Gini in the Taylor Rule: Should the Fed Care About Inequality?

1.1 Related Literature

This paper is primarily related to the literature looking at the welfare implication of a more inclusive monetary policy. Hansen, Lin, and Mano (2020) find that a more inclusive monetary policy can improve social welfare by becoming more accommodative when the consumption gap between Ricardian and rule-of-thumb households widens within a two-agent New Keynesian model with no savings or investment. Baek (2021) constructs a New Keynesian model with regular and irregular labor types that reflect the cyclical nature of labor composition. The main finding of the paper is that if the central bank targets the deviations of cut-offs that determine the behavior of labor market participation, it can reduce the variation of the size of irregular employees, and in turn economic welfare can be improved. While previous literature only considered employment and labor income as relevant channels to determine the degree of inequality, the rich heterogeneity among households introduced in our model allows more complicated interactions between income and idiosyncratic states, such as labor efficiency, preferences, and asset holdings.

This study is also complementary to a chain of quantitative papers that incorporate heterogeneity across individual households to study the transmission mechanism of monetary policy. Seminal work by Kaplan, Moll, and Violante (2018) develops a HANK model that incorporates two types of assets with different degrees of liquidity and returns. Their main finding is that indirect channels from the general equilibrium effects, such as an increase in labor demand, are larger than the direct effects from intertemporal substitution channels. Auclert (2019) shows that redistribution channels, including the Fisher and earnings heterogeneity channels, amplify the real effect of monetary policy on aggregate consumption.^[3] Bayer, Born, and Luetticke (2020) estimate a HANK economy that enlarges the medium scale New Keynesian model studied in Smets and Wouters (2007), and argue that the estimated shocks, including monetary and fiscal policy shocks, significantly contributed to wealth and income inequality dynamics in the U.S. In addition, they also show that the systematic components of monetary and fiscal policy rules are important in shaping inequality. Ma (Forthcoming) studies a labor-supply-side story for the monetary transmission mechanism by developing a HANK model where a nonlinear mapping from hours worked into labor services generates an operative adjustment along the intensive and extensive margins of labor supply.^[4] Among the normative studies, Acharya, Challe, and Dogra (2020) explore an optimal monetary policy in a HANK economy and show that policy preventing the fall in output during recessions can mitigate the increase in inequality when income risk is countercyclical. On the other hand, Le Grand, Martin-Baillon, and Ragot (2020) find that an optimal monetary policy is still required to focus on inflation stability, and that redistribution is a matter of fiscal policy, by analyzing Ramsey monetary and fiscal policies within a HANK framework. Bhandari et al. (2021) show that the optimal monetary policy in HANK differs qualitatively as well as quantitatively from that in a representative agent model as monetary policy can provide insurance against aggregate shocks to heterogeneous agents. The work that is probably closest to this paper is Gornemann, Kuester, and Nakajima (2021), who develop a HANK economy where matching frictions generate countercyclical labor-market risk. They find that stabilization of unemployment is preferred by a majority of households, even if prices are more unstable. This paper differs from the previous literature as we focus on the importance of the systematic response of the monetary policy authority to inequality and evaluate whether there is policy room for reacting to inequality and introducing more inclusive policy goals into the monetary policy framework in the context of HANK economies.

There has been research that empirically evaluates the role of monetary policy in inequality. The conclusions from this literature are divided. For instance, Coibion et al. (2017), Furceri, Loungani, and Zdzienicka (2018), Casiraghi et al. (2018), and Lenza and Slacalek (2018) show that an expansionary monetary policy can ease income inequality. On the other hand, Andersen et al. (2021) and Cloyne, Ferreira, and Surico (2015) find that a softer monetary policy aggravates income inequality. Since empirical analyses generally study specific channels of monetary policy propagation, this difference can arise as documented in Colciago, Samarina, and de Haan (2019). Moreover, it is difficult to examine the role of systematic parts of monetary policy on inequality from those previous studies. This paper calls for a line of research that focuses more on the inequality implication of systematic monetary policy.^[5]

The remainder of the paper is organized as follows. In Section 2, the model that will be used in the subsequent analyses is introduced. Section 3 specifies the benchmark model economy with the standard Taylor rule. Sections 4 and 5 conduct the welfare analyses for various monetary policy rules. Finally, Section 6 concludes.

2.1 Heterogeneity

We build our model to reproduce substantial heterogeneity across characteristics of individual households, including wealth, income, employment, and consumption, as observed in U.S. data. To this end, we introduce two types of idiosyncratic shocks in the model economy: households are exposed to idiosyncratic risks of variations in time discount factor and labor efficiency. In particular, as documented in Krusell and Smith (1998) and Gornemann, Kuester, and Nakajima (2016), heterogeneity in the time discounting preference is known to be a crucial factor to match the empirically realistic wealth distribution. We assume that both shocks do not depend on the business cycles.

First, households are subject to idiosyncratic labor efficiency shocks, denoted by z. Labor efficiency, z, follows an AR(1) process in logs:

We discretize the continuous AR(1) process as a Markov chain, T z , by using the algorithm developed in Tauchen (1986). We assume that labor efficiency z takes on N _z values, i.e. z ∈ Z = z 1 , z 2 , … , z N z , and hence z follows an N _z -state first-order Markov process. The transition probability from i to j is given: T z ( i , j ) ≥ 0 , where ∑ j T z ( i , j ) = 1 for each i = 1, 2, …, N _z .

Second, individual households face idiosyncratic shocks to discount factors, β. The time discount factor, β, can take on two values, i.e. β ∈ B = β L , β H , where 0 < β _L < β _H < 1. Stochastic evolution of β is described by the transition matrix, T β . The probability of a transition from l to m is given T β ( l , m ) ≥ 0 , where ∑ m T β ( l , m ) = 1 for each l = L and H. Households cannot issue any assets contingent on their future idiosyncratic risks, β and z, which implies that asset markets are incomplete as in Huggett (1993) and Aiyagari (1994).

2.2 Households

The model economy is populated by a continuum of infinitely-lived households. Each household maximizes its expected lifetime utility by choosing consumption, c _t , and hours worked, h _t :

subject to

and

where σ is the inverse intertemporal elasticity of substitution, χ > 0 denotes a parameter for disutility from working, and ν is a parameter for a curvature in preferences over hours of work. B _t denotes the cumulative discounting between period 0 and t, i.e. B t = ∏ s = 0 t β s . In each period, an individual household is endowed with a unit of time, which is allocated between hours worked and leisure. We consider factors that generate nonconvex budget sets to operate adjustment along both the intensive and extensive margins of labor supply. A household with labor efficiency of z providing h units of time will generate φ(h)z efficiency units of labor, where φ(h) is the mapping from time devoted to work into units of labor services. As in Rogerson and Wallenius (2009) and Chang et al. (2019), we consider a nonconvexity that takes the form with time costs:

where 0 < Δ _h < 1 is time costs. The above functional form implies that (i) time costs arise at any time in which hours devoted to market work are positive, and (ii) hours of market work have a convex relationship with labor earnings. Accordingly, when a household supplies h units of labor, it earns w _t z _t φ(h _t ) as labor income, where w _t is the wage rate per effective unit of labor. Households can trade a claim for financial assets, a _t , which yields the real rate of return, r _t . Each household earns profit income, ξ _t , from firms. A household faces a borrowing constraint that limits the fixed amount of debt: the assets holding, a _t+1, should not be less than a ̲ for all t.

We define ω and Ω as the vectors of individual and aggregate state variables, respectively: ω ≡ (β, a, z) and Ω ≡ ( μ , S ) , where μ(ω) is the type distribution of households, and S denotes a vector of aggregate shocks.^[6] The value function for a household, denoted by V(ω, Ω), is defined as:

subject to

and

where Γ denotes a transition operator for μ.

2.3 The Representative Final Goods Producing Firm

It is assumed that the representative final goods producing firm operates in a competitive sector. The final goods firm uses y _t (j) units of each intermediate good j ∈ [0, 1] to produce a homogeneous output, Y _t , according to the constant-return-to-scale technology given by:

where ϵ > 1 is the elasticity of substitution for intermediate goods. The firm in this sector takes the final goods price, P _t , as given and purchases each of its inputs at the nominal price p _t (j), where p _t (j) is the price of the jth intermediate input. The profit maximization problem of the representative final goods producing firm is given by:

subject to Equation (3). The first order condition for the final goods firm’s problem and the zero profit condition yield the demand for intermediate good j:

2.4 Intermediate Goods Producing Firm

There is a continuum of monopolistically competitive firms indexed by j ∈ [0, 1], each of which produces a different type of intermediate good, y _t (j). Intermediate goods producing firms employ k _t (j) units of capital and n _t (j) units of effective labor in order to produce y _t (j) units of intermediate good j. Their production technology is represented by the Cobb–Douglas function:

where A _t is aggregate productivity, α is capital income share, and Δ _f ≥ 0 is the fixed cost of production.^[7] Aggregate productivity, A, follows a stationary AR(1) process in logs:^[8]

The cost minimization problem implies that intermediate goods producing firms must all have the same real marginal cost, mc _t , and capital-labor ratio, and i.e.

where Θ = (1 − α) ^α−1 α ^−α , and r t d = r t + δ . Price adjustment costs are introduced to generate sticky prices. Following the price setting mechanism as in Rotemberg (1982), we assume that when intermediate goods firms adjust their prices, they pay quadratic costs. Accordingly, an intermediate goods producing firm, j, maximizes its expected discounted profit by choosing its price p _t (j):

where, Λ _t,t+τ is the stochastic discount factor,^[9] θ > 0 represents the extent of nominal stickiness, and Π ̄ is the steady-state gross inflation. In the symmetric equilibrium conditions, i.e. p _t (j) = P _t and y _t (j) = Y _t ,^[10] the first order condition associated with the optimal price implies:

2.5 Mutual Fund and Central Bank

We follow Gornemann, Kuester, and Nakajima (2016) and assume that a representative mutual fund trades assets owned by all the households in the economy. This implies that there is no portfolio decision by individual households in the model economy. Mutual fund determines the price of claims based on the its shareholders’ period-to-period valuation, so it is important how to define the stochastic discount factor. We need to first discuss how monopoly profits from intermediate goods producing firms are distributed, since this issue is closely related to the definition of the stochastic discount factor. Similar in spirit to Kaplan, Moll, and Violante (2018), we assume that dividend, D, is proportionally distributed according to both asset holdings of households and labor efficiency of employed households:

where ψ a = a ∫ a d μ , ψ z = z ∫ z d μ E , γ is the fraction of profits for assets, 1 _h(β,a,z)>0 is an indicator function for working households, and μ ^E is the type distribution conditional on working. Accordingly, we can define the stochastic discount factor between t and t + 1, denoted by Λ _t,t+1:

where u _c (⋅) is the marginal utility of consumption.^[11] Note that the stochastic discount factor here is consistent with the distribution of profits described in Equation (4). We follow Woodford (1998) and assume that the gross nominal interest on risk-free bonds, R t f , is controlled by the central bank. Accordingly, the optimal bond investment decision of the mutual fund leads to a standard Euler equation:

where Π _t+1 is the gross inflation rate, P t + 1 P t . Q _t is aggregate demand shocks, which follow a stationary AR(1) process in logs:

The gross nominal interest rate on risk-free bonds, R t f , is assumed to follow a conventional Taylor rule by stabilizing the inflation and output gaps:

where ϕ _Π > 1, ϕ _Y ≥ 0, and R f ̄ and Y ̄ are the deterministic steady-state values of the corresponding variables.

2.6 Definition of Equilibrium

A recursive competitive equilibrium is a value function V(ω, Ω), a transition operator Γ(Ω), a set of policy functions c ( ω , Ω ) , a ′ ( ω , Ω ) , h ( ω , Ω ) , k j ( Ω ) , n j ( Ω ) , p j ( Ω ) , y j ( Ω ) , and a set of prices w ( Ω ) , r ( Ω ) , R f ( Ω ) , Π ( Ω ) such that:

1. Individual households’ optimization: given w(Ω) and r(Ω), optimal decision rules c(ω, Ω), a′(ω, Ω), and h(ω, Ω) solve the Bellman equation, V(ω, Ω).

2. Intermediate goods firms’ optimization: given w(Ω), r(Ω), Λ(Ω, Ω′), and P(Ω), the associated optimal decision rules are k _j (Ω), n _j (Ω), and p _j (Ω).

3. Final good firm’s optimization: given a set of prices P(Ω) and p _j (Ω), the associated optimal decision rules are y _j (Ω) and Y(Ω).

4. The stochastic discount factor, Λ(Ω, Ω′), satisfies E Λ ( Ω , Ω ′ ) Q R f ( Ω ) Π ( Ω ′ ) = 1 .

5. The gross nominal interest rate, R ^f (Ω), satisfies the Taylor rule (Equation (6)).

6. Market clearing: for all Ω,

   1. labor market clearing: N(Ω) = ∫zφ(h(ω, Ω))dμ, where N(Ω) = ∫n _j (Ω)dj

   2. capital market clearing: K(Ω) = ∫adμ, where K(Ω) = ∫k _j (Ω)dj

   3. goods market clearing: Y(Ω) = C(Ω) + I(Ω) + Ξ(Ω) where Y(Ω) = AK(Ω) ^α N(Ω)^1−α − Δ _f , C(Ω) = ∫c(ω, Ω)dμ, I(Ω) = K′(Ω) − (1 − δ)K(Ω), and Ξ ( Ω ) = θ 2 ( Π ( Ω ) − Π ̄ ) 2 Y ( Ω ) .

7. Consistency of individual and aggregate behaviors: for all B 0 ⊂ B , A 0 ⊂ A , and Z 0 ⊂ Z ,

2.7 Calibration

In this subsection, we describe how we calibrate the model economy. Table 1 summarizes the parameter values used for the benchmark model. A simulation period in the economy is a quarter.

We set the inverse intertemporal elasticity of substitution (IES), σ, to 1. Following Chang et al. (2019) and Ma (Forthcoming), we choose the curvature parameter, ν, to be 1.^[12] Given the value of ν, the disutility parameter of working, χ, and the nonconvexity parameter, Δ _h , are chosen so that the employment rate is 70 percent, and the average hours conditional on working are 0.26. The latter moment comes from the fact that prime-age men spend around 41 h per week (out of 160 h) working. Similar in spirit to Kaplan, Moll, and Violante (2018), the borrowing limit, a ̲ , is set to −0.2, which implies that the maximum debt is around the quarterly average earnings of a household.

We then calibrate the parameters related to the heterogeneity in the time preference and labor efficiency. These parameters are set to match the key moments related to the wealth and earnings distributions, respectively. We calibrate parameters associated with labor efficiency as follows. We obtain the transition matrix T z , by discretizing the log-normal process using the algorithm developed in Tauchen (1986) with 11 values of labor efficiency (N _z = 11). We set ρ _z to 0.95, based on the empirical fact that individual labor efficiency shocks have a high persistence (Chang, Kim, and Schorfheide 2013; Floden and Linde 2001). We parameterize σ _z to target the earnings Gini index of 0.63 in the steady state. For the time preference parameter, we follow Gornemann, Kuester, and Nakajima (2016) and assume that each household has the same probability of drawing each of the two states. This means that the transition matrix for β is symmetric, i.e. T β ( L , L ) = T β ( H , H ) . Given T β ( L , L ) , T β ( L , H ) can be obtained by the condition that T β ( L , L ) + T β ( L , H ) = 1 . Accordingly, there are three parameters related to the stochastic time preference to parameterize: β _L , β _H , and T β ( L , L ) . We calibrate T β ( L , L ) to capture changes in the saving behavior between generations (Krusell and Smith 1998). To be specific, we choose T β ( L , L ) to target the average duration of discount factors of 40 years, following Gornemann, Kuester, and Nakajima (2016). Regarding the remaining parameters, β _L and β _H , we choose them so that the model economy generates the quarterly return to capital of one percent (4 percent annualized) and the wealth Gini coefficient of 0.78 in the steady state.

We choose ρ _A = 0.8 and ρ _Q = 0.7 as the persistent parameters for aggregate productivity and demand shocks, respectively. These values are estimated from Stock and Watson (2003) and Alpanda and Zubairy (2021). The standard deviations, σ _A and σ _A are set to align with the output volatility and the cyclical behavior of inflation (its contemporaneous correlation with GDP). The capital income share, α, and the quarterly depreciation rate, δ, are calibrated to be 0.33 and 2.5 percent, respectively. The production fixed cost, Δ _f , is set for intermediate goods firm to have zero profit in the steady state. The elasticity of substitution across intermediate goods ϵ is equal to 10, which implies that a steady-state markup is 11 percent. The parameter for the Rotemberg price adjustment, θ, is set to 100, implying that firms, on average, update their prices every four quarters, given the choice of the elasticity of substitution.^[13] As in Kaplan, Moll, and Violante (2018), we assume that the fraction of profits for asset holdings, γ, is the same as α, i.e. γ = α = 0.33.

The Taylor rule coefficients of inflation and output, ϕ _Π and ϕ _Y , are chosen to be 1.5 and 0.15, respectively, which are conventional values in the New Keynesian literature. The steady-state gross inflation, Π ̄ , is set to 1.

The main results of the paper will be discussed in the following order. First, we examine if the benchmark model economy (i) generates empirical features of the heterogeneity in wealth, income, consumption, and earnings, and (ii) produces empirically realistic aggregate dynamics – business cycle moments and the impulse response to the productivity shock. Then we include an additional monetary policy objective that aims to reduce any inequality variation in the economy. As a natural starting point, we augment the income Gini coefficient in the benchmark Taylor rule. We study aggregate and disaggregate welfare implications of this more “inclusive” monetary policy. Then, we consider several other monetary policy rules as alternatives, since Gini coefficients are hard to obtain in real-time and are not suitable in practice.

3.1 Cross-Sectional Distributions

The main objective of this paper is to investigate welfare implications of an inequality-targeting monetary policy. To this end, it is important for our model economy to produce empirically realistic heterogeneity across households. In Table 2, we compare the Gini coefficients for income, earnings, net asset holdings, and consumption in the model to U.S. data.^[14] The benchmark model successfully targets the wealth and earnings distributions in the U.S. data. The earnings and wealth Gini coefficients in the benchmark model are 0.63 and 0.77, respectively, which are almost comparable to what we observe in the U.S. data. Untargeted distributions are also reasonably reproduced by the benchmark model. The model economy fits the income distribution in the data. The income Gini index (0.58) in the model economy is very similar to that in the data (0.57). Consumption inequality is also well replicated by the model. The Gini index for consumption is 0.38 in the model, which is comparable to what is observed in the U.S. data (0.33). From the results, we argue that our benchmark model is successful in generating reasonable cross-sectional distributions as found in the U.S. data.

3.2 Aggregate Dynamics

3.2.2 Transmission of Aggregate Shocks

Next we discuss how both aggregate shocks affect the economy. The responses of the key aggregate variables to an expansionary one-percent total factor productivity (TFP) shock for 40 quarters of horizon are shown in Figure 1.^[20] The transmission mechanism of the technology shock in the benchmark model is in play through a rise in overall productivity at all firms. An expansionary TFP shock makes intermediate goods firms more productive, which leads to an increase in the demand for both labor and capital inputs and, in turn, their prices. This causes households to provide more hours devoted to work by adjusting both margins of labor supply. Consumption and savings at the same time rise due the increase in household incomes. Accordingly, output, consumption, and investment rise. As expected, profits or dividends positively respond to a favorable aggregate productivity shock. The expansion makes an aggregate supply shift to the right, so inflation falls. In response to the significant decline in inflation, the Fed decreases nominal interest rates on risk-free bonds (or the federal funds rate, FFR) following the Taylor rule. As discussed above, an expansionary technology shock decreases income inequality, mainly due to a rise in employment from the bottom of the income distribution (Castañeda, Díaz-Giménez, and Ríos-Rull 1998; Kwark and Ma 2021). The responses to technology shocks are comparable to the other HANK literature (i.e. Bayer, Born, and Luetticke 2020) both quantitatively and qualitatively.

Figure 1:

Impulse responses to TFP shock. Note: Impulse response to a one-percent TFP shock. For inflation and the FFR, the y axis shows changes in annualized percentage points, while for the remaining variables, the y axis shows percent changes. The real rate refers to the ex-post real interest rate. The x-axis shows quarters after the shock.

Figure 2 illustrates the effects of an expansionary one-standard-deviation demand shock on aggregate variables over a horizon of 40 quarters. Consistent with standard New Keynesian models, an unexpected increase in demand primarily impacts economic activity through a sudden rise in aggregate demand. As a result, firms demand more inputs, leading to an increase in real factor prices. This, in turn, allows households to allocate more hours to market work and accumulate more assets, ultimately boosting consumption and leading to an uptick in inflation.

Figure 2:

Impulse responses to demand shock. Note: Impulse response to a one-percent demand shock. For inflation, the FFR, and the real interest rate, the y axis shows changes in annualized percentage points, while for the remaining variables, the y axis shows percent changes. The real rate refers to the ex-post real interest rate. The x-axis shows quarters after the shock.

When comparing the impulse responses to supply and demand shocks, a significant finding emerges in the opposite reactions of income inequality. In response to favorable TFP shocks, income inequality decreases owing to the rise in employment from the lower end of the income distribution. Conversely, in the case of aggregate demand shocks, the counter-cyclicality of markups (or profits) dampens labor earnings for employed households.^[21] This negative income effect is relatively stronger for lower-income households, leading to a decline in their employment levels. However, among households that remain employed, labor supply adjusts primarily along the intensive margin, with higher-income households significantly increasing their working hours. This compositional shift results in a net increase in total hours worked, despite a reduction in overall employment. Consequently, income inequality rises, as reflected in an increase in the Gini index. The procyclical inequality dynamics, contingent upon demand shocks,^[22] are well documented by recent empirical studies, such as Dolado, Motyovszki and Pappa (2020) and Cantore et al. (2022). It is important to note that the calibrated relative size of TFP shocks is large, resulting in a weakly countercyclical income Gini coefficient in the benchmark model, as shown in Table 3.

4.1 Augmented Taylor Rule

Our primary interest is in studying how monetary policy with an explicit targeting of inequality affects aggregate and disaggregate outcomes, as well as economic welfare. In this subsection, we assume a hypothetical situation where the central bank switches its policy rule to a more inclusive one to reduce inequality fluctuations over the business cycles in the economy. Then, we compare the aggregate and distributional outcomes and economy-wide welfare obtained under this alternative policy rule to those derived under the benchmark policy rule. To this end, we first consider a simple policy experiment: the central bank includes an inequality measure into the Taylor rule. The income Gini coefficient is the most widely-used single-summary number for judging the level of inequality in a particular country or region. Also, relative to earnings and wealth, income is a more general dimension of inequality since this variable includes both labor earnings and income generated by wealth. Accordingly, we assume that, among various measures and dimensions of inequalities, the Fed considers the income Gini index as a targeting variable. That is, we impose that the central bank tries to achieve equity by reducing the variability of the income Gini coefficient. We consider the following Taylor rule, which augments the income Gini coefficient as the third objective:

where ϕ _G is a weight on the income Gini index, and G ̄ is the deterministic steady-state value of the Gini coefficient of income. While the augmented rule is quite straightforward to understand, there are two practical issues to be settled before bringing it into the model. First, we need to determine the right sign of the coefficient ϕ _G . As discussed above (in Table 3 and Figure 1), the income Gini coefficient is countercyclical over the business cycles. In this respect, a natural candidate for ϕ _G is a negative sign as the Taylor rule coefficient for output, ϕ _Y , is positive. In other words, the central bank sets a lower nominal interest rate when the income Gini exceeds its steady state level. As an accommodating monetary policy boosts real activity and employment, we could expect that it can reduce inequality because it is believed that employment is a major source of economic inequality (Baek 2021; Ma 2023). Assigning a negative reaction coefficient for a measure of inequality is also implemented in previous studies, such as Hansen, Lin, and Mano (2020). However, this is still an open question, since the general equilibrium effect may affect inequality in a very different manner than we expect (Colciago, Samarina, and de Haan 2019). Therefore, we consider both signs for ϕ _G in this experiment.

The other issue is the range of the weight for the income Gini index, ϕ _G . It is unclear to what extent a central bank needs to respond to inequality measures. There is no consensus regarding the value of ϕ _G , while there are some ranges of empirical estimates for ϕ _Π and ϕ _Y . Put differently, in terms of the Taylor rule considered above, we do not have prior knowledge regarding the suitable magnitude of ϕ _G . For this reason, we consider a reasonable range of values for ϕ _G in order to illustrate how this affects outcomes from both a quantitative and qualitative perspective. Specifically, we normalize the changes in the Gini coefficient with its standard deviation, and then vary the coefficient for a reasonable range. We assume that the central bank changes the annualized interest rate on risk-free bonds by up to 1 percent point in response to a change in one standard deviation of the logged income Gini index. This assumption leads to a range that runs from −0.3 to 0.3.

4.2 Should the Fed Care About Inequality?

4.2.1 Aggregate Welfare Effect of Inequality Targeting

Should a central bank consider inequality when setting a systematic monetary policy? This subsection discusses this question, which is the main focus of this paper. We explore the welfare implication of the systematic response of monetary policy to inequality. The systematic reform of monetary policy may affect the shape of the business cycle. Moreover, any new monetary policy rules could affect welfare-related economic variables differently. They could stabilize or destabilize employment (or output) and inflation.^[23] Accordingly, it is natural to ask whether a systematic reaction of monetary policy to the income Gini index could improve economic welfare. Toward this end, we change the Taylor rule coefficient for the inequality gap, ϕ _G , while keeping the response to the inflation and output fixed at the benchmark levels (ϕ _Π = 1.5 and ϕ _Y = 0.15). That is, our purpose here is not to find the optimal monetary policy. Instead, we are looking for possible improvements in policymaking by introducing an additional target variable in the monetary policy rule that describes the status quo well. Our main finding is that there is a possibility that conducting a more inclusive monetary policy by negatively responding to a deviation in income Gini from its steady state could improve the average welfare of households, although employment and the income Gini index become more volatile.

We compute the welfare effect of the policy reform for an individual household by comparing value functions between different policy regimes. Let E [ V ( a , β , z ; A , Q , μ , τ ) ] be unconditional expectation of the value function for an individual household under a policy regime, τ. The unconditional expectation is taken over aggregate states A and μ, which is nothing but the long-run average welfare (or the value function) for each household type. Let τ′ be a new policy regime. Then the welfare effect of a regime change from τ to τ′ can be expressed as the consumption-equivalent measure, λ, which satisfies:

(8) E [ V ( a , β , z ; A , Q , μ ; τ ′ ) ] = E [ V ( a , β , z ; A , Q , μ ; τ , λ ) ] ,

where

E [ V ( a , β , z ; A , Q , μ ; τ , λ ) ] = max E 0 ∑ t = 0 ∞ B t log ( 1 − λ ) c t − χ h t 1 + 1 / ν 1 + 1 / ν

subject to the budget constraint (1) under a policy regime τ. It should also be noted that λ depends on individual state variables, i.e. λ = λ(a, β, z). Positive (Negative) λ means that the household is better off (worse off), relative to the benchmark policy regime.

Figure 3 shows the welfare consequences of switching to an inequality-targeting monetary policy with different values of the weight on the income Gini index, ϕ _G . Specifically, the welfare effects in the figure are measured as the average consumption-equivalent welfare gains, λ ̄ ( = ∫ λ ( a , β , z ) d μ ) . As found in Figure 3, the systematic change in monetary policy generates different welfare consequences from both the qualitative and quantitative perspective, depending on the size of the Taylor rule coefficient for the inequality gap, ϕ _G . The key quantitative finding is that the systematic reaction of monetary policy to inequality could be welfare-improving. The figure suggests that there is a region of ϕ _G that generates welfare gains. Specifically, households are better off on average when ϕ _G has a value between −0.2 and 0. Notably, the welfare gain peaks when ϕ _G = −0.06: the average consumption-equivalent welfare increases by 0.0216 percent compared to the benchmark model. This suggests that households benefit when central banks reduce the policy rate in response to inequality surpassing its long-run value. This finding is broadly in line with recent research, such as Acharya and Dogra (2020), Bhandari et al. (2021), Le Grand, Martin-Baillon, and Ragot (2020), who generally concur that monetary policy should be more accommodative during recessions (and conversely tighter during expansions) to alleviate inefficient fluctuations in inequality.

Figure 3:

Welfare effect of inequality targeting. Note: This figure shows the average consumption-equivalent welfare gains from a switch from the benchmark Taylor rule to one with a different weight on the income Gini index, ϕ _G .

Interestingly, in an economy where TFP shocks are the sole source of the business cycle, the value of ϕ _G at which the welfare gain peaks is −0.11, smaller than that of the benchmark model. In this scenario, households experience even greater improvement (0.0314 in consumption-equivalent units). This is mainly because the income Gini coefficient exhibits strong countercyclicality in the model with TFP shocks. In essence, in the benchmark model where both aggregate demand and supply shocks – each with opposing effects on income Gini dynamics – are considered, central banks need not respond as strongly to inequality variations to achieve welfare-improving reforms. This is because, as is well-known, markups are countercyclical conditional on demand shocks in a sticky-price setting. This implies that households have some degree of aggregate insurance against these shocks, lessening the need for substantial central bank intervention. Conversely, in the presence of TFP shocks where markups are procyclical, a stronger level of aggregate insurance is necessary to enhance welfare in the economy.

We also examine various measures to assess income inequality within the economy, with the outcomes presented in Table 4. One such measure is the quintile share ratio, defined as the ratio of total income received by the top quintile to that received by the lowest quintile. Another measure under consideration is the top 20 % income share. Irrespective of the inequality metrics utilized, the main message remains consistent: an inclusive monetary policy (where central banks reduce the policy rate when inequality surpasses its long-run value) could be welfare-improving. These findings are unsurprising, given the high correlation among the three measures.

Table 4:

Welfare effect with various specifications.

	Gini (both shock)	Gini (TFP shock only)	Quintile share ratio	Top 20 % share
ϕ G *	−0.06	−0.11	−0.03	−0.07
Welfare	0.0225	0.0314	0.0126	0.0139

1. Note: ϕ G * is the value at which the welfare gain peaks.

4.3 Disaggregate Welfare Effect: Who Benefits the Most?

As discussed above, monetary policy reform shapes the business cycles, and this will, in turn, affects household decisions. To restate it, switching to an inequality-targeting monetary policy with a small negative ϕ _G allows households to benefit from the reduced fluctuation in output or consumption, but this policy hurts households due to there now being more volatile inflation. In this unequal society, the extent to which households are exposed to the changes in the business cycles may be significantly different, depending on how they are well-insured. There are mainly two channels in our model economy through which households can insure against business cycle fluctuations: savings (or wealth) and labor supply. On the one hand, households that hold enough wealth are reasonably well insured, as found in standard incomplete market models. On the other hand, households also can adjust their labor supply to insure against business fluctuations (Cho, Cooley, and Kim 2015).^[25]

Table 6 shows the welfare effects of a switch from the benchmark monetary policy rule to one with ϕ _G = −0.06 by household type. Specifically, the table reports the consumption-equivalent welfare gains by labor efficiency (z), time discount factor (β), and net wealth (a), i.e. λ(a, β, z).^[26] As far as time discount factor heterogeneity is concerned, as expected, impatient households tend to have higher welfare gains than patient households. Households with the smaller time discount factor are willing to pay as much as 0.0261 percentage of their lifetime consumption for monetary policy reform, while the consumption-equivalent welfare gain for patient households is 0.0171 percent. Households with a lower preference for future consumption tend to be less affected by the destabilized inflation, which makes future consumption more uncertain.^[27] This is a well-known finding in the literature studying welfare analysis, in the presence of incomplete markets with time discount factor heterogeneity (Gornemann, Kuester, and Nakajima 2016; Krusell et al. 2009).

An important discovery reveals that, on average, households in the middle range of productivity distribution benefit more from an inequality-targeting monetary policy.^[28] As shown in Table 6, the welfare gain of households in the third efficiency group (Z3) is 0.223 percent in consumption equivalents, which is larger than that of households in Z1 and Z4. This pattern of the welfare gain can be attributed to the labor supply channel. In the model economy, households can insure against the business cycles by adjusting both margins of labor supply: being employed or providing more time devoted to work. The effects from this channel will be substantially different across households, since nonlinear mapping generates huge heterogeneity in labor supply elasticity across households. As discussed in Ma (2023), the non-linear budget constraint endogenously creates a different pattern of labor supply elasticity over the level of labor efficiency, and the substantial heterogeneity in labor supply elasticity is mainly due to the extensive margin. Essentially, households positioned in the middle of the labor efficiency distribution can adjust both their employment status and hours worked to mitigate the effects of aggregate fluctuations. Conversely, the most productive households are predominantly already employed, thus limited to adjustments solely on the intensive margin as an insurance mechanism. Similarly, the majority of households with the lowest productivity struggle to hedge against aggregate shocks due to their limited employment opportunities.

Lastly, regarding the asset dimension, consumption-equivalent welfare gains are U-shaped across wealth levels. The U-shaped welfare effects may be attributed to the relative availability of means of insurance – labor supply and wealth – against consumption risk among households. In particular, on the one hand, the wealth-poor are likely to utilize larger labor supply elasticity. That is why the welfare gains are largest for the wealth-poorest (households at the bottom 30 percent). On the other hand, as found in standard incomplete market models, wealth is an important tool of a household’s ability to smooth its consumption path. Wealthy households can use their savings to insure against the business cycle. This savings channel also works in this model economy: the welfare of the wealthiest is relatively large.

Who benefits the most from a systematic response by monetary policy to inequality? To answer this question, it is more instructive to take a closer look at the labor supply and savings channels. To this end, we report the welfare gains in greater detail in Figure 4.^[29] The upper and bottom panels in Figure 4 show the welfare effects for patient and impatient households, respectively (households with high and low time discount factors, β _H and β _L , respectively). In each panel, the horizontal axis shows the asset holdings of households by decile of the wealth distribution. For each decile, four household groups by labor efficiency (from lowest to highest) are reported using bars with different colors (red, yellow, purple, and green). We first discuss the asset channel. As shown in the upper panel of Figure 4, the welfare gains of households with the higher time discount factor tend to show an increasing pattern over asset holdings since they can use their savings to insure against the business cycle. The savings channel is clearer for productive and patient households. For these households, the labor supply channel is relatively small since most of them are already employed, and provide enough time devoted to work. For example, the consumption-equivalent welfare gain for the most productive households in the lowest wealth group is negative while it is around 0.03 for the corresponding households in the highest decile.

Figure 4:

Welfare gains of switching to ϕ _G = −0.06. Note: This figure shows the consumption-equivalent welfare gains of a switch from the benchmark Taylor rule to one with ϕ _G = −0.06, by the type of household: time discount factor (β), net wealth (a), and productivity (z). The dashed horizontal lines show the average welfare gain.

As far as the labor supply channel is concerned, this channel considerably affects households with lower labor efficiency. As seen in Figure 4, the welfare gain for less productive households tends to be relatively large, especially among wealth-poor households. For example, conditioning households with a higher time discount factor (the upper panel of Figure 4), the consumption-equivalent welfare gain for the least efficient households (Z1) in the lowest wealth group is around 0.02 percent while it is negative for the most productive households (Z4) in the same wealth group. The effect of the labor supply channel seems decreasing with the level of asset holding due to the conventional wealth effect. This finding implies that the savings channel is more dominant for households with a higher time discount factor while impatient households benefit more from the labor supply channel.^[30]

Importantly, it is impatient wealth-poor households with lower labor efficiency that have the biggest welfare gains from the monetary policy reform. The wealth-poorest households in the first or second productivity group gain around 0.03 percent if they are impatient, which is around 40 percent larger than the average welfare gain. This result implies that explicit inequality-targeting can improve the welfare of the poorest the most. It should be noted that for these households, the labor supply channel is more dominant than the savings channel. Who benefits the least? Patient and productive households at the bottom 30 percent of the wealth distribution gain the least welfare, since the effects from the two channels are very limited for them – lower labor supply elasticity and limited asset holdings.

In short, a monetary policy that explicitly considers the income Gini index as a targeting variable can improve economic welfare. The welfare gains are heterogeneous across households, but the poor can benefit more from this policy. This result is comparable to that in the previous literature that studies the welfare implication of a more inclusive monetary policy. In particular, Hansen, Lin, and Mano (2020) find that when the consumption gap between Ricardian and rule-of-thumb households widens within a two-agent New Keynesian model with no savings or investment, a more inclusive monetary policy can improve social welfare by becoming more accommodative. Similarly, Baek (2021) develops a New Keynesian model with regular and irregular labor types and finds that reducing the variation of the size of irregular employees can improve welfare on average.

4.4 Discussions

4.4.1 Paradox of Inequality Targeting

The systematic response of monetary policy to inequality has a critical limitation, even if it can be welfare-improving. According to Table 5, the cyclical variation in income inequality over the business cycle is larger in a monetary policy with ϕ _G = −0.06 than that in the benchmark model, even if this policy makes households in the economy better off.

To intuitively understand this paradoxical result, we compare the responses of key aggregate variables to an expansionary one-percent TFP shock in the benchmark model with those in the model with inequality targeting, as shown in Figure 5. Consider a hypothetical scenario where a favorable TFP shock impacts the economy, leading to an increase in output and a decrease in inflation. Since the inflation rate falls by more than the nominal interest rate, this results in a rise in the real interest rate.^[31] As the income Gini tends to be countercyclical, it also decreases. When we introduce an additional inequality target, the real interest rate rises even more compared to the benchmark without it.

Figure 5:

Impulse responses to TFP shock. Note: Impulse response to a one-percent TFP shock. For inflation and the real rate, the y axis shows changes in annualized percentage points, while for the remaining variables, the y axis shows percent changes. The real rate refers to the ex-post real interest rate. The x-axis shows quarters after the shock.

On one hand, the rise in the real rate reduces aggregate demand, leading to decreased cyclical fluctuations in output, as seen in Table 5. This means the central bank provides additional insurance only when the income Gini deviates from its steady-state value, indicating that with inequality targeting, the central bank takes extra steps to stabilize the economy by reducing inequality and offering insurance against consumption risks for lower-income brackets. On the other hand, as previously discussed, inequality targeting generates larger fluctuations in inflation. To hedge against volatile inflation, households adjust their labor supply. Employment dynamics become crucial, especially for less productive households. Lower-income households, previously non-employed, start working when the shock hits, leading to heightened employment volatility, as shown in Table 5. As a result, when a positive TFP shock occurs, the increased employment among lower-income groups contributes to reduced income inequality. Therefore, greater employment volatility leads to larger fluctuations in income inequality.

To clarify this mechanism further, it is crucial to examine whether less productive households are additionally employed during expansions. Figure 6 illustrates employment decision rules over productivity and asset (for high-β households) in both the benchmark model and the model with ϕ _G = −0.06 when a TFP shock increases by one standard deviation. In the figure, a blue color (value = 2) indicates that types are employed in both economies, a red color (value = 1) implies that a type is employed only in the model with ϕ _G = −0.06, and a white color (value = 0) signifies that types are not employed in either economy. As depicted in the figure, under the inclusive monetary policy, households with lower asset levels find employment opportunities increasing during economic upswings.

Figure 6:

Employment decision rules. Note: Employment decision rules over productivity and asset (conditioning on high β) in both the benchmark model and the model with ϕ _G = −0.06 when a TFP shock increases by one standard deviation. In the figure, a blue color (value = 2) indicates that types are employed in both economies, a red color (value = 1) implies that a type is employed only in the model with ϕ _G = −0.06, and a white color (value = 0) signifies that types are not employed in either economy.

This finding is a bit puzzling because the central bank intended to reduce the inequality variation by including the inequality gap in the monetary policy rule, but it ends up increasing the volatility of inequality. Hence, we refer to this anomaly as the paradox of inequality targeting. This paradox has an important policy implication. Social welfare is not directly observed in reality. Accordingly, in spite of its welfare improvement, an explicit targeting of inequality can be considered a failed policy due to the more volatile income Gini.

4.4.2 Efficiency-Equity Trade Off

Related to the paradox of an inequality-targeting monetary policy, another interesting finding is that there is a trade-off between output and inequality variations. According to Table 5, a more inclusive monetary policy with ϕ _G = −0.06 decreases cyclical variations in output, but increases fluctuations in income inequality over the business cycle. When ϕ _G = 0.06, on the contrary, the size of the output response increases, but the size of the income inequality response decreases, compared to those in the benchmark economy. This means that it is not possible to reduce the variability of the Gini coefficient by implementing a more accommodative monetary policy. The only way that the economy can achieve less volatile inequality is to have a more hawkish central bank. Hence, there is a trade-off between equity and economic stability.

Specifically, Figure 7 shows the fluctuations (measured by the HP-filtered standard deviation) of output and income inequality with the business cycle frequency across different values of weights on the income Gini index, ϕ _G .^[32] The figure clearly shows an efficiency-equity trade-off. There is an inverse relationship between output and income inequality variations. For example, when ϕ _G = −0.3, the cyclical variations in output and inequality are 1.08 and 1.14 percents, respectively, while the corresponding values are 1.37 and 0.56 percents, respectively, in a case that ϕ _G = 0.3. This result implies that an economy should sacrifice a more volatile output in order to have smaller cyclical variations in income inequality.

Figure 7:

Efficiency-equity trade off. Note: This figure shows the cyclical variations (standard deviation) in output and the income Gini index across different weights on the income Gini index, ϕ _G . Output and the Gini coefficients are quarterly values. Both variables are logged and detrended by the HP filter.

5.1 More Accommodative Policy

To begin with, we vary the benchmark Taylor rule to gauge the possibility of stabilizing inequality and improving welfare. To be precise, since the income Gini is countercyclical in the model, a more accommodative monetary policy may reduce the volatility of output and inequality at the same time. We postulate a more accommodative policy, while maintaining the dual mandate, by increasing the response of the interest rate to the output gap, ϕ _Y . This seems to be a natural starting point given the countercyclical nature of the income Gini coefficient.

Table 7 reports cyclical variations of the welfare and inequality-related variables and the welfare gains or losses under new monetary policy rules with various values of ϕ _Y . Similar to the previous analyses, more accommodating policies result in a more stable output at the expense of volatile inflation. For example, when ϕ _Y = 0.25, the cyclical variations in output and inflation are 1.10 and 0.39, respectively, while the corresponding values in the benchmark model are 1.23 and 0.31. These are obvious consequences since these policies have accommodative characteristics compared to the benchmark model. Moreover, employment and the income Gini also become more volatile as in the previous analyses. Under the more accommodative monetary policy with ϕ _Y = 0.25, the volatilities of employment and the income Gini coefficient are 1.20 and 0.83, respectively, which are larger than those in the benchmark economy. As discussed above, in this case, households in the lower income group rely more on their employment to hedge against aggregate shocks, which increases the inequality variation.

Next, the welfare gains under the new policies are evaluated in the last column of Table 7. When the central bank reacts stronger to the output, households are always worse off with values of ϕ _Y under consideration. This is mainly due to the significant increase in the inflation variation. When ϕ _Y = 0.25, for instance, the average household is willing to forgo about 0.0125 percent of its consumption every period to stay in the benchmark economy.^[33] This is a well-known finding in the optimal monetary policy literature. For example, Schmitt-Grohe and Uribe (2007) show that the welfare costs of a more accommodating monetary policy can be large, thereby underlining the importance of not responding to output. Therefore, attempts to achieve higher welfare through a more accommodative monetary policy have not been successful.

The reason why a more accommodating monetary policy yields different outcomes compared to directly targeting inequality is as follows. While both policies involve additional stabilizing efforts over the business cycle, the distinction lies in their mechanisms of providing insurance. In the case of a more inclusive monetary policy, it offers a form of insurance against consumption risk for those at the lower end of the income distribution, as the central bank stabilizes the economy in response to decreased inequality. On the other hand, a more accommodating monetary policy targets the efficiency unit of labor rather than employment or relative earnings/income. This approach does not necessarily guarantee greater benefits for poorer households. For example, the central bank might achieve its goal of stabilizing output (efficient units of labor) by also providing insurance to highly productive households. In this case, the resulting welfare gain may even be negative, as it could result in excessive insurance for productive households.

5.2 Employment Targeting

According to the Federal Reserve Act of 1977, which modified the original act establishing the Federal Reserve in 1913, the Fed’s goals include maximum employment, not maximum GDP. To be more precise, the Act clarified the roles of the Board of Governors and the Federal Open Market Committee (FOMC), by explicitly stating that the Fed’s goals include maximum employment, stable prices, and moderate long-term interest rates. Furthermore, many papers based on the incomplete market models show that employment is more closely related to inequality than aggregate output over the business cycles (Castañeda, Díaz-Giménez, and Ríos-Rull 1998; Chang and Kim 2007; Kwark and Ma 2021) or in the transmission of monetary policy (Baek 2021; Gornemann, Kuester, and Nakajima 2016; Ma 2023). Indeed, in our model, even if there is a strong positive relationship between output and employment, they may not always show the same direction over the business cycles. For example, if already employed households in the top productivity group increase hours of work, output can increase significantly without a rise in employment. Hence, employment may be a more valid proxy for an inequality target. Aggregate employment targeting also benefits from the fact that employment can be measured in a timely manner with higher precision, compared to Gini coefficients. In this regard, we modify the benchmark monetary policy rule and consider an additional employment target with a weight on the employment gap, ϕ _E :

where E _t and E ̄ are employment at t and its steady state value, respectively.

Table 8 reports the cyclical variations of the key variations and the welfare effects under alternative monetary policy rules with various values of ϕ _E . Similar to the more accommodative monetary policy rule, employment-targeting generates more stable output and more volatile inflation. For example, when ϕ _E = 0.20, the cyclical variations in output and inflation are 1.19 and 0.62, respectively, while the benchmark model produces the corresponding values of 1.23 and 0.31, respectively. Interestingly, similar to the paradox of inequality targeting, another anomaly is found in the employment-targeting monetary policy. Under this policy, employment becomes more fluctuating, although the central bank explicitly considers the employment gap as an additional target variable. When ϕ _E = 0.20, the cyclical variation in employment is 1.87, which is greater than the 1.13 in the benchmark economy, as is shown in Table 8. Intuitively, poor households tend to adjust the extensive margin of labor supply to hedge against inflation risks.^[34] The larger variation in employment ends up also making the income Gini coefficient more volatile, as in previous analyses. For example, in the model with ϕ _E = 0.20, the volatility of the income Gini index increases to 1.19, which is much larger than that in the benchmark model.

As far as the welfare effect is concerned, the last column of Table 8 reports the welfare gains under the employment-targeting rule. When the central bank considers an additional target of employment, it results in very unstable inflation, so households should pay welfare costs for any value of ϕ _E . When ϕ _E = 0.20, for instance, the welfare losses are 0.0383 percent. On average, households are willing to forgo about 0.04 percent of their life-time consumption to stay in the benchmark economy. Therefore, an employment-targeting monetary policy also fails to achieve higher welfare. This implication is in line with that in Baek (2021), where it is shown that targeting the aggregate unemployment gap is less preferred than targeting statistics related to different subgroups in the labor market.

5.3 Subgroup Employment Targeting

Lastly, we test whether monetary policy rules with an additional target regarding the employment of specific subgroups can improve welfare. In particular, we consider the following subgroup targeting rule: one cares about an employment gap for impatient households (low β). We think that the subgroup can reflect wealth-poor households in practice. This subgroup-targeting monetary policy is quite intuitive, since it is natural to think that the employment of poorer households may have a tighter link with inequality than aggregate-level employment.

This consideration has appeal on both the policy and academic sides. When it comes to calls for an “inclusive monetary policy” in policy circles, a substantial amount of discussion is associated with the economic well-being, including the employment, of disadvantaged groups, such as ethnic or racial minorities or low income families, not those of average households (Daly 2020; Powell 2020). In addition, while targeting only subgroups of the economy through a monetary policy has not been widely analyzed in the literature, research on this topic is becoming more common nowadays (Baek 2021; Bartscher et al. 2021). The analysis in this subsection tries to shed some light on the possibility of an inclusive monetary policy by targeting subgroups in the economy through the lens of a HANK model.

We evaluate the welfare gain for the case that the central bank additionally targets the employment of impatient households as shown below:

where E t β and E β ̄ are the number of employed among impatient households and its steady state value, respectively. As impatient households tend to retain a relatively smaller amount of assets, this rule can be implicitly interpreted as a policy rule that cares more about the economic conditions of low asset households. Before proceeding, we need to specify the values for ϕ _β . As in the previous analysis, we choose positive values for those parameters so that the central bank decreases its nominal interest rate more when the employment of impatient households goes below its steady state value.

Table 9 reports the cyclical variations of the key variations and the welfare gains under the subgroup-targeting monetary policy rule.^[35] A monetary policy with the subgroup employment-targeting results in less volatile output, but more volatile inflation. For example, when ϕ _β = 0.20, the cyclical variations in output and inflation are 1.16 and 0.43, respectively, while the corresponding values in the benchmark model are 1.23 and 0.31. It should be noted that similar to the case where the central bank includes the income Gini into the Taylor rule, employment becomes more fluctuating under the subgroup-targeting monetary policy rule. When ϕ _β = 0.20, the cyclical variation in employment is 1.43, which is greater than the 1.13 in the benchmark economy, as is shown in Table 9.^[36] The larger variation in employment leads to an increase in the income Gini coefficient variation, as in previous analyses. For example, in the model with ϕ _β = 0.20, the volatility of the income Gini index increases to 0.94, which is larger than that in the benchmark model. This result implies that the subgroup-targeting policy cannot address the paradox of inequality targeting either.

Importantly, when the central bank considers an additional target of subgroup employment, households can be better off. For example, when ϕ _β = 0.20, households are willing to forgo about 0.0180 percent of their life-time consumption to stay in the economy with this alternative monetary policy rule. While the changes in aggregate dynamics, such as lower output variation, can be attributed to higher welfare, it should be noted that the distributional dimension still matters and the targeted households benefit from this policy the most. To be precise, when ϕ _β = 0.20, the average welfare gain of the impatient households is 14 percent higher than those of the average household.

Therefore, the subgroup-targeting monetary policy rule – though more implementable – has a similar welfare effect as the monetary policy with an explicit targeting of the income Gini. In other words, welfare improvement can be achieved within a single implementable policy framework. This result calls for further research on the usefulness of a version of the subgroup targeting monetary policy as a tool for a more inclusive monetary policy.