Financial market segmentation, stock market volatility and the role of monetary policy

European Economic Review 63 (2013) 256–272

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European Economic Review journal homepage: www.elsevier.com/locate/eer

Financial market segmentation, stock market volatility and the role of monetary policy Anastasia S. Zervou n Department of Economics, Texas A&M University, College Station, TX 77843, USA

a r t i c l e in f o

abstract

Article history: Received 31 January 2012 Accepted 14 June 2013 Available online 24 June 2013

We study a segmented financial markets model where only the agents who trade stocks encounter financial income risk. In such an economy, the welfare-maximizing monetary policy attains the novel role of redistributing the traders' financial market risk among all agents in the economy. In order to do that, optimal monetary policy reacts to financial market movements; it is expansionary in bad times for the financial markets and contractionary in good ones. In our quantitative exercise, a dividend shock generates different policy responses and consumption paths among the optimal and the 2% inflation targeting policy. The latter implies large distributional welfare losses and risk sharing losses of similar magnitude with those generated by business cycle fluctuations. In addition, the optimal monetary policy does not minimize stock price volatility and implies lower inflation volatility than other commonly used policies. & 2013 Elsevier B.V. All rights reserved.

JEL classification: E44 E52 G12 Keywords: Limited participation Optimal monetary policy Distributional effects Stock price volatility

1. Introduction Should financial market developments be a matter of monetary policy? This is a widespread concern among central bankers, especially aggravated by the 2007–2009 recession. The Federal Reserve and central banks of other developed countries seem to follow expansionary policies in response to financial market distress.1 Previous literature regarding how a monetary authority should respond to asset market advances focuses on policy responses to asset price changes (e.g., Bernanke and Gertler, 2000, 2001; Cecchetti et al., 2001; Faia and Monacelli, 2007; see Gilchrist and Leahy, 2002 for a review on the topic). This paper studies new aspects of the interaction of the monetary authority with the stock market. Specifically, we develop a cash-in-advance model and study the distributional and risk-sharing implications of an optimal, welfare-maximizing monetary policy in the presence of segmented financial markets. In a quantitative exercise we find large welfare losses resulting from following a 2% inflation targeting policy instead of the optimal one. We also find risk sharing losses similar in magnitude with a natural benchmark, associated with the welfare cost of smoothing business cycle fluctuations. In addition, we address the question of whether the optimal policy entails lower fundamentals originated stock price volatility when compared with other, widely used monetary policy rules. We find that this is not necessarily the case. Financial market segmentation is well documented (Mankiw and Zeldes, 1991; Guiso et al., 2002; Vissing-Jørgensen, 2002) and previously used in monetary models as an apparatus for studying the liquidity effect (Alvarez et al., 2001), forms

n

Corresponding author. Tel.: +1 3143979967. E-mail addresses: [email protected], [email protected] 1 E.g., the Federal Reserve consistently decreased the federal funds rate target for almost every meeting from August 2007 until the end of 2008, after which the target was too low to further decrease it. See Bernanke (2009). Also, the marginal lending facility of the European Central Bank has been consistently decreasing through 2008–2009. 0014-2921/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.euroecorev.2013.06.005

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of non-neutrality of money (Williamson, 2005, 2006) and a positive inflation target (Antinolfi et al., 2001).2 Our model is based on two implications of financial market segmentation. First, as previous literature points out (Grossman and Weiss, 1983; Rotemberg, 1984; Lucas, 1990; Fuerst, 1992; Alvarez et al., 2001; Williamson, 2005, 2006), monetary policy's actions diffuse in the economy through the financial system, affecting those who are connected to the financial system and those who are not in a different manner. During open market operations the Federal Reserve interacts with large financial institutions, directly affecting financial market participants, yet affecting non-participants indirectly through price adjustments. For example, a monetary expansion benefits those who are at the receiving end of the expansion, i.e., the financial market participants. However, because it increases prices, it hurts those who are not connected to the financial system. Thus, monetary policy has distributional effects.3,4 Second, segmentation implies that only a fraction of the population is connected to the financial system, so that only a fraction of the population is subject to financial income risk. Although agents' heterogeneity with respect to their connection to the financial markets has been addressed in previous models (Grossman and Weiss, 1983; Rotemberg, 1984; Lucas, 1990; Fuerst, 1992; Alvarez et al., 2001; Williamson, 2005, 2006), agents heterogeneity in terms of their financial risk holding has not yet been explored and introduces additional considerations for monetary policy. Specifically, these distributional effects that monetary policy exhibits under stock market segmentation affect the way financial income risk is shared between financial market participants and non-participants. This happens automatically, through monetary policy's usual operation. Our model studies how a monetary authority that cares equally about every agent, connected or not to the financial markets, becomes risk sharing, redistributing the financial risk among all agents in the economy. Financial markets' distress translates into lower dividend income; monetary policy optimally expands and benefits financial market participants. However, expansionary policy increases the price of the consumption good, decreasing the consumption of those who do not participate in the financial markets. By contrast, monetary policy optimally tightens whenever financial markets flourish and dividend income is higher than expected. Such a reaction reduces the financial market participants' consumption; it also makes the consumption good more affordable, increasing the consumption of non-participants. Answering the question asked above, whether and how monetary policy should respond to stock market advances, this paper suggests that optimal monetary policy should be expansionary in bad times for the financial markets and contractionary in good times. This result assigns to monetary policy the novel role of redistributing risk among heterogeneous agents; in this case among financial market participants and non-participants. We address the importance of the above mechanism quantitatively. We compare the optimal monetary policy with a 2% inflation targeting policy. We find that compared to the optimal policy, the 2% inflation targeting policy induces large losses for those who do not participate in the financial markets and large gains for those who do participate. We find large welfare effects which highlight the distributional role of monetary policy. Isolating the risk-sharing gains of optimal monetary policy, we calculate them to be at the order of magnitude of the gains from smoothing the business cycle, which we regard as the benchmark for our analysis. In addition, we find that the two policies respond in the opposite direction after a dividend shock. For example, after a negative dividend shock the optimal monetary policy becomes expansionary in order to redistribute resources to the financial market participants. On the contrary, the 2% inflation targeting policy becomes contractionary in order to keep inflation at its target. The consumption paths implied are also different across the two policies. Motivated by recent work on the response of monetary policy to the stock price (Bernanke and Gertler, 2000, 2001; Cecchetti et al., 2001; Gilchrist and Leahy, 2002; Faia and Monacelli, 2007) we study this relationship in our model. We find that the optimal monetary policy responds to the stock price due to its risk sharing consideration; it becomes expansionary in response to a stock price increase. The 2% inflation targeting policy is also responsive to a stock price increase; however, it is over-expansionary compared to the optimal policy. We further investigate the role of monetary policy in our model and compute stock price volatility and inflation volatility implied by the optimal monetary policy rule; we compare these volatilities with those implied by the constant money supply, inflation targeting and nominal interest rate peg policy rules. There is vast finance literature related to one or more of this model's elements, studying stock price volatility (Allen and Gale, 1994; Guo, 2004; Guvenen and Kuruscu, 2006; Chien et al., 2011). We abstract from other issues this literature has considered (e.g., endogenous participation, idiosyncratic shocks or heterogeneous preferences), in order to focus on the importance of monetary policy regimes in generating stock price volatility. We find that the optimal monetary policy does not necessarily produce lower stock price volatility compared to the other policy rules and thus, stock price volatility should not be an integral part of monetary policy. Furthermore, the policy that minimizes stock price volatility also reduces welfare. In addition, our findings suggest that contrary to previous literature (Bernanke and Gertler, 2000, 2001) that does not account for financial market segmentation, the inflation targeting policy is not associated with minimal stock price volatility. Optimal monetary policy in our model does however associate with inflation stability; it produces half the inflation

2

For its empirical importance see LandonLane and Occhino (2008) and Mizrach and Occhino (2008). Early work on the distributional effects of monetary policy involves models that are not very tractable (Grossman and Weiss, 1983; Rotemberg, 1984), although important attempts to obtain tractability resulted, contrary to this paper, in models that suggest limited role for monetary policy (Lucas, 1990; Fuerst, 1992). 4 There is, of course, large literature exploring the distributional effects of inflation (Erosa and Ventura, 2002; Doepke and Schneider, 2006). In addition, recent work studies monetary policy regimes and the distributional effects that the resulted inflation has (Meh et al., 2010). However, here we are exploring direct distribution effects that monetary policy exerts. 3

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volatility that the constant money supply policy does. Also, contrary to previous literature (Allen and Gale, 1994) high financial market participation does not necessarily lead to low stock price volatility. This is because in our model, stock price volatility depends on the type of policy rule the monetary authority follows. Recent work attempts to specify optimal monetary policy in limited participation New Keynesian models.5 Bilbiie (2008) focuses on assigning relative weights on output and inflation in an interest rate Taylor-type rule, and Andres et al. (2010) focus on addressing trade-offs between monetary authority's stabilization goals. We use a very different model to focus on the risk sharing role of optimal monetary policy and address the issue of how stock price volatility is affected by monetary policy. Overall, this paper suggests that in the presence of segmented financial markets monetary policy should react to financial market changes through channels that previous literature has ignored. Monetary policy attains the role of redistributing financial income risk among financial market participants and non-participants. This policy is, to some extent, concerned with inflation stability but is not concerned with stock price volatility. The rest of the paper is organized as follows. Section 2 introduces the model economy and studies the competitive equilibrium and asset pricing. Section 3 describes the implications and role of the optimal monetary policy rule. Section 4 examines the stock price, stock price volatility and inflation volatility for various policy rules. Section 5 presents the results of our quantitative exercise. Section 6 concludes. 2. The model economy 2.1. Environment The model economy consists of the goods market and three asset markets: nominal bond, stock and money market. The bond and stock markets are segmented, so that from a continuum of infinitely lived households of measure one, only λ∈ð0; 1Þ fraction participates in these markets although 1−λ does not. The stock market is introduced in a way similar to the Lucas (1978) model, i.e., participating agents receive a share of the stochastic dividend tree in proportion to the quantity of shares they hold. The bonds are introduced for examining the asset pricing of the model. All agents have identical preferences and seek to maximize ∞

E0 ∑ βt uðcit Þ; t¼0

where β is the discount factor with 0 oβ o 1 and cit ≥0 denotes consumption at time t by consumer of type i, with i∈fT; Ng. Consumers' types T and N are described below. We assume that u′ð:Þ 40 and u″ð:Þ o0. The fraction 1−λ of the population that does not participate in the financial markets, or the non-traders (i¼N), receives every period a fixed real endowment yN 4 0 of the non-storable consumption good. The fraction λ of the population that participates in the financial markets, or the traders (i¼T), receives every period a fixed real endowment yT 4 0 and a share of the stochastic real total dividend εt . We assume that there is a firm which receives endowment εt in period t and distributes it as dividends to its share holders. The total dividend εt is random, has mean ε 4 0 and is described as follows: εt ¼ ε þ η t ;

ð1Þ

where ηt is an iid shock with mean zero, variance and support ½−ε; ∞Þ. The stochastic dividend is distributed among traders proportionally to the quantity of shares they own. Consequently, traders have a risky component in their income, although non-traders collect only the fixed endowment yN. Total income in this economy equals yt, yt ≡εt þ λyT þ ð1−λÞyN , and thus mean income is given by s2ε

y ¼ ε þ λyT þ ð1−λÞyN :

ð2Þ

In order for total output to be independent from the financial market participation rate λ, we let the mean income of the traders equal to that of the non-traders, i.e., yT þ ε=λ ¼ yN . Besides traders having a risky component in their income (although non-traders do not), there is one more difference between financial market participants and non-participants. That is, financial market participants are directly affected by monetary policy's actions. As is typical in the limited participation literature (Grossman and Weiss, 1983; Rotemberg, 1984; Lucas, 1990; Fuerst, 1992; Alvarez et al., 2001; Williamson, 2005, 2006), this model reflects the fact that initially, open market operations affect only the financial sector of the economy. We employ this feature by having the monetary authority distributing transfers τt only to the traders, although the non-trades do not collect such transfers.6 The timing of the model is as follows. Agents enter period t with money balances mit ≥0 for type i∈fT; Ng. At the beginning of the period the dividend shock εt is realized, although given a cash-in-advance assumption is not available to the traders 5 Related topics have also been studied using full participation models, e.g., Challe and Giannitsarou (2011) develop a full participation asset pricing New Keynesian model in order to match the empirical findings of the stock price response to monetary policy shocks (Rigobon and Sack, 2004; Bernanke and Kuttner, 2005). 6 The cash provision to traders through this practice is equivalent to open market operations, which in fact affects directly only the financial market participants.

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until the end of the period. The financial markets open first (while the goods market remains closed) and while open, the monetary transfer is distributed to the traders. In period t traders can sell the zt amount of stock they bought in period t−1 and buy new stock at price qt. Bonds bought in period t−1 at price st−1 o 1 expire and pay one unit of money in period t. T Using their money holdings mt , the money from selling zt stocks, the returns from holding bt bonds and the monetary transfer τt , traders can decide their new stocks and bonds purchases, ztþ1 and btþ1 . After the financial markets close, the goods market opens. In order for money to have value we assume that no agent consumes her own endowment and dividends but needs cash to finance consumption. Each household consists of a shopper–seller pair. The shopper receives the cash remaining after completing transactions in the financial markets and buys consumption good from other agents. The seller sells at price pt 40 the real endowment yT and share ztþ1 of the real dividend εt , if she is a trader, or just real endowment yN, if she is a non-trader. After the operations in the goods market conclude the seller and the shopper meet again, consume the consumption good the shopper purchased and keep the cash the seller received as money holdings for next period. That is, consumption is subject to the following cash-in-advance constraints, for traders and non-traders respectively: mTt þ qt zt þ bt þ τt ≥pt cTt þ qt ztþ1 þ st btþ1 ;

ð3Þ

N mN t ≥pt ct :

ð4Þ

The budget constraints for the traders and non-traders are given respectively by mTt þ qt zt þ bt þ τt þ pt ztþ1 εt þ pt yT ≥mTtþ1 þ pt cTt þ qt ztþ1 þ st btþ1 ;

ð5Þ

N N N mN t þ pt y ≥mtþ1 þ pt ct ;

ð6Þ

where ztþ1 εt is the real dividend payment distributed in period t (but available to use in period t þ 1). The monetary authority operates by setting the money growth each period t. Whenever money supply increases, the extra cash is distributed as transfers to the traders although whenever money supply decreases, traders are taxed. M t ¼ λτt þ M t−1

or equivalently; M t ¼ M t−1 ð1 þ μt Þ;

ð7Þ

where μt ∈½−1; ∞Þ denotes money growth rate from time t−1 to time t and Mt denotes money stock in period t, with a nonnegative initial value. The extra money supplied at time t is distributed as transfers to the λ traders. 2.2. Equilibrium and asset pricing We now explore the model's equilibrium and asset pricing. In equilibrium the four markets operating in this economy clear. The real total endowment and dividend are consumed by traders and non-traders: εt þ λyT þ ð1−λÞyN ¼ λcTt þ ð1−λÞcN t : Using Eq. (2), which defines mean income, the goods market clearing condition becomes y þ εt −ε ¼ λcTt þ ð1−λÞcN t :

ð8Þ

Traders hold all shares of the firm and the stock market clears λztþ1 ¼ 1⇒ztþ1 ¼

1 : λ

ð9Þ

The bond market clears too λbt ¼ 0:

ð10Þ

Finally, the money market clears λmTtþ1 þ ð1−λÞmN tþ1 ¼ M t ;

ð11Þ

where M t is given by Eq. (7). The maximization problem of each household is subject to constraints (3) and (5) for the traders, and (4) and (6) for the non-traders. Because the financial markets operate before the goods market does, holding money after the financial markets close bears positive opportunity cost when the return on bonds or stocks is positive. Only the amount of money required for purchasing the desired amount of consumption good is held and the equilibrium is constructed for binding cash-in-advance constraints. The budget constraints also bind, as usual. The implications for the budget constraints are pt ztþ1 εt þ pt yT ¼ mTtþ1 ;

ð12Þ

for traders, and pt yN ¼ mN tþ1 ;

ð13Þ

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for non-traders. The above equations reveal that the cash balances with which the agents begin period t þ 1 match the fraction of their wealth that the cash-in-advance constraints prevented them from using in period t. These are, the proceeds from selling in the goods market the real endowments, and for the case of traders, the real dividends distributed in period t. Furthermore, from the goods, stock, bond and money market clearing conditions, (8), (9), (10), and (11) respectively, the cash-in-advance constraints (3) and (4) holding with equality and the money supply equation (7), we get a version of the quantity equation where velocity equals one, and total output equals the sum of the deterministic part, λyT þ ð1−λÞyN ¼ y−ε, and the stochastic part, εt : pt ¼

Mt : y þ εt −ε

ð14Þ

Equilibrium consumption for the two groups of agents is derived as follows. Combining the non-traders binding cash-inadvance constraint (4) with Eq. (13) and the goods price (14) we find that the non-traders' consumption is given as follows: cN t ¼

pt−1 y þ εt −ε 1 y ¼y : pt y þ εt−1 −ε 1 þ μt

ð15Þ

The above equation together with the market clearing condition for the goods market, given by Eq. (8), imply that the traders' consumption can be written as follows:
 p 1 τt cTt ¼ t−1 y þ ðεt−1 −εÞ þ λ pt pt y þ εt −ε ðεt−1 −εÞð1 þ μt Þ þ yðλ þ μt Þ : ð16Þ ¼ λ ðy þ εt−1 −εÞð1 þ μt Þ Eqs. (15) and (16) reveal the distributional effects that monetary policy exhibits in this segmented financial markets model.7 Monetary policy affects indirectly, through prices, all agents in the economy; however, it affects directly, through transfers or taxes, only the financial market participants. In an expansion, monetary policy creates an inflation tax for all households, but distributes monetary transfers only to the traders; traders' consumption increases and non-traders' consumption decreases. In contrast, in a tightening, consumption becomes cheaper for both types of agents; however, only the traders get taxed and thus their consumption shrinks, although non-traders' consumption rises. Note also that monetary policy affects risk sharing between traders and non-traders. Any monetary policy rule that reacts to real activity affects the risk sharing between the two groups of agents. In the next section we study how monetary policy can redistribute this risk optimally. Also, notice how, in the case of limited participation, dividend income affects the consumption of the two groups, assuming that monetary policy does not react to such a shock. The equilibrium consumption equations reveal that an increase in the current total dividends distributed, εt , implies lower price for the consumption good in period t, increasing consumption for both traders and non-traders. On the other hand, an increase in total real dividends distributed the previous period, εt−1 , decreases the price of the consumption good in period t−1 and thus the value of the consumption good carried in the form of money balances from period t−1 to period t. For iid dividend shocks, consumption in period t decreases for the non-participants although increases for the participants. The increase in traders' consumption depends on the participation rate; the more participating agents there are, the smaller the share of the εt−1 shock each of them receives is. Therefore, the increase in traders' consumption is negatively affected by the participation rate. Finally, it is important to notice that because of the cash-in-advance constraint, the dividend εt is currently distributed but is not currently consumed. It is the previous period dividend εt−1 that is consumed in period t. While the above analysis did not require solving the maximization problem, the study of asset prices requires such a procedure. In particular the traders' utility maximization problem needs to be solved, subject to the cash-in-advance constraints (3), (4) and budget constraints (5), (6). The first order conditions imply that the price of the bond is determined as follows: βEt

u′ðcTtþ1 Þ u′ðcTt Þ ¼ st : pt ptþ1

ð17Þ

Eq. (17) describes the usual pricing of nominal bonds: the utility increments traders expect to receive in period t þ 1, when the bond matures and pays back, equals the foregone utility they suffer from buying the nominal bond in period t. In addition, this equation reveals a Fisher effect, so the nominal interest rate is given by the real interest rate, augmented by an expected inflation premium. Note also that a strictly positive multiplier associated with the traders' cash-in-advance constraint (3) implies that st o1, so the nominal interest rate is strictly positive. For the case of certainty the usual condition is required to satisfy this assumption, i.e., that money growth must be greater than the discount factor. The first order conditions imply the following expression for the stock price: βEt

7

u′ðcTtþ1 Þ u′ðcTt Þ ðqtþ1 þ pt εt Þ ¼ qt ; pt ptþ1

Market segmentation allows for monetary policy's distributional effects, which are not present under full financial market participation.

ð18Þ

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which suggests that the discounted marginal utility expected in period t þ 1, when the dividends are paid and the share can be traded again, equals the forgone utility incurred from purchasing the share at time t. We will return to the stock price and its volatility later, when we will apply various policy specification in Eq. (18) and compare across them. 3. Optimal monetary policy In this section we study a new role for intermediation that optimal monetary policy acquires in our model. We consider a monetary authority that maximizes total welfare by choosing the money supply growth rate. We assume that the monetary authority assigns equal weight to each agent, independent of the group the agent belongs to. Then, λ weight is assigned to the group of traders and 1−λ to the group of non-traders. The maximization problem is as follows: ∞

max E0 ∑ βt ðλuðcTt Þ þ ð1−λÞuðcN t ÞÞ: μt

t¼0

The first order conditions imply the following: λu′ðcTt Þ

∂cTt ∂cN t þ ð1−λÞu′ðcN ¼ 0: t Þ ∂μt ∂μt

ð19Þ

From Eqs. (15) and (16) which determine consumption in equilibrium, we can calculate the derivatives of consumption with respect to money growth: ∂cN y þ ðεt −εÞ y t ¼− ; ∂μt y þ ðεt−1 −εÞ ð1 þ μt Þ2 and ∂cTt 1−λ y þ ðεt −εÞ y ¼ : λ y þ ðεt−1 −εÞ ð1 þ μt Þ2 ∂μt Note that non-traders' consumption decreases although traders consumption increases whenever monetary policy expands. This is because limited participation prevents the monetary authority from directing its transfers to all agents, but distributes them instead only among the agents who participate in the financial markets. Expansionary monetary policy increases the current goods price adversely affecting all agents; the traders, however, receive the monetary transfer and the positive effect prevails. Notice also that the higher the financial market participation rate λ is, the smaller the fraction of the monetary expansion each trader receives is. Substituting the above equations into Eq. (19) we find that optimal money growth is as follows: 1 þ μnt ¼

y : y þ ðεt−1 −εÞ

ð20Þ

The above expression reveals a new role for monetary policy, which is to redistribute the financial income risk that traders are exposed to, among all agents in the economy. When the total real dividend is low (lower than the total mean dividend ε) traders' consumption decreases. Optimal monetary policy becomes expansionary and increases traders' consumption by distributing to them higher transfers. As monetary policy expands, current goods price increases, reducing non-traders consumption. In contrast, whenever the total dividend is high (higher than the total mean dividend ε), traders' consumption is high. Optimal monetary policy becomes contractionary by taxing traders; the goods price decreases causing the nontraders' consumption to rise. Financial income risk is perfectly shared between financial market participants and nonparticipants, through optimal monetary policy.8 Financial market segmentation exposes only participants to financial income risk. In addition, it allows monetary policy to have distributional effects and the power to undo this market failure, so the dividend risk to be shared among all agents.9 Note that because of the cash-in-advance constraint, traders at time t consume the dividend of the previous period, εt−1 . The only relevant effect of εt in period t is through price changes, which affect both types of agents. Then, optimal policy at time t chooses to react to total dividend distributed at time t−1, because εt−1 is the source of differential effects across the two groups, i.e., positive effects for traders and negative for non-traders.10 As a result, this model suggests that optimal monetary policy responds to advances in the asset markets, however not in the way previous research has considered (e.g., Bernanke and Gertler, 2000, 2001; Cecchetti et al., 2001; Gilchrist and Leahy, 8 Modifying the model, allowing the monetary authority to have intertemporal considerations would not make the Friedman rule optimal. This is because monetary authority has distributional considerations in this model. This is similar to Williamson (2005). 9 We consider the case that limited participation is generated through entry, information, trading costs etc. Vissing-Jørgensen (2003) finds that these costs are very important for explaining financial market segmentation. 10 Following the standard CIA assumption and timing of Lucas (1982), we only allow cash to be used for consumption purchases. We have explored a version of the model where agents are allowed to use current real dividends for financing current consumption. Then, optimal monetary policy reacts to current real dividends in the exact same way that it reacts to lagged real dividends in Eq. (20).

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2002; Faia and Monacelli, 2007). Here the monetary authority responds to real dividend changes in order to redistribute wealth from the privileged financial market participants who were fortunate to encounter good financial markets conditions, to the rest of the population, or, from the rest of the population to the disadvantaged financial market participants who were hit by bad financial markets shocks. The above result holds for any concave utility function. In addition, it is not sensitive to the fixed endowment assumption. In the case of random mean endowment, optimal monetary policy would still redistribute the extra risk that participants hold between the two types of agents and increase in this way total welfare. Also note that in this model optimal monetary policy reacts to real shocks, without the assumption of price rigidities. This is because of redistribution concerns, similar to Williamson (2005). In our paper we take limited participation as given and ignore the interesting complications that the participation decision would introduce in the model.11 If participation cost, e.g., entry cost, trading cost or lack of information, discourages a positive mass of agents to participate in the financial markets, then financial markets are segmented and our model suggests that monetary policy bears real effects. If monetary authority follows the optimal rule, the consumption of traders and non-traders each period is given below: n Tn n cN t ¼ ct ¼ ct ¼ yt ¼ y þ εt −ε:

ð21Þ

We see that the optimal monetary policy is a risk sharing policy. In addition, although we are using an exogenous participation framework, optimal monetary policy makes agents indifferent between participating in the financial markets or not. Precisely, the traders would vote for any policy with μt 4 μnt as such a policy would increase their consumption relative to what they consume under the optimal monetary policy regime. On the contrary, the non-traders would vote for any policy with μt o μnt for the same reason. Optimal monetary policy equates consumption of the two groups and makes agents indifferent between participating or not in the financial markets. Finally, note that contrary to Bilbiie (2008), the optimal monetary policy in this model does not depend on the participation rate. This is true because monetary authority has direct effects on the same group of agents that faces the dividends risk. It is the traders' group that is exposed to financial income risk; the same group is directly affected by monetary policy. However, for monetary policy to have any real effect, the limited participation assumption is necessary. Hence, as soon as financial markets are segmented, no matter to what extent, monetary policy can operate in such a way that everybody shares and consumes the total output and becomes indifferent between participating or not in the financial markets. Our model implies that monetary policy affects the risk sharing between financial market participants and nonparticipants automatically, through its usual function. We suggest that policy makers should consider the direction of responses the model proposes in order for the redistribution from one group of agents to another to be welfare improving. Of course this does not mean that monetary policy does not have other considerations, which our parsimonious model has intentionally ignored in order to focus on a new one, the financial income risk sharing. In addition, we suggest that monetary policy is the relevant policy to consider for redistributing financial income risk. As previously suggested (e.g., Taylor, 2000), monetary policy does not require a special design of tax scheme and takes less time and resources to implement than fiscal policy. In our case, monetary policy affects financial income risk sharing automatically, through its usual operation, taking no extra time or resources to implement.

4. Stock price and inflation volatility Given that previous literature on monetary policy's response to financial market changes has been focused on exploring whether or not monetary authority should consider assets prices and their volatility when deciding its instruments (e.g., Bernanke and Gertler, 2000, 2001; Cecchetti et al., 2001; Gilchrist and Leahy, 2002; Faia and Monacelli, 2007), we study the implications for stock price and stock price volatility that monetary policy has in our model. In addition, we study monetary policy's implications for inflation volatility. Section 4.1 studies the relationship between optimal monetary policy and the stock price. We examine the role of financial market segmentation for the stock price, and we find that the optimal monetary policy eliminates the segmentation effect and makes the stock price behave as in the representative agent model. We also find that in the absence of other shocks, optimal monetary policy expands after an increase in the stock price, but its reaction is less expansionary compared to an inflation targeting policy with positive target. In Section 4.2 we compute the stock price volatility for four policy rules: optimal, constant money supply, inflation targeting and nominal interest rate pegging. We ask the question whether optimal monetary policy implies lower stock price volatility when compared to the other, frequently cited policy rules, and we find that this is not necessarily the case. Section 4.3 examines the inflation volatility that the above monetary policy rules produce. We find that optimal monetary policy is to some extent concerned with inflation volatility, but does not coincide with the policy that minimizes inflation volatility. 11

Alvarez et al. (2002) and Khan and Thomas (2007) have thoroughly examined cases of endogenous participation.

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In addition, we derive the policy rule associated with minimal stock price volatility and compute the welfare loss caused by implementing that policy instead of the optimal one. The analysis suggests that the welfare-maximizing monetary policy does not attempt to minimize stock price volatility, and thus, stock price volatility should not be an integral part of monetary policy. This analysis, however, does not suggest that monetary policy should not react to advances in the stock market. On the contrary, as analyzed in Section 3, optimal monetary policy reacts to dividend shocks by tightening in good times for the financial markets and expanding in bad ones, in order to perfectly share financial income risk. For convenience, we have summarized and discussed our main conclusions from this section, so the reader may refer directly to Section 4.4.

4.1. Optimal monetary policy and the stock price We study optimal monetary policy in relation to the stock price. Previous work in the topic prescribes inflation stabilization policies that do not respond to stock price per se. This is either because these policies stabilize the shocks that create the asset price volatility (Bernanke and Gertler, 2000, 2001), or because the welfare losses of inflation stabilization policies that do not react to asset prices compared to the optimal monetary policy are minimal (Faia and Monacelli, 2007). We find that monetary policy reacts differently to the stock price according to its consideration. The inflation targeting policy expands after an increase in stock price, and the expansion is sub-optimally large. Contrary to previous work, our model can address a distributional consideration of monetary policy, which affects the stock price. We show below the reaction mandated by the distributional consideration of monetary policy. For the analysis that follows we specify a utility representation in order to explicitly compute the stock price. We use the logarithmic utility function. We first calculate the real stock price, q^ t ¼ qt =pt , using Eq. (18). The recursive solution, assuming that there are no bubbles so that the transversality condition holds, is as follows: ∞

u′ðcTtþj Þ ptþj−1

j¼1

u′ðcTt Þ ptþj

q^ t ¼ Et ∑ βj

εtþj−1 ;

which for logarithmic utility can be written as ∞

q^ t ¼ Et ∑ βj j¼1

c~ Tt yt 1 εtþj−1 ; c~ Ttþj ytþj 1 þ π tþj

where x~ t ¼ xt =yt . The real stock price depends on the stochastic discount factor and the payoff. In this model the stochastic discount factor changes because of two reasons: (i) changes in the fraction of total consumption consumed by traders, i.e., the segmentation effect (c~ Tt =c~ Ttþj ), and (ii) changes in aggregate consumption, i.e., the typical representative agent effect (yt =ytþj ). The payoff 1=ð1 þ π tþj Þεtþj−1 depends on the stream of dividends and on inflation.12 Under the optimal monetary policy where the dividend shock is shared among financial market participants and nonparticipants, there is no variation of the relative consumption of the traders, and the segmentation effect disappears. Every period, traders and non-traders consume an equal part of total output and the discount factor is only affected by the change in total consumption, similar to the representative agent model.13 In addition, under optimal monetary policy, the effect of the previous period's shocks do not matter for inflation, and only current dividends can change current prices.14 The real stock price under the optimal policy is ∞

n q^ t ¼ Et ∑ βj

j¼1

∞ yt 1 y εtþj−1 ¼ Et ∑ βj t εtþj−1 ; ytþj 1 þ π ntþj y j¼1

where π n denotes inflation under the optimal monetary policy regime. We see that with optimal monetary policy the segmented markets effect disappears and the real stock price increases when current output or the stream of dividends increases. We now linearize the real stock price and find the response to monetary policy. Using the equations of goods price (14) and traders' consumption (16), we find the following expression for the stock price: ∞

q^ t ¼ Et ∑ βj j¼1

ðεt−1 −εÞð1 þ μt Þ þ yðλ þ μt Þ 1 ðy þ εt −εÞεtþj−1 ; ðεtþj−1 −εÞð1 þ μtþj Þ þ yðλ þ μtþj Þ ðy þ εt−1 −εÞð1 þ μt Þ

ð22Þ

12 Inflation affects the real payoff because the dividends are received and sold a period before the period they are used to buy consumption good. Thus, an increase in inflation rate decreases the real value of the payoff. 13 We thank a referee for pointing out this decomposition. 14 Note that the quantity equation is in place. Then if output increases, with no change in money, there is not enough cash to buy the goods, and thus prices decrease.

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where the first two fractions in the expression above come from the change in the fraction of consumption consumed by traders, and the last two portions are from the change in total consumption and the change in the payoff. We linearize the expression inside the expectation around ε and μ and we get the linearized stock price as follows:
 βε β εð1−λÞ β ε ðλ þ μÞy−εð1 þ μÞ þ þ ðεt−1 −εÞ þ ðεt −εÞ q^ t ¼ ð1−βÞð1 þ μÞ 1−β yð1 þ μÞðλ þ μÞ ð1 þ μÞy 1−β ðλ þ μÞ β ð1−λÞε þ ðμ −μÞ: 1−β ð1 þ μÞ2 ðλ þ μÞ t A monetary expansion increases the stochastic discount factor because the part of output that currently goes to traders increases. The loss of giving up current consumption in order to buy more stocks becomes less severe, stock demand increases and the stock price increases.15 Previous empirical work (Bernanke and Kuttner, 2005) finds this effect, which attributes to monetary policy changing consumers' expectations for future dividends and risk premiums. We find that monetary policy exhibits distributional effects currently, which alter the stock price. We can solve the above expression for the monetary policy action: ð1 þ μÞðλ þ μÞ 1−β ð1 þ μÞ2 ðλ þ μÞ 1þμ þ q^ t − ðεt−1 −εÞ 1−λ β ð1−λÞε y
 ð1−βÞðλ þ μÞð1 þ μÞ ε ðλ þ μÞy−εð1 þ μÞ þ ðεt −εÞ: − 1−β ðλ þ μÞ yð1−λÞε

μt ¼ μ−

Keeping the output (dividends) constant and treating the real stock price q^ t as a shock, we see that the response of monetary policy to this shock depends on the type of policy followed. For the optimal monetary policy the average money growth is μ n ¼ 0, and for the inflation targeting policy it is μ π ¼ π . This is n  ∂q^ t μt ¼ μ 1−β 2λ þ 1 4 0; ¼ β ð1−λÞε ∂μt  π n   ∂q^ t μt ¼ μ 1−β 1 þ π ∂q^ μt ¼ μ ð2ðλ þ π Þ þ ð1 þ π ÞÞ 4 t  ¼ :  β ð1−λÞε ∂μt ∂μt

The optimal monetary policy expands whenever there is an increase in the stock price, so it gives more cash to the traders to buy the now more expensive asset, sharing the extra cost the participants have, among everybody in the economy. The rational is the same as before; optimal monetary policy aims to smooth consumption across the two groups of agents, although now it reacts to the stock price. On the other hand, the inflation targeting policy sees that the price of the stock relative to the goods increases, destabilizing inflation. The inflation targeting policy expands in order to keep inflation on its target. Thus, the inflation targeting policy, targeting inflation more than 0%, is more expansionary and reacts stronger to stock price compared to the optimal one. 4.2. Stock price volatility In the examples that follow we use the linearized expression for the stock price (22) to compute the variance of the stock price for a choice of policy rules and compare the results. We first compute the stock price under the assumption that monetary policy is conducted optimally, following the optimal rule (20). We linearize around the dividend mean value, ε ¼ λðy−yT Þ, and find the unconditional variance of the stock price for the optimal monetary policy rule: β2 s2ε

n

Varðq^ t Þ ¼

ð1−βÞ2 y 2

½ð1−βÞy þ λðy−yT Þ2 ;

ð23Þ

where as discussed earlier, s2ε is the variance of the total dividend shock. A positive shock in current dividends under the optimal monetary policy rule would make traders want to acquire more shares, increasing the stock price. Higher dividend volatility in (23) translates into higher stock price volatility. Furthermore, under optimal monetary policy agents' consumption equals aggregate output, which is not affected by the financial markets' participation rate (see Eq. (21)). However, higher participation increases the mean total dividend, which in turn positively affects the stock price and its variance. We now compare the volatility produced by the optimal monetary policy rule with that produced by the zero money growth rule. To compute the latter, we substitute μt ¼ 0 for every period, in the real stock price equation (22) and linearize around the iid dividend shocks. Stock price volatility for a monetary authority that does not change its money supply is μ¼0

Varðq^ t

15

Þ¼

β2 s2ε ð1−βÞ2 y 2

fð1−λÞ2 ðy−yT Þ2 þ ½λðy−yT Þ þ ð1−βÞyT 2 g:

ð24Þ

We assume that μ 4 −λ. In case μ o −λ then the monetary policy is too contractionary and taxes more than what the traders started the period with.

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Table 1 Parameter values. Parameter

Symbol

Value

Mean income Trader's endowment Total dividend variation Discount factor

y yT sε β

1 0.9 0.06 0.9

Stock Price Variance 0.012 0.01 0.008 0.006 0.004 0.002 0.2

0.4

0.6

0.8

1

λ

Fig. 1. Stock price volatility of optimal (large-dashed line), constant money supply (solid line), π ¼ 2% inflation targeting (small-dashed line) and nominal interest rate peg at r þ 1 ¼ 2=β (thick line) policy rules, for the parameter values given in Table 1.

Higher dividend volatility translates into higher stock price volatility. However, the effect of the financial market segmentation on the stock price and its variance is ambiguous and depends on the parameter values. Comparing Eqs. (23) and (24) is not straightforward. To illustrate that optimal monetary policy is not necessarily associated with low stock price volatility we use the following example (for convenience, we summarize the parameter values in Table 1). For y ¼ 1, yT ¼ 0:9, β ¼ 0:9 and sε ¼ 0:06, Fig. 1 shows that there is a critical value for the participation rate λ below which optimal monetary policy produces less volatility than the constant money supply policy, and above which optimal monetary policy generates higher volatility.16 For a financial market participation rate of λ ¼ 0:35 it is true that the optimal monetary policy implies lower stock price volatility than the constant money supply policy; however, this result reverses as the financial market participation increases.17 We now explore the inflation targeting policy and its implications for stock price volatility. Inflation for any monetary policy rule μt is given below: πt ¼

pt −pt−1 ðy þ εt−1 −εÞð1 þ μt Þ −1; ¼ pt−1 y þ εt −ε

ð25Þ

and for inflation target π t ¼ π the corresponding monetary policy action is 1 þ μπt ¼ ð1 þ π Þ

y þ εt −ε : y þ εt−1 −ε

ð26Þ

This equation implies that whenever current dividends are low compared to the previous period, inflationary pressure increases. A monetary authority aiming in attaining its inflation target reduces money supply and reduces inflation back to its target level. To derive the stock price variance for the inflation targeting monetary policy rule, we linearize the real stock price (22) for this policy μt ¼ μπt , around the mean of the iid dividend shocks. The following expression is derived: π

Varðq^ t Þ ¼

β2 s2ε 2 2

ð1−βÞ y

½λð1 þ π Þðy−yT Þ þ ð1−βÞðλ þ π Þy2 ðλ þ πÞ2 ð1 þ π Þ2 :

ð27Þ

An increase in the variance of the dividend shock increases the volatility of the stock price. The effect of the degree of segmentation is not clear though, as it has ambiguous effects on consumption under this policy rule. Given the specific inflation target that the monetary authority chooses, we can compare the stock price volatility that the inflation targeting policy produces with that of the optimal and constant money supply policies. For example, compared to the optimal policy, a zero inflation targeting policy produces always higher stock price volatility. This is because of limited 16 17

sε ¼ 0:06 is between Shiller (1981)'s estimates of 0.01481 and 0.09828, based on two different data sets. λ ¼ 35% is approximately the percentage of the US population that Vissing-Jørgensen (2002) classifies as bondholders.

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financial market participation, although under full participation these two polices generate the same amount of stock price variance. As a second example we consider the policy implied by setting inflation target equal to π ¼ 2%. We use the same parameter values as before, summarized in Table 1. We see in Fig. 1 that choosing the policy that produces the least stock price variability depends crucially on the financial market participation rate and on the other parameter values. Another example of policy rule we consider is that of the nominal interest rate peg. By substituting in the equation for bonds price (17), the equilibrium price level (14), and traders' consumption (16), the bond price becomes st ¼ Et β

y þ εt −ε ðεt−1 −εÞð1 þ μt Þ þ yðλ þ μt Þ : ðy þ εt−1 −εÞð1 þ μt Þ ðεt −εÞð1 þ μtþ1 Þ þ yðλ þ μtþ1 Þ

Linearizing the expression inside the expectation around μtþ1 ¼ μt ¼ μ ¼ 0 and εt ¼ εt−1 ¼ ε, and assuming that all shocks are iid and uncorrelated to each other, the nominal interest rate, 1 þ r t ¼ 1=st−1 , equals 1 þ rt ¼

λy : βλy−βð1−λÞðεt−1 −εÞ þ βð1−λÞðεt−2 −εÞ þ βð1−λÞyμt−1 −βyEt−1 ðμt Þ

ð28Þ

Before we explore the stock price implications of the nominal interest rate peg policy, we first examine the liquidity effect of the model. Differentiating the above expression with respect to current money growth we see that ∂r t =∂μt−1 o0. Furthermore, this derivative becomes zero when there is full participation in the financial markets, signifying the liquidity effect. As in Alvarez et al. (2001), full participation implies that the only way monetary policy affects the nominal interest rate is through expected inflation, i.e., ∂r t =∂Et−1 μt 4 0. We compute the money supply policy implied by pegging the nominal interest rate at level r þ 1 ¼ 1=βð1−μÞ, computed by evaluating the nominal interest rate in Eq. (28) for mean values of the shocks, i.e., μt−1 ¼ μt ¼ Et−1 ðμt Þ ¼ μ and εt−2 ¼ εt−1 ¼ ε. Equating the nominal interest rate target r to Eq. (28) we find the monetary policy rule that pegs the nominal interest rate at level r: 1 þ μrt ¼ ð1 þ μÞ þ

εt −εt−1 : y

ð29Þ

The above equation reveals that whenever the dividend shock consumed in the current period is high, i.e., ηt−1 ¼ εt−1 −ε 40, traders are prompt to buy more assets and the price of the bond rises. A monetary authority that aims keeping the nominal interest rate at a specific level would then tighten and bring the nominal interest rate back to its target. In addition, whenever ηt ¼ εt −ε 40, future consumption is expected to rise; traders tend to buy fewer assets during the current period, forcing the price of the bond to fall. In order to keep the nominal interest rate at its target, monetary authority reacts by increasing money supply. Linearizing as usual around ε ¼ λðy−yT Þ and assuming iid dividend shocks we find the stock price variance for the interest rate pegging policy, μ ¼ μr , using the real stock price equation (22): " β2 s2ε λ2 ð1−λÞ2 ðy−yT Þ2 μ 2 r Varðq^ t Þ ¼ 2 2 ðλ þ μÞ2 ð1 þ μÞ4 ð1−βÞ y # 2 fλðy−yT Þ½1 þ λμ þ βμð1 þ μÞ þ ð1−βÞyðλ þ μÞð1 þ μÞg þ : ð30Þ ðλ þ μÞ2 ð1 þ μÞ4 The monetary authority's choice of interest rate peg, combined with the parameters values will determine whether or not this policy creates higher stock price volatility than the other policies considered. We first examine the example of pegging the equilibrium rate, r ¼ 1=β, derived by setting μ ¼ 0. It turns out that the stock price variance when pegging the r

π ¼0

Þ, which in turn is higher than equilibrium rate is equal to this produced by targeting zero inflation, i.e., Varðq^ t Þ ¼ Varðq^ t the stock price variance produced under the optimal monetary policy specification, as we explained earlier. As a second example we consider a monetary authority which pegs a rate of r þ 1 ¼ 2=β. Using for the rest of the parameters the same values as before, summarized in Table 1, we see in Fig. 1 that depending on the parameter values, a different policy produces the least stock price volatility. Overall, in our model, it is not the case that the optimal monetary policy is in general associated with minimal stock price volatility. We also derive the policy rule that a monetary authority interested in minimizing stock price volatility would implement. Then we calculate the welfare loss that this policy produces compared to the optimal policy. We consider a central bank that reacts to the distributed dividends in the previous and current period, εt−1 and εt , respectively. Specifically, we derive a linear function f ð  Þ, where f ðεt−1 ; εt Þ ¼ μqt , and μqt is the money growth associated with minimal stock price volatility. We substitute in Eq. (22) the monetary rule associated with minimum stock price volatility, μt ¼ μqt . Then, we linearize around the mean total dividend and find the linearized expression for the stock price, as given below: q q^ t ≃

βε 1 þ f ðεÞ þ yf 1 ðεÞ þ βεð1−λÞ ηt−1 ð1−βÞ½1 þ f ðεÞ ð1−βÞy½λ þ f ðεÞ½1 þ f ðεÞ2

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267

  ½λ þ f ðεÞ½1 þ f ðεÞ þ ð1−λÞyf 2 ðεÞ y½λ þ f ðεÞ−ε½1 þ f ðεÞ−εyf 1 ðεÞ ηt ; þ βε þβ 2 y½λ þ f ðεÞ½1 þ f ðεÞ ð1−βÞy½λ þ f ðεÞ½1 þ f ðεÞ where f ðεÞ is the money growth rate when the dividend shocks εt−1 , εt equal to their mean, and f 1 ðεÞ, f 2 ðεÞ are its first derivatives with respect to the first and second argument respectively, evaluated at the mean of the dividends shocks. Also, ηt is defined in Eq. (1). Letting the above expression to be invariant, and by assuming that mean money growth is zero, we can find the slope of the money growth function that minimizes stock price volatility, with respect to the two dividend shocks: f 1 ðεÞ ¼ −

1 y

f 2 ðεÞ ¼ −

and

λ½ε þ ð1−βÞy : ð1−λÞεy

We consider the case of a linear monetary policy rule, which is as follows: 1 λ½ε þ ð1−βÞy 1 þ μqt ¼ 1− ðεt−1 −εÞ− ðεt −εÞ: ð1−λÞεy y

ð31Þ

We compare this policy to the optimal one, in terms of total welfare: ∞

∞

t¼0

t¼0

N;q t Tn Nn W q −W n ¼ E0 ∑ βt ½λuðcT;q t Þ þ ð1−λÞuðct Þ− ∑ β ½λuðct Þ þ ð1−λÞuðct Þ; n

W qt

denote total welfare implied by the optimal monetary policy and the stock price targeting rule, where W t and respectively. After substituting for consumption implied by each policy, using Eqs. (15), (16) and (21), the logarithmic utility implies the following expression for the total welfare loss: ( " # " #) ∞ ðy þ εt−1 −εÞð1 þ μqt Þ−ð1−λÞy ðy þ εt−1 −εÞð1 þ μqt Þ q n t W −W ¼ E0 ∑ β λ ln − ln : λy y t¼0 The above expression shows that there is no welfare loss if there is full participation in the financial markets or the total dividend shocks are always equal to their mean. However, any other case produces positive welfare loss. Using the parameter values from Table 1 and financial market segmentation parameter λ ¼ 0:35 we find welfare losses for both positive and negative financial shocks. For a positive financial shock of 10% above the mean in period t, the welfare loss in period t and period t þ 1 from implementing stock price targeting versus the optimal policy rule adds to 1.43%.18 Calculated similarly, a negative financial shock of 10% below its mean in period t reduces welfare by 1.37%. This welfare loss is increasing with the rate of financial segmentation, suggesting that the optimal monetary policy rule becomes more vital in economies with high financial market participation.

4.3. Inflation volatility In this section we examine the inflation volatility that the optimal, constant money supply, inflation targeting, interest rate pegging and stock price volatility targeting policies imply, and we make comparisons across them. The general expression for inflation is given by Eq. (25), in which we substitute the relevant policy rule. To compute the inflation variance implied by the various policies, we first linearize the inflation equations around the mean dividend value ε and then calculate the variance for iid dividend shocks as follows: Varðπ nt Þ ¼

s2ε y2

;

for the optimal monetary policy rule; Varðπ μt ¼ 0 Þ ¼ 2

s2ε y2

;

for the constant money supply policy rule; Varðπ πt Þ ¼ 0; for the zero inflation targeting policy rule; Varðπ rt Þ ¼ 2μ 2

18

s2ε y2

;

We look at two consecutive periods because the stock price targeting policy involves responses in two periods.

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for the nominal interest rate pegging policy rule, and  Varðπ qt Þ ¼

ð1−βÞλy þ ε ð1−λÞε

2

s2ε y2

;

for the stock price targeting monetary policy rule. Inflation variance is minimized, as expected, under the inflation targeting policy. Additionally, the optimal policy is always associated with half the inflation volatility the constant money supply policy produces. The latter is true because under the optimal policy the dividend shocks from the previous period are offset, while under constant money supply they are not. These shocks increase the volatility of inflation. Furthermore, a monetary authority pegging the interest rate at its equilibrium level, r þ 1 ¼ 1=β, implies zero inflation volatility. Using the parameter values in Table 1 and for any other peg between zero and one, this policy implies lower inflation volatility than the optimal and constant money supply ones. Finally, using the parameter values in Table 1 and for λ ¼ 0:35, the optimal monetary policy implies lower inflation volatility than the stock price targeting policy.

4.4. Discussion In this section we first examined the relationship between monetary policy and stock prices. The evidence on whether or not monetary policy should respond to asset prices is conflicting (Cecchetti et al., 2001; Gilchrist and Leahy, 2002; Faia and Monacelli, 2007). We found that optimal monetary policy responds to stock price shocks, but only for redistributing the extra cost higher stock price implies for the traders, to all agents in the economy. The response to the stock price depends on the monetary authority's objective. The optimal monetary policy is typically less expansionary than the inflation targeting policy after an increase in the stock price (see Section 4.1). We also examined the implications that optimal monetary policy has for stock price volatility (Section 4.2) and inflation volatility (Section 4.3), and compare across various monetary policy rules. It is clear from our analysis that the optimal monetary policy does not necessarily associate with lower stock price volatility or inflation volatility when compared to the other policy rules considered. There are policies different from the optimal one that produce minimal stock price volatility and inflation volatility. Specifically, we find that the optimal monetary policy rule does not produce necessarily lower stock price volatility than what the constant money supply policy does; it produces lower stock price volatility than the inflation targeting policy for some targets and from the interest rate peg policy for some pegs. The results depend on the parameter values and on the choice of inflation target and peg. We conclude that the welfare-maximizing monetary policy is not in general concerned with minimizing stock price volatility. We also derive a monetary policy rule that aims in keeping constant the stock price and we find that there is welfare loss from implementing this rule instead of the optimal one. In our simple example, a 10% positive deviation from the dividends' mean produces welfare loss of 1.43%, if the stock price targeting versus the optimal monetary policy is followed. The welfare loss is increasing with the rate of financial segmentation and disappears under full financial market participation, revealing the misleading conclusions one can reach by omitting limited financial market participation from welfare comparisons of monetary policy rules. Previous literature suggests that monetary policy targeting inflation, takes care of stock price volatility (Bernanke and Gertler, 2000, 2001). This paper provides some counter examples: for the same parameter values, a policy that minimizes stock price volatility produces high inflation volatility and a policy that minimizes inflation volatility produces high stock price volatility. This is because, first, in our model we consider dividend type of shocks. Currently distributed dividends decrease current prices and inflation (through Eqs. (14) and (25)), so a monetary authority targeting inflation expands after high current dividend shocks (see Eq. (26)). However, currently distributed dividends increase the stream of future consumption, increasing the stock price, so a monetary authority targeting stock prices becomes contractionary after high current dividend shocks (see Eq. (31)). In addition, in our model we take into account the limited financial market participation, which affects the stock price targeting policy, but not the inflation targeting policy. Because it is affected differently by financial market participation and dividend shocks, the inflation targeting policy (that minimizes inflation volatility) does not necessarily minimize stock price volatility. Furthermore, we see in Fig. 1 that increased participation does not necessarily imply lower stock price volatility. This observation is in contrast to previous literature (Allen and Gale, 1994) arguing that high variability in stocks price is encouraged by low stock market participation. If monetary policy actions are taken into account, as they are in this model, the effect of the increased financial market participation on stock price volatility becomes more complicated, and depends on the specific monetary policy followed. Concerning inflation volatility we find that the optimal monetary policy always produces lower inflation volatility than what the constant money supply policy rule does. That is, the welfare-maximizing monetary policy is concerned, to some extent, with sustaining stable inflation.

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5. Quantitative analysis In this section we quantify the differences between an economy that follows a 2% inflation targeting policy and an economy that follows optimal monetary policy. We chose a 2% inflation target because it is often mentioned in policy talks, in academic work and was recently formally stated as the inflation target of the Federal Reserve.19,20 We use the mean and variance of the total dividend income.21 We estimate an ARð1Þ process for the de-trended part of the dividend income from which we use the persistence coefficient.22 We calibrate total endowment to match the 1997 average labor share of 66.1% from Ríos-Rull and Santaeulàlia-Llopis (2010).23 We take from Walentin (2010) the estimates of the shareholders' share of labor income, being λyT =ðλyT þ ð1−λÞyN Þ≡ηT ¼ 45:1% in 1997. We also use the stock market participation rate for 1997 from the same study, which equals to λ ¼ 27:3%, excluding retirement accounts.24 We use Eqs. (8), (15), (20), (21), (25), and (26) and re-write the model in terms of the estimated process and calibrated parameters as follows: yT ¼

ηT l; λ

yN ¼

ð1−ηT Þ l; ð1−λÞ

cN;π t

ð1−ηT Þ l pπt−1 N yN ð1−λÞ ¼ ; ¼ π y ¼ 1þπ ð1 þ π Þ pt

cT;π ¼ yT þ t 1 þ μnt ¼

εt 1−λ N N ðy −ct Þ; þ λ λ

yN ð1−ηT Þ l ð1−ηT Þ l ; ¼ ¼ 1−λ yt−1 1−λ εt−1 þ l yt−1

1 þ μπt ¼ ð1 þ π Þ 1 þ π nt ¼

yt εt þ l ; ¼ ð1 þ π Þ εt−1 þ l yt−1

yt−1 y ð1−ηT Þ l εt−1 þ l ð1−ηT Þ l ; ð1 þ μnt Þ ¼ t−1 ¼ εt þ l 1−λ εt−1 þ l yt yt 1−λ yt−1

n Tn cnt ¼ cN t ¼ ct ¼ l þ εt ¼ yt ;

yt ¼ l þ εt ; εt ¼ aε þ ρε εt−1 þ ζ εt ; W Tt ¼ log cT;π þ βW Ttþ1 ; t π N;π W πt ¼ λ logðcT;π t Þ þ ð1−λÞlogðct Þ þ βW tþ1 ;

W nt ¼ log cnt þ βW ntþ1 ; W gain ¼ W nt −W πt ; where W Tt is the welfare of the traders under the inflation targeting policy and W πt and W nt denote total welfare under the inflation targeting and the optimal monetary policy respectively. We use β ¼ 0:99. The estimated process for the de-trended 19

Leigh (2008) estimates the implicit inflation target which although unstable, is on average around 2% for the period we examine. Chairman Bernanke's Press Conference, January 25, 2012. 21 We define dividend income as the sum of Rental income of persons with CCAdj, Corporate profits with IVA and CCAdj, Net interest and miscellaneous payments and Current surplus of government enterprises from the Bureau of Economic Analysis, which we convert to real per capita values using CPI and Civilian population from FRED. We use quarterly, per capita data from the first quarter of 1960 until the second quarter of 2012. 22 For deriving the cyclical component we de-trend the data with HP filtering before estimating the ARð1Þ process. 23 We have also used Ríos-Rull and Santaeulàlia-Llopis (2010)'s processes for labor share to calculate a process for capital share. As expected, the capital share does not fluctuate much and the magnitude of the effects this shock has in our model is small. However, the direction of the responses is similar. 24 Walentin (2010) uses the Survey of Consumer Finances data to calculate λ. This calculation is close to Vissing-Jørgensen (2002)'s one which uses the U.S. Consumer Expenditure Survey. Bilbiie et al. (2008) and Bilbiie and Straub (2013) use dynamic stochastic general equilibrium models to estimate the fraction of households that does not smooth consumption over time, for the period 1983–2004 and 1984–2008, respectively. Their estimates are larger than the ones we use. We choose to use the data-based calculations because they fit the concept of our model better, as we are interested in having a fraction of the population exposed to considerable financial income risk. Using the model-based estimates does not alter our results qualitatively. 20

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money growth for 2% inflation target

output

dividend 0

0

0.02

0

−0.05 −0.02

−0.02

−0.1 −0.04

−0.04

−0.15

−0.2

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ζ

Fig. 2. Impulse response functions after a shock to the dividends, with s ¼ 0:4548. Percentage deviation form steady for dividend, output, money growth implied by the 2% inflation targeting policy, traders' consumption implied by the 2% inflation targeting policy, money growth implied by the optimal monetary policy, inflation implied by the optimal monetary policy, consumption implied by the optimal monetary policy, total welfare implied by the optimal monetary policy, traders' welfare implied by the 2% inflation targeting policy.

dividend income implies ρε ¼ 0:8. The mean of the dividend series data is ε ¼ 3:671 and the standard deviation sε ¼ 0:758. Then, we derive that aε ¼ 0:734 and sζ ¼ 0:4548 so as to match the mean and standard deviation of the dividend series in the data. The only shock in our economy is the shock to the dividends, ζ εt , which has mean zero and standard deviation sζ . Fig. 2 presents our results as percentage deviations from steady state values. From there we see that a negative dividend shock of 13.6% decreases output by more than 4% and traders' consumption by almost 7%, under the inflation targeting policy. Given that this shock decreases current total output, it puts upward pressure on prices so the inflation targeting policy must tighten by 4.34% to keep inflation at the 2% target. As the shock fades away and output goes back to its steady state, the inflation targeting policy becomes less and less contractionary, and there is some period that also expands. Under the optimal monetary policy money growth increases in response to the negative dividend shock, in order to redistribute the dividend shock among traders and non-traders. We see that a 13.6% decrease in per capita dividend income mandates a more than 4% increase in money growth. Optimal monetary policy allows inflation to temporarily increase, in order to transfer money to traders who are hit by the low dividend shock. Consumption of traders and non-traders is equal, given that optimal monetary policy in this model corrects the segmentation friction and makes traders and non-traders indifferent between participating or not in financial markets (see Section 3). Under the optimal policy, we see in Fig. 2 that consumption of traders' and non-traders' decreases by 4.34% with the dividend shock, and returns back to steady state as the shock fades away. The optimal monetary policy implies smaller decrease in traders' consumption, by smoothing the dividend shock across traders and non-traders. On the contrary, the 2% inflation targeting policy directs all the dividend volatility towards the traders. Our analysis suggests that the consumption paths that each of the two policies imply are very different. This is because the response that the two policies have to the negative dividend shock is very different.

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The inflation targeting policy becomes contractionary in order to keep inflation to its target, although optimal monetary policy becomes expansionary in order to redistribute the dividend loss. There is welfare loss from having a dividend shock compared to the steady state welfare for both policies. We use Lucas (1982)'s calculation to evaluate the welfare loss incurred because of dividend variation, for each of the two policies. Specifically, we compute consumption compensation required in order to stay in a world with fluctuations, away from the steady state. We find that for both policies the compensation is between 0.15 and 0.25% of consumption, which is comparable in magnitude to the benchmark welfare gains for smoothing business cycle fluctuations as computed by Lucas (1982).25 This is not surprising given that the welfare cost of fluctuations is usually low for symmetric shocks like ours, and our analysis is bound by that cost. However, we calculate very large welfare loss that results from implementing inflation targeting instead of the optimal monetary policy. In order to calculate that cost we ask consumers to evaluate welfare under the following two scenarios. The first scenario is the optimal monetary policy scenario, where dividend income is shared among the two types of agents, and both types consume the same amount of goods. Total welfare equals in this case: W nt ¼ log cnt þ βW ntþ1 . The alternative scenario is the one under inflation targeting policy that keeps inflation constant and equal to 2%. Welfare under this policy is N;π π W πt ¼ λ logðcT;π t Þ þ ð1−λÞlogðct Þ þ βW tþ1 . In order to calculate the welfare cost we ask the consumers how much extra consumption they would need in order to accept the second scenario instead of the first: ∞

∞

t¼0

t¼0

N;π π π t n E0 ∑ βt ½λuðcT;π t ð1 þ Θ ÞÞ þ ð1−λÞuðct ð1 þ Θ ÞÞ ¼ E0 ∑ β uðct Þ;

so β logð1 þ Θπ Þ ¼ W gain : 1−β We calculate that Θπ ¼ expðð1−βÞ=ðβW gain ÞÞ−1 ¼ 33:24%. Thus, consumers need compensation equal to 33.24% of consumption in order to reside in an inflation targeting economy instead of the optimal one. This is a very large welfare cost which includes steady state differences between the two policies. We repeat the same exercise but we now shut down all differences in mean income across traders and non-traders, and we compute the welfare gain from switching from the inflation targeting policy to the optimal one. This exercise isolates the risk-sharing effect. We find that the welfare gain is 0.15% of average consumption; it is at the order of magnitude of the welfare gains for smoothing business cycle fluctuations as calculated by Lucas (1987), which we consider as our benchmark. We analyze the mechanism behind our result. The intuition is the same for both types of economies, with or without same mean income for the two groups. The non-traders have welfare gains from switching to the optimal monetary policy. This is because under the optimal monetary policy they are sharing the large positive mean dividend, and they have minimal cost from accepting the volatility of the dividend shock. The traders on the other hand have welfare losses from switching to the optimal monetary policy. They lose from sharing the mean dividend income and there is no much gain from decreasing the volatility of their dividend risk. However, given that the non-traders have higher mass, the total welfare increases when switching from the inflation targeting to the optimal monetary policy. 6. Concluding remarks Our model of segmented financial markets suggests that monetary policy should respond to stock market advances. However, it does for reasons that the previous literature has not considered. In our model, a novel role arises for welfare maximizing monetary policy through redistributing the financial income risk that only the financial market participants face, to all agents in the economy. In order to do so, optimal monetary policy is expansionary in bad times for the financial markets and contractionary in good ones. Moreover, this policy equalizes consumption of financial market participants and non-participants. If given the choice, all agents would be indifferent between participating or not in the financial markets. These results hold for any concave utility function and are not sensitive to the degree of market segmentation. We also examine optimal monetary policy's implications for stock price volatility and inflation volatility, and compare it with other, commonly used, monetary policy rules. Our analysis suggests that optimal monetary policy is not concerned with asset price volatility, but is concerned, to some extent, with keeping inflation stable. We perform a quantitative exercise where we find welfare gains from following the optimal monetary policy compared to an inflation targeting policy. In particular, a 2% inflation targeting policy involves large welfare losses for those who do not participate in the financial markets and large welfare gains for those who do. Our model and quantitative exercise suggest that monetary policy has distributional and risk-sharing effects that produce welfare differences among financial market participants and non-participants. We argue that monetary authorities should consider these effects. Some questions concerning the role of monetary policy in a segmented financial market remain open. It would be desirable to allow for correlation between work effort and financial market participation. In this environment, our optimal monetary policy is likely to be sub-optimal, for it penalizes those who exert higher effort. Finally, our model does not 25 Given that the dividend shock fluctuates more than consumption, we do find slightly higher welfare gain of smoothing the fluctuation of dividend income, compared to the gains that Lucas (1987) finds for smoothing the business cycle fluctuations.

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address the relative importance of financial market segmentation compared to price stickiness. The evaluation of these effects is a promising avenue for further research. Acknowledgments I thank the referees, the associate editor and the editor for useful comments. I am very grateful to Stephen Williamson and to Costas Azariadis and James Bullard for their constructive comments. I also thank Jacek Suda and the entire Macro Reading Group at Washington University. I thank YiLi Chien, Dennis Jansen, Ryo Jinnai, Filippo Occhino, Juan Sanchez, Rodrigo Velez, Yuzhe Zhang, seminar participants at Athens University of Economics and Business, Bank of Cyprus, University of Cyprus, University of Piraeus, Rice University and participants of the 2011 American Economic Association Meetings, 10th Econometric Society World Congress, 2010 Midwest Macro Meetings, 2009 European Meeting of the Econometric Society, 2009 North American Summer Meeting of the Econometric Society, 7th Conference on Research on Economic Theory & Econometrics, 12th ZEI International Summer School on Monetary Macroeconomics and 2008 Missouri Economics Conference for helpful comments. I thank Yulei Peng for excellent research assistance. Finally, I thank the Olin Business School's Center for Research in Economics and Strategy (CRES) for funding. References Allen, F., Gale, D., 1994. Limited market participation and volatility of asset prices. American Economic Review 84, 933–955. Alvarez, F., Atkeson, A., Kehoe, P.J., 2002. Money, interest rates, and exchange rates with endogenously segmented markets. Journal of Political Economy 101, 73–112. Alvarez, F., Lucas, R.E., Weber, W.E., 2001. Interest rates and inflation. American Economic Review 91, 219–225. Andres, J., Arce, O., Thomas, C., 2010. Banking competition, collateral constraints and optimal monetary policy. Banco de España Working Paper 1001. Antinolfi, G., Azariadis, C., Bullard, J.B., 2001. The optimal inflation target in an economy with limited enforcement. Federal Reserve Bank of St. Louis Working Paper Series 037B. Bernanke, B.S., 2009. The crisis and the policy response. Federal Reserve System Chairman Speech at the Stamp Lecture, London School of Economics. Bernanke, B.S., Gertler, M., 2000. Monetary policy and asset price volatility. NBER Working Paper Series 7559. Bernanke, B.S., Gertler, M., 2001. Should central banks respond to movements in asset prices? American Economic Review 91, 253–257. Bernanke, B.S., Kuttner, K.N., 2005. What explains the stock market's reaction to federal reserve policy? The Journal of Finance 60, 1221–1257. Bilbiie, F.O., 2008. Limited asset markets participation, monetary policy and (inverted) aggregate demand logic. Journal of Economic Theory 140, 162–196. Bilbiie, F.O., Meier, A., Müller, G., 2008. What accounts for the changes in U.S. fiscal policy transmission? Journal of Money, Credit and Banking 40, 1439–1470. Bilbiie, F.O., Straub, R., 2013. Asset-market participation, monetary policy rules, and the Great Inflation. Review of Economics and Statistics, forthcoming. Cecchetti, S.G., Genberg, H., Lipsky, J., Wadhwani, S., 2001. Asset prices and Central Bank policy. ICMB: Geneva reports on the world economy 2. Challe, E., Giannitsarou, C., 2011. Stock prices and monetary policy shocks: a general equilibrium approach. Banque de France Working Paper 330. Chien, Y., Cole, H., Lustig, H., 2011. A multiplier approach to understanding the macro implications of household finance. The Review of Economic Studies 78, 199–234. Doepke, M., Schneider, M., 2006. Inflation and the redistribution of nominal wealth. Journal of Political Economy 114, 1069–1097. Erosa, A., Ventura, G., 2002. On inflation as a regressive consumption tax. Journal of Monetary Economics 49, 761–795. Faia, E., Monacelli, T., 2007. Optimal interest rate rules, asset prices, and credit frictions. Journal of Economic Dynamics and Control 31, 3228–3254. Fuerst, T.S., 1992. Liquidity, loanable funds, and real activity. Journal of Monetary Economics 29, 3–24. Gilchrist, S., Leahy, J.V., 2002. Monetary policy and asset prices. Journal of Monetary Economics 49, 75–97. Grossman, S.J., Weiss, L.M., 1983. A transactions-based model of the monetary transmission mechanism. American Economic Review 73, 871–880. Guiso, L., Haliassos, M., Jappelli, T., 2002. Household Portfolios. The MIT Press. Guo, H., 2004. Limited stock market participation and asset prices in a dynamic economy. Journal of Financial and Quantitative Analysis 39, 495–516. Guvenen, F., Kuruscu, B., 2006. Does market incompleteness matter for asset prices? Journal of the European Economic Association 4, 484–492. Khan, A., Thomas, J., 2007. Inflation and interest rates with endogenous market segmentation. Federal Reserve Bank of Philadelphia Working Paper Series 07-1. Landon-Lane, J., Occhino, F., 2008. Bayesian estimation and evaluation of the segmented markets friction in equilibrium monetary models. Journal of Macroeconomics 30, 444–461. Leigh, D., 2008. Estimating the federal reserves implicit inflation target: a state space approach. Journal of Economic Dynamics and Control 32, 2013–2030. Lucas, R.E., 1978. Asset prices in an exchange economy. Econometrica 46, 1429–1445. Lucas, R.E., 1982. Interest rates and currency prices in a two-country world. Journal of Monetary Economics 10, 335–359. Lucas, R.E., 1987. Models of Business Cycles (Yrjo Jahnsson Lectures). Wiley-Blackwell. Lucas, R.E., 1990. Liquidity and interest rates. Journal of Economic Theory 50, 237–264. Mankiw, G., Zeldes, S.P., 1991. The consumption of stockholders and nonstockholders. Journal of Financial Economics 29, 97–112. Meh, C.A., Rios-Rull, J.V., Terajima, Y., 2010. Aggregate and welfare effects of redistribution of wealth under inflation and price-level targeting. Journal of Monetary Economics 57, 637–652. Mizrach, B., Occhino, F., 2008. The impact of monetary policy on bond returns: a segmented markets approach. Journal of Economics and Business 60, 485–501. Rigobon, R., Sack, B., 2004. The impact of monetary policy on asset prices. Journal of Monetary Economics 51, 1553–1575. Ríos-Rull, J.V., Santaeulàlia-Llopis, R., 2010. Redistributive shocks and productivity shocks. Journal of Monetary Economics 57, 931–948. Rotemberg, J.J., 1984. A monetary equilibrium with transactions costs. Journal of Political Economy 92, 40–58. Shiller, R.J., 1981. Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review 71, 421–436. Taylor, J.B., 2000. Reassessing discretionary fiscal policy. Journal of Economic Perspectives 14, 21–36. Vissing-Jørgensen, A., 2002. Limited asset market participation and the elasticity of intertemporal substitution. Journal of Political Economy 110, 825–853. Vissing-Jørgensen, A., 2003. Perspectives on behavioral finance: Does “irrationality” disappear with wealth? evidence from expectations and actions. NBER Macroeconomics Annual. Walentin, K., 2010. Earnings inequality and the equity premium. The B.E. Journal of Macroeconomics, Contributions 10. Williamson, S.D., 2005. Limited participation and the neutrality of money. Federal Reserve Bank of Richmond Economic Quarterly 91, 1–20. Williamson, S.D., 2006. Search, limited participation and monetary policy. International Economic Review 47, 107–128.