Yuri Bedjanian
email: yuri.bedjanian@cnrs-orleans.fr

Reaction of O( 3 P) with Carbon Disulfide: Kinetics and Products

Keywords: carbon disulfide, oxygen atom, OCS, kinetics, atmospheric chemistry TOC

The kinetics and products of the reaction of ground-state O atom with carbon disulfide, of interest for atmospheric and combustion chemistry, were studied using a discharge-flow system combined with modulated molecular beam mass spectrometry. The total reaction rate constant was determined either in an absolute way from kinetics of CS 2 consumption and reaction product, SO radical, formation and employing a relative rate method with two reference reactions: k 1 = (3.35±0.10)×10 -11 exp(-(665±15)/T) cm 3 molecule -1 s -1 at T= 220-960 K, with estimated independent of temperature uncertainty of 15 %. The yields of two reaction products, SO and OCS, were determined at T = 220 -960 K, resulting in the following expressions for the branching ratio of the corresponding (SO + CS and OCS + S forming) reaction pathways: k 1a /k 1 = (0.935±0.005)×exp(-(7.4±0.2)/T) and k 1b /k 1 = (0.067±0.002)×exp(80±8/T), where the uncertainties reflect the statistical 2 precision. The reaction rate constant and product data from the present work are discussed in comparison with previous experimental and theoretical studies.

INTRODUCTION

Oxidation of reduced sulfur species such as H 2 S, OCS and carbon disulfide (CS 2 ) is of great interest for atmospheric chemistry, 1 combustion 2 and a number of industrial processes. [START_REF] Monnery | Modelling the Modified Claus Process Reaction Furnace and the Implications on Plant Design and Recovery[END_REF] In the present work, we report the results of an experimental kinetics and product study of the reaction of ground-state oxygen atom with carbon disulfide. CS 2 is one of the principal sulfur compounds in the atmosphere. Emitted by biomass burning, oceans and industrial processes, CS 2 is relatively rapidly oxidized in the troposphere (mainly, in reaction with OH radicals, lifetime of  1 week) leading to production of OCS. [START_REF] Seinfeld | Atmospheric Chemistry and Physics: From Air Pollution to Climate Change[END_REF] Tropospheric oxidation of CS 2 is an important source of OCS, the further photooxidation of which in the stratosphere leads to the formation of sulphate aerosols impacting the concentration of stratospheric ozone and the radiative properties of the atmosphere. [START_REF] Seinfeld | Atmospheric Chemistry and Physics: From Air Pollution to Climate Change[END_REF] O-atom initiated oxidation of CS 2 is negligible in the troposphere due to low concentrations of oxygen atoms; however, the title reaction can be an important removal process of CS 2 in the stratosphere upon direct injection of carbon disulfide into the stratosphere during volcanic eruptions. The estimated global volcanic input of CS 2 into the stratosphere is comparable with that of OCS: (1.3×10 7 -4.4×10 [START_REF] Slagle | Kinetics of the Reaction between Oxygen Atoms and Carbon Disulfide[END_REF] ) and (9.4×10 7 -3.2×10 [START_REF] Wei | Esr Study of the Kinetics of the Reactions of O( 3 P) Atoms with CS 2 and OCS[END_REF] ) g/yr, respectively. [START_REF] Halmer | The Annual Volcanic Gas Input into the Atmosphere, in Particular into the Stratosphere: A Global Data Set for the Past 100 Years[END_REF] In this respect, the information on the kinetics of the title reaction O + CS 2  products (1) at low stratospheric temperatures as well as at high near-source volcanic plume temperatures is of importance.

In the past, the kinetics of the title reaction has been extensively studied. [START_REF] Homann | Geschwindigkeit Von Elementarreaktionen Teil I[END_REF][START_REF] Smith | Rate Parameters for Reactions of O( 3 P) with CS 2 , NO 2 and Olefins[END_REF][START_REF] Westenberg | Atom-Molecule Kinetics Using Esr Detection. V. Results for O+OCS, O+CS 2 , O+NO 2 , and H+C 2 H 4[END_REF][START_REF] Callear | Flash Spectroscopy with Mercury Resonance Radiation. Part 1.-an Experimental Method with Microwave-Pulse Excitation[END_REF][START_REF] Slagle | Kinetics of the Reaction between Oxygen Atoms and Carbon Disulfide[END_REF][START_REF] Wei | Esr Study of the Kinetics of the Reactions of O( 3 P) Atoms with CS 2 and OCS[END_REF][START_REF] Graham | Temperature Dependence of Rate Constants and Branching Ratios for the Reaction of Oxygen Atoms with Carbon Disulfide[END_REF][START_REF] Hsu | Dynamics of Reactions of O( 3 P) Atoms with CS, CS 2 and OCS[END_REF][START_REF] Cooper | An Infrared Laser Study of the Atomic Oxygen (3P) + Carbon Disulfide Reaction[END_REF][START_REF] Borissenko | Experimental Study of SO 2 Formation in the Reactions of CH 3 SO Radical with NO 2 and O 3 in Relation with the Atmospheric Oxidation Mechanism of Dimethyl Sulfide[END_REF] The interest in this reaction was mainly due to its importance for the development of a chemical laser based on the emission of the vibrationally excited carbon monoxide formed in the sequence of the reactions:

O + CS 2  CS + SO (1a) O + CS  S + CO* (2)
The previous kinetic data obtained for k 1 in different and limited temperature ranges (between 218 and 500 K) are generally consistent within a factor of 1.5. However, only one measurement is available for k 1 at T > 500K. [START_REF] Homann | Geschwindigkeit Von Elementarreaktionen Teil I[END_REF] Reaction 1 has three exothermic channels: [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] O + CS 2  SO + CS  r H° = -19.4 kcal mol -1 (1a)

 S + OCS  r H° = -55.1 kcal mol -1 (1b)  CO + S 2  r H° = -83.1 kcal mol -1 (1c)
Information on the branching ratios of different reaction pathways as a function of temperature is important for atmospheric chemistry and combustion, CS 2 based laser performance and is of great fundamental interest for the theory of elementary reactions.

Despite this, the current quantitative data on the products of O+CS 2 reaction are extremely scarce and are limited to two determinations of k 1b /k 1 [START_REF] Slagle | Kinetics of the Reaction between Oxygen Atoms and Carbon Disulfide[END_REF][START_REF] Cooper | An Infrared Laser Study of the Atomic Oxygen (3P) + Carbon Disulfide Reaction[END_REF] and k 1c /k 1 . [START_REF] Hsu | Dynamics of Reactions of O( 3 P) Atoms with CS, CS 2 and OCS[END_REF][START_REF] Cooper | An Infrared Laser Study of the Atomic Oxygen (3P) + Carbon Disulfide Reaction[END_REF] The aim of this work was to fill the gaps in the available data on the kinetics and products of reaction 1 by measuring the total reaction rate constant and determining the branching ratios for the possible reaction pathways over an extended temperature range, T = 220 -960 K.

EXPERIMENTAL

Experiments have been carried out in a discharge-flow apparatus at total pressure of 2 Torr of Helium using electron-impact ionization (25-30 eV energy) mass spectrometry to measure the concentrations of the species involved. [START_REF] Morin | Experimental Study of the Reactions of OH Radicals with Propane, n-Pentane, and n-Heptane over a Wide Temperature Range[END_REF][START_REF] Bedjanian | Rate Constants of the Reactions of O( 3 P) Atoms with Br 2 and NO 2 over the Temperature Range 220-950 K[END_REF][START_REF] Bedjanian | Experimental Study of the Reaction of O( 3 P) with Carbonyl Sulfide between 220 and 960 K[END_REF][START_REF] Bedjanian | Rate Constant and Products of the Reaction of O( 3 P) Atoms with Thiirane over the Temperature Range 220-950 K[END_REF] The flow reactor used at low temperatures, T = 220 -320 K, consisted of a halocarbon wax coated Pyrex tube (45 cm length and 2.4 cm i.d.)

(Figure S1, Supporting Information (SI)). The temperature in the reactor was controlled by circulating thermostated ethanol. The high temperature reactor, employed at T = 300 -960 K, was an electrically heated Quartz tube (45 cm length and 2.5 cm i.d.) with water-cooled extremities (Figure S2, SI). [START_REF] Morin | Experimental Study of the Reactions of OH Radicals with Propane, n-Pentane, and n-Heptane over a Wide Temperature Range[END_REF] Oxygen atoms detected by mass spectrometry at their parent peak, m/z = 16 (O + ), were produced using two different methods: discharging of trace amounts of O 2 in He and through rapid reaction of N atoms (produced in a microwave discharge of N 2 /He mixtures) with NO, [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] To ensure accurate measurements of the absolute concentrations of O atoms, three independent methods were used, all of which gave consistent results with an accuracy of 10%.

N + NO  O + N 2 ( 2
)
k 2 = 2.1  10 -11 exp(100/T) cm 3 molecule -1 s -1 (T = 196 -370 K),
In

k 3 = (6.1 ± 0.4)  10 -12 exp((155 ± 18)/T) cm 3 molecule -1 s -1 (T = 220 -950 K), [START_REF] Bedjanian | Rate Constants of the Reactions of O( 3 P) Atoms with Br 2 and NO 2 over the Temperature Range 220-950 K[END_REF] and their absolute concentrations could be determined from the consumed fraction of NO 2 :

[O] = [NO 2 ]. Finally, the absolute concentrations of oxygen atoms could also be determined

using their titration by C 2 H 4 S ([O] = [SO] = [C 2 H 4 S]): O + C 2 H 4 S  SO + C 2 H 4 (4)
k 4 = 1.13×10 -12 (T/298) 2.18 exp(733/T) cm 3 molecule -1 s -1 (T = 220 -950 K) [START_REF] Bedjanian | Rate Constant and Products of the Reaction of O( 3 P) Atoms with Thiirane over the Temperature Range 220-950 K[END_REF] This procedure was also employed for the measurements of the absolute concentrations of SO.

All stable species (CS

' = k 1 [O]
. The consumption of oxygen atom was observed to be negligible (no more than a few percent) in all the experiments due to its high enough excess over CS 2 and relatively low rate of heterogeneous loss on the wall of the flow reactor (k w < 2 s -1 ). Examples of the observed concentration-time profiles of CS 2 are shown in Figure S3 (SI). Figure 1 shows the pseudofirst order rate constants,

k 1 ' = k 1 [O]
, as a function of the concentration of oxygen atoms. The slopes of the straight lines in Figure 1 (linear through origin fit to the experimental data)

provide the values of k 1 at respective temperatures, shown in Table 1.

For more confidence in the above measurements carried out in an excess of oxygen atoms, we conducted additional experiments (at T = 815 K), where k 1 was determined under pseudo-first order conditions, however, this time in an excess of CS 2 over the oxygen atoms.

Due to the difficulty of controlling low concentrations of oxygen atoms with mass spectrometry, in these experiments, the kinetics of SO formation was monitored. The kinetics of the reaction product follows the following expression:

[SO] = ×([O] 0 -[O] 0 ×exp(-k 1 't)),
where  is the branching ratio for SO forming channel of reaction (1) ( 0.93 at T = 815 K,

see below). Rearrangement of this expression results in [SO

]  -[SO] = [SO]  ×exp(-k 1 't), where [SO]  = ×[O] 0 and k 1 '  k 1 ×[CS 2 ]
, considering negligible heterogeneous loss of O atoms. In experiments, the kinetics of SO growth was monitored and [SO]  was determined upon total consumption of oxygen atoms. The observed dependence of the pseudo-first-order rate constant,

k 1 '  k 1 ×[CS 2 ],

Relative measurements of k 1 .

In this series of experiments, the rate constant of reaction 1 was determined using conventional relative rate method, which consisted of the measurements of the consumption of CS 2 and reference compound, NO 2 (reaction 3) or Br 2 , in reactions with oxygen atoms:

O + CS 2  products (1)
O + Br 2  Br + BrO (5) k 5 = 9.8510 -16 ×T 1.41 exp(543/T) cm 3 molecule -1 s -1 (T = 220 -950 K) [START_REF] Bedjanian | Rate Constants of the Reactions of O( 3 P) Atoms with Br 2 and NO 2 over the Temperature Range 220-950 K[END_REF] The relative consumptions of CS 2 and reference compound in the reaction with O-atoms are related by the ratio of the corresponding rate constants:

(I)
The These data as well as the final values of k 1 calculated with k 3 = 6.1  10 -12 exp(155/T) and k 5 = 9.8510 -16 ×T 1.41 exp(543/T) cm 3 molecule -1 s -1 (T = 220 -950 K) [START_REF] Morin | Experimental Study of the Reactions of OH Radicals with Propane, n-Pentane, and n-Heptane over a Wide Temperature Range[END_REF] are given in Table 2.

The possible impact of secondary chemistry on the results of the relative rate measurements can be discussed. When reaction 5 is used as a reference one, the most probable secondary reactions potentially leading to the additional consumption of CS k 8 = (9.5 ± 1.7)10 -11 cm 3 molecule -1 s -1 (T = 298 K) [START_REF] Clyne | Rate Constant Measurements for Rapid Reactions of Ground State Sulphur 3p 4 ( 3 P j ) Atoms[END_REF] Overall, the impact of the secondary reactions was minimized by use of the relatively low concentrations of CS 2 and Br 2 : (4 -5)×10 10 and ((5 -6)×10 11 molecule cm -3 , respectively, and short reaction time ≤ 0.01 s. Reactions of Br and BrO with CS 2 are too slow to contribute to CS 2 consumption. This could be verified directly by mixing Br and BrO, generated in the reaction of O atoms with excess Br 2 in the movable injector, with CS 2 in the main reactor. For example, the upper limit of 10 -15 cm 3 molecule -1 s -1 was determined for the rate constant of reaction 6 at T = 298 -960 K. Although the rate constant of reaction 8 is very high, S-atoms formed in reactions 1b and 2 are partly removed by O 2 , which was present in the reactive system in concentrations at least by two orders of magnitude higher than that of Br 2 :

S + O 2  SO + O (9)
k 9 = 1.610 -12 exp(100/T) cm 3 molecule -1 s -1 (T = 252 -878 K) [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] In addition, in order to minimize the possible contribution of reaction 8 to the consumption of Br 2 compared to the primary reaction with oxygen atoms, the initial concentrations of Br 2 in these experiments were more than an order of magnitude higher than those of CS , estimated total uncertainty on k 1 is nearly 20% and includes that on reference reaction.

Temperature dependence of k 1 .

All available kinetic data for the temperature dependence of k 1 are shown in Figure 3. One can note good agreement between the results obtained in the present work using different methods: the absolute one with monitoring of CS 2 and SO kinetics and relative rate method employing two reference reactions. The exponential fit to the present absolute measurements of k 1 (solid line in Figure 3) yields the following Arrhenius expression: k 1 = (3.35±0.10)×10 -11 exp(-(665±15)/T) cm 3 molecule -1 s -1 at T= 220-960 K, where quoted uncertainties represent statistical 2 precision on the fit. The overall uncertainty on k 1 was estimated to be about 15% combining statistical error (≤ 2%) and those on the measurements of the absolute concentration of O atoms (10%), flows (3%), pressure (2%) and temperature (1%).

The present value of the rate constant at T = 300 K, k 1 = (3.65±0.55)×10 -12 cm 3 molecule - 1 s -1 , is in good agreement with previous room temperature measurements (T = 298-302 K, not shown in Figure 3) of Callear and Hedges, 3.65, [START_REF] Callear | Flash Spectroscopy with Mercury Resonance Radiation. Part 1.-an Experimental Method with Microwave-Pulse Excitation[END_REF] Slagle et al., 4.0±0.3 [START_REF] Slagle | Kinetics of the Reaction between Oxygen Atoms and Carbon Disulfide[END_REF] and Borisenko et al., (3.6±0.1)×10 -12 cm 3 molecule -1 s -1 . [START_REF] Borissenko | Experimental Study of SO 2 Formation in the Reactions of CH 3 SO Radical with NO 2 and O 3 in Relation with the Atmospheric Oxidation Mechanism of Dimethyl Sulfide[END_REF] Temperature dependent data from the present work agree within the experimental uncertainty with previous measurements by Smith, [START_REF] Smith | Rate Parameters for Reactions of O( 3 P) with CS 2 , NO 2 and Olefins[END_REF] Westenberg and deHaas, [START_REF] Westenberg | Atom-Molecule Kinetics Using Esr Detection. V. Results for O+OCS, O+CS 2 , O+NO 2 , and H+C 2 H 4[END_REF] Wei and Timmons, [START_REF] Wei | Esr Study of the Kinetics of the Reactions of O( 3 P) Atoms with CS 2 and OCS[END_REF] Graham and Gutman. [START_REF] Graham | Temperature Dependence of Rate Constants and Branching Ratios for the Reaction of Oxygen Atoms with Carbon Disulfide[END_REF] However, the present measurements of k 1 at high temperatures are lower by a factor of 1.5-1.9 than those of Homann et al. (T = 695 -920 K). [START_REF] Homann | Geschwindigkeit Von Elementarreaktionen Teil I[END_REF] Homann et al., [START_REF] Homann | Geschwindigkeit Von Elementarreaktionen Teil I[END_REF] using an experimental setup similar to that of the present study, determined the rate constant of reaction 1 from the kinetics of CS 2 consumption and SO formation in an excess of O atoms over CS 2 . In our opinion, the most likely reason for the discrepancy between the two studies is the accuracy of the measurement of the absolute concentrations of oxygen atoms in the work of Homann et al., [START_REF] Homann | Geschwindigkeit Von Elementarreaktionen Teil I[END_REF] although, unfortunately, the relevant experimental details are not presented in their work. It can be added that in this work we used four different methods for determining k 1 at elevated temperatures (Figure 3), and all of them led to similar (within an uncertainty of 15%) values of the rate constant.

Current recommendation of the NASA Panel for data evaluation, k 1 = 3.210 -11 exp(-650/T) cm 3 molecule -1 s -1 at T = (218 -543) K (dotted line in Figure 3), [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] is practically identical to the Arrhenius expression for k 1 derived in the present study. In a theoretical study of the O+CS 2 reaction, Saheb [START_REF] Saheb | Quantum Chemical and Theoretical Kinetics Study of the O( 3 P) + CS 2 Reaction[END_REF] calculated the following non-Arrhenius expression for the overall rate constant: k 1 = 8.38×10 -13 ×T 0.54 ×exp(-506/T) cm 3 molecule -1 s -1 . The calculations of Saheb [START_REF] Saheb | Quantum Chemical and Theoretical Kinetics Study of the O( 3 P) + CS 2 Reaction[END_REF] are in very good agreement with our experimental data, although we do not observe a slight curvature of the Arrhenius plot predicted by theory (Figure 3). The rate of CS 2 removal in the stratosphere by atomic oxygen can be roughly compared with that in reaction with OH radical:

OH + CS 2  CS 2 OH (+O 2 ) products (12)
k 12 = (1.256×10 -16 exp(4550/T))/(T+1.81×10 -3 exp(3400/T)) cm 3 molecule -1 s -1 16

So, for example, at altitudes of 25-30 km, the rate constants of the respective reactions are: k 1  2×10 -12 cm 3 molecule -1 s -1 (this work) and k 12 ≤ 10 -11 cm 3 molecule -1 s -1 (upper limit because the recommended expression is for the total pressure of one atmosphere). [START_REF] Burkholder | Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies[END_REF] Considering that concentration of atomic oxygen at these altitudes (> 10 7 molecule cm -3 ) [START_REF] Anderson | The Absolute Concentration of O(³P) in the Earth's Stratosphere[END_REF][START_REF] Bekki | Stratospheric Ozone: History and Concepts and Interactions with Climate[END_REF] is by two orders of magnitude higher than that of OH radicals ( 10 5 molecule cm -3 ), [START_REF] Li | Tropospheric OH and Stratospheric OH and Cl Concentrations Determined from CH 4 , CH 3 Cl, and SF 6 Measurements[END_REF] the O-atom initiated oxidation of stratospheric CS 2 is much more efficient process compared with OH+CS 2 reaction, and should be taken into account when modeling the chemistry of sulfur compounds in the stratosphere.

Products of reaction 1.

Experiments were focused on the measurements of SO and OCS yields corresponding to the branching ratios for the reactions 1a and 1b, respectively.

The yield of SO in reaction 1 was measured relative to that in reaction of O atoms with thiirane (reaction 4), for which the yield of SO is known to be of nearly 100%. [START_REF] Bedjanian | Rate Constant and Products of the Reaction of O( 3 P) Atoms with Thiirane over the Temperature Range 220-950 K[END_REF] Experiments consisted in a consecutive titration of oxygen atoms with CS 2 and C 2 H 4 S and detection of the SO formed. Typical experimental data observed at extreme temperatures of the study are

shown in Figure 4. The branching ratios for the SO forming channel of reaction 1, determined at different temperatures between 220 and 960 K from slopes of the straight lines like those in Figure 4, are summarized in Table 3. In these experiments, the formed concentration of OCS was also measured as a function All the results obtained for k 1a /k 1 and k 1b /k 1 between 220 and 960 K are presented in Table 3 and Figure 6. The errors on k 1a /k 1 and k 1b /k 1 shown in the forming, channel of reaction 1 with a branching ratio of a few percent. Indeed, Slagle et al. [START_REF] Slagle | Kinetics of the Reaction between Oxygen Atoms and Carbon Disulfide[END_REF] in their molecular crossed beam study with photoionization mass spectrometry as a detection method observed, although not quantified, S 2 as the product of reaction 1. Hsu et al. [START_REF] Hsu | Dynamics of Reactions of O( 3 P) Atoms with CS, CS 2 and OCS[END_REF] and Cooper and Hershberger 14 reported the branching ratios of (1.4 ± 0.2) % and (3.0 ± 1.0) %, respectively, for the reaction channel (1c) based on the measurements of the other reaction product, CO.

Figure 1 .

 1 Figure 1. Pseudo-first order rate constant, k 1 ' = k 1 [O], as a function of the O-atom concentration at different temperatures.

  versus CS 2 concentration is shown in Figure S4 (SI). The slope of the straight line in Figure S4 provides k 1 (± 2) = (1.53±0.04)×10 -11 cm 3 molecule -1 s -1 at T= 815 K, in good agreement with the k 1 data obtained from the kinetics of CS 2 consumption (

Figure 2 .

 2 Figure 2. Examples of the dependence of ln([CS 2 ] 0 /[CS 2 ]) on ln(NO 2 ] 0 /[NO 2 ]) observed at different temperatures.

Figure 3 .

 3 Figure 3. Summary of the temperature dependent measurements of the rate constant of the reaction O+CS 2 . Partially shown error bars on the values of k 1 from the present study correspond to the estimated 15 and 20% uncertainties on the absolute and relative measurements, respectively.

Figure 4 .

 4 Figure 4. Yield of SO radicals in reaction of O atoms with CS 2 relative to that in reaction O+C 2 H 4 S upon consumption of the same concentration of oxygen atoms.

  of consumed concentration of oxygen atoms at T = 380 -960 K. However, in contrast to the relative measurements of SO yield, the determination of the branching ratio for the OCSforming channel of reaction 1 required the measurements of the relatively low absolute concentrations of oxygen atoms and those of OCS. The initial concentration of oxygen atoms was determined through their conversion to SO in reaction with excess thiirane: [O] 0 = [SO]. The methods employed for the absolute calibration of SO and OCS signals are given in the Experimental section. At lower temperatures (T = 220 -335 K), where the possible impact on [OCS] of the secondary reaction O + OCS  products (13)k 13 = 1.92×10 -12 ×(T/298) 2.08 ×exp(-1524/T) cm 3 molecule -1 s -1 at T= 220-960 K.[START_REF] Bedjanian | Experimental Study of the Reaction of O( 3 P) with Carbonyl Sulfide between 220 and 960 K[END_REF] could be neglected, we conducted a series of experiments in an excess of oxygen atoms over CS 2 . Reaction time was in the range (0.02-0.03) s and consumption of CS 2 was more than 95%. The formed concentration of OCS was measured as a function of [CS 2 ] consumed, i.e.only the stable species were involved in the determining of the branching ratio k 1b /k 1 . Some typical experimental data obtained with two methods are shown in Figure5. The slopes of the straight lines in Figure5provide the branching ratios for the OCS forming channel of reaction 1.

Figure 5 .

 5 Figure 5. Concentration of OCS formed in reaction of O atoms with CS 2 as a function of the consumed concentration of CS 2 or O atoms.

Figure 6 .

 6 Figure 6. Branching ratio of the SO+CS (k 1a /k 1 ) and S+OCS (k 1b /k 1 ) forming channels of the reaction O+CS 2 as a function of temperature. Partially shown error bars for the present data correspond to estimated uncertainty of 10 % on the measurements of k 1b /k 1 .

  the first one, the O concentrations were determined from the decrease in the O 2

	concentration upon initiation of the microwave discharge ([O 2 ] = 2[O]). In another method,
	oxygen atoms were titrated with an excess of NO 2 ,
	O + NO 2  NO + O 2

RESULTS AND DISCUSSION 3.1. Absolute measurements of k 1 . In

	He (carrier gas) and O 2 were taken directly from high-pressure tanks and had stated
	purities better than 99.99% (Alphagaz). NO 2 , NO were Alphagaz products (> 99.9%). The
	purities of CS 2 (Aldrich), OCS (15% in He, Messer), C 2 H 4 S (Merck) and Br 2 (Aldrich) were ≥
	99.9, 99.99, 98 and 99.99%, respectively.
	3. most experiments, the rate constant of the title
	reaction was determined from decays of CS 2 ([CS 2 ] 0 = (4-7)×10 10 molecule cm -3 ) monitored
	under pseudo-first order conditions in excess of oxygen atoms (see Table 1 for concentrations
	of O). Under the employed pseudo-first-order conditions, the concentration of CS 2 may be
	expressed as [CS 2 ] = [CS 2 ] 0 ×exp(-k 1 '×t) with the pseudo-first-order rate constant given by k 1
	2 , OCS, C 2 H 4 S, O 2 , NO 2 , NO and Br 2 ) were detected by mass
	spectrometry at their parent peaks. Their absolute concentrations were derived from measured
	flow rates of their manometrically prepared gas mixtures.

Table

Table 1 . Experimental Conditions and Results of the Absolute Measurements of the Rate Constant of Reaction 1

 1 0  1.5×10 11 molecule cm -3 ) to minimize the potential impact of the secondary

	reaction
	O + CS  CO + S

). It should be noted that initial concentration of O atoms in these experiments was low enough

([O]

  2 . Similarly, in the experiments where reaction O+NO 2 was used as a reference, to minimize the relative contribution of the reactions of S and SO with NO 2 much higher concentrations of NO 2

	compared to [CS 2 ] were used ([NO 2 ] 0 /[CS 2 ] 0 > 50):
	S + NO 2  SO + NO	(10)
	k 10 = 4.910 -10 exp(84/T) cm 3 molecule -1 s -1 (T = 296 -410 K) 22
	SO + NO 2  SO 2 + NO	(11)
	k 11 = 6.7×10 -12 exp(295/T) cm 3 molecule -1 s -1 (T = 220 -960 K) 23

Table 2 . Summary of the Relative Measurements of k 1

 2

	T (K)	k 1 /k ref (±2)	k 1 a	Reference reaction
	260	0.232±0.002	2.56	O+NO 2
	285	0.307±0.007	3.22	O+NO 2
	305	0.374±0.005	3.79	O+NO 2
	345	0.254±0.008	4.57	O+Br 2
	380	0.603±0.010	5.53	O+NO 2
	530	0.486±0.016	9.25	O+Br 2
	620	1.350±0.022	10.6	O+NO 2
	850	0.582±0.009	14.7	O+Br 2
	925	2.068±0.016	14.9	O+NO 2
	a Units of 10	-12 cm 3 molecule -1 s -1

Table 3 . Branching Ratio Data (%) for the Channels (1a) and (1b) of the O+CS 2 Reaction.

 3 The quoted errors represent the statistical 2 fit precision, the estimated total uncertainty on k 1b /k 1 is about 10%.

	T (K)	100 × k 1a /k 1 (± 2) a	100 × k 1b /k 1 (± 2) a	100 × (k 1a /k 1 +k 1b /k 1 )
	220	91.2±0.4	9.60±0.12	100.8
	235	90.3±0.6	9.90±0.06	100.2
	250	91.2±0.2	9.06±0.06	100.3
	270	91.1±0.2	8.88±0.08	100.0
	298	90.4±0.6	8.49±0.04	98.9
	320	91.5±0.6	9.01±0.02	100.5
	335	90.6±1.8	8.70±0.08	99.3
	380	91.0±1.4	8.17±0.11	99.2
	445	92.1±0.8	7.90±0.08	100.0
	545	92.2±0.6	7.70±0.07	99.9
	695	93.2±1.0	7.48±0.06	100.7
	960	92.9±0.6	7.52±0.06	100.4

a

  Table correspond to the statistical2 precision of the fit to the respective experimental data. The estimated total uncertainty on k 1b /k 1 is around 10% and is due to combined uncertainty on the measurements of the absolute concentrations of SO, OCS and CS 2 . The sum of the branching ratios for two reactions channels (1a) and (1b) shown in the last column of Table3is nearly 100 % at all temperatures of the study. However, this by no means excludes the possible presence of the third, CO+S 2


Alina K Bartscher

Moritz Kuhn
email: mokuhn@uni-bonn.de

Moritz Schularick
email: moritz.schularick@sciencespo.fr

Paul Wachtel
email: pwachtel@stern.nyu.edu

Klaus Adam

Adrien Auclert

James Bullard

Ellora Derenoncourt

Keshav Dogra

Michael Fleming

Linda Goldberg

Jordi Galí

Bev Hirtle

Ethan Ilzetzky

Chi Hyun Kim

Anna Kovner

Alexander Kriwoluzky

Keith Kuester

Òscar Jordà

David Lucca

Ben Moll

Emanuel Mönch

Gernot Müller

Marco Del Negro

Emil Holst Partsch

Pascal Paul

Anna Rogantini Picco

Andrea Tambalotti

Alan Taylor

John Williams

Monetary Policy and Racial Inequality

Keywords: JEL classification: E40, E52, J15 monetary policy, racial inequality, income distribution, wealth distribution, wealth effects _________________

This paper aims at an improved understanding of the relationship between monetary policy and racial inequality. We investigate the distributional effects of monetary policy in a unified framework, linking monetary policy shocks both to earnings and wealth differentials between black and white households. Specifically, we show that, although a more accommodative monetary policy increases employment of black households more than for white households, the overall effects are small. At the same time, an accommodative monetary policy shock exacerbates the wealth difference between black and white households, because black households own fewer financial assets that appreciate in value. Over a fiveyear horizon, the employment effects remain substantially smaller than the countervailing portfolio effects.

Introduction

The racial tensions that spread across the United States in 2020 attracted the attention of monetary policymakers. Fifty years past the accomplishments of the Civil Rights Movement, racial gaps in income and wealth remain enormous. There is widespread recognition thatdespite a decline in overt labor market discrimination and gains in educational opportunities since the onset of the Civil Rights movement -racial gaps persist and have even grown larger by some measures [START_REF] Bayer | Divergent Paths: A New Perspective on Earnings Differences Between Black and White Men Since 1940[END_REF][START_REF] Dettling | Recent Trends in Wealth-Holding by Race and Ethnicity : Evidence from the Survey of Consumer Finances[END_REF][START_REF] Kuhn | Income and Wealth Inequality in America, 1949-2016[END_REF][START_REF] Thompson | Updating the Racial Wealth Gap[END_REF][START_REF] Wolff | Household Wealth Trends in the United States, 1962 to 2016: Has Middle Class Wealth Recovered? Working Paper 24085[END_REF]. The size and persistence of the gaps between both the income and wealth of black and white households are striking [START_REF] Chetty | Race and Economic Opportunity in the United States: An Intergenerational Perspective[END_REF][START_REF] Emmons | Housing Wealth Climbs for Hispanics and Blacks, Yet Racial Wealth Gaps Persist, Federal Reserve Bank of St[END_REF]. According to the 2019 Survey of Consumer Finances (SCF), the median wealth of a white household was $181,400, compared to only $20,700 for the median black household, implying that the typical black household owns only about 11 percent of the wealth of the typical white household. The income ratio is smaller but still large: the median income of black households ($38,700) is 58 percent of the median income of white households ($67,200).

Traditionally, macroeconomists and monetary policymakers held the view that racial inequities were outside their purview. However, the view that central banks should pay attention to racial inequalities in income and wealth has recently gained ground. For instance, Raphael Bostic, president of the Federal Reserve Bank of Atlanta, suggests that the Federal Reserve "can play an important role in helping to reduce racial inequities and bring about a more inclusive economy." 2 Yet so far we lack a deeper understanding of how monetary policy impacts racial inequities, a topic that has for a long time received little attention from the research community. Our goal in this paper is to examine the effects of monetary policy on the income and wealth of black and white households.

One line of thinking that links monetary policy to distributional outcomes runs as follows: at the business cycle frequency, a more accommodative monetary policy lowers unemployment and increases labor income for workers who would otherwise have become or stayed unemployed. Marginal workers that are drawn into the labor market by such accommodative policies are often low-income and minority households. Consequently, the gap between unemployment rates of black and white households can be expected to shrink under a more accommodative policy. 3 In support of this view, [START_REF] Carpenter | The Disparate Labor Market Impacts of Monetary Policy[END_REF] find a higher sensitivity of black workers' labor market outcomes to monetary policy shocks. [START_REF] Coibion | Innocent Bystanders? Monetary Policy and Inequality[END_REF] call this effect on low-income workers the earnings channel.

Yet at the same time, monetary policy affects heterogeneous household balance sheets through its impact on asset prices [START_REF] Brunnermeier | Redistributive Monetary Policy[END_REF][START_REF] Kaplan | Monetary Policy According to HANK[END_REF]. Asset price changes will affect the racial wealth distribution if portfolios differ systematically between black and white households. Using SCF data, we show that portfolio heterogeneity is a very pronounced fact in the data: black households hold substantially different portfolios and in particular less financial assets than white households, so that monetary policy shocks potentially have larger effects on white households' portfolios. The median black household has no stock holdings, nor owns a house. Thus, any effect that monetary policy has on the price of such assets bypasses the majority of black households.

The effects could be particularly pronounced in the case of unconventional monetary policy, which explicitly aims at affecting asset prices [START_REF] Bernanke | The New Tools of Monetary Policy[END_REF][START_REF] Wu | Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound[END_REF].

In addition to the earnings and portfolio effects, monetary policy will impact interest rates and dividends directly. We call the effect on interest earnings on savings and bonds, dividend earnings and the gains or losses from mortgage refinancing the capital income effect. To the extent that black and white households' portfolios differ, there will be differential capital income effects of monetary policy.

Since accommodative monetary policy boosts asset returns, it is likely that the portfolio and earnings effects go in opposite directions. On the one hand, more accommodative monetary policy may benefit black households by reducing unemployment and increasing labor market participation and earnings, thereby helping to reduce the racial income gap -and over time even the wealth discrepancy, if part of the additional income is saved. But on the other hand, the same policies may widen racial wealth differences if white households benefit more from rising asset prices than black households due to their different portfolio composition and greater wealth. The capital income effects can go in either direction, since lower interest rates reduce household interest income but the opportunity to refinance mortgages at a lower rate can have positive effects on disposable income. This paper quantifies and compares the size of the earnings, portfolio and capital income effects of monetary policy. We begin with a comparative statics exercise, examining the impact of a given change in asset prices and interest rates. We then develop a unified empirical framework that uses instrumental variable local projections (LP-IVs) following [START_REF] Stock | Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments[END_REF] and Jordà, Schularick, and Taylor (2020) to study the effects of a monetary policy shock on asset prices, interest rates and black-white employment gaps over a five-year horizon. For this analysis, we rely on the most widely used monetary policy shock series --the (extended) Romer-Romer shocks [START_REF] Coibion | Innocent Bystanders? Monetary Policy and Inequality[END_REF]. We apply the asset price and interest rate changes to the portfolios of white and black households from the most recent SCF wave in 2019, and determine the effect on the net wealth of black and white households. We further combine the estimated effects on the unemployment gap with unemployment and earnings data from the SCF and compare them to the portfolio effects in response to the estimated monetary policy shocks over different time horizons.

Our core finding is that an accommodative monetary policy shock leads to larger employment gains for black households, but also to larger wealth gains for white households.

More precisely, the black falls more than the white unemployment rate after an unexpected accommodative interest rate shock. This translates into a relative earnings gain for the mean black household relative to the mean white household. Our results indicate that after five years, the relative cumulative earnings gain for black households is $134.

The same monetary policy shock pushes up stock prices by up to 5 percent, and house prices by 2 percent, while lowering bond yields on corporate and government debt and increasing dividend payments. Since portfolio size and composition of black and white households differ, there are large differences in the effects on the wealth of black and white households. For white households, we find that on average, a 100bp accommodative policy shock leads to a peak effect on capital gains from asset price changes of $25,000, which is about a quarter of their average annual income. The wealth gains for black households are substantially smaller, about $4,000, corresponding to 7 percent of their average annual income. The larger capital gains for white households mainly stem from the stock market, as most stocks are owned by white households. Although housing is more equally owned, capital gains from the housing market still fall disproportionately to white households, as do interest savings from lower mortgage interest rates. The effect of a policy shock on the earnings gap pales in comparison to its effects on the wealth gap.

Our empirical findings strongly suggest that monetary policymakers face a trade-off: Monetary accommodation widens racial wealth inequality as it reduces income inequality.

There is little reason to think that monetary policy can play a significant role in reducing racial inequities in both income and wealth at the same time. The conventional tools of monetary policy seem ill suited for these important tasks.

CHANNELS OF MONETARY POLICY EFFECTS.

There are at least three notable channels through which policy-induced asset price changes can affect the macroeconomy. First, asset price changes can affect household consumption through a standard wealth effect. [START_REF] Berger | House Prices and Consumer Spending[END_REF] demonstrate that a calibrated heterogeneous agent model is quantitatively consistent with large estimated asset price effects on consumption. In our setting, such wealth effects on the consumption of white households are under plausible assumptions substantially larger than the relative earnings effects for black households. For instance, estimates indicate that the marginal propensity to consume out of capital gains is about 3 cents per dollar. 4 This means that our estimated difference between the capital gain received by white and black households after five years, which is roughly $15,300, translates into additional consumption expenditures of around $500 -about four times our estimate of the cumulated relative earnings effect for black households over five years. An accommodative monetary policy shock would need to have a much larger effect on black unemployment and earnings than what is typically estimated in order to offset the impact of changes in asset prices on the consumption of white households.

Second, asset price changes lead to redistribution between prospective buyers and sellers of assets, as emphasized in [START_REF] Moll | Discussion of "Sources of US Wealth Inequality: Past, Present, and Future[END_REF]. Households planning to buy the asset that appreciates in value will experience welfare losses, while households who plan to sell will experience gains. For instance, households at different points of the life cycle differ in whether they plan to buy and sell assets (cf. also [START_REF] Greenwald | Financial and Total Wealth Inequality with Declining Interest Rates[END_REF]. [START_REF] Glover | Intergenerational Redistribution in the Great Recession[END_REF] explore such life-cycle redistribution with a focus on the consequences of the large asset price changes during the financial crisis. A similar logic can be applied to racial differences in asset holdings. If past discrimination in housing markets implies that black households are structurally "short" in housing and have plans to become homeowners, asset price increases would tend to make those households worse off.

Third, rising asset prices may also temporarily relax collateral constraints, e.g. for business formation. To the extent that such effects predominantly fall on white households, they can induce permanent effects on income and wealth through entrepreneurial activity [START_REF] Boerma | Reparations and Persistent Wealth Gaps[END_REF]. Similarly, after an accommodative monetary policy shock households can permanently lock in lower mortgage rates through refinancing. The evidence we present below is consistent with such permanent gains accruing predominantly to white households. This implies that even if monetary policy shocks only have temporary effects on asset prices, they can have persistent economic consequences. Moreover, our estimated effects of a policy rate shock on asset prices remain visible over a multi-year period, as in other recent research [START_REF] Paul | The Time-varying Effect of Monetary Policy on Asset Prices[END_REF]. Hence, even temporary policy shocks can alter the equilibrium characteristics of the economy with long-lasting effects.

PREVIOUS LITERATURE.

Much of the existing literature on the distributional consequences of monetary policy focuses on income and consumption inequality. [START_REF] Coibion | Innocent Bystanders? Monetary Policy and Inequality[END_REF] find that a contractionary monetary policy shock increases inequality in pre-tax incomes and consumption. They estimate the effects of monetary policy shocks in the spirit of [START_REF] Romer | A New Measure of Monetary Shocks: Derivation and Implications[END_REF] on aggregate inequality measures. Using a similar approach and administrative data from Norway, [START_REF] Holm | The Transmission of Monetary Policy under the Microscope[END_REF] find evidence that contractionary monetary policy shocks increase inequality in disposable income and consumption, but decrease wealth inequality. By contrast, [START_REF] Andersen | Monetary Policy and Inequality[END_REF] find an increase in disposable income inequality after an accommodative monetary policy shock.

They use Danish microdata and exploit the peg of the Danish krone to the euro in order to identify monetary policy shocks. Unlike the previous two studies, the authors consider households along the within-age total income distribution, and estimate inequality effects based on income effects at the household level, instead of estimating the effects on aggregate measures of inequality. While [START_REF] Andersen | Monetary Policy and Inequality[END_REF] find monotonically increasing effects of accommodative monetary policy shocks on disposable incomes along the income distribution, Amberg et al. (forthcoming) find U-shaped income effects based on Swedish administrative data. They identify monetary policy shocks with a high-frequency approach and study the effects on total post-tax income. Similar to [START_REF] Andersen | Monetary Policy and Inequality[END_REF], they compute inequality effects from income effects at the individual level. Due to the U-shape of income effects, the overall effects on income inequality depend on the considered in-equality measure. For instance, they find that inequality increases as measured by the Gini coefficient, yet decreases as measured by the ratio of the 90th to the 10th percentile.

Only a few papers have explicitly focused on the effect of monetary policy on wealth inequality. For instance, [START_REF] Adam | Distributional Consequences of Asset Price Inflation in the Euro Area[END_REF] use Euro-area data from the Household Finance and Consumption Survey to estimate the impact of changes in different asset prices along the wealth distribution. [START_REF] Albert | Monetary Policy and the Redistribution of Net Worth in the US[END_REF] use the high-frequency monetary policy shocks of [START_REF] Gertler | Monetary Policy Surprises, Credit Costs, and Economic Activity[END_REF] in a structural VAR model to estimate the effects on interest rates, dividends and stock and house prices. They link these effects to data from the 2016 SCF and find that an expansionary monetary policy shock increases wealth inequality, especially in the long run. Moreover, the effects of housing, stock prices and interest rates differ along the wealth distribution.

Although we are not aware of any other examination of the effect of monetary policy on the racial wealth gap, the size and persistence of the wealth gap has been shown in previous work, most recently by [START_REF] William | Just How Severe Is America's Racial Wealth Gap?[END_REF], [START_REF] Kent | Wealth Gaps between White, Black and Hispanic Families in[END_REF] and [START_REF] Aladangady | Wealth Inequality and the Racial Wealth Gap[END_REF]. The differential effect of monetary policy on black and white unemployment rates was observed in the 1990s, see for example [START_REF] Zavodny | Monetary Policy and Racial Unemployment Rates[END_REF]. [START_REF] Carpenter | The Disparate Labor Market Impacts of Monetary Policy[END_REF] find a higher sensitivity of black workers' labor market outcomes to monetary policy shocks. Finally, [START_REF] Rodgers | African American and White Differences in the Impacts of Monetary Policy on the Duration of Unemployment[END_REF] explores differential effects of monetary policy on the duration of unemployment for black and white workers. His evidence points towards a stronger effect on the unemployment duration of black workers than for white workers after contractionary monetary policy shocks.

Recent theoretical macro models with heterogeneous agents have emphasized the asset price channel of monetary policy transmission [START_REF] Auclert | Monetary Policy and the Redistribution Channel[END_REF][START_REF] Auclert | Micro Jumps, Macro Humps: Monetary Policy and Business Cycles in an Estimated HANK Model[END_REF][START_REF] Caramp | Monetary Policy and Wealth Effects: The Role of Risk and Heterogeneity[END_REF][START_REF] Kekre | Monetary Policy, Redistribution, and Risk Premia[END_REF]. Heterogeneous agent models bring important new elements to the study of the distributional effects of monetary policy, but the exisiting literature does not discuss our topic, racial inequality.

STRUCTURE OF PAPER.

In Section 2, we discuss racial inequalities in income and wealth, present the data and discuss portfolio differences between black and white households. In Section 3 we examine the effect of a 10-percent change in asset prices and a 100bp change in interest rates on the portfolios of black and white households. We present our estimates of the effects of a monetary policy shock on asset prices, interest rates, dividends and the wage and unemployment gaps in Section 4. In Section 5, we examine the impact of a typical monetary policy shock on black and white wealth and capital income and compare the wealth effects to the estimated earnings effects. The last section concludes.

Racial inequalities in income and wealth

In this section, we describe the Survey of Consumer Finances (SCF) data and present summary statistics. The data from the 2019 SCF indicate that the median wealth of white households was almost nine times higher than for black households, while white median income was 1.7 times larger than for black households. Not only is the wealth gap between black and white households large, it has hardly changed over the last 50 years. We show trends in the financial situation of black and white households with the data compiled by [START_REF] Kuhn | Income and Wealth Inequality in America, 1949-2016[END_REF] from early waves of SCF going back to 1950.

SCF data

The SCF provides representative data on the financial situation of U.S. households, employing a survey design that oversamples wealthy households. The detail of the financial information, the data quality, and the extent of the household coverage have made the SCF the primary source for studying the distribution of income and wealth among U.S. households. In the 2019 SCF data, 68 percent of household heads reported being white, 16 percent answered being non-black and non-white, and 16 percent of households answered that they have a black household head. For our analysis, we focus on households who either have a black or a white head. 5We follow the definitions of income and wealth in the previous literature [START_REF] Bricker | Measuring Income and Wealth at the Top Using Administrative and Survey Data[END_REF]; [START_REF] Kuhn | 2013 Update on the US Earnings, Income, and Wealth Distributional Facts: A View from Macroeconomics[END_REF]; [START_REF] Kuhn | Income and Wealth Inequality in America, 1949-2016[END_REF]). In particular, wealth is the sum of all assets minus all debt of a household. We consider marketable wealth so that we do not include claims against social security or defined-benefit retirement plans. Defined-contribution retirement plans are part of marketable wealth and constitute 17 percent of wealth in the United States [START_REF] Kuhn | 2013 Update on the US Earnings, Income, and Wealth Distributional Facts: A View from Macroeconomics[END_REF]. Housing includes the primary residence, other residential real estate, and the net value of non-residential real estate. For income, we consider income from all sources; for earnings, we use wage and salary income. We convert all nominal variables throughout the paper to 2019 dollars using the Consumer Price Index (CPI).

We use the approach of [START_REF] Bricker | Changes in US Family Finances from 2013 to 2016: Evidence from the Survey of Consumer Finances[END_REF] to construct household holdings of all asset classes, calculating total stock and bond positions as the sum of direct and indirect holdings. Directly held bond and stock investments are allocated to their respective positions. For indirect holdings, we allocate stock and bond investment components for stock and bond mutual funds, annuities and trusts, retirement accounts and investment savings accounts to the respective total stock and bond holdings. In the end, total stock holdings are the sum of directly held stocks, stock mutual funds, where we take 50 percent of the holdings of combination mutual funds, and the share of retirement plans, other managed investments and investment saving accounts which are invested in stocks, as reported by the survey participants. We proceed accordingly for bonds.

Summary statistics, 2019 SCF

Table 1 provides a summary of the financial situation of black and white households in the United States in 2019. We report several asset components from household balance sheets, as well as total debt, wealth, and income. 6 We report means and medians for asset positions, wealth, debt and income, and in addition the share of households with positive holdings of each asset class.

The SCF data show that the average black household has 51 cents for each dollar of white household income. The average wealth gap is dramatically larger; the average black household has only 15 cents per dollar of white household wealth. The racial wealth gap is prevalent on the entire household balance sheet but it is much smaller for non-financial assets. For example, for housing, the average black household owns 30 cents per dollar of the average white household. By contrast, if we look at equities, black households hold on average only 9 cents for every dollar held by white households.

Comparing means and medians highlights the large skewness of the U.S. wealth distribution, with means being much larger than medians. The racial wealth gap is larger at the median than at the mean, with the typical black household owning only about 11 percent of the wealth of the typical white household.7 For many asset types, the median is zero or close to zero because the share of households with holdings is small. The last two columns of Table 1 show that only 35 percent of black households own equities, just a bit more than half the share of white households. Black households are heavily underrepresented at the top of the U.S. wealth distribution, where financial wealth is concentrated [START_REF] Kuhn | 2013 Update on the US Earnings, Income, and Wealth Distributional Facts: A View from Macroeconomics[END_REF]. Many black households in the U.S. do not have any financial assets at all, so if asset prices increase, they will not benefit.

Figure 1 displays the portfolio composition of black and white households by showing the average share of each asset class in total assets.8 Housing is the largest portfolio component for both black and white households. The housing share is larger for white households, who on average hold 44 percent of their assets in housing, compared to an average share of 33 percent for black households.

The equity share of white households (around 16%) is about twice as high as for black households. For bonds, the discrepancy in average portfolio shares between black and white households is smaller. Differences in portfolio composition translate into differences in exposure to asset price changes [START_REF] Kuhn | Income and Wealth Inequality in America, 1949-2016[END_REF]. The portfolio shares for housing, equities and bonds are larger for white households, making them more exposed to changing asset prices than black households, who have a larger share of low-return liquid assets, life insurances and non-financial assets such as vehicles. For the wage gap, we use data for black and white workers from the Current Population Survey (CPS) [START_REF] Flood | Integrated Public Use Microdata Series, Current Population Survey: Version 9.0[END_REF]. Wage data for all employed workers paid by the hour in the CPS outgoing rotation groups are available from January 1982 onward. The racial wage gap shown in Figure 4b is the difference between log wages of black and white workers.

The series has a slight upward trend from 8 percent lower wages for black workers in 1982

to almost 15 percent today. The wage gap does not show systematic cyclical fluctuations around this secular trend. The increasing wage gap counteracts some of effects of the historical decline in the racial unemployment gap shown in Figure 4a.12 3. Household portfolios, asset prices and interest rates

In the following, we will illustrate the different sensitivity of black and white household asset portfolios to changes in asset prices and to interest rates.

Portfolio composition and asset price changes

To illustrate the effect of asset price changes, we consider a 10-percent increase in the price of each asset and look at how this affects the wealth of the average black and white household. 13 Figure 5a shows the dollar wealth changes for three major asset classesbonds, equity, and housing -following a 10-percent asset price increase. Changes in asset prices lead to much larger capital gains for white compared to black households, which is not surprising given the large differences in the average wealth levels shown in Table 1.

that the capital gains as a fraction of income are now even larger for black than for white households because of the underlying racial income gap.

Whether it is red-lining, other forms of discrimination or other factors that have led to black households owning fewer and less valuable homes, these differences mean that black households gain less from overall home price appreciation. This potentially fuels further racial inequalities when monetary policy leads to capital gains in the housing market.

Portfolio composition and interest rate changes

Black and white households are also affected differently when interest rates and dividend payments change. Households are affected by such changes in several ways after an accommodative monetary policy shock. First, lower interest rates will lead to lower interest income on bank accounts and deposit-type assets. Unlike for fixed-rate bonds that will increase in value, the money value of an account balance will not change. What will change are the future income flows from this balance, making a household with a positive balance poorer in expectation. Falling interest rates also reduce the interest earnings on bonds when maturing bonds are reinvested at a lower rate. Around 13.4 percent of corporate and 20.6 percent of mortgage-backed bonds are refinanced each year, which leads to a loss in interest income when rates fall. 15 . Second, we assume that a policy accommodation that leads to increased equity prices and profits will also lead to an increase in dividend payments. Given the higher stock market participation and average stock holdings of white compared to black households, this source of income mainly matters for white households.

The final way in which households are affected by lower interest rates is via borrowing, in particular if the household borrows with a mortgage contract that allows refinancing at a lower interest rate. Most U.S. mortgages are fixed-rate mortgages with a built-in call option that allows for the opportunity to prepay. Although refinancing is costly and cumbersome, refinancing activity typically increases when interest rates fall. The lower rates will persist for the remaining duration of the mortgage [START_REF] Bhutta | Interest Rates and Equity Extraction during the Housing Boom[END_REF]. Refinancing activity is therefore an important example where even transitory changes in interest rates resulting from monetary policy can have long-lasting redistributive effects as households "lock in" the lower interest rate for the remaining maturity of the mortgage. If the mortgage balance is not increased upon refinancing, but future interest payments are lowered, the household interest income of the average black household goes down by about 160 dollars and it goes down about four times as much for white households. Expressing these losses relative to income, Figure 7b shows that they are small: about 0.6 percent of annual income for white households and about half as much for black households.

Mortgage debt balances of U.S. households are, after four decades of growth, large, and correspond to almost 100 percent of SCF household income [START_REF] Bartscher | Household Debt and Inequality in the U.S[END_REF]. The dollar decline in mortgage payments from refinancing after a 100bp decrease in interest rates is shown in Figure 7a, along with the gain from higher dividend incomes, which is small. We find that the mortgage payments per household decline by 800 dollars for white households and by roughly half as much, 400 dollars, for black households.

Figure 7b shows that as a fraction of current annual income, the responses are almost equal.

For both black and white households, the reduction in mortgage payments corresponds to roughly 0.7 percent of annual income. It is however important to keep the distribution of homeownership in mind; more than every second black household does not own a house and therefore typically also does not owe mortgage debt. Moreover, the calculations are based on a scenario in which all households actually take advantage of the fall in the mortgage interest rate and refinance. Yet recent evidence by Gerardi, Willen, and Zhang (2021) suggests that black households benefit less because they are substantially less likely to refinance when interest rates decline.

Monetary policy, asset prices and the unemployment gap

In Section 2, we showed the heterogeneity in portfolio composition between black and white households and differences in their labor market outcomes, specifically the racial unemployment and wage gaps. In Section 3, we showed that portfolio heterogeneity leads to different gains when a loose monetary policy results in an increase in asset prices and dividends and a decline in interest rates. In the following, we will develop estimates of the effects of a monetary policy shock on the prices of assets -equities, houses, bonds -as well as on interest rates, dividends and labor market outcomes. In Section 5, we will combine these estimates with the household portfolio data from the SCF in order to investigate the wealth and capital income effects of an accommodative policy shock for black and white households and compare them to the earnings effects that result from changes in the racial unemployment gap.

To study the effects of monetary policy shocks on asset prices and other outcomes, we use instrumental variable local projections (LP-IV) following [START_REF] Stock | Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments[END_REF] and Jordà, Schularick, and Taylor (2020). We employ the widely used extended Romer and Romer series for policy shocks [START_REF] Coibion | Innocent Bystanders? Monetary Policy and Inequality[END_REF] and [START_REF] Romer | A New Measure of Monetary Shocks: Derivation and Implications[END_REF]) as an instrument for the change in the Funds rate. In the interest of comparability and transparency, we will also show simple local projection results for uninstrumented changes in the Fed Funds rate. Although there is a wide range of estimates of the effects of policy shocks on macro outcomes, we maintain that the estimates provide plausible approximations that illustrate the underlying economic mechanisms.

We show estimates of the impact of monetary policy shocks over a five-year period. There is a growing consensus in the literature that monetary policy moves asset prices over extended periods. [START_REF] Rigobon | The Impact of Monetary Policy on Asset Prices[END_REF] and [START_REF] Bernanke | What Explains the Stock Market's Reaction to Federal Reserve Policy?[END_REF] pioneered empirical approaches. Both studies found substantial effects of policy surprises on stock prices that mainly come from changes in risk premia (excess returns). In both studies, a surprise 100bp shock lowers stock prices by between 5 and 7 percent. [START_REF] Jordà | Leveraged Bubbles[END_REF] document substantial effects of exogenous changes in monetary conditions on all major asset classes over multi-year horizons in a long-run cross-country data set.

A recent paper by [START_REF] Paul | The Time-varying Effect of Monetary Policy on Asset Prices[END_REF] argues that monetary policy today has larger and more persistent effects on asset prices than in the past. Similar findings have been reported

for non-conventional monetary policy [START_REF] Bernanke | The New Tools of Monetary Policy[END_REF][START_REF] Wu | Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound[END_REF]. The same mechanism that we describe in this paper -greater wealth effects for white households than for black households following monetary policy-induced asset price gains -can be applied to these findings as well. Only the size and duration of the effects will vary across different studies.

Estimation of the effects of monetary policy

We will first show simple local projections based on OLS. In a second step, we will treat the monetary policy shock measure as a proxy for the structural shocks in the LP-IV set-up. The intuition is that surprises and structural shocks are imperfectly correlated.

Monetary surprise measures suffer from measurement error due to noise and random zero observations in months without FOMC meetings. Instrumenting the Federal Funds rate (FFR) instead of future rates also reduces the problems raised by the potential release of private central bank information [START_REF] Nakamura | Identification in Macroeconomics[END_REF]. Throughout the analysis, we will scale the policy shocks to represent a 100bp surprise cut in the current FFR.

Let ∆r t denote the change in the FFR at time t. We denote as x the vector of controls, which includes two lags of the outcome and the interest rate variables, as well as other variables such as the unemployment rate, inflation, industrial production, corporate bond yields, the dividend-price ratio, money growth, and asset prices. Consider the following set of local projections relating future economic outcomes such as stock and house price changes, as well as the black-white unemployment rate, to changes in interest rates today:

y t+h = α h + ∆r t β h + x t γ h + ν t+h ; for h = 0, . . . , H -1, (1)
where t = 1, . . . , T.

Estimates of this equation will show the effects of changes in the Fed Funds rate, but will not allow for a causal interpretation, as changes in the interest rates are endogenous to the state of the economy. To obtain exogenous variation in ∆r t , we will use the structural policy shocks introduced by [START_REF] Romer | A New Measure of Monetary Shocks: Derivation and Implications[END_REF]. The Romer-Romer (RR) shocks are the component of policy changes that are orthogonal to the Fed's information set, Federal

Reserve Greenbook projections for GDP, inflation and unemployment. Taking account of the delay in the publication of the Greenbook, the data are currently available for the period from 1969 to 2015. More specifically, let ∆z t denote the surprise component. We will estimate the following set of local projections using instrumental variables (LP-IV):

y t+h = α h + ∆ r t β h + x t γ h + ν t+h ; for h = 0, . . . , H -1 , (2)
which can be compared to the LP-OLS etimation from [START_REF] Bricker | Measuring Income and Wealth at the Top Using Administrative and Survey Data[END_REF]. The estimates of ∆ r t come from return to their original level after about three years. The coefficient estimates at projection horizons ranging from impact to five years are shown in Table 3.16

Labor market outcomes

Both the results with the instrumented and uninstrumented change in the Funds rate indicate that there is a small effect on the unemployment gap, which is sometimes significant at the 90 percent level. After a 100bp expansionary shock, the unemployment gap closes by 0.14pp. Similar results are reported in [START_REF] Carpenter | The Disparate Labor Market Impacts of Monetary Policy[END_REF], who find that a one-standard-deviation monetary policy shock reduces the black unemployment rate on average by 0.15pp more than the white unemployment rate. Their estimated effect is also persistent; it declines slightly over time, but remains significant even after four years.

The results above do not suggest any discernible effect of an expansionary monetary policy shock on the mean black-white hourly wage gap. We also examined alternative measures effects are often wide. Thus, we do not claim to have identified precise point estimates for policy effects, but we suggest that our benchmark estimates with the RR-shocks are within a plausible range suggested by different approaches.

In Appendix B we show that results with three other shock series are broadly similar to the results shown above. The first series shown is the measure introduced by Bernanke and Kuttner ( 2005) that sparked interest in the effect of monetary policy on asset prices. It is based on the difference between the Funds target rate and the rate implied by futures contracts. We then show shocks based on [START_REF] Gertler | Monetary Policy Surprises, Credit Costs, and Economic Activity[END_REF] that use high-frequency responses from the Fed Funds futures markets immediately following each FOMC meeting to identify a policy shock.

We also show results with a time-varying VAR (TV-VAR) approach following Paul (2020).

The TV-VAR aims to capture different responses of asset prices to monetary policy shocks over time, depending, for instance, on whether risk appetite in markets is high. The TV-VAR methodology is described in Appendix C and the estimates are presented in Appendix

Earnings and portfolio effects of monetary policy

The empirical results in Section 4 show substantial and persistent positive asset price effects of a surprise monetary easing, in combination with a reduction in the black-white unemployment gap. In this section, we use these estimates to calculate the effects of a monetary policy shock on the wealth of the average black and white household. Since the wealth distribution is highly skewed, we also examine the portfolio effects along the wealth distribution and around the median. Finally, we calculate the effect of a monetary policy shock on the gap between black and white earnings and compare the size of the portfolio and earnings effects over different horizons.

Effects on household wealth

One additional step is needed before we can estimate the impact of a monetary policy shock on wealth. For bonds, we need to transform the effect on interest rates into a change in the asset price using an assumption about duration. We use duration estimates from Bloomberg for the average duration of outstanding 10-year Treasuries (7.07), mortgage-gap between black and white households [START_REF] Gerardi | Mortgage Prepayment, Race, and Monetary Policy[END_REF].

A note on the persistent effects of policy shocks

It is important to note that while monetary policy shocks by construction capture cyclical variation, they can still have persistent effects on inequality. First, we find that asset prices change after monetary policy shocks for an extended period of five years. Our results build on a growing literature that estimates persistent asset price changes in response to monetary policy shocks [START_REF] Bernanke | What Explains the Stock Market's Reaction to Federal Reserve Policy?[END_REF][START_REF] Jordà | Leveraged Bubbles[END_REF][START_REF] Paul | The Time-varying Effect of Monetary Policy on Asset Prices[END_REF][START_REF] Rigobon | The Impact of Monetary Policy on Asset Prices[END_REF]. Such a period can easily account for 10 percent of the economically active lifetime of a household.

Second, recent theoretical and empirical work suggests that monetary policy shocks can affect the long-run equilibrium interest rate (Bianchi, Lettau, and Ludvigson, forthcoming;[START_REF] Rungcharoenkitkul | Monetary Policy Hysteresis and the Financial Cycle[END_REF]. Bianchi, Lettau, and Ludvigson (forthcoming) show that monetary policy leads to regime shifts with long-lasting effects on relative asset prices. In this case, there can be permanent impacts on asset prices.

Moreover, distributional effects may be persist even if gains and losses average out over time and asset prices revert to an equilibrium, as indicated in theory [START_REF] Auclert | Monetary Policy and the Redistribution Channel[END_REF]. This is because portfolio decisions by households are often driven by changes in their life-cycle situation rather than financial returns. For example, household formation or changes in family composition can lead to portfolio adjustments such as the purchase or sale of a house. In such instances, households cannot simply wait for asset prices to revert back to their long-run level without welfare consequences from not adjusting their asset positions.

In general, the life cycle puts young households systematically on the buyer side and older households on the seller side of the market and will induce constant trading needs that are not governed by asset price movements. That is, capital gains are often realized by households due to life-cycle events such as marriage, divorce, family formation, job loss or job change. Hence, differences along racial lines in household demographic structure or unemployment experience can induce differences in the propensity to buy and sell assets, in addition to the racial differences in the exposure to asset price change.

Also, asset prices changes may alleviate or tighten collateral constraints as, for example, discussed in [START_REF] Iacoviello | House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle[END_REF]. An expansionary monetary policy shock relaxes borrowing constraints and offers the opportunity to access additional credit for consumption or investment. This collateral effect will likely play out differently along racial lines, as the around the median differ in their composition relative to the mean effects because of the differences in the portfolio composition along the wealth distribution. We find that around the median, most of the gains stem from housing, whereas equity gains are the largest part at the mean. As a result, it takes about two years for gains to accumulate and they are persistent after that. The capital gains are about the same size in year 5 as in year 3.

In Table 1, we reported that a large share of black households do not own any assets of several types and if they do, their holdings are often small. To see the implications of this, we look at the shares of black and white households who have portfolio gains that are less than one percent of their annual income 5 years after an expansionary shock. We refer to households with a portfolio gain below one percent of income as having no portfolio effect.

We find that about one fourth of white households (24 percent) have no portfolio effect after 5 years. By contrast, the share among black households is more than twice as large (53 percent). Hence, almost half of black households are left with no portfolio gains 5 years after an expansionary monetary policy shock. 19By construction, black and white households with similar portfolios will have similar capital gains. Figure 15a shows that capital gains for black and white households are Figure 15b looks at capital gains for black and white households around the median of the aggregate income distribution. Here, we again see pronounced differences between black and white households. In other words, even black households who by construction have similar incomes as white households do have lower wealth and therefore reap lower capital gains after expansionary monetary policy shocks. On average, the capital gains of white households between the 40th and 60th percentile of the aggregate income distribution are two to three times larger than those of their black counterparts.

For our calculation, we focus on prime-age household heads (age 25-55) and on the information if the head has been unemployed during the 12 months before the interview.21

There are large differences in the unemployment experiences of black and white households.

The share of black household heads experiencing unemployment in the year prior to the interview is 12.4 percent, while the share for white heads is 8.3 percent. Comparing earnings of households who have been and who have not been unemployed during the past 12 months, we find that average earnings of black households whose head has not been unemployed are $56,200. For households whose head experienced unemployment within the last 12 months, the average annual labor income is $27,500. 22 By contrast, we find that white households who experienced unemployment during the last 12 months still report average earnings of $50,300 -almost the level of black households without unemployment experience. White households without unemployment experience over the last 12 months report an average labor income of more than $103,000 in the 2019 SCF data.

To derive the earnings effect, we multiply the difference in earnings between black households that have and have not experienced unemployment by our estimates of the impact of monetary policy on the differential between black and white unemployment rates from Table 3. We then make a conservative assumption in order to relate the change in the unemployment gap to earnings changes. In particular, we assume that each household who finds employment receives the average earnings gain of a black household finding employment, such that the earnings gain is $56,200 -$27,500 = $28,700. The relative income gain of black households is computed by multiplying the estimated impact of the monetary policy shock on the unemployment gap with the average earnings gain of $28,700.

More formally, let us denote the estimated effect on the unemployment gap at projection horizon h by ∆ h u and the earnings gain from leaving unemployment for black households by ∆Y B = Y B E -Y B U where Y B E denotes average labor income of black households who have not been unemployed over the past 12 months and Y B U denotes labor income of black households who have been unemployed at least for some time in the past year. In the 2019 SCF data, we find ∆Y B = $28, 700. Our estimate for the relative earnings gain for black households relative to white households in period h after the shock, ∆ h Y, is thus

∆ h Y = ∆ h u∆Y B = ∆ h u(Y B E -Y B U )
The effect on the unemployment gap in Table 3 peaks after 2 years, when the unemployment rate gap is reduced by 0.137 percentage points. The relative earnings gain is found by multiplying this number with the average earnings gain, which yields a relative gain per black household of $39.3, or 0.07 percent of annual total income for all black households.

Comparing earnings and portfolio effects

∆ h Y is the impact of the monetary policy shock on the difference in earnings between black and white households. Thus, the appropriate comparison is to the difference in capital gains accruing to black and white households. Continuing with the above calculation, where we found ∆ 2 Y = $39.3, the corresponding portfolio effect after 2 years estimated is about $20,300 for white households and $3,000 percent for black households. The differential gain of white households relative to black households is thus $17,300. This comparison suggests that the portfolio effect for white households is substantially larger than the earnings effect for black households. Put differently, the differential capital gain of white households as a fraction of income is two orders of magnitude larger than the earnings effect.

However, there is an important conceptual difference between the two effects. The earnings effect applies to the flow of earnings, while the capital gains are a gain on the stock of wealth. Thus, the capital gain is a one-time change in the valuation of assets, while the earnings effect applies to incomes year by year. To take this into account, we compare the difference in capital gains between white and black households over the five-year horizon to the accumulated estimate of the differential earnings effect over this time period.

After five years, the accumulated earnings effect of the benchmark monetary policy shock is $134. In Figure 17, we show the year-by-year accumulated earnings effects and the difference in the portfolio effects on black and white households in percent of each group's from a monetary policy shock. Note that for easier comparison, we construct the differences to be always positive; capital gains are larger for white households and earnings gains are larger for black households. The estimates shown use our benchmark shock series to estimate the impact of monetary policy shocks on asset prices, interest rates and the unemployment gap. Even as the earnings effect accumulates over time, it remains orders of magnitude smaller than the effects from capital gains.

In a final step, we compare the wealth effect on consumption to the earnings effect and find that under plausible assumptions, the wealth effect on consumption for white households is larger than the earnings effect for black households. There is a large literature that estimates

Conclusion

We have shown that policy shocks that change asset prices have differential effects on the wealth of black and white households. White households gain more because they have more financial wealth and hold portfolios that are more concentrated in interest-rate-sensitive assets such as equities. At the same time, monetary policy shocks reduce the gap between black and white unemployment rates and entail larger earnings gains for black households.

Bringing the two together, however, leads to a stark finding: the reduction in the earnings gap pales in comparison to the effects on the wealth gap.

Our analysis therefore does not bode well for the suggestion made by politicians and central bankers that a more accommodative monetary policy helps alleviate racial inequalities.

With the instruments available -all of which work through effects on asset prices and interest rates -a central bank would not be able to design policies for an income gap reduction objective without increasing wealth inequality. Clearly, this does not mean that achieving racial equity should not be a first-order objective for economic p olicy. We strongly think it should. But the tools available to central banks might not be the right ones, and could possibly be counter-productive.

B. Alternative shock estimates

Figure A.5 shows the impact on key outcome variables of the alternative monetary policy shocks discussed in Section 4.2.2. The measure introduced by Bernanke and Kuttner (2005) (BK) produces substantially larger asset price effects than the benchmark RR-series. The effects of an 100bp exogenous decline in the Fed Funds pushes up both stock and house prices by 20 percent or more over an extended period. Also the effects on the unemployment gap are larger than with the RR estimate. The shocks based on Gertler and Karadi (2015) (GK) that use high-frequency Fed Funds futures markets data show smaller asset price effects. In this case, stock prices rise by a little less than 10 percent over a three year horizon, but the response is similar and more persistent in the case of house prices. By contrast, with the GK shock series, the unemployment gap is essentially unaffected for three years following a monetary shock. All in all, the alternative shock series lend support to the idea that more accommodative monetary policy boosts asset prices over some time horizon. In many of our estimates that time horizon is an extended one, encompassing multiple years. There is also evidence, mixed with respect to statistical significance, that accommodative monetary policy has a short-run effect on the unemployment gap between black and white workers. The wage gap is never really affected.

Similar results are shown with a time-varying VAR (TV-VAR) approach following Paul (2020) (PP).

The TV-VAR aims to capture different responses of asset prices to monetary policy shocks over time, depending, for instance, on whether risk appetite in markets is high. The TV-VAR methodology is shown in Section C and the estimates are in Table A.1. It is noteworthy that the equity price response reaches double-digits with the TV-VAR set up. Stock prices rise and remain more than 10 percent higher over a five year period. Statistical significance here is borderline, while the confidence intervals for BK-shocks are extremely wide for asset and labor market responses.

C. TV-VAR Estimates

Consider the structural form of the evolution of a set of macroeconomic variables and controls, Y t , relative to a series of structural shocks, t :

HY t = C 0 + k ∑ i=1 C k Y t-k + t
Solving for Y t yields the following expression, in which u t = H -1 t represents reduced-form innovations which pick up the contemporaneous effects of the structural shocks on all the variables within Y t :

Y t = B 0 + k ∑ i=1 B k Y t-k + u t
The t are not directly observable, so an external instrument related to the shock must be introduced. Let 1,t be the primary structural shock of interest, so that the instrument z t can be related as z t = φ 1,t + η t , where η t is normally distributed with mean zero and independent of all other variables. We use the shocks calculated in Paul (2020) as our instrument. These can be directly integrated into the model as follows: A3 Notes: The table shows TV-VAR response estimates for asset prices, interest rates, and the unemployment gap after a 100bp expansionary monetary shock for the monetary policy shock series of [START_REF] Paul | The Time-varying Effect of Monetary Policy on Asset Prices[END_REF]. The rows show the point estimates of the response after 1 to 5 years. Brackets below the point estimates at each horizon show the 90-percent confidence intervals. TV-VAR method uses Gibbs sampling to uncover the distribution of responses over different time periods

D. Demographic composition of households

The results in the body of the paper take all black and all white households together without any attention paid to other demographic differences. The portfolio holdings and unemployment responses of households might differ for reasons other than race, such as marital status and the sex of the household head. If households with a single versus a married or male versus female head have different asset portfolios, they are likely to be affected differently by a monetary policy shock.

In this Appendix, we will examine the impact of monetary policy shocks on the income and wealth of black and white households of different types.

Since only 15% of the SCF households have a black head, the granularity of other demographic characteristics will be limited. We start with a distinction between households with a single rather than married head, where married includes cohabiting couples. Two-thirds of white households are married, while the proportion for black households is only 35%. Households with a single head can further be distinguished into male and female heads, whereas the head is always male for married couples by the SCF's convention. Among black single households, 66% have a female head, while among white single households 56% have a female head.27

Summary statistics for black and white households by type are shown in Appendix Table A.2. The racial wealth gap is large for all household types. White single and married households have about 5 times as much wealth as comparable black households. Average income of white single households with male or female heads is about 1.3 times the average income of the corresponding

  Bureau of Labor Statistics (BLS) data on unemployment rates starting in 1972, when black unemployment rate data become available. 11 Figure 4a shows the black-white annual unemployment gap from 1972 to 2020. The gap has rarely been smaller than 4 percentage points. It reached 12 percentage points during the 1982 recession and reached a low of 3 percentage points in the tight labor market prior to the Covid-19 pandemic.

  Brackets below the point estimates at each horizon show the 90-percent confidence intervals. * indicates significance at the 10 percent level, * * indicates significance at the 5 percent level, and * * * indicates significance at the 1 percent level.

Table A. 1 .

 1 The effects of the alternative shock series on key outcome variables are shown in Appendix Figure A.5.

  indeed similar when looking at households between the 40th and 60th percentile of the overall wealth distribution. The effects are only slightly smaller for black households, mostly due to somewhat smaller housing capital gains. The remaining differences in capital gains disappear when normalizing by income, as shown in Appendix Figure A.3. However, black households are underrepresented in the middle and upper parts of the aggregate wealth distribution. Appendix Figure A.4 shows that the share of black households in the upper half of the wealth distribution has consistently been lower than the overall population share of black households since the 1950s. Moreover, black households have become less likely to make it to the top 10%, and more likely to be in the bottom 50%, since the 1970s.

Table 1 :

 1 Mean and median black and white wealth and income in the 2019 SCF

		Means	Medians	Share with
						holdings (%)
		White	Black	White	Black	White	Black
	Bonds	122,700	19,600	0	0	47	27
	Housing	353,500	104,700	170,000	0	75	46
	Equity	474,000	40,900	9,000	0	64	35
	Other non-financial assets	33,400	13,500	17,000	8,000	90	72
	Liquid assets	57,000	13,900	8,000	1,400	99	95
	Other financial assets	28,400	7,600	0	0	37	30
	Net wealth	951,300	139,800	181,400	20,700
	Debt	117,300	60,400	35,000	10,100
	Income	113,300	58,100	67,200	38,700

Notes: The table shows mean and median asset positions, wealth, debt and income for black and white households from the 2019 SCF. All dollar values are rounded to the nearest 100 dollars. The last two columns show the share of black and white households with positive holdings of each asset classes in percent.

Table 2 :

 2 Macroeconomic dataThe table summarizes the macroeconomic time series used in the LP-IVs. It shows the different variables with descriptions, the time period for which the data are available, and the source of the data.

	Variable	Description	Time Period	Source
	Federal Funds Rate	Federal Funds Target	11/1988 -9/2017 FRB
	Unemployment rate	seasonally adjusted unemployment	1/1960 -9/2017	BLS
	Unemployment gap	difference in black and white unemployment rates 1/1972 -9/2017	BLS
	Hourly wages	Black and white workers	1/1982 -9/2017	BLS
	Weekly earnings	Black and white workers	1/1982 -9/2017	BLS
	Industrial production industrial production index	1/1960 -9/2017	FRB
	Stock price	S&P500 price	1/1960 -9/2017	S&P
	Inflation	CPI, all urban consumers	1/1960 -9/2017	BLS
	M2 growth	Real money stock	1/1960 -9/2017	FRB
	House price	Case-Shiller house price index	1/1975 -9/2017	S&P Corelogic
	Dividends	Real dividends, S&P500	1/1960 -9/2017	R. Shiller
	Corporate debt yield	Moody's seasoned corporate BAA yield	1/1960 -9/2017	FRB
	Treasury yield	10-year constant maturity T-note yield	1/1960 -9/2017	FRB
	Notes:

Table 3 :

 3 LP-IV estimates for response to 100bp expansionary monetary policy shock(Romer-Romer)

	Horizon	Unemployment Gap	Wage Gap	Stocks	Houses	Treasury	Dividends
		%	%	pp	pp	pp	%
	0M	0.038	-0.004	1.268*	-0.074	-0.236***	0.026
		(0.121,-0.045)	(0.011,-0.018) (2.461,0.074) (0.069,-0.217) (-0.117,-0.355) (0.119,-0.067)
	6M	0.004	-0.008	2.479	0.080	-0.299**	0.548*
		(0.161,-0.154)	(0.008,-0.024) (5.254,-0.295) (0.687,-0.527) (-0.082,-0.516) (1.088,0.007)
	12M	-0.009	-0.008	0.463	-0.118	-0.420*	0.787*
		(0.111,-0.308)	(0.007,-0.024) (3.903,-2.976) (0.835,-1.070) (-0.055,-0.785) (1.553,0.020)
	24M	-0.137	-0.006	2.089	1.046	-0.505**	0.566
		(0.123,-0.396)	(0.013,-0.025) (5.346,-1.169) (2.475,-0.383) (-0.085,-0.925) (1.731,-0.598)
	36M	-0.038	-0.006	3.206*	2.047*	-0.143	0.328
		(0.253,-0.328)	(0.011,-0.023) (6.333,0.078)	(4.044,0.051)	(0.148,-0.434) (1.575,-0.918)
	48M	-0.104	-0.011	1.905	2.230	0.154	0.001
		(0.061,-0.269)	(0.008,-0.029) (5.211,-1.401) (5.049,-0.589) (0.500,-0.192) (1.195,-1.193)
	60M	-0.129	-0.011	2.564	2.383	0.097	0.334
		(0.084,-0.342)	(0.004,-0.025) (5.493,-0.365) (5.299,-0.533) (0.393,-0.199) (1.723,-1.054)

Notes: The table shows LP-IV response estimates for the unemployment and wage gaps, stock prices, house prices, 10-year treasury yields and dividends after a 100bp expansionary monetary shock for Romer-Romer (RR) shocks. The rows for each variable show the point estimates of the response after 0, 6, 12, 24, 36, 48 and 60 months.

Table A . 1 :

 A1 TV-VAR estimates for response to 100bp expansionary monetary policy shock

	Shock	Horizon House prices Stock prices Treasury yield BAA yield
			%	%	pp	pp
	Paul (2020) 1y	1.4	13.85	0.24	-0.11
			(-3.1, 5.82)	(-0.99, 29.48)	(-0.76, 1.29)	(-0.61, 0.34)
		2y	1.98	12.41	0.16	-0.1
			(-5.34, 9.54)	(-4.2, 30.69)	(-0.96, 1.36)	(-0.69, 0.47)
		3y	2.19	11.29	0.14	-0.09
			(-6.51, 12.1) (-6.49, 30.95)	(-1.14, 1.39)	(-0.82, 0.54)
		4y	2.14	10.64	0.13	-0.06
			(-8.03, 14.24) (-8.69, 31.45)	(-1.24, 1.5)	(-0.88, 0.62)
		5y	1.95	10.12	0.12	-0.04
			(-9.02, 16.24) (-9.84, 32.93)	(-1.37, 1.67)	(-0.93, 0.73)

https://www.rev.com/blog/transcripts/joe-biden-racial-equity-plan-speech-transcript-july-

https://www.frbatlanta.org/about/feature/2020/06/12/bostic-a-moral-and-economicimperative-to-end-racism

This channel is often emphasized in policy discussions[START_REF] Aliprantis | What Is Behind the Persistence of the Racial Wealth Gap? Working Paper February[END_REF]. In the words of Atlanta Fed President Bostic (see footnote 2): "The Federal Reserve acts to create a foundation upon which businesses, families, and communities can thrive. Our success means that businesses can grow faster and hire more workers and that more innovation can be supported, which would mean more opportunities for African Americans and others who have not been as attached to the economy."

The literature on the marginal propensity to consume out of capital gains on housing and the stock market is summarized in[START_REF] Poterba | Stock Market Wealth and Consumption[END_REF] and[START_REF] Paiella | The Stock Market, Housing and Consumer Spending: A Survey of the Evidence on Wealth Effects[END_REF]. More recently Di[START_REF] Maggio | Stock Market Returns and Consumption[END_REF] and[START_REF] Chodorow-Reich | Stock Market Wealth and the Real Economy: A Local Labor Market Approach[END_REF] present similar estimates based on micro data.

The SCF convention is that in a couple the male spouse is the household head and we follow this convention.

Housing includes other real estate. Equity includes business wealth. Liquid assets are the sum of checking accounts, saving accounts, call accounts, money market deposit accounts, prepaid accounts and certificates of deposit. Other financial assets include the cash value of life insurance. Non-financial assets are the value of vehicles and other non-financial assets, e.g., jewellery or gold.

Medians are computed within asset classes and might therefore not correspond to the asset holdings of the median-wealth household.

Note that the figure shows average portfolio shares, which differ from the portfolio shares of the average household obtained by dividing the average holdings of each asset class by average total assets (as found in Table1). The latter would amount to an asset-weighted average of the household-level portfolio shares.

The gap is the difference between black and white unemployment rates, where the data are seasonally adjusted with Census X-12 ARIMA.

Another reason for the trend might be changes in the group of workers who are paid by the hour. We also considered data on the racial gap in mean and median weekly earnings and found our results to be robust.

A 10-percent changes seem to be a reasonable benchmark in light of the substantial increases in asset prices that have occurred during the past 15 years. Over this time period, U.S. home prices rose by 69 percent, stock prices by 95 percent and bond prices by 22 percent. These numbers are based on the annual average S&P Case Shiller U.S. National Home Price Index, the end of year S&P 500 stock price index and the annual average U.S. 10-year government bond yield with the assumption that duration is 7 years.

The proportions of bonds maturing are estimated as total issuance less the change in bonds outstanding as a fraction of bonds outstanding, averaged over the ten years since 2011, based on data from the Securities Industry and Financial Markets Association

The effects of the policy shock on inflation and the corporate bond yield are not shown to conserve space.

If we consider a 5-percent threshold instead of the 1-percent threshold, the shares increase to 41 percent for white households and 68 percent for black households.

We consider the last 12 months rather than the current labor force status at the interview because the surveyed labor income also refers to the previous calendar year.

Sample sizes are small: we observe 182 white households and 64 black households whose head reports unemployment during the last 12 months.

Single households include both individuals living alone and individuals with children. A further breakdown is not feasible because of small sample sizes in sub-categories. There are only 166 black households with a single male head, our smallest category.

not be interpreted as reflecting the views of the Federal Reserve Bank of New York or the Federal Reserve System. Dean Parker, Sven Eis, Francisco Ruela, and Siddhi Jagdale provided excellent research assistance. The project received support from the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy -EXC 2126/1 -39083886. The paper has benefited from a visit by Paul Wachtel as a fellow at the Frankfurt Center for Advanced Studies: Foundations of Law and Finance funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) -project FOR 2774.

This paper presents preliminary findings and is being distributed to economists and other interested readers solely to stimulate discussion and elicit comments.