معافیت های ساختاری و غیر خطی در قوانین سیاست های پولی با قیمت های سهام

This paper introduces nonlinearity and a structural break to the US forward-looking Taylor rule with a stock price gap, thereby alleviating the robustness problem that the linear Taylor rule is sensitive to minor changes of the sample period since 1991. The path of the time-varying inflation coefficient shows that, unlike in the linear model, the Fed consistently responds to inflationary pressures in an aggressive manner even after 1991. The stock price coefficient stays positive since 1991. However, its time-varying pattern does not show active responses in the early periods of stock price hikes, which is counter to the view that the Fed has preemptively reacted to stock price bubbles

Modeling how monetary policy changes in response to economic circumstances has long been an interesting topic in macroeconomics, for various reasons. The policy reaction function is an important element in macroeconomic models, which helps to forecast changes in the federal funds target rate, plays an important role in evaluating the Federal Reserve's monetary policy, and provides a better understanding of various macroeconomic issues. Robust estimation of the Fed's reaction function is consequently of central importance in empirical macroeconomic analysis. This paper has two objectives. The first is to examine the Fed's response to stock prices, as well as expected inflation, using a forward-looking interest rate rule with addition of a stock price variable. The role of stock prices in the setting of monetary policy has long been an important issue, both in policy making and in academic research. The current research focuses on two questions: 1) should the Fed respond to a stock price change? and 2) has the Fed responded to stock price changes? This paper does not attempt to answer the first question. For detailed discussion, however, see Bernanke and Gertler, 1999 and Bernanke and Gertler, 2001 for the standard policy view that, before a bubble collapses, monetary policy should consider changes in stock prices only when they are strongly associated with future inflation expectations. See also Cecchetti et al., 2000 and Cecchetti et al., 2002, Borio and Lowe (2002), Bordo and Olivier (2002), Filardo (2004), Tetlow (2004), Akram et al. (2006) and Kannan et al. (2009), for the alternative policy view that the central bank should preemptively respond to non-fundamental stock price changes to obtain macroeconomic and financial stability. In this paper we focus on the second question, that is, we examine whether and how the federal funds target rate has moved in accord with the movements of stock prices. Existing work suggests non-unified answers to this question. Rigobon and Sack (2003) and Björland and Leitemo (2005) find evidence of monetary policy responses to stock price movements, while Fuhrer and Tootell (2008) and Hayford and Malliaris (2005) show that policy responses to stock price changes are not evident. We can also find various empirical findings analyzing the policy behavior of the European Central Bank (ECB). Botzen and Marey (2010) find that the ECB adjusted interest rates in response to deviations of stock prices from their average values before the recent financial crisis. Siklos et al. (2004) on the other hand, find asset prices to be highly relevant as instruments rather than as separate arguments in forward-looking Taylor rules estimated via GMM. Most of the existing studies assume that the Fed's reaction process is stable and linear. There may however be a structural break in the policy response to inflation, even in the last two decades, as shown in Estrella and Fuhrer (2003) and Jouini and Boutahar (2003). Stock and Watson (2007) find that the explanatory power of stable models of US inflation has diminished in recent decades. Moreover, the estimation results of existing models depend highly on the choice of sample period, another sign of possible instability in the reaction function. This leads us to our second objective in this paper: to construct a more robust model of monetary policy response, by explicitly considering both the time variation in the Fed's response and the structural break. Dupor and Conley (2004) consider a structural break in the reaction function to have occurred in 1991:II, in that, inflation has since then never exceeded 4%. However, their estimation provides the counterintuitive result that the Fed's response to inflation is not clear since this break. Moreover, we find that the estimated inflation coefficient in the linear forward-looking rule shows a substantial change in accordance with a minor shift in the breakpoint, implying that a more rigorous choice of the breakpoint and a more robust model are required. To tackle this problem, we introduce a nonlinearity based on the ‘Series method’, along with a single structural break, which allows us to keep using the original GMM representation. Applying the Series method allows for a temporary time variation and smooth change between any two regimes, as well as asymmetry in the responses to inflationary and deflationary pressures, making it possible to capture the nonlinearity due to asymmetric preferences (see Cukierman and Muscatelli, 2008, Dolado et al., 2005 and Ruge-Murcia, 2003 for details). Consequently, together with the structural break which captures a permanent change, our method covers a wide range of possible transitory time variations of the response function. Our nonlinear model captures nonlinear dynamics different from those of the Threshold or Smooth Transition Model of Bunzel and Enders (2010) and Lo and Piger (2005), in that they focus only on identifying recurrent regimes. We test whether both nonlinearity and a structural break are present in the reaction function. The test results strongly support nonlinearity in the Fed's responses to inflation pressures. The structural break test detects the existence of a break at 1989:III, even in the nonlinear model. The time-varying dynamics of the expected inflation coefficient support the asymmetric response of the Fed: the coefficient shows an aggressive Fed monetary policy under high inflationary pressures and a moderate response when inflation is low. However, unlike in the case with linear models such as in Dupor and Conley (2004), we find little evidence of a significant change in the Fed's behavior since the structural break. The estimated coefficient still supports active responses to increased future expected inflation, even after the break, while staying low in the other periods of stable inflation. These results also coincide with the finding of Stock and Watson (2007), that the inflation model is better explained by time-varying coefficients since the 1990s. The stock price coefficient remains positive for most of the time since the break. This, however, does not necessarily imply that the Fed has preemptively responded to possible stock market bubbles. Note that it is generally expected that the Fed has two possible responses to movements in stock prices: one is the standard policy of responding to stock prices when they convey information about the future paths of inflation and output. The other is the more contentious, so-called bubble policy, of preemptive reaction to reduce a possible stock price bubble. If the Fed responds actively to possible bubbles, it can be expected to respond more actively in the early periods of bubbles. However, the time-varying pattern of the stock price coefficient reveals that it remains low until the late periods of bubbles, when it then quickly spikes. The remainder of this paper is organized as follows. Section 2 derives and specifies the forward-looking interest rate rule including a stock price gap variable. Section 3 discusses the results of linear estimation and the instability issue. Section 4constructs a nonlinear model based on the Series method and discusses its estimation results and the movement of its time-varying coefficients. Section 5 explores the test of structural change for the nonlinear framework, and Section 6 concludes.

The Fed's behavior raises many macroeconomic and econometric issues. After observing the non-robustness of the linear set-up around the breakpoint, we construct an alternative nonlinear model. Allowing for the time variations of the reaction coefficients provides a more robust view of the Fed's behavior over the past thirty years. It is hard to find a change in the Fed's fundamental response to inflationary pressures since 1990. When the linear estimation is used the Fed appears to respond to changes in stock price changes. But the time-varying pattern of its responses does not necessarily suggest response to be due to preemptive actions against stock market bubbles. Examining the precise reason for this is beyond the scope of this paper, and further research is required. Our structural break test is restricted, in that it focuses on the possibility of a break at around 1991 only. But other breaks at around 1987 and 1982 are still plausible, which would affect estimation in the pre-break period. Further investigation in the periods between 1979 and 1991 is thus reasonable. We expect that the time variation could possibly capture those breaks, although it is not a perfect approach in that temporary movements and structural breaks are observationally equivalent in a short time-period.