REDISTRIBUTION IN THE MONETARY TRANSMISSION MECHANISM
EVIDENCE FROM THE EURO AREA
Elin Colmsjö
&
Luca Restaldi
Supervisor: Kathrin Schlafmann
Master’s Thesis Copenhagen Business School In Partial Fulfilment of the Requirements
for the degree of Master of Sciences in Advanced Economics and Finance May 2021
Contract number: 18690
Number of characters with spaces: 154 338 Number of CBS pages: 81
ABSTRACT
We evaluate the relationship between redistribution and monetary transmission (MT) in Euro area (EA) countries, empirically testing the prevalence of three redistribution channels (RC);
The Earnings Heterogeneity channel (EHC), the Fisher channel (FC) and the Interest Rate Exposure channel (IEC). We do so by first estimating a statistical measure of the difference in countries’ aggregate output responses to a common MP shock by using a Local Projections Instrumental Variable (LP-IV) technique. Subsequently, we relate this measure to micro variables meant to capture heterogeneities in household balance sheets and the marginal propensity to consume (MPC). The findings support a positive relationship between MT and variable proxies for the redistribution of income, but not for the redistribution of wealth. While a higher share of low-income households in reference to the EA income levels amplifies MT, supporting the prevalence of the EHC, the evidence for the FC and the IEC remains weak.
Finally, accounting for the spread of Hand-to-Mouth (HtM) households across the channel proxies indicates that the EHC is partly driven by a redistribution from low to high-MPC households.
Keywords: Household heterogeneities, Monetary policy, Redistribution, Local Projections, Hand-to-Mouth, Marginal Propensity to Consume, Eurosystem Household Finance Consumption Survey
ACRONYMS & ABBREVIATIONS
Abbreviation/Acronym Definition
EA Euro Area
EHC Earnings Heterogeneity Channel
EONIA Euro Overnight Index Average
FC Fischer Channel
GDP Gross Domestic Product
HANK Heterogeneous Agent New Keynesian
HtM Hand-To-Mouth
HICP Harmonized Index of Consumer Prices
IEC Interest rate Exposure Channel
IRF Impulse Response Function
LP-IV Local Projections Instrumental Variable
MP Monetary Policy
MPC Marginal Propensity to Consume
MT Monetary Transmission
MTM Monetary Transmission Mechanism
NNP Net Nominal Position
NK New Keynesian
OIS Overnight Index Swap
PP Percentage Points
RC Redistribution Channels
URE Unhedged interest Rate Exposure
TABLE OF CONTENT
1. INTRODUCTION 7
2. THEORY 11
2.1. THE TRANSITION FROM RANK TO HANK 11
2.1.1. MARGINAL PROPENSITY TO CONSUME 12
2.2. REDISTRIBUTION IN MONETARY TRANSMISSION 13
2.2.1. FRAMEWORK SUMMARY 13
2.2.2. REDISTRIBUTION CHANNELS 16
2.2.3. THE MODEL 18
2.2.4. OPEN ECONOMY ADJUSTMENTS 21
3. LITERATURE REVIEW 24
3.1. ESTIMATING MONETARY TRANSMISSION 25
3.1.1. CHOOSING THE MODEL: S-VAR VERSUS LOCAL PROJECTIONS 25
3.1.2. INSTRUMENTAL VARIABLE SPECIFICATIONS 26
3.1.3. THE APPLICATION TO MONETARY POLICY SHOCKS 27
3.2. RELATING MACRO-DYNAMICS TO MICRO-HETEROGENEITIES 28
3.2.1. METHODOLOGICAL OVERVIEW 28
3.2.2. THE “BOTTOM-UP” APPROACH 28
3.2.3. THE “TOP-DOWN” APPROACH 29
3.3. THE ROLE OF REDISTRIBUTION 30
3.3.1. THE EFFECTS OF MONETARY POLICY ON REDISTRIBUTION 30
3.3.2. THE EFFECTS OF REDISTRIBUTION ON MONETARY TRANSMISSION 31
3.4. HYPOTHESES 34
4. DATA 35
4.1. MACRO VARIABLES 35
4.1.1. OIS RATE 35
4.1.2. INCOME GINI 36
4.2. MICRO VARIABLES 37
4.2.1. THE HOUSEHOLD FINANCE & CONSUMPTION SURVEY 37
4.2.2. INCOME 38
4.2.3. MARGINAL PROPENSITY TO CONSUME 38
4.2.4. HAND-TO-MOUTH HOUSEHOLDS 39
4.2.5. LOW INCOME HOUSEHOLDS 40
4.2.6. NET NOMINAL POSITION 41
4.2.7. UNHEDGED INTEREST RATE EXPOSURE 42
4.2.8. INTERTEMPORAL SUBSTITUTION 43
4.3. DESCRIPTIVE STATISTICS 44
5. METHODOLOGY 45
5.1. ESTIMATING AGGREGATE RESPONSES TO MONETARY POLICY SHOCKS 45
5.1.1. MONETARY POLICY SHOCK IDENTIFICATION 45
5.1.2. THE LP-IV MODEL 46
5.1.3. EXTRACTING IRF PEAKS 48
5.1.4. ALTERNATIVE SPECIFICATIONS 49
5.2. RELATING IRF PEAKS TO REDISTRIBUTION INDICATORS 49
5.2.1. ECONOMETRIC MODELS 49
5.2.2. ESTIMATION STRATEGY: ORDINARY LEAST SQUARES 51
6. RESULTS 54
6.1. MONETARY TRANSMISSION ACROSS EURO AREA COUNTRIES 54
6.2. THE RELATIONSHIP BETWEEN MPC AND REDISTRIBUTION INDICATORS 57
6.3. THE EFFECT OF REDISTRIBUTION ON MONETARY TRANSMISSION 61
6.3.1. THE EARNINGS HETEROGENEITY CHANNEL 61
6.3.2. THE FISHER & INTEREST RATE EXPOSURE CHANNEL 65
6.3.3. COMBINED EFFECTS 67
6.3.4. OPEN VERSUS CLOSED ECONOMY FRAMEWORK 69
7. DISCUSSION 72
7.1. REDISTRIBUTION EFFECTS IN MONETARY TRANSMISSION 72
7.1.1. HETEROGENEOUS REACTIONS TO MONETARY POLICY 72
7.1.2. THE ROLE OF INCOME REDISTRIBUTION 73
7.1.3. THE ROLE OF WEALTH REDISTRIBUTION 76
7.1.4. TOWARDS AN INTERNATIONAL HANK FRAMEWORK 78
7.2. LIMITATIONS 80
7.2.1. VALIDITY OF THE EHC PROXY 80
7.2.2. VALIDITY OF THE INTERTEMPORAL SUBSTITUTION PROXY 81
7.2.3. OLS ESTIMATION ISSUES 81
8. CONCLUSION 82
9. BIBLIOGRAPHY 83
10. APPENDIX 89
10.1. HFCS VARIABLES 89
10.2. TECHNICAL COMPARISON: LP AND S-VAR 92
10.3. ROBUSTNESS CONTROLS 94
1. INTRODUCTION
This study investigates the role of redistribution in the transmission mechanism of MP. Recent studies indicate that differences in certain household characteristics can amplify or reduce countries’ reactions to aggregate shocks (see for example Almgren et al. 2019; Carroll et al., 2017 and Gornemann et al., 2016). For this reason, micro-heterogeneities among economic agents are becoming increasingly integrated into the conventional New Keynesian (NK) models.
At the core of this development is the Heterogeneous Agent New Keynesian (HANK) framework, highlighting the importance of indirect ‘general equilibrium’ channels of MP in addition to the direct ‘partial equilibrium’ channels (Kaplan et al., 2018). Particularly, in an economy where households are non-representative, these channels capture the potential effects of redistribution on aggregate consumption and output following a change in the policy rate.
The Eurozone is a unique economic experiment because it unites a group of countries under the same currency. Although the European Central Bank (ECB) applies a uniform MP in all EA member states, the economic consequences across the countries differ vastly (Corsetti et al.
2020). From a political point of view, such asymmetric reactions are undesirable because they suggest that MP has distributional or disproportional effects, which goes beyond its purpose of maintaining price stability. Accordingly, it is of interest to further the current knowledge of the underlying forces at play. So far, the variation in responses has been attributed to household differences in consumption, unemployment, housing prices (Corsetti et al., 2020) and liquidity constraints (Almgren et al., 2019). It is therefore surprising that, although a bourgeoning literature confirms a prominent impact of household heterogeneities on aggregate dynamics, so few empirical studies consider the potential of redistribution in explaining cross-country discrepancies.
In a recent paper, Auclert (2019) proposes a theoretical framework on how redistribution affects MT. According to this framework, redistribution enters into the MT mechanism (MTM) in the form of three ‘transmission channels’; The EHC, the FC and the IEC. Underpinning these pathways are heterogeneities in the income, Net Nominal Position (NNP) and Unhedged Interest Rate Exposure (URE) of households, signaling the sensitivity of their balance sheets to changes in the real interest rate or price levels. The effects of redistribution on MT subsequently work in two steps. Firstly, the redistribution indicators determine who increases (winners) and who decreases (losers) in their income or wealth following a monetary expansion. Specifically,
agents that are low income or have negative levels of URE or NNP capture the majority of the economic gains triggered by a monetary expansion. Secondly, provided that all gains translate into losses, redistribution will amplify MT if the winners have a higher MPC than the losers.
Specifically, the latter implies that a decrease in the interest rate will generate a redistribution of wealth and income from low to high-MPC households.
The MPC is a key component of the HANK literature since it determines which households in the economy that are the most sensitive to economic shocks in regard to their consumption. For this reason, several studies explore the determinants of economic agents’ MPC (such as the work of Carroll et al. (2014) or Carroll et al. (2017)). Many of these emphasize liquidity constraints, referred to by Kaplan et al. (2014) as “Hand-to-Mouth” behavior, as a consistent inflator of household MPC. Due to a lack of effective MPC measures in existing micro-datasets, HtM households have proved useful in approximating consumption behavior across country populations (Almgren et al., 2019) (Bilbiie, 2020).
Utilizing the above theoretical predictions and empirical insights, this study aims to contribute to the literature on the relationship between redistribution and MT by evaluating data from the Eurosystem Household Finance & Consumption Survey (HFCS). Particularly, the study addresses the following questions:
• Can cross-country variation in aggregate reactions to common monetary policy in the Euro area be attributed to indicators of redistribution?
• Does European (HFCS) household data support Auclert’s (2019) theoretical prediction that redistribution amplifies expansionary monetary policy through an Interest Rate Exposure channel, a Fisher channel and an Earnings Heterogeneity channel?
• Can accounting for the spread of Hand-to-Mouth households across the redistribution indicators of NNP, URE and income empirically capture the effects of redistribution from low to high-MPC households?
We empirically test our main questions by relating household redistribution proxies to aggregate reactions in real output and consumption following a negative shock in the Euro Overnight Index Average (EONIA). Our methodological approach retraces parts of the work by Almgren et al. (2019) and can be summarized in two stages. Firstly, we derive individual country-responses in real output triggered by a common MP shock in 18 EA countries using a
Local Projections Instrumental Variable (LP-IV) technique. We then extract the maximum point (peak) of the impulse response function (IRF) in each country and use this as a statistical measure for MT effectiveness. Secondly, we estimate the country means of NNP, URE as well as two measures of income inequality as proxies for each redistribution channel (RC), relating these to the IRF peaks through cross-sectional ordinary least squares (OLS) regressions.
Specifically, while we use the income Gini as the relevant ‘closed economy’ proxy of the EHC, we compute the share of households that belong in the 1st quintile of the EA income distribution as our ‘open economy’ proxy. We expect the aggregate values of URE and NNP to be negatively associated to MT, and the proxies for income inequality to show a positive relationship. To further account for the distribution of MPC across the redistribution indicators of interest, we use the HtM binary qualification as a measure of high-MPC status and isolate the share of the redistribution variables that is held by these agents. If the high-MPC households are overrepresented in the group of winners from monetary expansions, the effect of the redistribution proxies on MT should be greater once isolated for the HtM households.
The exercise above yields several interesting results. Firstly, in line with the evidence of Almgren et al. (2019), we find that MT differs widely across EA countries, both in strength and persistence. The peak reaction in real output from a 100 basis point decrease in the EONIA reaches from 0.05 % in Portugal to 0.43 % in Latvia. Moreover, the time point where MT reaches maximum effectiveness averages from 8 months ex-post the expansion in Cyprus and Greece to 30 months in France. Secondly, in our attempt to explain the variation in aggregate responses to MP across the EA, we confirm the importance of accounting for redistribution in the MTM.
We find a positive and robust relationship between the share of low income households and MT, supporting the existence of an EHC. In reference to the EA average change in output from a monetary expansion, increasing the share of low income households by 20 percentage points (PP) is associated with a 40 % amplification of MT. This relationship is strengthened when isolating for the share of low income households that are also liquidity constrained (HtM).
Intuitively, while we interpret the former correlation as the impact of disproportional income gains across countries, it appears that the latter also captures the effect of redistribution from low to high-MPC households. This result is consistent with the previous literature emphasizing that low income households benefit disproportionately from MP expansions (Slacalek et al., 2020) and that HtM households amplify countries’ reaction to aggregate shocks (Bilbiie, 2020)(Kaplan et al., 2014).
The NNP and URE variables do not show any significant relationship with MT once regressed individually. However, when analyzing the three redistribution indicators combined, the regressions indicate that cross-country discrepancies in aggregate reactions to MP can be attributed to all three channel proxies. While the coefficients of the country mean of NNP as a proxy for the FC has the expected negative sign, the household mean of URE is positively related to aggregate output reaction, contradicting theory. The observed estimates increase in absolute size once accounting for the distribution of HtM households across NNP/URE. However, the variables are sensitive to the inclusion of liquidity constraints depending on the model specification. Accordingly, we conclude that the evidence for the FC and the IEC is weak, and that these are more likely to be captured through less macro-oriented modeling techniques.
Finally, the spread of HtM households across the redistribution indicators of NNP, URE confirms the Auclert (2019) assumption that the winners of MP also have a higher MPC than the losers. While this pattern is strongest for the relationship between MPC and income, the distribution of MPC across the deciles of NNP/URE is hump-shaped, with the highest average MPC levels at the perfectly hedged positions of these variables (where NNP or URE = 0). These results indicate that HtM households (1) are winners of monetary expansions and (2) possess less exposed asset positions to inflation or real interest rate changes, compared to the remaining population.
Concerning the main questions, we find evidence of a positive relationship between our open economy proxies for income redistribution (the EHC), but no robust relationship between proxies for redistribution in financial balance sheets (the FC or IEC) and MT. In other words, our macro-analysis consistently captures one out of three RC as suggested by Auclert (2019).
Finally, the effects of redistribution from low to high-MPC households appears to be empirically captured by controlling for the spread of HtM households across the redistribution indicators of NNP, URE and income. Thus, comparing these variable estimates in a regression with MP peaks to the estimates that do not account for HtM behavior produces results that are aligned with theoretical predictions on the spread of MPC across the population. Our results demonstrate the potential value of the micro-interaction approach described herein. We believe it may lend value to forthcoming research in the field and we encourage its application in future works.
2. THEORY
This chapter introduces the theoretical framework of this study by describing some main concepts that are important to the analysis of the empirical results. Part 2.1 reports an overview of the theoretical background, which derives from the contemporary discussion on the role of heterogeneous agents in New Keynesian (NK) models. Part 2.2. presents the theoretical framework of Auclert (2019) on how redistribution affects MT.
2.1. THE TRANSITION FROM RANK TO HANK
The Representative Agent New Keynesian (RANK) model is frequently used by major economic institutions as the standard workhorse model for interpreting economic fluctuations. As the name suggests, this framework lays its microeconomic foundation onto infinitely lived representative agents, which are thought to fully explain the economic reaction to shocks through their household’s Euler equation (Kaplan et al., 2018). The precision of these models began to be strongly questioned after the 2008 financial crisis. Thus, empirical evidence indicated that the bust in housing and mortgage prices had strikingly different effects on households, depending on their balance sheet composition (Kaplan & Violante, 2018).
Thereafter, macroeconomists started to consider extended models, which would account for diversity in portfolio composition, credit exposure and income across households. This process cumulated in the development of the Heterogeneous Agents New Keynesian (HANK) model, initially proposed by Kaplan et al. (2018)).
Technically, HANK extends the conventional New Keynesian (NK) framework by incorporating (1) idiosyncratic income risk which creates a precautionary savings motive amongst economic agents and (2) two asset types with different returns and levels of liquidity through which individuals insure themselves against negative shocks by trading assets in the free capital markets. Under these modifications, the HANK model captures the pro-cyclicality of demand for liquidity constrained (HtM) agents occurring through their inability to smooth consumption.
Importantly, such agents have a higher MPC than the average population, which makes their prominence a strong determinant of aggregate reactions in output to sudden income shocks (Kaplan et al., 2014). Because of these modifications, the HANK framework so far represents the most complete tool available for thoroughly examining the relationship between MP changes and household heterogeneities.
2.1.1. MARGINAL PROPENSITY TO CONSUME
As mentioned, the MPC of households is a crucial cornerstone of the HANK framework because it captures heterogeneities in household consumption behavior, which are strong determinants of aggregate reactions to macroeconomic shocks. The “MPC out of current income” is defined as the share of an aggregate increase in income that is spent on consumption directly:
𝑀𝑃𝐶$ =Δ𝐶$
Δ𝑌$ (1)
Where Δ𝐶$ is the change in consumption and Δ𝑌$ is the change in income at time 𝑡. In an attempt to capture the heterogeneity in households’ reaction to the Great Recession, MPC proved to be a plausible explanation for the magnitude discrepancies between households’ registered income loss and fall in consumption (Kaplan & Violante, 2018). For this reason, the indicator is also relevant when studying redistribution effects on MT. In fact, identifying how MPC is distributed across balance sheet indicator variables at the micro-level allows for an evaluation of the redistribution from low to high-MPC households.
Recent studies indicate that certain household characteristics correlate more strongly with MPC. As mentioned above, the HANK literature emphasizes liquidity constraints as important drivers of aggregate spending behavior. Thus, households that are constrained in their liquid assets have been shown to spend almost all of their available resources in every pay period.
Such households were labeled “Hand-To-Mouth” (HtM) by Kaplan, Violante, & Weidner (2014)1. Since their establishment, the HtM has gained a lot of attention in the empirical literature due to their convenient computation in household data (see Slacalek et al., 2020, Almgren et al.
(2019) and Bilbiie (2020)). In this study, we exploit the HtM qualification to approximate the distribution of MPC across country populations and our relevant redistribution indicators.
Importantly, we use this measure to evaluate the effects of redistributing income and wealth from agents with low to those with high MPC.
In summary, the HANK model and households’ MPC represent a theoretical base on which the effects of household heterogeneities in MT can be understood. Importantly, these concepts allow
1 By definition: ”A household is categorized as living HtM if its liquid wealth is smaller than a certain
share of monthly income” (see Almgren (2019) and Kaplan, Violante, & Weidner, (2014) for rigorous definition).
us to navigate the role of redistribution in the MTM. The following part specifies in detail the identification of this process.
2.2. REDISTRIBUTION IN MONETARY TRANSMISSION
Auclert (2019) proposes a framework identifying the role of inequality and the redistribution of income and wealth in MT. The framework unifies the distributional impact of MP with the effect of disproportional wealth and income gains on MT. Specifically, part 2.2.1. outlines a summary of the theoretical framework while part 2.3.2. introduces in detail the RC that we aim to test.
Part 2.3.3 contains an exposition of the derived model adopted by Auclert (2019). Finally, part 2.3.4 introduces some modifications that are necessary when the framework is applied to open economies.
2.2.1. FRAMEWORK SUMMARY
According to Auclert (2019), the effects of redistribution on MT can be understood in two steps:
STEP 1. MP affects the margins of the wealth and income distribution in countries through its disproportional effects on household balance sheets. Thus, during a monetary expansion, some agents gain while others shrink in their nominal accounts. Following Auclert (2019), we refer to the prior group as ‘winners’ and the latter as ‘losers’ of MP.
Specifically, the net-of-consumption wealth change (𝑑Ω+) from a monetary expansion for a household 𝑖 can be defined as:
𝑑Ω+= 𝑑𝑦.+ 𝑛.𝑑𝑤.− (𝑁𝑁𝑃.)𝑑𝑃
𝑃 + (𝑈𝑅𝐸.)𝑑𝑖9
𝑖9 (2)
Where the two first terms correspond to the increase in unearned income 𝑦. and earned income (𝑛. hours times the change in the wage 𝑤.) effects on wealth from a decrease in the policy rate. The third term represents the effect of nominal wealth exposure to increases in the price levels. This term is negatively related to 𝑑Ω+ and depends on the size of households’ Net Nominal Position (𝑁𝑁𝑃.), which is the present value of their nominal assets. Finally, the fourth term quantifies the change in wealth triggered by a decrease in the real interest rate. Since ;.<
.< < 0, an increase in the Unhedged Interest
Rate Exposure (𝑈𝑅𝐸.), which is the difference between all maturing assets and liabilities at one point in time, results in a negative effect on 𝑑Ω+. Accordingly, equation (2) suggests that agents with negative values of 𝑁𝑁𝑃. or 𝑈𝑅𝐸. are ‘winners’ (increases in their net-of- consumption-wealth) while agents with positive levels of these variables are ‘losers’
(decrease in their wealth) of monetary expansions.
STEP 2. If the winners of MP have a higher MPC than the losers, the final effect on consumption and output will be amplified. This prediction stems from Auclert’s (2019) expression defining the change in consumption 𝐶. for household 𝑖 following a decrease in the interest rate:
𝑑𝐶. = 𝑀𝑃𝐶?.@𝑑𝑌.− 𝑁𝑁𝑃.𝑑𝑃
𝑃 + 𝑈𝑅𝐸.𝑑𝑅
𝑅A − 𝐶.𝜎.C1 − 𝑀𝑃𝐶?.E𝑑𝑅
𝑅 (3)
2Where 𝜎. is the elasticity of intertemporal substitution, 1 − 𝑀𝑃𝐶?. = 𝑀𝑃𝑆?. is the marginal propensity to save and 𝑑𝑌. denotes the overall change in income. According to equation (3), increasing 𝑀𝑃𝐶?. strengthens the effect of income, 𝑁𝑁𝑃., 𝑈𝑅𝐸. and savings 𝑠. = 𝐶.(1 − 𝑀𝑃𝐶.) on the change in individual consumption 𝑑𝐶. ex-post a negative MP shock.
Following market clearing conditions and the fiscal rule, the change in aggregate consumption for a closed economy 𝐼 is defined as:
𝑑𝐶I= 𝐸IJ𝑌.
𝑌𝑀𝑃𝐶?.K 𝑑𝑌 LMMMMNMMMMO
PQQ9RQS$R ITUVWR UXSTTRY
+ 𝑐𝑜𝑣I]𝑀𝑃𝐶?., @𝑑𝑌.− 𝑌.𝑑𝑌. 𝑌 A_
LMMMMMMMMNMMMMMMMMO
`S9T.TQa bR$R9VQRTR.$c UXSTTRY
−𝑐𝑜𝑣IC𝑀𝑃𝐶?., 𝑁𝑁𝑃.E𝑑𝑃 LMMMMMMNMMMMMMO𝑃
d.aXR9 UXSTTRY
+ e 𝑐𝑜𝑣LMMMMMNMMMMMOIC𝑀𝑃𝐶?., 𝑈𝑅𝐸.E
IT$R9Ra$ fS$R `ghVai9R UXSTTRY
− 𝐸LMMMMMNMMMMMOIj𝜎.C1 − 𝑀𝑃𝐶?.E𝑐.k
lima$.$i$.VT UXSTTRY
n𝑑𝑖9
𝑖9
(4)
Here, 𝐸I stands for the aggregated expected value for all households within the economy.
The change in countries’ aggregate consumption from a decrease in the nominal interest rate depends on an aggregate income channel 𝐸Ioppq𝑀𝑃𝐶.r, a substitution channel
2 𝑀𝑃𝐶? =stuvstlstu =wvxstystu ≥ 𝑀𝑃𝐶.
𝐸I[𝜎.(1 − 𝑀𝑃𝐶.)𝑐.];.<
.<, an Earnings Heterogeneity channel 𝑐𝑜𝑣I@𝑀𝑃𝐶., }𝑑𝑌.− 𝑌.;p
p~A, a Fisher channel c𝑜𝑣I(𝑀𝑃𝐶., 𝑈𝑅𝐸.);t
t and an Interest Rate Exposure channel 𝑐𝑜𝑣I(𝑀𝑃𝐶., 𝑈𝑅𝐸.);.<
.<. While the prior two are standard textbook model channels of MP, the latter three captures the effects of redistribution on MT. Particularly, redistribution amplifies the aggregate response in countries consumption and output (𝑑𝐶I) provided that the following conditions hold:
𝑐𝑜𝑣IC𝑀𝑃𝐶? , 𝑌• .E < 0 (5) 𝑐𝑜𝑣IC𝑀𝑃𝐶? , 𝑁𝑁𝑃• .E < 0 (6) 𝑐𝑜𝑣IC𝑀𝑃𝐶? , 𝑈𝑅𝐸• .E < 0 (7)
Equation (5)-(7) implies that redistribution of income and wealth positively affects MT if and only if the covariance terms have negative signs. Thus, this ensures that redistribution occurs in the direction from low to high MPC agents.
To summarize, following this framework, inequality of income and wealth affects MT by establishing conditions that determine the redistribution of wealth from agents with positive or high levels of income, NNP and URE to agents with low or negative values of these indicators.
The redistribution from losers to winners matters to MT because it affects households’
consumption behavior. Specifically, redistributing resources from agents with low (high) to those with high (low) MPC will amplify (dampen) MT.
Positive NNP Negative NNP
Positive URE Negative URE High income
Expansive MP shock
Low income
Aggregate consumption
STEP 1 STEP 2
Image 1: Own illustration of Auclert’s (2019) theoretical framework,
Low MPC High MPC
EHC FC IEC
2.2.2. REDISTRIBUTION CHANNELS
As outlined above, the Auclert (2019) framework highlights three main channels of redistribution in MT. To illustrate in greater detail how these channels operate, we consider a monetary expansion transmitting to the economy in the following way:
𝑀 ↑ ⟹ 𝑖9 ↓ ⟹ 𝐼 ↑ ⟹; 𝑌 ↑; 𝑃 ↑ (8)
When the money base (𝑀) expands, the real interest rate (𝑖9) falls. Since a fall in the real rate lowers the cost of capital, this triggers an increase in investment spending (𝐼) which increases real income (𝑌) and price levels (𝑃) (Mishkin, 1996). This process has disproportional effects on households’ income and wealth, which also determines the subsequent effects on aggregate consumption through the distribution of MPC across NNP, URE and income. The procedure is captured by the following channels, illustrating the role of redistribution in MT:
(1) The Earnings Heterogeneity channel (EHC) illustrates the uneven effects on household income that stems from differences in income sources across the population. It has been shown that, under a monetary expansion, the positive effects of lower unemployment disproportionately benefit low-income households (Lenza &
Slacalek, 2018). Auclert (2019) argues that such a redistribution of income can itself amplify MT. Specifically, the EHC relies on (1) that low-income agents increase more in their income from a monetary expansion than the average population and (2) that these households also have a higher MPC. If the prior is true, the elasticity of agent 𝑖’s income relative to aggregate income, approximated by some constant 𝛾, is negative:
𝛾. ≡𝜕 }𝑌. 𝑌 − 1~
}𝑌. 𝑌 − 1~
𝑌
𝜕𝑌≈ 𝛾 < 0 (9)
In other words, increasing agent 𝑖’s income will result in a lower gain from increases in the aggregate income level 𝑌. Several empirical studies show that expansive MP reduces income inequality (Coibion et al., 2017) and that income risk is countercyclical (Guvenen et al., 2014), supporting the statement of equation (9).
Accepting this and substituting 𝛾𝑐𝑜𝑣I}𝑀𝑃𝐶? ,ppq~ for 𝑐𝑜𝑣I@𝑀𝑃𝐶? , }𝑑𝑌.− 𝑌.;pq
p ~A in equation (4) suggests that that the EHC amplifies MT as long as 𝑐𝑜𝑣I}𝑀𝑃𝐶? ,ppq~ < 0.
(2) The Fisher channel (FC) refers to the effect of an unexpected increase in the price level 𝑃 on the value of nominal balance sheets. Particularly, inflation leads to a nominal denomination of assets and liabilities, lowering the debt burden for borrowers and the value of nominal assets for creditors (Doepke & Schneider, 2006).
Accordingly, under a monetary expansion, wealth is redistributed from nominal creditors to borrowers3. A convenient measure of households’ exposure to changes in price level is their Net Nominal Position (NNP), which is defined as the present value of their nominal assets (Auclert, 2019):
𝑁𝑁𝑃$ ≡ ˆ𝑄𝑡
𝑡≥0
Š−1 𝑡𝐵
𝑃0 Œ (10)
Where 𝑄$ is the price of a nominal zero-coupon bond paying at time 𝑡. •w $𝐵 is the quantity of consolidated nominal claims such as long term bonds, mortgages or deposits inherited from period 𝑡 = −1 and 𝑃Ž is the price level at 𝑡 = 0. According to equation (2), a higher 𝑁𝑁𝑃 is linearly associated with a negative change in wealth from a permanent increase in the price level •tt at 𝑡 = 0. Specifically, following an unexpected increase in the price levels, nominal wealth will be distributed from households with positive to those with negative NNP levels. Provided that equation (6) holds, this redistribution will amplify MT. Thus, this implies that the gains are held by agents with a higher MPC than the remaining population.
(3) The Interest Rate Exposure channel (IEC) captures the uneven change in wealth from a falling real interest rate 𝑖9 that stems from differences in the asset position and maturity structure of household balance sheets. Specifically, if the assets of a household have a longer (shorter) duration than its liabilities, a negative shock to the real rate will lower (increase) their wealth. A comprehensive measure of households’
3 By “nominal” we refer to the asset/liability positions denominated in Euros.
exposure to changes in the interest rate is their Unhedged Interest Rate Exposure (URE). In the Auclert (2019) definition, it is computed as:
𝑈𝑅𝐸 ≡ 𝑦 + 𝑤𝑛 + Š−1 0𝐵 𝑃0
Œ+−1𝑏0− 𝑐 (11)
Where 𝑦 denotes unearned income and 𝑤𝑛 equals earning salary. ’“ ”t‘
” denotes the consolidated claims of nominal assets at 𝑡 = 0 from the perspective of 𝑡 = −1 and •w𝑏Ž refers to the consolidated claims of real assets given the same time perspective.
Finally, 𝑐 denotes total consumption. Accordingly, equation (11) gives the difference between the total amount of maturing assets and liabilities, which signals the exposure to a temporary change in the real interest rate at 𝑡 = 0. Similar to the FC, a monetary expansion will redistribute wealth from households with positive to those with negative URE. Thus, lowering the real interest rate results in a negative effect on wealth when 𝑈𝑅𝐸 > 0 and to a positive effect when 𝑈𝑅𝐸 < 0. Again, provided that equation (7) holds, the IEC will amplify MT since the winners of lower real rates will also have a higher MPC than the losers.
The combined effect of the three channels together with the standard substitution and income channel will determine the total impact on the change in aggregate consumption from a shock in the policy rate, as illustrated by equation (4).
2.2.3. THE MODEL
This part presents in detail the model derived by Auclert (2019), identifying the role of RC in the MTM. Auclert assumes a closed economy where households have separable preferences over consumption 𝑐$ and hours of work 𝑛$. Economic agents solve the following optimization problem:
max ˆ 𝛽${𝑢(𝑐$) − 𝑣(𝑛$)}
$
(12) Subject to a ‘flow’ budget constraint:
𝑃$𝑐$= 𝑃$𝑦$+ 𝑊$𝑛$+ C$•w $𝐵 E + ˆ( 𝑄$ $va)(
ažw
C$•w $va𝐵 − 𝐵$ $vaE + 𝑃$C$•w $𝑏 E
+ ˆC 𝑞$ $vaE
ažw
𝑃$vaC$•w $va𝑏 − 𝑏$ $vaE
(13)
Importantly, equation (13) states that the total consumption at time 𝑡 must equal the value of unearned income, 𝑃$𝑦$, earned income,𝑊$𝑛$, an inherited portfolio of zero coupon bonds (ZCB) from 𝑡 − 1 ($•w $𝐵 ), the value of nominal ZCBs paying at 𝑡 + 𝑠 (∑ažw( 𝑄$ $va)((𝐵$va$•w− 𝐵$va$ )) and real ZCBs (∑ažw(𝑞$va$ )𝑃$va(𝑏$va$•w− 𝑏$va$ )). While $ $va𝑄 denotes the time 𝑡 price of a nominal ZCB paying at 𝑡 + 𝑠, $ $va𝑞 refers to the price for a real ZCB with similar time frame.
The nominal term structure is determined by the Fisher equation through the assumption of no-arbitrage:
𝑄$va = C 𝑞$ $vaE 𝑃$
𝑃$va, ∀ 𝑡, 𝑠 (14)
Under a terminal condition of a finite horizon economy or a transversality condition that the economy has an infinite horizon, the flow budget constraint turns into an intertemporal budget constraint:
ˆ 𝑞$𝑐$
$žŽ
= ˆ 𝑞$(𝑦$+ 𝑤$𝑛$) LMMMMNMMMMO$žŽ
¢£
+ ˆ 𝑞$
$žŽ
](•w𝑏$) + @(•w𝐵$) 𝑃$ A_
LMMMMMMMMNMMMMMMMMO
¢¤
= 𝜔 (15)
Which implies that the present value of consumption needs to equal total wealth, which is the sum of human wealth (𝜔b) and financial wealth (𝜔d).
We now consider a monetary expansion at 𝑡 = 0 with macroeconomic outcomes as in equation (8). This yields the following marginal changes in consumption (𝑐), hours worked (𝑛) and utility (𝑈):
𝑑𝑐 = 𝑀𝑃𝐶(𝑑Ω + 𝜓𝑛𝑑𝑤) − 𝜎𝑐𝑀𝑃𝑆𝑑𝑖9
𝑖9 (16)
𝑑𝑛 = 𝑀𝑃𝑁(𝑑Ω + 𝜓𝑛𝑑𝑤) + 𝜓𝑛𝑀𝑃𝑆𝑑𝑖9
𝑖9 + 𝜓𝑛𝑑𝑤
𝑤 (17)
𝑑𝑈 = 𝑢§(𝑐)𝑑Ω (18)
Here, MPN refers to the marginal propensity to work and 1 − 𝑀𝑃𝐶 = 𝑀𝑃𝑆 is the marginal propensity to save. 𝑑Ω is the net-of-consumption change in wealth, which is defined as:
𝑑Ω = 𝑑𝑦 + 𝑛𝑑𝑤 − ˆ 𝑄$
$žŽ
Š•w $𝐵 𝑃Ž Œ𝑑𝑃
𝑃 + Š𝑦 + 𝑤𝑛 + Š•w Ž𝐵
𝑃Ž Œ + C 𝑏•w ŽE − 𝑐Œ𝑑𝑅
𝑅 (19)
Here, we call the nominal value of the financial assets ∑$žŽ𝑄$@’“ ¨‘
t” A the NNP of households.
Furthermore, the net saving requirement of a household at 𝑡 = 0 from the view of 𝑡 = −1 equals 𝑦 + 𝑤𝑛 + @’“ ”‘
t” A + C 𝑏•w ŽE − 𝑐, which corresponds to household URE. Equation (19) hence becomes:
𝑑Ω = 𝑑𝑌 + 𝑛𝑑𝑤 − (𝑁𝑁𝑃)𝑑𝑃
𝑃 + (𝑈𝑅𝐸)𝑑𝑖9
𝑖9 (20)
Given a change in total income 𝑑𝑌 = 𝑑𝑦 + 𝑛𝑑𝑤 + 𝑤𝑑𝑛, we get the household response to the monetary expansion by substituting equation (20) into (16):
𝑑𝑐 = 𝑀𝑃𝐶? @𝑑𝑌 − 𝑁𝑁𝑃𝑑𝑃
𝑃 + 𝑈𝑅𝐸𝑑𝑖.
𝑖9A − 𝜎𝑐C1 − 𝑀𝑃𝐶? E𝑑𝑅
𝑅 (21)
where 𝑀𝑃𝐶? = 𝑀𝑃𝐶
𝑀𝑃𝐶 + 𝑀𝑃𝑆= 𝑀𝑃𝐶
1 + 𝑤𝑀𝑃𝑁≥ 𝑀𝑃𝐶 (22)
So the specific definition of 𝑀𝑃𝐶? is how much of the remaining amount of income that is consumed.
Now, imagine that this economy has 𝐼 heterogeneous households 𝑖 with different incomes, NNP and URE. The labor market clearing conditions after the monetary shock imply that the aggregate change in gross income equals the total change in the Gross Domestic Product (GDP), 𝑑𝑌 = 𝐸I[𝑑𝑌.]. Moreover, market clearing for nominal assets results in that all nominal positions cancel each other out except for the assets of the government:
𝐸I[𝑁𝑁𝑃.$] = 𝑏© = −𝑁𝑁𝑃Q$, ∀𝑡 (23) 𝐸I[𝑈𝑅𝐸.$] = 𝑌$− 𝐸I[𝑡.$] +𝐵$
𝑃$− 𝐶$= 𝐺$+𝐵$
𝑃$− 𝐸I[𝑡.$] = −𝑈𝑅𝐸Q$ (24) Aggregating the effect change in individual consumption across all households yields:
𝑑𝐶I= 𝐸IC𝑀𝑃𝐶?.E ∗ @𝐸I(𝑑𝑌.) − 𝐸I(𝑁𝑁𝑃.)𝑑𝑃
𝑃 + 𝐸I(𝑈𝑅𝐸.)𝑑𝑅
𝑅A − 𝜎𝐶I}1 − 𝐸UC𝑀𝑃𝐶?.E~𝑑𝑅
𝑅 (25)
Following market clearing conditions and the fiscal rule, the change in aggregate consumption from the transitory shock can be decomposed into 5 channels:
𝑑𝐶I= 𝐸IJ𝑌.
𝑌𝑀𝑃𝐶?.K 𝑑𝑌 LMMMMNMMMMO
PQQ9RQS$R ITUVWR UXSTTRY
+ 𝑐𝑜𝑣I]𝑀𝑃𝐶?., @𝑑𝑌.− 𝑌.
𝑑𝑌. 𝑌 A_
LMMMMMMMMNMMMMMMMMO
`S9T.TQa bR$R9VQRTR.$c UXSTTRY
−𝑐𝑜𝑣IC𝑀𝑃𝐶?., 𝑁𝑁𝑃.E𝑑𝑃 LMMMMMMNMMMMMMO𝑃
d.aXR9 UXSTTRY
+ e 𝑐𝑜𝑣LMMMMMNMMMMMOIC𝑀𝑃𝐶?., 𝑈𝑅𝐸.E
IT$R9Ra$ fS$R `ghVai9R UXSTTRY
− 𝐸LMMMMMNMMMMMOIj𝜎.C1 − 𝑀𝑃𝐶?.E𝑐.k
lima$.$i$.VT UXSTTRY
n𝑑𝑖9 𝑖9
(26)
Note that (26) is identical to equation (4).
2.2.4. OPEN ECONOMY ADJUSTMENTS
The theoretical conclusions of equation (26) rely on the assumptions of closed economies and on the equalities of equations (23) and (24). These imply that within the Auclert (2019) theoretical framework, all losses and gains from MP amongst households cancel out due to market clearing and closed borders. In an open economy framework, (23) and (24) does not hold because the redistribution of income, NNP and URE occur between domestic countries and the rest of the world. In other words, when borders are open, economies can benefit or suffer on average from a monetary expansion, which is determined by the respective levels of 𝐸I(𝑁𝑁𝑃.), 𝐸I(𝑈𝑅𝐸.) and 𝐸I}pq
p¬~, where the latter denotes the relative income level of each country in reference to the global average 𝑌x4. Although this changes the precise predictions of equation (26)5, the RC still work in the same direction. The difference is that some countries will have more winners than losers ex-post a monetary expansion, in which case MT should be stronger. To adjust the Auclert (2019) framework to an open economy one, we rewrite equation (26) accordingly:
4 Auclert (2019) also mentions this in his paper, briefly elaborating on the implications of country net gains and the role of outside rebates.
5 For example, it is not possible to replace 𝐸I(𝑀𝑃𝐶.∗ 𝜃.), 𝜃 = ¯pq
p, 𝑈𝑅𝐸, 𝑁𝑁𝑃°, to covariance terms of 𝑐𝑜𝑣I(𝑀𝑃𝐶., 𝜃.).
𝑑𝐶I= 𝐸IJ𝑌.
𝑌𝑀𝑃𝐶?.K 𝑑𝑌 LMMMMNMMMMO
PQQ9RQS$R ITUVWR UXSTTRY
+ 𝐸I]𝑀𝑃𝐶?.∗ @𝑑𝑌.− 𝑌.
𝑑𝑌. 𝑌 A_
LMMMMMMMMNMMMMMMMMO
`S9T.TQa bR$R9VQRTR.$c UXSTTRY
−𝐸IC𝑀𝑃𝐶?.∗ 𝑁𝑁𝑃.E𝑑𝑃 LMMMMMMNMMMMMMO𝑃
d.aXR9 UXSTTRY
+ e 𝐸LMMMMNMMMMOIC𝑀𝑃𝐶?.∗ 𝑈𝑅𝐸.E
IT$R9Ra$ fS$R `ghVai9R UXSTTRY
− 𝐸LMMMMMNMMMMMOIj𝜎.C1 − 𝑀𝑃𝐶?.E𝑐.k
lima$.$i$.VT UXSTTRY
n𝑑𝑖9
𝑖9
(27)
Equation (2) and (27) now illustrates the main theoretical effects of heterogeneities in MT. Thus, assuming an open economy framework, MT can be affected by a redistribution across agents with different MPC and by the average household position of NNP, URE and income. If we would like to separate the aggregate effects of wealth or income gains (step 1 of 2.2.1) from the effect that is caused by the redistribution from low to high MPC agents (step 2 of 2.2.1), a relevant indicator would be the difference in effect between 𝐸Ij𝑀𝑃𝐶?.∗ 𝜃gk and 𝐸I[𝜃g], 𝜃g = {𝑑𝑌𝑖− 𝑌𝑖𝑑𝑌𝑖
𝑌 , 𝑁𝑁𝑃., 𝑈𝑅𝐸.} on MT. Thus, while 𝐸I[𝜃g] signal a country’s net effect of NNP, URE or income levels on MT, 𝐸Ij𝑀𝑃𝐶?.∗ 𝜃.k captures the effect of redistribution from low to high MPC households. Below we list some theoretical modifications in regard to the RC.
2.2.4.1. THE EARNINGS HETEROGENEITY CHANNEL
The open economy adjustments have implications for the choice of appropriate proxy for the EHC on the country-level. To see this, consider a closed economy where we know that income is redistributed from high to low-income households following a monetary expansion. Provided that the latter group has higher MPC, the relationship between income inequality and MT should be positive. In other words, we require a measure of income inequality to test the mechanism underpinning the EHC. One appropriate such measure is the income Gini, which captures the frequency of individuals that are low income compared to those that are high income. However, in the case of open economies, the disproportional income gain caused by heterogeneities in earnings stands in relation to the average income levels of all countries affected by the policy rate change. In this context, we cannot ensure that redistribution only happens between agents within the domestic economy, implying that the classification of low- income households is no longer dependent on the income distribution (the income Gini) in each country. Instead, it depends on the ‘global’ income distribution across all countries affected by
the common MP shock. Therefore we require a measure describing the prevalence of low-income agents relative to the Euro area average to capture the EHC in open economies.
2.2.4.2. THE FISHER CHANNEL & INTEREST RATE EXPOSURE CHANNEL As for the EHC, the derived measures for the FC and the IEC depend on the degree of openness in economy 𝐼. In equation (26), these are expressed as the covariance between MPC and NNP or URE. When economies are open, the covariance terms fail to capture the complete effects of balance sheet differences on MT since they rely on the assumption that all gains and losses net out. Instead, computing the proxies as 𝐸Ij𝑀𝑃𝐶?.∗ 𝜃.k, 𝜃 = {𝑈𝑅𝐸., 𝑁𝑁𝑃.} ensures that the average exposure of the economy as a whole is accounted for.
The open economy framework suggests that two components are underpinning the FC and IEC on the country-level. Firstly the average values 𝐸U(𝑁𝑁𝑃.) and 𝐸U(𝑈𝑅𝐸.) signal the NNP or URE position of countries on average, indicating the wealth exposure of each country’s population.
For example, while a country with an average negative URE or NNP will gain wealth from a monetary expansion (all else equal), a country with a positive URE or NNP average will experience a loss in the value of nominal or real assets following a negative shock in the interest rate. Arguably, countries with a greater wealth effect should also increase more in their consumption, amplifying the response to MP. Secondly, the MPC-weighted share of NNP and the URE, 𝐸U(𝑀𝑃𝐶. ∗ 𝑁𝑁𝑃.) and 𝐸U(𝑀𝑃𝐶.∗ 𝑈𝑅𝐸.), captures the effect of redistribution from low to high-MPC households. Hence, although a country would have zero exposures to inflation or real rate changes on the aggregate level (implying that 𝐸U(𝜃.) = 0), the response in consumption may still be affected by a redistribution on the household level. For example, if 𝐸U(𝑀𝑃𝐶.∗ 𝑁𝑁𝑃.) <
𝐸U(𝑁𝑁𝑃.), this implies that agents with higher MPC have a lower NNP on average, so wealth will be redistributed from low to high MPC agents following a monetary expansion. This process should also amplify MT.
We keep these important realizations in mind while computing our channel proxies in chapter 4 as well as the econometric models in chapter 5.
3. LITERATURE REVIEW
This chapter contains an in-depth summary of the existing literature on redistribution in the MTM. In particular, it specifies the context of our study in the light of existing theoretical models and empirical evidence.
In summary, our contribution to the field is twofold. Firstly, while many existing studies point towards disproportional effects of MP across households, we check whether such differences can explain the variation in aggregate reactions to MP across countries. As opposed to the existing studies that investigate the interplay between redistribution and MT through enriched DSGE models, we propose a more immediate empirical approach to evaluate the pattern of correlations on the macro level. Specifically, we employ a Local Projections Instrumental Variable (LP-IV) technique to estimate countries’ aggregate reactions to MP, relating the cross-country variation to indicators of household heterogeneities. In doing so, we follow closely the work of Almgren et al. (2019) in regard to the overall empirical methodology and to the estimation strategy of MP shocks. In their study, the authors estimate the effect of liquidity constraints on the strength of output responses to MP shocks in EA countries. By estimating separate country impulse responses, relating these to microdata on liquidity constraints, they find that a larger fraction of liquidity constrained households amplifies MT. Our work replicates this method, but instead relates the IRF peaks to redistribution indicators. Secondly, using this approach, we explore the prevalence of the specific RC presented by Auclert (2019) across 18 EA countries. Surprisingly, although many studies consider the distributional effects of MP, few studies empirically test for the subsequent effects of redistribution on MT. Here our study brings new evidence, especially in regard to explaining cross-country variation in MT through heterogeneities in household balance sheets and MPC.
To outline the previous methods used to estimate aggregate reactions to MP shocks, and the existing evidence on redistribution effects in MT, this chapter prevails as follows. Part 3.1.
contains an in-depth overview of the use of LP-IV in empirical work and its comparison with the S-VAR approach. Part 3.2. presents the existing literature on the effects of household heterogeneities in MT. Part 3.3. summarizes the contemporary evidence on MP and redistribution.
3.1. ESTIMATING MONETARY TRANSMISSION
3.1.1. CHOOSING THE MODEL: S-VAR VERSUS LOCAL PROJECTIONS The empirical practice of recovering structural shocks to estimate their propagating effects on economic variables has typically relied on two types of econometric model specifications: the Structural Vector Autoregression (S-VAR) introduced by Sims (1980) and the Local Projections (LP) technique, initially proposed by Jordà (2005). These methods are used in combination with several identification schemes, all justified by models of full-information rational expectations, to compute dynamic multipliers of interest such as impulse responses and forecast error variance decompositions (Miranda-Agrippino & Ricco, 2017). Our work employs the latter technique due to its simplification of the computational complexity of the S-VAR approach. In particular, thanks to a horizon-specific regression, the LP allows one to skip the iterated one- period-ahead estimation of impulse responses that is typical for a VAR specification (Ramsey, 2016). Thus, each equation of the LP model can be estimated individually by least squares (Kilian & Lütkepohl, 2017). In addition to this, Jordà (2005) claims that the LP approach is also more robust to model misspecification. In fact, it is argued that the VAR process cannot be assumed as an accurate representation of the Data Generating Process (DGP) with absolute certainty. Therefore, given a misspecified S-VAR, the derived impulse responses will generate a biased estimation because specification errors get compounded at each horizon. Finally, Jordà (2005) also highlights that the LP offers superior accommodation to non-linear specifications.
In order to furtherly clarify the differences between the two methods, we include a technical comparison of the IRF construction using LP and S-VAR in the Appendix (10.2).
In the literature, the acknowledgment of Jordà (2005) improvements to the existing S-VAR methodology is highly debated. Kilian & Lütkepohl (2017) argue that LP impulse response estimator still depends on the S-VAR estimate of the structural impact multiplier matrix. In other words, the LP method does not relax any of the assumptions of the S-VAR model. On top of this, Kilian & Kim (2011) and (Lütkepohl et al., 2015) claim that the confidence intervals of the structural Impulse Response Functions (IRF) generated by the LP estimator are less accurate than those of obtained through VAR estimation. More recent studies, such as Brugnolini (2018), show equal and even better performance of LPs when the lag lengths for each forecast horizon are adequately fixed. This intuition has been supported lately by Plagborg- Møller & Wolf (2020) whose simulations demonstrate that linear LP and S-VAR models in fact estimate the same impulse responses in the population of interest. This is due to the fact that
the LP IRF can only be obtained through an appropriately ordered recursive S-VAR, and that any S-VAR IRF can be only obtained through a LP with appropriate control variables.
3.1.2. INSTRUMENTAL VARIABLE SPECIFICATIONS
Despite the above critiques, the LP approach has been used broadly in applied research. To facilitate various applications, a wide range of evolved specifications of the model have been developed. Especially relevant to our work is the instrumental variable (IV) modification of the LP model as developed by Jordà et al. (2015) and Valerie A. Ramey & Zubairy (2018). This LP- IV method allows for the identification of an exogenous shock is fully unexpected. Importantly, due to its exogenous identification strategy, the LP-IV approach is immune to the critiques outlined in part 3.1.1 regarding the dependence of the LP method on the VAR specification.
The purpose of the IV modification is thus to isolate the share of the shock in the model that is exogenous, estimating its causal effect on macroeconomic outcomes. Technically, introducing the IV in the LP setting implies including a variable that is strictly correlated with the shock of interest, yet that it is not correlated with any other shock outside the model. If this exogeneity condition holds, the instrumental variable captures the exogenous variation which can only be attributed to the shock of interest (Stock & Watson, 2018). Both Stock & Watson (2018) and V.
A. Ramey, 2016 highlight that the validity of the instrument is not only conditional to its contemporaneous exogeneity but also to its “lead-lag” exogeneity, implying exogeneity with respect to past shocks. Under the breach of the latter, the authors propose an inclusion of additional regressors which can control for the lagged shocks.
In using the LP-IV, we add to the increasing amount of literature using LP-IVs in exiguous shock identification exercises. These include the study by Jordà et al. (2015) which assesses the reaction of house prices to the unexpected changes in interest rates, the work of Alpanda &
Zubairy (2019) which considers the efficiency of MP depending on households’ debt levels. In addition to these works, Coibion et al. (2017) uses the LP-IV technique to empirically evaluate the effects of MP shocks on various income and wealth inequality measures. Finally, the novel publication of Barnichon & Mesters (2021) highlights the LP-IV as a valid approach to estimate the Phillips multiplier.
3.1.3. THE APPLICATION TO MONETARY POLICY SHOCKS
In our work, we attempt to estimate countries’ output responses to unexpected innovations in the policy rate. Therefore, our choice of method particularly relates to the literature on the external identification of MP shocks. V. A. Ramey (2016) provides a detailed summary that divides the existing empirical literature on this matter into two approaches. The first one, outlined by Romer & Romer (2004), combines the use of Greenbook forecasts6 with narrative methods to construct a new measure of MP shocks. This approach involves deriving intended federal funds rate changes during Federal Open Market Committee (FOMC) meetings using narrative methods, regressing these on the current rate and on the Greenbook forecasts of output growth and inflation at each FOMC date. The residuals of such regressions can be used as MP shock measures since they closely capture exogenous reactions, while the rest of the regression captures the endogenous response of policy to information about the economy.
The second approach is known as High Frequency Identification (HFI), which exploits the fact that a considerable amount of monetary announcements usually take place, and the jumpy way in which monetary news is revealed allows for an identification scheme based on discontinuity.
The application of HFI was initially introduced in a S-VAR framework by the study of Gertler and Karadi (2015), which uses high-frequency movements in the Federal Funds futures rates around the MP announcements by the FOMC to capture MP shocks. More recent studies highlight the applicability of this method in a EA framework (see Ampudia & Van den Heuvel ( 2017), Almgren et al. (2019) and Jarociński & Karadi (2020)). Specifically, the EA application involves a rolling window of the Overnight Interest Swap (OIS) rate as the relevant instrument when identifying an MP shock orchestrated by the ECB.
Due to our focus on EA economies, we choose to employ the HFI approach rather than the one by Romer & Romer (2004) because of its immediate applicability to the European framework.
Accordingly, in addition to the baseline LP-IV framework outlined above, our methodological approach draws extensively on the works by Ampudia & Van den Heuvel ( 2017), Almgren et al. (2019) and Jarociński & Karadi (2020) in estimating the MP shock caused by a decrease in the EONIA.
6 Projections of various macroeconomic indicators for the economy of the US produced by the FED before each meeting of the FOMC. These forecasts are made available to the public five years after their realization.
3.2. RELATING MACRO-DYNAMICS TO MICRO- HETEROGENEITIES
3.2.1. METHODOLOGICAL OVERVIEW
To evaluate the theoretical predictions of HANK models, the exogenous shock identification outlined above is useful in producing variables that can be related to indicators of micro- heterogeneities. Due to the development of such methods, researchers can produce studies that jointly evaluate the impact of micro-heterogeneities on macro-dynamics.
Especially relevant to our study is the previous research that considers household heterogeneities in monetary transmission. In the choice of estimation method, Colciago et al.
(2019) categorize the existing literature into two groups7. Firstly, the “Bottom-Up” approach, refers to the models derived from the micro-level to the macro-level. By establishing a theoretical framework subject to economic assumptions, this approach provides a detailed image of the dynamic relationship between household heterogeneities and aggregate dynamics.
Secondly, the “Top-Down” approach refers to the studies that test the significance of household heterogeneities ex-post the estimation of aggregate shocks. While our study belongs in the latter category, the prior is crucial to the hypotheses and theoretical predictions underpinning our analysis.
3.2.2. THE “BOTTOM-UP” APPROACH
The majority of studies considering the interplay between household heterogeneities and monetary transmission employs the Bottom-Up approach. The typical aim of these works is to quantify the role of various microeconomic conditions in macroeconomic outcomes. According to Slacalek et al. (2020), two specific methods permeates the literature. On the one hand, some studies develop rich DSGE models that test the validity of HANK predictions through calibration techniques. The simulated dynamics generated by such models are then typically compared to observed aggregate data to evaluate the precision of theoretical predictions.
Gornemann et al. (2016) builds an NK model featuring labor-market risk and preferences for the stabilization of unemployment vis á vi price stability, and find that such modifications affect the MT to consumption, but not to output. Moreover, Kaplan et al. (2018) establish a model incorporating liquidity constraints and income-risk, which generates distributions of MPC and
7 Note that: the criteria for this categorization do not match the ones in (Colciago et al., 2019)
wealth across the population which are similar to the ones observed in empirical data. Finally, Luetticke (2020) uses a HANK framework to explore the driving forces of investment and redistribution in MT. He finds that, while investments are significant drivers of MT, redistribution dampens the elasticity of investment via household heterogeneities in the liquidity premium and in the marginal propensity to invest. On the other hand, other studies rely on more simplifying model assumptions to provide straightforward analytical insights. For example, Slacalek et al. (2020) evaluate the RC of MP by applying a “back of the envelope approach”, which consists of an analytical decomposition that categorizes the population into different groups according to assumed economic behavior8. Bilbiie (2020) constructs economic multipliers as indicators of aggregate demand by exploiting heterogeneity features in the population. Finally, Auclert (2019) estimates the components of his derived model on redistribution in MT using US and Italian household data and concludes that the model reproduces realistic predictions of macroeconomic outcomes.
While the prior group of studies facilitates a comprehensive business cycle analysis subject to endogenous MP, the second minimizes computational complexity and offers a clear insight into the nature of existing economic forces.
3.2.3. THE “TOP-DOWN” APPROACH
This study employs the Top-Down approach due to its usefulness in explaining variations in aggregate dynamics across countries. The Bottom-Up approach would be the more appropriate choice if we were to consider the detailed impact of redistribution within one economy. However, while the latter investigation was already executed by Auclert (2019), no study has yet tested the explanatory strength of redistribution in regard to cross-country MT differences.
The Top-Down approach provides an immediate empirical way of testing theoretical predictions.
Thus, this method typically relies on analyzing the pattern of correlations between macro and aggregated micro variables. Examples include the work of Almgren et al. (2019) from which our methodology closely derives, where the authors relate countries’ reactions from MP announcements to liquidity constraints. Furthermore, in our estimation set-up, we draw inspiration from Voinea et al. (2018) in capturing how household responses to MP depends on
8 Specifically, the authors use different HtM qualifications to identify how these households interact with various MT channels.
