E0 | Macro Paper Warehouse

A Housing Portfolio Channel of QE Transmission

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper identifies and quantifies a housing portfolio channel of quantitative easing (QE) transmission that operates through household portfolio rebalancing toward second homes (as opposed to the well-studied bank credit channel). The central question is whether, and how much, the ECB’s formal adoption of QE in January 2015 induced households with larger pre-existing bond holdings to shift wealth into residential real estate—specifically second homes held for investment—and what the downstream effects on regional housing market outcomes were.

Setting and Motivation

Germany is used as the empirical laboratory because it experienced a sustained housing boom from 2009 onward that was not accompanied by a household credit boom—a “housing boom without a credit boom.” The national house price-to-rent ratio rose markedly from 2009, especially accelerating after QE adoption in 2015, while the stock of mortgage credit to households as a share of GDP was flat or declining. This decoupling makes Germany well-suited for isolating a non-credit portfolio rebalancing mechanism.

Data

Household-level data come from the Deutsche Bundesbank’s Panel on Household Finances (PHF), a triennial survey fielded in 2011, 2014, and 2017, from which the authors construct a panel of 1,651 households. The key exposure variable is each household’s pre-QE (2014) share of total wealth invested in bonds, both directly and indirectly via mutual funds and insurance. Regional housing outcomes (prices, rents, rental yields) are from Bulwiengesa AG for all 401 German administrative regions (Kreise) at annual frequency, and listing data come from Immoscout 24, Germany’s largest online real estate platform.

Methodology

The household-level analysis uses a difference-in-differences (DiD) specification comparing changes in housing portfolio shares between the pre-QE wave (2014) and the post-QE wave (2017), against the pre-period change (2011 to 2014), with the degree of exposure measured by the 2014 bond share. The specification includes household and time fixed effects. A parallel-trends check using all three survey waves (Figure 2) shows that more- and less-exposed households tracked identically before QE adoption, diverging sharply thereafter. Two indirect placebo tests—using households’ share in non-financial, non-housing assets as a spurious treatment, and using the change in non-financial assets as a spurious outcome—both return null results, supporting the identification assumption. For regional housing outcomes, the authors use a panel regression interacting lagged ECB debt-securities-to-GDP (the QE intensity measure) with a regional exposure variable—the 2008 pre-QE share of refugees housed in independent accommodations—across 401 regions from 2010 to 2017.

Main Findings with Quantitative Magnitudes

Benchmark portfolio rebalancing: A household with an ex-ante bond share that is 10 percentage points higher (roughly the interquartile range of the bond share distribution) increases its portfolio share of second homes by 1.72 to 1.87 percentage points more than a less-exposed household after QE adoption, conditional on household and time fixed effects. This result is statistically significant at the 1% level across multiple specifications and is robust to alternative bond share definitions, alternative portfolio denominators, and controlling for negative interest rate policy exposure (via initial deposit shares).
Equity rebalancing: Controlling for risk aversion does not attenuate the second-home result. Strikingly, households with larger ex-ante bond shares reduce, rather than increase, their equity shares after QE (coefficient: −0.042, significant at 5%), ruling out the interpretation that the housing result merely picks up broad rebalancing toward all risky assets. This implies that cash purchases of second homes are funded by liquidating bonds, drawing down deposits, and also selling equities.
Heterogeneity—household characteristics: Rebalancing is stronger for (a) bank-advised households (triple-interaction significant at 5%), (b) financially more literate households (significant at 1%), and (c) households aged 40–60 (significant at 5%), consistent with a lifetime-income-peak, tax-optimization motive rather than a bequest motive. The result for age 61+ is positive but statistically insignificant.
Tax-motive heterogeneity: In Germany, rented-out second homes (or those declared for future letting) benefit from substantial tax deductions not available for owner-occupied primary residences, with the advantage rising in marginal tax rates. Rebalancing is stronger for higher-income households (triple interaction with income per capita positive and significant, especially after controlling for deposit shares) and for church-affiliated households, who face an additional 8–9% church tax surcharge on their regular tax bill, amplifying the tax gain from rental property deductions. For church members, the income-interaction triple coefficient is statistically significant; for non-church members it is not, directly linking the rebalancing gradient to the church tax burden.
Buy-to-let motive: The benchmark result is driven entirely by households that already owned a second home in the pre-QE period and were generating rental income from it (coefficient 0.821, significant at 1%); households without a pre-owned second home show a near-zero, statistically insignificant coefficient (0.000). This establishes that the rebalancing is driven by experienced buy-to-let investors, not vacation-home buyers or commuters.
Credit channel control: The portfolio rebalancing result is not driven by credit access or credit growth. The triple interactions of the bond-share × Post term with both (a) pre-QE leverage (mortgage credit to housing wealth) and (b) post-QE mortgage credit growth are statistically insignificant. Restricting the sample to households with no mortgage credit growth leaves the main coefficient essentially unchanged (0.175, significant at 1%). Nonetheless, an independent credit-channel effect is also present: mortgage credit growth has its own positive and significant effect on second-home share increases, confirming the two channels operate in parallel but independently.
Regional housing market outcomes—prices and yields: In regions more exposed to rental market tightness (higher refugee-in-independent-accommodation share), QE is associated with larger declines in rental yields. A one-standard-deviation increase in QE (approximately 4.3 pp higher ratio of ECB debt securities to GDP) reduces the rental yield in the 75th-percentile-exposure region relative to the 25th-percentile region by 2 to 12 basis points per year (depending on whether the refugee share or the renter share is used as the exposure measure). As ECB holdings rose from 7% of GDP in 2014 to 24% in 2017, the cumulative implied rental yield decline at the regional interquartile range is 8 to 48 basis points, sizable relative to the average regional rental yield decline of 140 basis points (from 7.4% to 6.0%) over the same period. House prices increase more than rents in more exposed regions.
Regional housing market outcomes—listings: Using Immoscout 24 data, both sale and rental listings decline in more exposed regions as QE expands, but the ratio of sale to rental listings falls significantly: sale listings decrease significantly more than rental listings in more exposed regions. This relative shift in supply toward the rental market is interpreted as evidence consistent with the buy-to-let motive documented at the household level and as potentially having benign implications for housing affordability through increased rental supply.

Scope Conditions

All household-level findings are conditional on the German institutional setting: Germany’s combination of a low-homeownership norm, substantial tax incentives favoring rental properties, triennial household survey data spanning one pre- and one post-QE wave, and a housing boom that was decoupled from household credit prior to 2015. The regional results apply to 401 German administrative regions (Kreise) over 2010–2017, using exposure instruments that are argued to capture rental-market tightness or depth rather than direct household bond holdings.

In depth

Q1. What is the housing portfolio channel of QE transmission, and how does it differ mechanically from the credit channel?

A: In the housing portfolio channel, the ECB’s bond purchases reduce the net supply of bonds available to private investors, raising bond prices and reducing expected bond returns. Under the assumption that bonds and houses are substitutes in household portfolios, households with larger initial bond positions rebalance toward housing to restore their target allocation, bidding up house prices. This mechanism operates through changes in risk premia rather than through future short-term rates or bank reserves and loan supply. The credit channel, by contrast, operates through increased bank reserves enabling expanded mortgage lending. The authors show empirically that the two channels operate in parallel and independently, but that greater prior credit access and post-QE mortgage credit growth do not amplify the portfolio rebalancing effect.

Q2. What is the key exposure variable and why is it a valid identification strategy?

A: The exposure variable is each household’s 2014 (pre-QE) share of total wealth invested in bonds, including both direct holdings and indirect holdings via mutual funds and insurance companies. The logic, drawn from the bank-portfolio-rebalancing literature (Rodnyansky and Darmouni, 2017; Luck and Zimmermann, 2020) and from the authors’ own portfolio model, is that the larger a household’s bond share, the stronger its incentive to rebalance when the central bank reduces bond supply. Identification rests on the parallel-trends assumption: Figure 2 shows that before 2015, more- and less-exposed households (defined by a median split on the 2014 bond share) followed identical trends in second-home shares; the trends diverge sharply post-QE. Two indirect placebo tests corroborate this: using a spurious treatment variable (non-financial, non-housing asset share) and using a spurious outcome (change in non-financial, non-housing asset share) both yield null results.

Q3. What is the benchmark magnitude of the portfolio rebalancing effect and how robust is it?

A: A 10-percentage-point higher 2014 bond share (the approximate interquartile range) is associated with a 1.72–1.87 percentage point larger increase in the second-home portfolio share post-QE relative to the pre-QE period (Table 3, columns 1–2, significant at 1%). This result is robust to: scaling second-home shares by a model-consistent denominator (bonds + housing + deposits, column 3); using total housing wealth instead of second-home wealth alone (column 4); using the count of second homes rather than their value share to rule out valuation-effect confounds (column 5); using direct bond holdings without imputation, or indirect holdings only, as alternative exposure measures (columns 7–8, where the coefficients are if anything larger at 0.403 and 0.420); controlling for a broad set of time-varying household characteristics including net worth, age, household size, financial literacy, and risk aversion (Table 4, range 0.19–0.23); and explicitly controlling for the deposit-share post-interaction to rule out the negative interest rate policy as a driver (column 6, main bond coefficient unchanged at 0.122).

Q4. Do households with higher bond exposure also rebalance toward equities after QE?

A: No. Column (7) of Table 4 shows that households with larger ex-ante bond shares reduce their equity shares after QE adoption (coefficient: −0.042, significant at 5%). This rules out the interpretation that the second-home finding merely captures broad rebalancing toward all risky assets due to general risk-appetite changes. Combined with the evidence that deposit shares also decline (though not precisely estimated), the result implies that households fund second-home purchases by selling bonds, drawing down deposits, and reducing equity positions.

Q5. Which household characteristics amplify the rebalancing, and what do they reveal about the mechanism?

A: Five characteristics are shown to amplify rebalancing (Table 5 and Table 7): (1) being actively advised by a bank on asset allocation (triple interaction significant at 5%), consistent with banks that own real estate agencies steering clients toward property; (2) higher financial literacy (significant at 1%), consistent with more informed investors acting more quickly on QE-induced return differentials; (3) middle age (40–60), significant at 5%, but not older age (61+), ruling out bequest motives and pointing to households near their lifetime income peak optimizing their tax burden; (4) higher income per capita (positive and significant, especially among church members), reflecting the progressive German tax schedule that makes property-related deductions more valuable; and (5) church affiliation (the income-triple interaction is significant only for church members, who face an 8–9% church tax surcharge, amplifying the tax advantage of rental property ownership). Tenure status (renter vs. owner of main residence) shows that both groups rebalance, but the triple interaction is significant only at 10%, suggesting the effect is not confined to existing homeowners.

Q6. How is the buy-to-let motive established directly in the data, as opposed to vacation-home or commuter motives?

A: The authors use variation in whether households owned a second home and generated rental income from it before QE adoption (Table 8). Households that owned a second home and reported rental income in the pre-QE wave rebalance very strongly (coefficient 0.821 on Bonds × Post, significant at 1%). Households that owned a second home but did not generate rental income show a positive but imprecisely estimated coefficient (0.641, significant at 10% in a very small sub-sample of 138 households). Critically, households that did not own any second home prior to QE show a coefficient of essentially zero (0.000). This pattern establishes that rebalancing is driven by experienced buy-to-let investors rather than by households acquiring second homes for personal use, and is consistent with the income-seeking motive documented in the Australian context by Gargano and Giacoletti (2022).

Q7. How does the paper demonstrate that the effect is independent of the credit channel, while also acknowledging the credit channel operates?

A: The paper employs three complementary tests (Table 6). First, triple interactions of the Bonds × Post coefficient with pre-QE leverage (mortgage-to-housing-wealth ratio) and with post-QE mortgage credit growth are both statistically insignificant (columns 5–6 of Table 5), meaning that greater credit access does not amplify the bond-share rebalancing effect. Second, restricting the sample to households with zero mortgage credit growth between 2014 and 2017 leaves the main coefficient unchanged at 0.175 (column 1 of Table 6). Third, including the two credit variables as additional controls only marginally reduces the bond-share coefficient without affecting its significance (columns 2–3 of Table 6). At the same time, column 3 of Table 6 shows that mortgage credit growth does have its own statistically significant positive effect on second-home shares (coefficient 0.009, significant at 1%), confirming a separate, independently operating credit channel.

Q8. How is regional exposure to the channel proxied, given that household survey data cannot be aggregated to the regional level?

A: Because the 1,651-household panel provides only 3–4 observations per region on average across 401 German Kreise, the authors cannot construct representative regional averages of household bond shares. Instead, they use the pre-QE (2008) share of refugees housed in independent accommodation in each region as developed by Bednarek et al. (2021), arguing that a larger refugee share creates tighter rental housing market conditions and therefore makes buy-to-let investment more attractive. For robustness, they also use the 2011 census share of renters in each region as an alternative measure of rental market depth. Both regional exposure variables take higher values in urban areas (refugee share: 21% urban vs. 10% rural; renter share: 70% urban vs. 46% rural), consistent with household-level rebalancing being stronger in urban regions.

Q9. What are the quantitative effects on regional rental yields, house prices, and rents?

A: Table 9 shows that a one-standard-deviation increase in QE (approximately 4.3 percentage points higher ECB debt securities-to-GDP ratio) reduces the rental yield in a region at the 75th percentile of the refugee-share exposure distribution relative to the 25th percentile by 2 basis points per year (using the refugee share) to 12 basis points per year (using the renter share). Comparing the 5th vs. 95th percentile of exposure, the yield differential is 5–24 basis points per year. Over the full 2014–2017 QE expansion (from 7% to 24% of GDP), the cumulative implied rental yield decline at the interquartile range of exposure is 8 to 48 basis points—sizable relative to the average regional decline of 140 basis points. House prices increase more than rents in more exposed regions. Using the Campbell-Shiller decomposition, about 70% of return variation is attributable to future price-to-rent increases, 36% to lower future rent growth (consistent with more rental supply), and only 5% to discount rate differentials.

Q10. What do the listing data reveal about the supply implications of the channel?

A: Table 10 shows that QE reduces both sale and rental listings in more exposed regions (both significant at 1%), consistent with the aggregate national decline visible from 2015 onward. Critically, the ratio of sale listings to rental listings declines significantly in more exposed regions: sale listings fall more than rental listings (columns 3 and 6, significant at 1% with both exposure measures). This relative shift implies that the share of properties available for rent increases relative to properties available for sale in regions more exposed to the portfolio rebalancing channel, providing evidence of an expanded rental supply. This finding is interpreted as a potentially beneficial side effect of QE-induced buy-to-let investment for housing affordability, to the extent that a larger rental supply mitigates rent increases even as house prices rise.

Q11. What is the theoretical model underlying the empirical analysis?

A: The model (Appendix C) features a representative local household with mean-variance preferences managing a portfolio of bonds, housing, and cash (equities are omitted for tractability). Preferred habitat investors segment both the national bond market and the local housing market. QE reduces the fixed net supply of bonds, raising bond prices and reducing expected bond returns. Under the substitutability of bonds and houses, households rebalance toward housing to restore optimal allocation, bidding up house prices; the larger the initial bond share, the larger the required rebalancing. Housing supply constraints determine how much rebalancing depresses expected housing returns (rental yields). The model does not unambiguously predict the response of the cash (deposit) share, motivating the empirical investigation reported in column (6) of Table 3.

Q12. What are the aggregate household balance sheet patterns consistent with the individual-level results?

A: Table 1 shows that Germany’s aggregate household real estate share rose from 55% of total assets in 2014 to 56–57% in 2017–2018, while the bond share declined by roughly 0.5 percentage points. The homeownership rate declined by about 2 percentage points over the sample period (from 52.5% in 2014 to 51.4–51.5% in 2017–2018), consistent with an increasing share of landlords and renters—which is compatible with the buy-to-let mechanism since more than 60% of German renters lease from other households. Household leverage also declined (loans-to-assets from 13% in 2014 to 12% in 2017), consistent with portfolio rebalancing rather than credit-driven housing acquisition. The deposit share remained constant over the period, weighing against the negative-interest-rate policy as a driver of portfolio rebalancing.

Key Concepts

Housing portfolio channel of QE transmission: The paper’s central concept—a mechanism by which central bank bond purchases (QE) induce households holding bonds to rebalance their portfolios toward second homes held for investment (buy-to-let), operating through changes in risk premia (bond prices and expected returns) rather than through bank lending channels or future short-term interest rates.

Ex-ante bond share (QE exposure measure): Each household’s share of total wealth invested in bonds (direct holdings plus indirect holdings via mutual funds and insurance) measured in the 2014 pre-QE survey wave. Used as a continuous household-level treatment intensity: the larger this share, the stronger the portfolio pressure to rebalance when the ECB reduces bond supply to the private sector. Corresponds roughly to 10 percentage points per interquartile range.

Buy-to-let motive: In the paper’s usage, the investment purpose of purchasing second homes specifically to rent them out—or to declare them for future letting—in order to exploit Germany’s substantial tax advantages for rented properties (depreciation allowances, deductibility of mortgage interest, management costs, and property taxes against rental income), which are unavailable for owner-occupied primary residences. Distinguished from vacation-home or commuter motives by the presence of pre-QE rental income.

Segmented housing markets / preferred habitat investors: Assumptions embedded in the paper’s theoretical model (following Flavin and Yamashita, 2002; Gete and Reher, 2018; Greenwald and Guren, 2021) that local real estate markets are insulated from national or international housing markets, and that some investors have a binding preference to hold bonds or local housing, so that QE-induced price changes in the bond market are not fully arbitraged away by shifting into liquid alternatives.

Parallel trends (DiD validity): The identifying assumption that, absent QE, households with larger and smaller initial bond shares would have followed the same trajectory in their second-home portfolio shares. The paper documents this graphically using all three survey waves (Figure 2) and supports it with two indirect placebo tests involving unrelated treatment and outcome variables.

Regional rental yield: The rent-to-price ratio at the regional (Kreise) level, derived from Bulwiengesa data. Used as the primary regional outcome variable because it jointly captures discount rate, rent-growth, and price-to-rent dynamics. A Campbell-Shiller decomposition decomposes its predictive content into three components: discount rates (5%), future rent growth (36%), and future price-to-rent ratio changes (70%) in the German regional panel.

Sale-to-rental listing ratio: The ratio of sale listings to rental listings for apartments on Immoscout 24, used as a quantity-side outcome variable. A decline in this ratio in more-exposed regions is interpreted as evidence of a relative increase in rental supply, consistent with the buy-to-let motive and with potentially beneficial implications for housing affordability.

Church tax (Kirchensteuer): A German institutional feature—formally affiliated church members pay an additional 8–9% surcharge on their regular income tax bill (varying by state). Because the tax advantage of owning rental property is proportional to the marginal tax rate, church members face a higher effective marginal tax rate and thus derive larger tax benefits from buy-to-let investment, producing stronger QE-induced portfolio rebalancing for this sub-group.

Bottom-Up Markup Fluctuations

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

The paper asks how firm-level, sector-level, and aggregate markups comove with output at different levels of aggregation, and whether a single structural model can reconcile seemingly contradictory empirical findings about markup cyclicality that arise when researchers use different aggregation schemes.

Model

The authors build a granular macroeconomic model featuring oligopolistic competition with a nested constant-elasticity-of-substitution (CES) demand structure following Atkeson and Burstein (2008). The economy contains N sectors, each with a discrete number of firms competing under Cournot oligopoly with flexible prices. Firm-level markups are endogenously increasing in within-sector market shares: under Cournot, the sectoral markup is a simple function of the sector’s Herfindahl-Hirschman index (HHI), and the aggregate markup is a function of the expenditure-share-weighted average of sectoral HHIs. Firm-level productivity follows a discretized random growth (Gibrat’s law) process as in Carvalho and Grassi (2019), generating fat-tailed firm-size distributions and granular aggregate fluctuations. The baseline calibration features only idiosyncratic firm-level productivity shocks and abstracts from aggregate shocks, because—in the model—aggregate shocks that move all firms proportionately do not affect relative market shares and hence do not affect markups.

Data

The empirical analysis uses French administrative firm-level data from the FICUS-FARE datasets covering the universe of French firms from 1994 to 2019, yielding approximately 9.38 million firm-year observations across 26 years, 22 two-digit sectors, and 275 five-digit NAF sectors. Firm-level markups are estimated following De Loecker and Warzynski (2012) using a translog production function estimated by GMM (following De Ridder et al. 2024) on a subsample of approximately 220,733 firm-year observations where physical output quantity is available from the Enquete Annuelle de Production survey (2009-2019). Using quantity rather than revenue as the output measure avoids the measurement biases documented in Bond et al. (2021).

Main Findings and Quantitative Magnitudes

Markup-market-share relationship (firm level): Regressions of the change in the inverse firm markup on the change in firm market share yield a negative and significant coefficient of approximately -0.268 to -0.293 (depending on fixed-effect specification), consistent with the model prediction that markups rise with market share. Sector-level analogues yield a slope of the change in inverse sector markup on the change in sector HHI of approximately -0.37, which is simultaneously a calibration target (implying sigma = 1.8 given epsilon = 5) and an empirical moment the model closely matches (model counterpart: -0.36).
Within-between decomposition of sector markup changes: In the model under Cournot competition, changes in firm-level markups (the “within” term) account for exactly 50% of changes in sector-level markups, with between-firm reallocation accounting for the other 50%. In the French data, for the median sector, the within term accounts for 59% of changes in sector markups (interquartile range across sectors: 34%-81%).
Firm-level markup cyclicality with sector output (heterogeneous by size): The average firm’s markup is countercyclical with respect to own-sector output (beta_1 approximately -0.073 in levels specification), but this relationship reverses for large firms: firms with market shares roughly above 10% (top 0.1% of the market-share distribution) have procyclical markups (interaction coefficient beta_2 approximately 0.574 in levels). The model qualitatively and roughly quantitatively reproduces this heterogeneity.
Sector-level markup cyclicality with sector output (procyclical): Following Nekarda and Ramey (2013), sector markup changes comove positively and significantly with sector output changes: estimated coefficient of 0.160 (standard error 0.040) in first-differences. The calibrated model yields a median coefficient of 0.139 (std dev 0.057 across 5,000 simulated 25-year samples), close to the data. Consistently, sector concentration (HHI) is also procyclical with sector output (estimated coefficient 0.332, std error 0.067 in first-differences).
Sector-level markup cyclicality with aggregate output (acyclical to weakly countercyclical): Following Bils et al. (2018), the comovement between sector markups and aggregate output is fragile in sign and significance: the French data yields a point estimate of -0.239 (std error 0.116) in first-differences, marginally significant (t-stat 2.06) and with sign sensitive to detrending method. The model without aggregate shocks predicts positive comovement (median coefficient 0.165) that is not statistically different from zero across samples. Adding aggregate productivity shocks (calibrated to match French aggregate output volatility) brings the model-implied coefficient close to zero (median 0.008), with 20-30% of 25-year simulated samples displaying countercyclical sectoral markups relative to GDP—consistent with the ambiguity in the data.
Aggregate output volatility: The baseline calibration with only granular firm-level shocks generates a standard deviation of detrended aggregate output of 0.83%, equal to 26% of the 3.16% observed in the French data. (The comparable granular ratio from Carvalho and Grassi 2019 for a perfectly competitive US model is 30%.) Variable markups dampen granular aggregate volatility: the standard deviation of aggregate output under variable markups is 0.87 times that under heterogeneous-but-constant markups (95% CI: 0.82-0.97), because incomplete pass-through reduces the effective weight of large firms in the price index.
Aggregate markup volatility: In the data, the relative standard deviation of aggregate markup to aggregate output is 0.40-0.50 (depending on detrending). The model generates a relative volatility of 0.36 (median across samples). The correlation between aggregate markup and output in the data is at most 0.06; the model without aggregate shocks implies a counterfactually large median correlation of 0.91, which falls to 0.27 when aggregate TFP shocks are superimposed (with 16% of 25-year samples displaying countercyclical aggregate markups).

Scope Conditions

Results pertain to French private-sector firms (including formerly government-owned firms, most of which privatized during the sample period) across manufacturing and some non-manufacturing sectors at the national-market level. The analysis abstracts from import competition (market shares are computed relative to all French firms in the sector), local geographic markets (relevant for non-tradeable goods where national-level shares understate local concentration), and multi-product firm structure. Findings are for a flexible-price model driven by idiosyncratic productivity shocks; the paper explicitly discusses how nominal rigidities would further strengthen procyclicality at the sector level.

In depth

Q1. What is the central mechanism by which granular firm-level shocks generate markup cyclicality?

A: Because markups are endogenously increasing in within-sector market shares under oligopolistic competition, a firm that receives a positive productivity shock gains market share and therefore raises its markup, while its competitors lose market share and lower their markups. The net effect on the sectoral markup depends on the shocked firm’s initial size: a positive shock to a sufficiently large firm (above a threshold market share) raises the sectoral markup, while a positive shock to a small firm lowers it. Since sectoral expansions in a granular economy are disproportionately driven by large firms, sector output and sector markup tend to comove positively in the medium run.

Q2. Why does the sign of markup cyclicality differ depending on the level of aggregation?

A: Sector-level markups react only to within-sector idiosyncratic shocks, so sectors that happen to be driven by large-firm booms display positive comovement between sector markup and sector output. However, a given sector’s markup is uncorrelated with aggregate output movements coming from other sectors. In small samples (such as 25-year windows), whether a sector’s markup comoves positively or negatively with aggregate output depends on whether the sector happens to lead or lag the aggregate cycle. Over sufficiently long samples, the model implies positive comovement of sector markups with aggregate output, but in finite samples the relationship is indeterminate. This asymmetry across aggregation levels explains why researchers using different reduced-form specifications in the same dataset can reach opposing conclusions about procyclicality versus countercyclicality.

Q3. What is the within-between decomposition of sectoral markup changes and what does it imply quantitatively?

A: Changes in the inverse sectoral markup can be decomposed into (i) a within term—changes in firm-level markups holding market shares fixed—and (ii) a between term—changes in market shares holding firm-level markups fixed. Under Cournot competition, the within and between terms are analytically equal in every period, so each accounts for exactly 50% of the change in sectoral markups; this 50-50 split holds globally (not only to first order). In the French data, for the median sector, within-firm markup changes account for 59% of sector markup changes (interquartile range across sectors: 34%-81%), close to but slightly above the model’s 50% prediction.

Q4. How do variable markups affect granular aggregate output volatility relative to a model with constant markups?

A: Variable markups (endogenous pass-through that is decreasing in firm size) reduce granular aggregate output volatility relative to a model where markups are heterogeneous but fixed. The intuition is that larger firms have lower pass-through rates, so their productivity shocks translate into smaller price changes and therefore smaller output responses than they would under constant markups—effectively reducing the weight of large firms in the aggregate price index in a way similar to a decline in market concentration. Quantitatively, using first-order approximations around equilibrium distributions from the calibrated model, the standard deviation of aggregate output under variable markups is 0.87 times that under heterogeneous-but-constant markups (95% confidence interval: 0.82-0.97). The overall standard deviation under variable and heterogeneous markups is only 1.02 times that under homogeneous and constant markups (95% CI: 0.99-1.14), meaning markup heterogeneity and variability together have limited net effects on aggregate output volatility.

Q5. What does the model predict for firm-level markup cyclicality, and how heterogeneous is this across firm size?

A: Proposition 4 states that, in the asymptotic limit, firm-level markups comove positively with own-sector output for firms with market shares above a threshold, and negatively for firms below it. This occurs because large firms have a disproportionate impact on sector-level price and output (when the product of market share and pass-through rate is increasing in size), so large-firm shocks simultaneously drive sector expansions and raise large-firm markups while compressing small-firm markups. In the French data, the average firm’s markup is countercyclical with respect to sector output (beta_1 approximately -0.073 in log-levels with firm and year fixed effects), but firms with market shares above roughly 10% (top 0.1% of the distribution, since the average market share is only 0.07%) display procyclical markups (interaction coefficient beta_2 approximately 0.574). The model reproduces this qualitative pattern and the order of magnitude of these estimates.

Q6. How does the paper calibrate the key demand elasticities, and what are the resulting pass-through implications?

A: The within-sector substitution elasticity is set to epsilon = 5, a standard value. The cross-sector substitution elasticity sigma is calibrated to match the slope of the inverse sector markup on sector HHI in first-differences. The empirical slope is -0.37; under the model, the slope equals -(epsilon/sigma - 1)/(epsilon - 1), and given epsilon = 5, sigma = 1.8 delivers a model counterpart of -0.36. These parameter values imply own-cost pass-through rates that are decreasing in firm size; for large firms (with market share >= 57%, approximately the top 0.004% of the distribution), the implied pass-through rate is 0.63, within the confidence intervals reported in Amiti, Itskhoki, and Konings (2019) for large Belgian firms.

Q7. Why do aggregate productivity shocks not affect markups in the model, and what are the implications for aggregate markup cyclicality?

A: In the model, firm-level markups are functions of within-sector market shares, not the level of productivity. An aggregate shock that shifts all firms’ productivity proportionately leaves relative market shares unchanged and therefore leaves all markups unchanged. This means aggregate shocks increase aggregate output volatility but leave markup volatility unchanged, reducing the correlation between aggregate markup and aggregate output. When aggregate TFP shocks are added to match French aggregate output volatility, the model-implied median correlation between aggregate markup and output falls from 0.91 (without aggregate shocks) to 0.27 (with aggregate shocks), while 16% of 25-year simulated samples display countercyclical aggregate markups—more consistent with the weak and fragile empirical relationship.

Q8. How does the paper address the potential measurement-error bias in the negative correlation between markups and marginal costs?

A: Since marginal cost is computed as price divided by estimated markup, regressing market shares or markups on marginal costs risks spurious correlation via measurement error in the markup (which appears in both sides). The authors address this concern by constructing an instrumental variable for marginal cost based on firm-specific energy intensity interacted with energy price changes, following Ganapati, Shapiro, and Walker (2020). Table A10 confirms that instrumenting for marginal cost yields negative effects on both markup and market share with larger point estimates than the OLS specifications in Table 4, validating the baseline findings.

Q9. Is the 50-50 within-between decomposition of sectoral markup changes robust to the choice of competition mode?

A: No. The exact 50-50 split of within and between terms in sectoral markup changes is a specific property of Cournot competition and holds globally (not just as a first-order approximation). Under Bertrand competition, the within and between terms are generally not equal to each other. The paper derives analytic results under both competition modes and focuses on Cournot for quantitative work because it generates more markup variation and better matches the estimated pass-through rates and markup-size relationship.

Q10. What do model simulations imply for the magnitude and cyclicality of aggregate markups versus the data, and what is the role of variable versus constant markups?

A: In the data (detrended), the standard deviation of aggregate markup is 1.27% with a relative volatility (to output) of 0.40 and a correlation with output of 0.03. The baseline model with only granular shocks yields a median markup standard deviation of 0.30%, relative volatility of 0.36, and correlation with output of 0.91. The model with aggregate shocks added yields median markup standard deviation of 0.30%, relative volatility of 0.09, and correlation of 0.27. Counterfactually fixing markups at their initial heterogeneous levels while keeping the same market shares and shock variance yields aggregate markup standard deviation approximately 0.93 times the variable-markup value (standard deviation of markups under variable markups is 1.08 times that under constant markups, with a 95% CI of 1.00-1.18), and a correlation with output of 0.92 versus 0.87 under variable markups. Overall, the magnitude and cyclicality of aggregate markups are not substantially different between variable and constant-markup specifications.

Q11. How does the paper reconcile its findings with prior literature on markup cyclicality (Bils et al. 2018 vs. Nekarda and Ramey 2013)?

A: Nekarda and Ramey (2013) find procyclical sector markups with respect to sector output in US data—a result replicated in French data (beta approximately 0.160). Bils, Klenow, and Malin (2018) find countercyclical sector markups with respect to aggregate output in US data. Both results can be generated simultaneously in the model: sector markups are positively correlated with own-sector output because granular booms in a sector are driven by large-firm expansions that raise sector markups; however, a given sector’s markup is weakly and ambiguously correlated with aggregate output because aggregate fluctuations reflect shocks across many sectors, only some of which are in the same sector. The model can therefore simultaneously predict procyclicality with respect to sector output and an acyclical-to-weakly-countercyclical relationship with aggregate output—explaining why both empirical findings can be correct.

Q12. What are the data limitations and how do they affect the interpretation of results?

A: Three limitations are noted. First, market shares are computed relative to total revenue of all French firms in the sector without accounting for imports, so foreign competition is ignored and domestic concentration may be overestimated. Second, revenues are reported at the national level, so for non-tradeable goods (whose relevant market is local) the paper underestimates true local market concentration, attenuating the markup-concentration relationship in those sectors. Third, the model abstracts from entry and exit (the number of firms per sector is held fixed at sector-year averages), though Appendix D demonstrates robustness of main empirical results to restricting the sample to continuing firms.

Key Concepts

Granular macroeconomic model: A model in which the economy consists of a finite (large but discrete) number of firms, so that idiosyncratic firm-level shocks to large firms do not average out and instead generate aggregate fluctuations. In the paper’s usage, granularity means that sectoral and aggregate business-cycle fluctuations are driven primarily by shocks to the largest firms, which also have the highest markups and market shares.

Nested CES demand structure (Atkeson-Burstein): A two-level constant-elasticity-of-substitution aggregation where the final good aggregates N sectors with cross-sector elasticity sigma, and each sector aggregates the output of its Nk firms with within-sector elasticity epsilon > sigma. This structure generates firm-level markups that are endogenously increasing in within-sector market shares (under both Cournot and Bertrand competition) and yields closed-form expressions for sector-level markups as a function of sector HHI and aggregate markups as a function of the expenditure-weighted average of sector HHIs.

Markup elasticity with respect to market share (Gamma_ki): Under Cournot competition, the semi-elasticity of firm i’s log markup with respect to its log market share, equal to (epsilon/sigma - 1)s_ki / (epsilon/(epsilon-1) - (epsilon/sigma - 1)s_ki). This is strictly positive for epsilon > sigma and increasing in market share, implying that larger firms have markups that are more responsive to changes in their competitive position.

Pass-through rate (alpha_ki): The fraction of an idiosyncratic cost shock that is passed into the firm’s price relative to the sectoral price index, given by 1/(1 + (epsilon-1)Gamma_ki). Pass-through is decreasing in market share (larger firms have lower pass-through), which dampens their price response to own shocks and mutes the impact of large-firm shocks on aggregate price volatility—acting like a reduction in market concentration.

Within-between decomposition of sector markup changes: The change in inverse sector markup decomposed into (i) a within term measuring changes in firm-level markups holding market shares fixed, and (ii) a between term measuring reallocation of market shares across firms with heterogeneous markups. Under Cournot competition, these two terms are exactly equal (each 50%) for any firm-level shocks—a result that holds globally (not merely as a first-order approximation)—because the forces that increase the within term (higher markup sensitivity) also raise heterogeneity between firms (increasing the between term).

Sectoral markup (mu_kt): Defined as the ratio of sectoral revenues to total wage payments in the sector, equal to the harmonic mean of firm-level markups weighted by market shares. Under Cournot competition, this is a simple increasing function of the sector’s HHI: mu_kt = (epsilon/(epsilon-1))[1 - (epsilon/sigma - 1)/(epsilon-1) x HHI_kt]^(-1). This mapping between concentration and the markup price-cost wedge gives the central empirical prediction tested at the sector level.

Markup cyclicality (at different aggregation levels): The comovement between markups and output, which the paper distinguishes sharply across three levels: (i) firm markup vs. own-sector output—countercyclical for small firms, procyclical for large firms; (ii) sector markup vs. own-sector output—procyclical (positive covariance) under conditions proven in Proposition 3; (iii) sector markup vs. aggregate output—theoretically positive over long samples but ambiguous and close to zero in short samples, because aggregate output also reflects shocks to other sectors whose markups are uncorrelated with the focal sector’s markups. The paper’s central insight is that the same underlying model generates all three empirical patterns simultaneously.

Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Mon, 01 Jan 0001 00:00:00 +0000

Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Research Question

The paper addresses two questions about government debt rollover. First, a positive question: what is the maximum ratio of government bonds to capital that can be sustained forever without any primary budget surpluses? Second, a normative question: among sustainable bond-capital ratios along a balanced growth path, which one maximizes the welfare (steady-state utility) of consumers? The analysis is motivated by Blanchard’s (2019) AEA presidential address and the fiscal responses to the COVID-19 pandemic.

Setting and Mechanism

The baseline environment is a standard two-generation (young and old) overlapping-generations model. Young consumers earn labor income and save; old consumers live off portfolio returns. The production function is Cobb-Douglas, Yt = (GtN)^(1−α) K^α, where G = 1+g is the gross growth rate of labor-augmenting productivity. Uncertainty enters exclusively through a stochastic i.i.d. durability shock ε_t to the depreciation rate of capital (δ − ε_t), so the rate of return on capital r = αk^(α−1) − δ + ε is stochastic even though the capital stock per unit of effective labor k is deterministic along a balanced growth path. Consumers have Epstein-Zin-Weil utility with an intertemporal elasticity of substitution equal to one. Because IES = 1 and labor income is earned only when young, aggregate saving of young consumers is a constant fraction β of their wage income, making total assets (capital plus bonds) non-stochastic.

This structure creates a key wedge: the expected rate of return on capital R can exceed the growth rate g (dynamic efficiency) while the riskfree interest rate rf — determined by the portfolio equilibrium between risky capital and riskless bonds — can remain below g. In deterministic economies these two rates coincide, so dynamic efficiency and the infeasibility of permanent debt rollover always go together. In this stochastic model they can be decoupled.

Main Findings

Positive finding. The maximum sustainable bond-capital ratio, Bmax, is attained precisely when rf = g (equivalently, when the adjusted gross riskfree rate Rf = 1). Starting from a bond-less economy with rf < g (which may itself be dynamically efficient), introducing government bonds crowds out capital, raises the marginal product of capital and the constellation of returns, and drives rf upward toward g. Once rf = g is reached, any further increase in bonds would require rf > g, making rollover infeasible without primary surpluses. The maximum sustainable ratio Bmax is characterized as the unique root of f(Bmax, 1) = 0, and it is finite.

Normative finding. The welfare-maximizing sustainable bond-capital ratio equals Bmax. Proposition 6 establishes that u′(B) ≥ 0 for all B ∈ [0, Bmax] whenever Rf ≤ 1, with strict inequality unless Rf = 1. Proposition 7 therefore concludes that the welfare-maximizing B is the corner solution Bmax. Intuitively, increasing B reduces capital and wages but raises the rate of return on capital. When rf ≤ g, the welfare gain from a higher return on capital in old age dominates the welfare loss from a lower wage when young (via the factor-price frontier and the intertemporal optimality condition E{uo′(co)} ≥ uy′(cy)). When rf = g (at Bmax), a marginal increase in bonds also provides no additional welfare improvement if all seignorage is transferred to young consumers (ζ = 1), but still raises welfare if some seignorage is wasted (ζ < 1). In either case, Bmax is the optimum. Critically, at the optimum the economy is dynamically efficient — even though the government is running permanent primary deficits.

Dual role of bonds. At the optimal bond-capital ratio, government bonds serve two purposes simultaneously: (1) they crowd out any dynamically inefficient overaccumulation of capital that might prevail without bonds, and (2) they supply riskfree assets to risk-averse consumers who would otherwise hold only risky capital, improving risk sharing.

Quantitative Illustration

The paper calibrates a 30-year-period OLG model with α = 0.33, β = 0.353 (annual discount rate 2%), annual productivity growth g = 1% (G = 1.35), and target mean return on unlevered equity m = 3% per year. Risk aversion γ ∈ {1, 3, 8, 10} and annualized standard deviation of capital returns s ∈ {0.02, …, 0.22}. Key results (ζ = 0): at γ = 10 and s = 0.22, Bmax = 0.478 and B∗ (the bond-capital ratio needed just to eliminate dynamic inefficiency) = 0.083, so there is a wide interval [0.083, 0.478] of dynamically efficient, permanently rollable bond-capital ratios. For a capital-output ratio of 2, the debt-GDP ratio corresponding to Bmax = 0.478 is approximately 0.956. Bmax is strictly increasing in both γ and s, and is invariant to ζ (the share of seignorage transferred rather than wasted).

Scope Conditions

Results hold along balanced growth paths with constant g and constant rf; the sustainability characterization is more complex if either rate is stochastic.
The key sufficient condition for Rf to be increasing in B (Proposition 1) is that risk aversion γ < Λ, a model-dependent upper bound that is always positive. All subsequent propositions assume R′f(B) > 0, which is satisfied for a potentially larger set of γ.
The paper focuses on welfare along the balanced growth path; it does not study transition dynamics or welfare during convergence from an initial state.
The No Ponzi Game (NPG) condition is violated by design in the feasible-rollover region (rf ≤ g); the value of government bonds is positive even though the present value of all future primary surpluses is non-positive.

In depth

Q1. Why can an economy be both dynamically efficient and able to roll over government bonds forever, when this is impossible in deterministic models?

In a deterministic economy, the riskfree rate rf and the rate of return on capital r are equal, so the conditions rf < g (feasibility of rollover) and r < g (dynamic inefficiency) are identical. In a stochastic economy, aggregate uncertainty drives a wedge between rf and the expected return on capital. Risk-averse consumers require a premium to hold risky capital over riskless bonds, so rf < E{r}. It is therefore possible that E{ln R} > 0 (the Zilcha sufficient condition for dynamic efficiency holds) while Rf < 1, i.e., rf < g. This decoupling is the central theoretical contribution of the paper.

Q2. What is the formal criterion the paper uses for dynamic efficiency, and how does it relate to the AMSZ criterion?

Abel, Mankiw, Summers, and Zeckhauser (AMSZ, 1989) show that if the rate of return on capital exceeds g in all states (R > 1 always), the economy is dynamically efficient, and since rf < r, the economy has rf > g so rollover is infeasible; conversely if r < g always, the economy is dynamically inefficient. The AMSZ criteria are silent when R sometimes exceeds and sometimes falls short of one. Building on Zilcha (1991), the paper uses E{ln R} ≥ 0 as a sufficient condition for dynamic efficiency. In the five-region diagram (Figure 1), Region E satisfies E{ln R} > 0 (Zilcha-efficient) and Rf < 1 (rollover feasible simultaneously), which is the case of central interest.

Q3. How does the model achieve a deterministic capital stock despite stochastic capital returns?

The durability shock ε_t affects depreciation but is additively separable from the production function. Because (1) IES = 1 and (2) consumers earn income only when young, aggregate saving is the fixed fraction β of wage income, which depends only on capital k (itself non-stochastic). Total assets At+1 = Kt+1 + Bt+1 = St are thus non-stochastic. The stochastic shock to depreciation makes the rate of return on capital r = αkα−1 − δ + ε stochastic even though k is deterministic. Online Appendix B establishes that this model is isomorphic to a model with production function shocks, extending the scope of the results.

Q4. What is the financial market equilibrium condition that pins down the riskfree rate?

Young consumers optimally choose the portfolio share λ in riskfree bonds. The first-order condition for this portfolio problem along a balanced growth path is E{(λRf + (1−λ)R)^(−γ)(Rf − R)} = 0 (equation 20). In equilibrium, λ = B/(1+B) (the bond-capital ratio determines the portfolio share), so the equilibrium riskfree rate Rf satisfies the implicit equation f(B, Rf) = 0 (equation 21). Lemma 1 establishes that Rf = E{R^(1−γ)_a}/E{R^(−γ)_a}, a ratio-of-moments formula analogous to an Euler equation.

Q5. Why is the riskfree rate Rf an increasing function of the bond-capital ratio B, and what is the sufficient condition for this?

Lemma 2 shows ∂f/∂B > 0; intuitively, more bonds reduce capital, raise the marginal product of capital, and raise R, inducing consumers to demand more capital and less bonds, pushing Rf up to restore equilibrium. Lemma 3 provides a sufficient condition for ∂f/∂Rf < 0, namely γ < Λ (where Λ is a positive parameter-dependent bound). Under this condition, the implicit function theorem implies Rf′(B) > 0 (Proposition 1). The condition γ < Λ is sufficient but not necessary, so the results of all downstream propositions hold potentially for a wider parameter range.

Q6. What is the maximum sustainable bond-capital ratio Bmax, and how is it characterized?

By definition, a bond-capital ratio B is sustainable if and only if Rf(B) ≤ 1. If Rf(0) ≥ 1, then Bmax = 0 (no positive amount of bonds is sustainable). If Rf(0) < 1, Bmax is the unique positive root of Rf(B) = 1, i.e., f(Bmax, 1) = 0 (Proposition 4). At Bmax, the riskfree rate exactly equals the growth rate: rf = g. The paper also shows Bmax ≤ (1−α)β/α − 1, an upper bound that depends only on production and preference parameters. Notably, Bmax is invariant to the parameter ζ (the share of seignorage transferred to young consumers rather than wasted), because at Bmax transfers are always zero regardless of ζ.

Q7. Why does the welfare-maximizing sustainable bond-capital ratio equal Bmax rather than some interior value?

Proposition 6 shows that u′(B) ≥ 0 for all B ∈ [0, Bmax] whenever Rf ≤ 1, with strict inequality unless Rf = 1 and (1−ζ)B = 0. Since utility is weakly increasing throughout the feasible set, the optimum is the corner solution Bmax (Proposition 7). The mechanism: increasing B reduces k, lowering wages (bad for utility when young) but raising the marginal product of capital and hence the rates of return on capital and bonds (good for utility when old). The factor-price frontier ensures that the wage reduction equals the income gain accruing to initial capital, and the intertemporal optimality condition uy′(cy) = Rf E{uo′(co)} implies that when Rf ≤ 1 (so E{uo′(co)} ≥ uy′(cy)/Rf ≥ uy′(cy)), the welfare gain in old age dominates.

Q8. How does Proposition 5 square with the optimality of Bmax? Does reducing expected consumption not reduce welfare?

Proposition 5 shows that when ζ = 1, a marginal increase in B at Bmax reduces expected aggregate consumption (dE{c}/dB < 0). However, welfare is not simply expected aggregate consumption: it also depends on the distribution of consumption across states. At Bmax, even though expected consumption falls, the increased risk sharing from holding more riskfree bonds — which smooth consumption between the high-return and low-return states of capital depreciation — is large enough to leave welfare unchanged (u′(Bmax) = 0 when ζ = 1) or to increase it (u′(Bmax) > 0 when ζ < 1). This illustrates that in stochastic economies, the welfare criterion diverges from the aggregate consumption criterion that characterizes dynamic inefficiency in deterministic economies.

Q9. How does the paper’s welfare analysis relate to the No Ponzi Game (NPG) condition and the fiscal theory of the price level?

The standard NPG condition requires that the value of government debt equals the present value of future primary surpluses. In the paper’s feasible-rollover region (rf ≤ g), the NPG condition is violated by design: the present value of future primary surpluses is non-positive (all primary balances are deficits or zero), yet the market value of outstanding bonds is strictly positive. This is possible because, as Santos and Woodford (1997) show, when the present value of aggregate consumption is infinite, the NPG can fail. The market value of the capital stock remains finite (it is the value of profits on a depreciating capital stock approaching zero), but the bubble value of government bonds is positive.

Q10. What does the quantitative calibration reveal about the range of dynamically efficient, permanently rollable bond-capital ratios?

With α = 0.33, β = 0.353, g = 1% per year, G = 1.35, target mean equity return m = 3% per year, and risk aversion γ = 10 with annualized return standard deviation s = 0.22, the paper finds Bmax = 0.478 and B∗ = 0.083 (ζ = 0, Table 1). The interval [B∗, Bmax] = [0.083, 0.478] is the range of bond-capital ratios for which the economy is both dynamically efficient and able to roll over bonds permanently. For an economy with a capital-output ratio of 2, these bond-capital ratios correspond to debt-GDP ratios of up to 0.956. Both Bmax and B∗ are increasing in risk aversion γ and in the standard deviation of capital returns s; Bmax is independent of γ in any given column of the table for the ζ = 0 case (since R is independent of γ there), but rises substantially with γ in the ζ = 1 case.

The parameter ζ governs what the government does with seignorage revenue: transfer it to young consumers (ζ = 1) or waste it (ζ = 0), or some mix. Corollary 1 shows that Bmax is completely invariant to ζ, because at Bmax, rf = g so seignorage (g − rf)Bt = 0 in any case. The value ζ does affect u′(Bmax): if ζ < 1, u′(Bmax) > 0; if ζ = 1, u′(Bmax) = 0. Both configurations yield Bmax as the welfare-maximizing level. The parameter ζ matters for welfare levels and for B∗ (only in the ζ = 1 case, where transfers are positive and boost saving capacity), but not for the main positive or normative results.

Q12. In what sense is the model tractable, and what are its key limitations?

Tractability comes from three design choices: (i) the durability shock is additively separable from the production function, so labor income and aggregate saving are non-stochastic; (ii) IES = 1 with Epstein-Zin-Weil preferences, making saving a constant fraction of income; (iii) along balanced growth paths, g and rf are constant, so sustainability reduces to comparing two constants. Limitations acknowledged by the authors: the paper analyzes only balanced growth paths and does not characterize transition dynamics; the framework does not directly address economies where g or rf are stochastic; and the two-period OLG structure is stylized. The authors pose as an open question whether the result that optimal borrowing equals maximal borrowing generalizes to settings with random g.

Key Concepts

Bond-capital ratio (B): The ratio of outstanding government bonds to the capital stock, Bt/Kt. This is the paper’s central state variable and policy instrument. A value B is “sustainable” if the government can roll over its debt forever at the riskfree interest rate without any primary budget surpluses. The paper distinguishes B from the more commonly reported debt-GDP ratio (which equals B times the capital-output ratio).

Adjusted gross rate of return / riskfree rate (R, Rf): R ≡ (1+r)/G and Rf ≡ (1+rf)/G, where r is the net return on capital, rf is the riskfree interest rate on bonds, and G = 1+g is the gross growth rate. Expressing returns in these “adjusted” gross units scales out balanced growth and simplifies the sustainability condition to Rf ≤ 1 (equivalently, rf ≤ g).

Dynamic efficiency (Zilcha criterion): In the paper’s stochastic setting, the relevant criterion for dynamic efficiency is E{ln R} ≥ 0 (Zilcha 1991, as amended by Rangazas-Russell 2005 and Barbie-Kaul 2009), meaning the geometric mean of the adjusted gross return on capital is at least one. This differs from the deterministic condition r ≥ g. The paper’s Region E in Figure 1 is the key zone where E{ln R} > 0 (dynamically efficient) and Rf < 1 (rollover feasible) simultaneously.

Bmax (maximum sustainable bond-capital ratio): The largest value of B for which the bond-capital ratio is sustainable, defined as the unique root of Rf(B) = 1. At Bmax, the riskfree rate exactly equals the growth rate (rf = g). The paper proves Bmax is finite, invariant to ζ, and equals the welfare-maximizing sustainable bond-capital ratio.

B∗ (dynamic efficiency threshold): The bond-capital ratio at which the economy crosses from Zilcha-inefficiency into Zilcha-efficiency, defined by E{ln R} = 0. For B ∈ [B∗, Bmax], the economy is dynamically efficient and debt rollover is feasible. B∗ < Bmax when risk aversion γ or return volatility s is large enough, defining a non-trivial interval of dynamically efficient, permanently rollable bond levels.

Durability shock (ε): An i.i.d. random variable with mean zero that enters the capital depreciation rate as δ − ε_t. This shock makes the rate of return on capital r = αkα−1 − δ + ε stochastic while leaving the capital stock per unit of effective labor, aggregate wages, and aggregate saving non-stochastic. It is the only source of aggregate uncertainty in the model and is the mechanism that drives a wedge between rf and E{r}.

No Ponzi Game (NPG) condition: The condition that the present discounted value of government debt converges to zero (equivalently, debt equals the present value of future primary surpluses). Standard fiscal sustainability analyses assume this condition holds. The paper explicitly violates it: in the feasible-rollover region rf ≤ g, the present value of aggregate consumption is infinite and the NPG fails, yet government bond values are positive and debt rollover is sustainable.

Seignorage (ζ): The revenue the government obtains by issuing new bonds in excess of interest payments on existing bonds, equal to (g − rf)Bt when rf < g. The parameter ζ ∈ [0,1] governs the share transferred to young consumers (as lump-sum transfers τt) versus wasted (captured by the government but yielding no utility). A key finding is that Bmax is invariant to ζ, since seignorage is zero at rf = g regardless of ζ.

Temporary Layoffs, Loss-of-Recall, and Cyclical Unemployment Dynamics

Mon, 01 Jan 0001 00:00:00 +0000

This paper measures and models the role of temporary layoffs (TL) in cyclical unemployment dynamics, motivating the analysis by the extraordinary surge in temporary layoffs at the onset of the pandemic recession — roughly 15% of employed workers moved to temporary-layoff status from March to April 2020. The paper documents two opposing effects of temporary layoffs on total unemployment: a stabilizing direct effect (workers on TL return to employment rapidly via recall) and a destabilizing indirect effect through “loss-of-recall” — workers initially on temporary layoff who fail to be recalled and instead transition to jobless unemployment (JL), inheriting that state’s far lower reemployment probability. A new recursive accumulation method is used to construct a time series of the stock of workers in jobless unemployment whose most recent exit from employment was to temporary-layoff status (JL-from-TL); this stock has a standard deviation 16 times that of GDP and 2 times that of total unemployment, and is a high-correlation indicator of labor market slack. A search-and-matching model with staggered Nash wage bargaining, endogenous layoff thresholds, and separate recall and new-hire channels replicates the pre-pandemic cyclical behavior of TL and JL flows. Applying the model to the pandemic recession, the paper finds that the Paycheck Protection Program (PPP) reduced employment shortfalls by roughly 2 percentage points at peak, primarily by dampening loss-of-recall — the program’s forgivable loan structure reduced firms’ incentive to permanently separate workers who had been placed on temporary layoff.

Summary of a published paper based on the NBER working paper full text (w30134), AI-assisted, pending human review. See the linked original for the authoritative claims and full conditions.

Layer 1: Overview

Gertler, Huckfeldt, and Trigari study two distinct features of temporary layoffs in aggregate unemployment dynamics: the well-documented stabilizing role of recall hiring, and a less-studied destabilizing mechanism they term “loss-of-recall” — the countercyclical flow of workers from temporary-layoff unemployment into jobless unemployment. Using monthly CPS data from 1979 through the pandemic period, they construct a four-state Markov transition matrix (employment, TL unemployment, JL unemployment, inactivity) and develop a novel recursive method to track the accumulated stock of jobless unemployed workers whose most recent employment exit was via temporary layoff (JL-from-TL). This stock is small on average (roughly 40% of the average TL stock) but highly volatile — its standard deviation is 16 times GDP and twice total unemployment — and strongly co-moves with total unemployment (correlation 0.93) and the vacancy-unemployment ratio (0.83). Across historical recessions: TL unemployment contributed 36.1% of the increase in total unemployment during the 1980s recessions (25.1% direct, 11.0% indirect via loss-of-recall); 17.2% during the Great Recession (8.7% direct, 8.5% indirect — nearly equal); and 98% during the pandemic recession (almost entirely direct, because PPP dampened loss-of-recall). The structural model — DMP with staggered multiperiod Nash wage bargaining, firm-specific overhead cost shocks that generate endogenous exit and temporary layoffs, and separate hiring and recall margins — captures pre-pandemic dynamics and shows that loss-of-recall amplifies unemployment persistence following recessionary TFP shocks. In the pandemic recession application, the PPP counterfactual finds that without PPP: peak unemployment would have been roughly 2 percentage points higher; jobless unemployment would have peaked at 7.0% versus 5.9% in the PPP scenario; and cumulative TL-to-JL flows would have been roughly double, amounting to 47.4% of what they would otherwise have been.

In depth

Q1. What distinguishes temporary-layoff unemployment from jobless unemployment in the data, and why does the distinction matter for cyclical dynamics?

Temporary-layoff unemployment (TL) is the state in which a CPS respondent indicates an expectation of recall — either a specific return date or a stated expectation of recall within six months — while jobless unemployment (JL) is unemployment without such an expectation; the two states have starkly different reemployment probabilities, with TL workers returning to employment at substantially higher rates than JL workers, making the composition of total unemployment — not just its level — a key determinant of unemployment persistence. In the Markov transition matrix estimated from CPS data 1979-2019 (Table 2), TL is a transient state: workers on TL transition to employment at a far higher rate than workers in JL, reflecting the attached recall relationship. The stock of TL unemployment is consequently small — averaging roughly one-eighth of total unemployment — even though TL separations account for roughly one-third of all separations from employment to unemployment. The distinction matters for aggregate dynamics because a recessionary increase in TL generates both a direct, relatively transient component (elevated TL stock) and an indirect, more persistent component (heightened loss-of-recall feeding into JL stock). Standard two-state unemployment models that lump TL and JL together miss the indirect channel entirely, understating both the volatility and persistence of total unemployment in the presence of countercyclical loss-of-recall.

Q2. What is the recursive accumulation method for estimating JL-from-TL, and what does it reveal about the indirect contribution of temporary layoffs?

The paper proposes a novel method to estimate the time series stock of jobless unemployed workers whose most recent employment exit was through temporary-layoff unemployment — the JL-from-TL stock — by propagating forward through the Markov transition matrix each cohort of workers who enter TL from employment, tracking the fraction that survive in any unemployment state without returning to employment, and summing across all past cohorts. Formally, if $x_{t-m,t}$ denotes the distribution of workers at time $t$ whose last exit from employment was to TL at time $t-m$, then $x_{t-m,t} = \tilde{P}t x{t-m,t-1}$ where $\tilde{P}t$ is a modified transition matrix, and the JL-from-TL stock is $u^{JL,TL}t = \sum{j=0}^{T} e’{JL} x_{t-j-1,t}$. The method requires only the Markov transition matrix — no individual-level panel data — and extends the Shimer (2012) / Elsby-Hobijn-Sahin (2015) variance decomposition approach to level decompositions. Applied to CPS data, the JL-from-TL stock has a standard deviation 16 times that of GDP (versus 2 times for TL itself) and a correlation of 0.93 with total unemployment — substantially higher than the 0.83 correlation of the vacancy-unemployment ratio with total unemployment. The large relative volatility reflects that the JL-from-TL stock compounds both the volatility of TL separations and the cyclical variation in the TL-to-JL transition probability (loss-of-recall); both components are countercyclical, so they co-amplify in recessions.

Q3. How does the paper’s structural model generate endogenous temporary versus permanent layoffs and a procyclical recall probability?

Temporary layoffs and permanent exits arise endogenously from two cost shocks in the model: an employee-specific cost shock (ϑ) and a firm-specific overhead shock (γ), with thresholds ϑ and γ determined by firm optimization; workers whose idiosyncratic cost exceeds ϑ* are placed on temporary layoff (retaining recall rights), while firms whose overhead shock exceeds γ* exit, converting their TL workers to jobless unemployment.** The framework is a modified DMP model with staggered Nash wage bargaining (following Gertler-Trigari 2009), where firms can expand their workforce either by recalling workers from TL unemployment or by hiring new workers from JL unemployment, with separate quadratic adjustment costs for each margin ($\kappa$ for new hires, $\kappa_r$ for recalls). The recall elasticity exceeds the new-hire elasticity, consistent with the lower cost of re-integrating previously attached workers. Recall hiring (xr) and new hiring (x) are both driven by the discounted value of a worker to the firm, J(w,s), but respond with different sensitivities governed by their respective adjustment cost parameters. The TL-to-JL (loss-of-recall) flow is endogenous and driven by firm exit: when the overhead shock γ exceeds γ*(w,s), the firm exits and its TL workers lose their recall option, converting to JL unemployment. Because γ* rises in bad times (higher firm insolvency), loss-of-recall is countercyclical, matching the data pattern. An exogenous loss-of-recall probability $(1-\rho_r)$ is also included to capture TL-to-JL flows that occur even when the firm survives (e.g., firm restructuring or expiration of recall expectations), and this parameter is calibrated to long-run flow moments.

Q4. What does the calibrated model reveal about the amplification role of loss-of-recall, and how is this quantified?

A counterfactual exercise that sets the TL-to-JL transition probability to zero (shutting off loss-of-recall) shows that total unemployment peaks earlier and at a lower level following a recessionary TFP shock, and that unemployment displays markedly less persistence — revealing loss-of-recall as an important amplification mechanism by which a recessionary increase in temporary layoffs can generate persistently higher total unemployment. The model is calibrated to monthly frequency with 16 parameters: 9 assigned externally (β=0.991^{1/3}, δ=0.025^{3}, α=1/3, standard AR(1) TFP parameters, matching function elasticity σ=0.5, bargaining power η=0.5, λ=8/9 targeting quarterly wage adjustment frequency), and 7 calibrated to long-run flow moments and business cycle volatility moments (Table 8-9). The calibrated model captures the cyclical volatility of aggregate labor market stocks and flows, and the impulse response to a negative 1% TFP shock shows a hump-shaped increase in total unemployment with TL unemployment recovering within roughly two years (due to lower recall costs) while JL unemployment recovers more slowly (due to lower job-finding rates). The countercyclical overshooting of employment-to-JL transition probabilities during the subsequent expansion reflects the procyclicality of the reservation wage — workers are less willing to accept pay cuts in good times, triggering exits from employment at the margin. The overall result is that loss-of-recall accounts for a quantitatively significant share of unemployment persistence in recessions, particularly in the later part of the sample.

Q5. How is the model adapted for the pandemic recession, and what are the specific mechanisms through which PPP reduced jobless unemployment?

The pandemic application introduces two temporary shock processes: (i) a “virus shock” that exogenously raises the TL rate above the threshold determined by ϑ (capturing mandatory closures and social distancing-induced reductions in effective labor demand), and (ii) a productivity shock from social-distancing requirements; PPP is modeled as a policy that subsidizes firms’ wage bills conditionally on maintaining worker-firm attachments, reducing firms’ incentive to exit and thereby directly dampening the endogenous TL-to-JL (loss-of-recall) flow.* With these modifications the model captures the key features of pandemic labor market dynamics: the extraordinary March-April 2020 TL spike, the rapid initial recall, and the subsequent slow recovery of employment. In the PPP counterfactual (no PPP), cumulative TL-to-JL flows over the pandemic period would have been approximately double their actual levels — the model generates a 47.4% ratio of actual-to-counterfactual cumulative TL-to-JL flows, indicating PPP prevented roughly 53% of the loss-of-recall that would have otherwise occurred. At peak (six months after the shock), employment under the no-PPP counterfactual is 8.8% below pre-pandemic levels versus 6.8% with PPP — a 2 percentage point gap. Jobless unemployment peaks at 7.0% without PPP versus 5.9% with PPP. Consistent with estimates from Hubbard and Strain (2020), the estimated average monthly PPP employment gain is approximately 2.0% over the first six months, with gains of 1.57% through February 2021 before convergence toward zero.

Q6. What does the evidence on reemployment probabilities of workers who transition from TL to JL establish, and why is it important for identifying loss-of-recall?

Workers in jobless unemployment who were in temporary-layoff unemployment in the previous period have reemployment probabilities virtually indistinguishable from those of the full population of jobless unemployed (Table 3), which — because JL workers have far lower reemployment probabilities than TL workers — establishes that the TL-to-JL transition is a true loss-of-recall event: the worker has genuinely lost the recall relationship and now faces the same search frictions as other permanently separated workers. This finding is important for the paper’s empirical strategy because it validates the interpretation of CPS-recorded TL-to-JL transitions as genuine loss-of-recall rather than mismeasurement or recategorization without substantive change in the worker’s employment prospects. The result also implies that TL-to-JL transitions create true duration dependence in reemployment probabilities among workers initially on TL: workers who spend longer in TL unemployment are more likely to lose recall, so the average reemployment probability of the TL cohort declines with duration. This duration dependence is consistent with the model’s mechanism — exit probability rises over time as firms facing prolonged overhead cost shocks eventually breach the exit threshold — and provides a micro-level validation of the endogenous loss-of-recall channel.

Key Concepts

temporary-layoff (TL) unemployment : the labor market state in which an unemployed worker retains an expectation of recall to the prior employer (either a specific return date or an indication of recall within six months, per CPS classification); characterized by substantially higher reemployment probabilities than jobless unemployment, accounting for roughly one-third of separations from employment but only one-eighth of the total unemployment stock due to the transient nature of TL spells.

loss-of-recall : the conversion of a temporary layoff into a permanent separation — the event by which a worker initially on TL status transitions to jobless unemployment because the prior employer exits or cannot recall; the paper’s central amplification mechanism, shown to be countercyclical (higher in recessions), to account for 8.5–11.0% of unemployment increases in pre-pandemic recessions, and to be substantially dampened by PPP during the pandemic.

JL-from-TL stock : the accumulated stock of workers currently in jobless unemployment whose most recent exit from employment was through temporary layoff — constructed via the paper’s novel recursive accumulation method; has a standard deviation 16 times GDP and 2 times total unemployment, correlates 0.93 with total unemployment, and constitutes a leading slack indicator that captures the indirect destabilizing contribution of temporary layoffs to unemployment dynamics.

recall hiring versus new-hire margin : the model’s two channels through which firms can expand their workforce — recalling workers from their own TL pool (lower adjustment cost, higher recall elasticity) versus hiring new workers from the pool of jobless unemployed (higher cost); both margins respond positively to the discounted firm value J(w,s) but with different sensitivities calibrated to match the differential volatility of TL-to-E and JL-to-E transition probabilities in the CPS.

staggered Nash wage bargaining : the model’s wage rigidity mechanism (following Gertler-Trigari 2009), in which firms and workers negotiate base wages with probability (1-λ) each period; the calibrated λ=8/9 targets a wage adjustment frequency of roughly one per quarter, consistent with Taylor (1999) and Gottschalk (2005) evidence; wage rigidity — combined with the allowance for temporary pay cuts to prevent exit — is quantitatively important for replicating the observed volatility of labor market flows and stocks.

E0 | Macro Paper Warehouse

A Housing Portfolio Channel of QE Transmission

Layer 1 — Overview

In depth

Q1. What is the housing portfolio channel of QE transmission, and how does it differ mechanically from the credit channel?

Q2. What is the key exposure variable and why is it a valid identification strategy?

Q3. What is the benchmark magnitude of the portfolio rebalancing effect and how robust is it?

Q4. Do households with higher bond exposure also rebalance toward equities after QE?

Q5. Which household characteristics amplify the rebalancing, and what do they reveal about the mechanism?

Q6. How is the buy-to-let motive established directly in the data, as opposed to vacation-home or commuter motives?

Q7. How does the paper demonstrate that the effect is independent of the credit channel, while also acknowledging the credit channel operates?

Q8. How is regional exposure to the channel proxied, given that household survey data cannot be aggregated to the regional level?

Q9. What are the quantitative effects on regional rental yields, house prices, and rents?

Q10. What do the listing data reveal about the supply implications of the channel?

Q11. What is the theoretical model underlying the empirical analysis?

Q12. What are the aggregate household balance sheet patterns consistent with the individual-level results?

Key Concepts

Bottom-Up Markup Fluctuations

Layer 1 — Overview

In depth

Q1. What is the central mechanism by which granular firm-level shocks generate markup cyclicality?

Q2. Why does the sign of markup cyclicality differ depending on the level of aggregation?

Q3. What is the within-between decomposition of sectoral markup changes and what does it imply quantitatively?

Q4. How do variable markups affect granular aggregate output volatility relative to a model with constant markups?

Q5. What does the model predict for firm-level markup cyclicality, and how heterogeneous is this across firm size?

Q6. How does the paper calibrate the key demand elasticities, and what are the resulting pass-through implications?

Q7. Why do aggregate productivity shocks not affect markups in the model, and what are the implications for aggregate markup cyclicality?

Q8. How does the paper address the potential measurement-error bias in the negative correlation between markups and marginal costs?

Q9. Is the 50-50 within-between decomposition of sectoral markup changes robust to the choice of competition mode?

Q10. What do model simulations imply for the magnitude and cyclicality of aggregate markups versus the data, and what is the role of variable versus constant markups?

Q11. How does the paper reconcile its findings with prior literature on markup cyclicality (Bils et al. 2018 vs. Nekarda and Ramey 2013)?

Q12. What are the data limitations and how do they affect the interpretation of results?

Key Concepts

Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Running Primary Deficits Forever in a Dynamically Efficient Economy: Feasibility and Optimality

Research Question

Setting and Mechanism

Main Findings

Quantitative Illustration

Scope Conditions

In depth

Q1. Why can an economy be both dynamically efficient and able to roll over government bonds forever, when this is impossible in deterministic models?

Q2. What is the formal criterion the paper uses for dynamic efficiency, and how does it relate to the AMSZ criterion?

Q3. How does the model achieve a deterministic capital stock despite stochastic capital returns?

Q4. What is the financial market equilibrium condition that pins down the riskfree rate?

Q5. Why is the riskfree rate Rf an increasing function of the bond-capital ratio B, and what is the sufficient condition for this?

Q6. What is the maximum sustainable bond-capital ratio Bmax, and how is it characterized?

Q7. Why does the welfare-maximizing sustainable bond-capital ratio equal Bmax rather than some interior value?

Q8. How does Proposition 5 square with the optimality of Bmax? Does reducing expected consumption not reduce welfare?

Q9. How does the paper’s welfare analysis relate to the No Ponzi Game (NPG) condition and the fiscal theory of the price level?

Q10. What does the quantitative calibration reveal about the range of dynamically efficient, permanently rollable bond-capital ratios?

Q11. What is the role of the parameter ζ (the share of seignorage transferred vs. wasted)?

Q12. In what sense is the model tractable, and what are its key limitations?

Key Concepts

Temporary Layoffs, Loss-of-Recall, and Cyclical Unemployment Dynamics

Layer 1: Overview

In depth

Q1. What distinguishes temporary-layoff unemployment from jobless unemployment in the data, and why does the distinction matter for cyclical dynamics?

Q2. What is the recursive accumulation method for estimating JL-from-TL, and what does it reveal about the indirect contribution of temporary layoffs?

Q3. How does the paper’s structural model generate endogenous temporary versus permanent layoffs and a procyclical recall probability?

Q4. What does the calibrated model reveal about the amplification role of loss-of-recall, and how is this quantified?

Q5. How is the model adapted for the pandemic recession, and what are the specific mechanisms through which PPP reduced jobless unemployment?

Q6. What does the evidence on reemployment probabilities of workers who transition from TL to JL establish, and why is it important for identifying loss-of-recall?

Key Concepts