterminacy and belief-driven fluctuations. A relatively simple (but preliminary) approach to this issue is to estimate a VAR on artificial data generated by our model under indeterminacy, and then compare the resulting impulse responses to those in the empirical VAR literature.42 Although the results of such exercise provide some support for our modeling framework, we believe that a more extensive and fully structural analysis is needed.