From He-Cession to She-Stimulus? The labor market impact of fiscal policy across gender

Bonk, Alica Ida; Simon, Laure Article From He-Cession to She-Stimulus? The labor market impact of fiscal policy across gender SERIEs - Journal of the Spanish Economic Association Provided in Cooperation with: Spanish Economic Association Suggested Citation: Bonk, Alica Ida; Simon, Laure (2022) : From He-Cession to She-Stimulus? The labor market impact of fiscal policy across gender, SERIEs - Journal of the Spanish Economic Association, ISSN 1869-4195, Springer, Heidelberg, Vol. 13, Iss. 1, pp. 309-334, https://doi.org/10.1007/s13209-021-00250-8 This Version is available at: https://hdl.handle.net/10419/286556 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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The labor market impact of fiscal policy across gender Alica Ida Bonk1 ·Laure Simon2 Received: 11 February 2021 / Accepted: 8 June 2021 / Published online: 21 October 2021 © The Author(s) 2021 Abstract Men, especially those that are young and less educated, typically bear the brunt of recessions because of the stronger cyclicality of their employment and wages relative to women’s. We study the extent to which fiscal policy may offset or worsen these asymmetric effects across gender. Using micro-level data for the U.S. from the Current Population Survey, we find that the effects of fiscal policy shocks on labor market outcomes depend on the type of public expenditure. Women benefit most from increases in the government wage bill, while men are the main beneficiaries of higher investment spending. Our analysis further reveals that the fiscal component most efficient at closing gender gaps is least suitable for offsetting inequitable business cycle effects across other socioeconomic dimensions. Keywords Fiscal policy ·Gender gaps ·Heterogeneous labor market outcomes · Business cycles 1 Introduction Despite substantial progress in the labor market fortunes of women over recent decades, gaps in wages and employment rates between male and female workers remain significant. In addition, gender differences in industry composition can generWe are grateful to Evi Pappa, Leonardo Melosi, Axelle Ferriere, Juan Dolado and Alexandra Fotiou for their helpful comments. We also thank Dimitrios Bermperoglou for sharing his codes with us. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Swiss National Bank or the Bank of Canada. BLaure Simon [email protected] Alica Ida Bonk [email protected] 1Swiss National Bank, Börsenstrasse 15, 8001 Zurich, Switzerland 2Bank of Canada, 234 Wellington Street, Ottawa, ON K1A 0G9, Canada 123 310 SERIEs (2022) 13:309–334 ate cyclical fluctuations in labor market gaps, as men tend to be employed in sectors more exposed to business cycles.1Notably, young, less-educated and blue-collar men are particularly strongly affected.2The role of fiscal policies in reducing inequalities has recently received increasing interest in the literature, with less attention paid to the gender dimension. Evaluating the ability of government spending to address both policy goals, i.e., to reduce inequalities not only within gender (to assist crisis-hit male groups) but also between genders (to close gender gaps), is important to shed light on potential trade-offs involved.3We find that these trade-offs depend crucially on the type of public expenditure considered. Using micro-level data for the U.S. from the Current Population Survey (CPS), our study provides policy-making insights on the importance of the composition of government expenditure for understanding the impact of fiscal shocks on labor market outcomes across gender. We also examine the impact on demographic subgroups to assess whether fiscal expansions that close gaps can simultaneously offset inequitable business cycle impacts that particularly affect some categories of male workers. Our main findings can be summarized as follows. First, the composition of fiscal shocks matters. Spending on the government wage bill narrows gender gaps in wages and employment rates, while government purchases from the private sector and investment expendituretendto stimulatemen’swages relativelymore thanwomen’s. Theseresults are likely driven by spending components that target specific occupations and sectors which differ in their gender composition. Second, promoting gender equality through fiscal expansions is not fully compatible with offsetting other types of inequalities. The spending component that best closes gender gaps has adverse effects on labor market outcomes of cyclically vulnerable male subgroups: young, less-educated and blue-collar workers. Similarly, investment spending, which fosters employment of these crisis-hit men, is not able to reduce gender inequalities but rather contributes to widening them. Government spending can impact labor market outcomes unequally across gender for four main reasons. First, because men and women sort into different occupations, their labor demand will shift to different extents following fiscal shocks. Such shifts will depend on which type of government spending is boosted. This motivates us to distinguish between different fiscal components in our analysis. Second, since women aremore mobileacrossindustriesandoccupations,4theymay bethemainbeneficiaries of higher wages and expanded employment opportunities after a fiscal expansion. Third, there is solid empirical evidence that female labor supply is relatively more 1Men incurred around three-quarters of the net job losses during the Great Recession, with similar magnitudes during previous downturns (Wall and Engemann 2009). This can be ascribed partly to men’s employment in more cyclical industries such as manufacturing and construction. See for instance Clark and Summers (1981), Solon et al. (1994) and Hoynes et al. (2012). 2Figure 13 shows unemployment rates for men, women and vulnerable male subgroups for the period 1979–2019. For a more detailed analysis see Bredemeier et al. (2017b). 3Note that fiscal policy may have long-term effects on labor market outcomes (see, e.g., Fatás and Summers 2018; Saez et al. 2019) and therefore on gender gaps. Notably, Saez et al. (2019) find evidence of stronger hysteresis effects of employment subsidies on women than men. Fiscal policy may also have a lasting impact on female labor force participation with family-friendly policies (see, e.g., Blau and Kahn 2013). 4See, e.g., Shin (1999). 123 SERIEs (2022) 13:309–334 311 elastic than male labor supply.5Consequently, female employment may respond more strongly than male employment to fiscal shocks. Fourth, women taking up jobs may hire (usually female) caregivers for children and elderly dependents, inducing secondround employment and wage effects. These insights can be valuable for macroeconomists and policy makers. First, our resultshelptogaugetowhatextentgovernmentexpenditureisableto“assistthosemost impacted by the recession,” which was the explicit purpose of the American Recovery and Reinvestment Act of 2009.6Second, our analysis is insightful for policy makers whose goal is to promote female employment and gender equality, independently of the cycle.7Conversely, this paper highlights the potential damaging effect that cutting government expenditure, especially the wage bill, may have by widening existing gender gaps. Hence, we underline the gender non-neutrality of budgetary decisions and substantiate the importance of implementing “gender budgeting” as suggested by the International Monetary Fund (2017) and the European Parliament (2015). Third, our analysis hints at the importance of encouraging women’s labor force participation as this may increase the effectiveness of fiscal policy as an aggregate stabilization tool. To measure the effects of fiscal policy shocks on gender gaps in the labor market, we estimate several vector autoregressive models using Bayesian estimation techniques. Following Mountford and Uhlig (2009), we identify the fiscal shocks using an agnostic sign restriction approach. The main advantage of this identification strategy is that it allows us to eliminate the confounding influence of other macroeconomic shocks: namely, business cycle, monetary policy and tax revenue shocks. We examine the impulse response functions (IRFs) of gender gaps in wages and employment rates to different types of government spending shocks. Our study encompasses the analysis of two dimensions of heterogeneity. First, we investigate whether the effects of fiscal policy shocks on gender gaps differ depending on the type of public expenditure. Second, we explore how the effects vary across male and female workers with different characteristics, such as age, education and occupation. This paper relates to a strand of the literature that reports heterogeneous effects of fiscal policy across households with different characteristics (such as Giavazzi and McMahon 2012; Misra and Surico 2014 and Anderson et al. 2016), and across industries (notably, Nekarda and Ramey 2011 and Bredemeier et al. 2020). Several studies have emphasized the crucial role of industry composition in shaping gender differences in labor market outcomes, including Hoynes et al. (2012), Olivetti and Petrongolo (2014) and Bredemeier et al. (2017b). However, despite a growing interest in the evolution and the determinants of gender gaps in the labor market,8the literature 5See, e.g., Cogan (1981), Eckstein and Wolpin (1989), van der Klaauw (1996) and Francesconi (2002). 6This stimulus package, worth $787 billion, consisted of a mix of tax credits, spending on social welfare, consumption spending (mainly on education and healthcare) and investments in infrastructure and the energy sector. 7Our results suggest that the impact of fiscal policy on gender gaps can be quite persistent. In addition, government expenditure shocks show a high degree of persistence. We find estimates of the autocorrelation coefficients of the cyclical component for government spending instruments that are larger than 0.9 and highly statistically significant. 8See, e.g., Blau and Kahn (2000), Blau and Kahn (2017), Ngai and Petrongolo (2017) and Albanesi and ¸Sahin (2018). 123 312 SERIEs (2022) 13:309–334 on the impact of fiscal policy on gender equality is scarce. A few recent studies document that fiscal expansions stimulate primarily female employment, in particular Bredemeier et al. (2017b) and Akitoby et al. (2019). These papers focus on the effects of total government spending. Our main contribution to the existing literature is to explore the effects of various components of public expenditure. We argue that who benefits from fiscal stimuli depends on the type of expenditure under consideration. We also analyze labor market outcomes for male subgroups that are hurt most during recessionstobetter understandthetrade-offsinvolved whenattemptingto closegender gaps. Furthermore, our identification strategy is able to better isolate the variations in fiscal policy variables from automatic responses to other macroeconomic shocks. The remainder of this paper is structured as follows. Sections 2and 3describe the data and the econometric approach. Results are presented in Sect. 4and robustness checks and extensions are described in Sect. 5. Section 6concludes by offering directions for future research. The appendices contain some stylized facts about the components of government expenditure and gender compositions across occupations and sectors. Furthermore, we provide a description of the data and of the algorithm used for estimating the impulse response functions. 2 Data We construct labor market series using micro-level data from the Centre for Economic Policy Research (CEPR) extracts of the CPS Merged Outgoing Rotation Groups.9We build quarterly series for real hourly wages and employment rates for each gender and for subgroups most exposed to cyclical fluctuations, i.e., those (i) without college education, (ii) aged 16 to 30 and (iii) in blue-collar occupations (mainly production, construction, transport, and installation).10 Following the approach described in the seminal paper by Deaton (1985), we build pseudo-panels by aggregating individual observations into pseudo-cohorts of workers with similar characteristics and computing averages for each period.11 We restrict the sample to full-time workers aged 16–64, i.e., who have worked at least 35 hours a week.12 Self-employed workers are excluded.13 All variables are seasonally adjusted by X-12 ARIMA. Data on fiscal vari9The CPS is the source of official US government statistics on employment, wages and unemployment, with interviewed households selected to be representative of the US population. 10 To build occupational employment groups, we use the conversion factors from the U.S. Census Bureauas theoccupationandindustrycodesintheCPSweresubjecttoseveralrevisions.AsdefinedinBredemeieretal. (2020), blue-collar occupations include construction and extraction occupations; installation, maintenance, and repair occupations; production occupations; and transportation and material moving occupations. Note that these occupations have a female share of less than 50% for the whole sample period. 11 We compute quarterly averages of monthly observations. 12 In Sect. 5, we also conduct the analysis for non-married individuals, to exclude partner effects, and for part-time workers. 13 We have excluded the self-employed since their wages, employment status and hours worked are difficult to measure accurately. As Hamilton (2000) points out, earnings of business owners are less reliable because oftaxincentivesto under-reportincome.Moreover,otherformsof“indirect”compensation,suchaspensions and health insurance contributions that are paid for employees by the employer, are not received by the self-employed, making it hard to compare incomes. 123 SERIEs (2022) 13:309–334 313 ables, GDP and inflation are from the U.S. Bureau of Economic Analysis, on civilian population from the U.S. Bureau of Labor Statistics, and on the federal funds rate from FRED. Details of sources and definitions of the data are provided in Appendix E. Figure 12 shows the historical evolution of each fiscal component between 1979 and 2019. Total government spending consists of government consumption expenditures and gross investment.14 In turn, consumption expenditures include compensation of general government employees (the wage bill), consumption of fixed capital, and purchases of intermediate goods and services from the private sector. While real government spending per capita has nearly quintupled since the start of our sample, the relative shares of its components have remained fairly stable, except for purchases from the private sector, which have grown from 21% in 1979 to 28% in 2019. The wage bill is the largest component, with a share of 45% of total government expenditure on average over 1979–2019, while investment spending accounts for about 19% of total government spending. Gender gaps have narrowed over the sample period, especially during the 1980s, driven by the rise in female labor force participation; but they remain significant. In 1979, full-time female workers earned around 40% less per hour than male workers and their employment rate was 27% lower than men’s. In 2019, gaps in wages and employment were about 18% and 15% respectively (see also Appendix A). 3 Econometric approach 3.1 VAR model To measure the effects of different types of government expenditure on gender gaps in the labor market, we estimate several structural vector autoregressive (VAR) models with up to nine endogenous variables. In our baseline specification, the vector of endogenous variables first includes the three fiscal components of interest: namely, the log of real per capita government expenditure on goods and services from the private sector, the log of real per capita government investment expenditure and the log of real per capita expenditure on the government wage bill.15 Next, the variables included are the log of real per capita net (of transfers) tax revenue, the log of real per capita GDP, the labor market gap variable, inflation and the federal funds rate. The labor market gap variable alternates between the gender gap in (i) hourly wages and (ii) employment rates. The gender wage gap is measured as the difference between the log of real male wages and the log of real female wages. The gender gap in employment rates is defined as the difference between male and female rates. 14 Consumption expenditures consist of spending by the government to produce and provide services to the public, such as national defense and public school education. Gross investment consists of expenditure by the government in structures that directly benefit the public, such as highways, as well as in equipment, software and R&D that assist government agencies in their production activities, such as purchases of military hardware. 15 Results for government expenditure on purchases of goods and services are similar to those obtained using non-wage government consumption, i.e., the sum of expenditure on purchases of goods and services and expenditure on fixed capital. 123 314 SERIEs (2022) 13:309–334 To control for fiscal foresight, we include eight lags of an exogenous war dummy following Ramey (2011). The VAR models are estimated with two lags, on quarterly data from 1979Q1 to 2019Q4.16 Following Mountford and Uhlig (2009), we include neither a constant nor a time trend.17 In addition, we repeat the above analysis including male and female series of log real wages (respectively, employment rates) instead of gender gaps. Estimating the effects of fiscal shocks on male and female labor market outcomes separately allows us to better understand the mechanism behind changes in gender gaps and to draw finer policy conclusions. 3.2 Identification FollowingMountfordandUhlig(2009),Pappa(2009),Ariasetal.(2018)andBermperoglou et al. (2017) among others, we identify the fiscal shocks using an agnostic sign restriction approach that sets a minimum number of restrictions on impulse responses, while controlling for other macroeconomic shocks. These identifying sign restrictions are summarized in Table 1. The shocks are identified sequentially, as in Mountford and Uhlig (2009), Arias et al. (2018) and Bermperoglou et al. (2017). First, we identify a generic business cycle shock that leads to a positive comovement between output and government net tax revenue for four quarters. Second, we follow Bermperoglou et al. (2017) and identify a monetary policy shock by combining zero and sign restrictions. In particular, the federal funds rate should react positively and contemporaneously to output and inflation deviations only, to approximate the Taylor rule.18 We also impose orthogonality between the monetary policy shock and the business cycle shock. Third, the government revenue shock is identified as a shock that raises net tax revenues for four quarters and that is orthogonal to the monetary and business cycle shocks. Lastly, we identify shocks to government goods purchases, a government investment shock and a government wage bill shock sequentially. We impose that these shocks increase the corresponding fiscal variable for four quarters while being orthogonal to the business cycle, monetary policy and other fiscal shocks. Orthogonality to the other fiscal shocks ensures that our results are driven exclusively by the fiscal instrument of interest and not by any other expenditure component. Following Uhlig (2005), we estimate the model using a Bayesian approach with flat priors for model coefficients and the covariance matrix of shocks (see Appendix D). The estimations are based on 400 draws from the posterior distribution of VAR parameters and 4000 draws of orthonormal matrices. We compute the median, the 68% and the 90% confidence bands of impulse responses to a shock that raises the government expenditure component of interest by 1% on impact. 16 The starting date of the sample is constrained by the availability of CPS MORG data. Results are qualitatively similar when the sample ends in 2007Q4. 17 We checked that the results are qualitatively robust when a constant and a time trend are included. 18 Since we use quarterly data, we believe that the assumption that the policy rate only responds within the first quarter and shows no sign of inertia is reasonable. In particular, Rudebusch (2006) finds little evidence of a sluggish adjustment of interest rates for the Fed at the quarterly frequency. 123 SERIEs (2022) 13:309–334 315 Table 1 Identifying sign restrictions Restricted variables Shocks εGP tεGI tεGW tεT tεMP tεBC t Output + Inflation rate Interest rate Government revenue + + Government purchases + Government investment + Government wage bill + This table reports the sign restrictions on impulse responses for each identified shock. εGP tdenotes a shock to government purchases of goods and services, εGI tdenotes a government investment shock, εGW t a government wage bill shock, εT ta government revenue shock, εMP ta monetary policy shock, and εBC ta business cycle shock. To identify the monetary policy shock, we do not impose restrictions on the impulse response functions but on the structural impact matrix. All restrictions apply for periods 0–3 after the shock occurred 4 Results This section reports our results for different government spending components. Section 4.1 looks at gender gaps among all full-time employees aged 16–64, and Sect. 4.2 analyzes heterogeneities across subgroups, obtained by further splitting the sample by age, education and occupation. The purpose of this exercise is threefold. First, it helps us to gain insights into whether spending components have asymmetric effects across men and women. Second, it allows for a better assessment of how to use fiscal policy to offset inequitable business cycle effects across other socioeconomic dimensions. Third, the analysis highlights trade-offs involved when attempting to close gender gaps since demographic subgroups may not react equally to fiscal stimuli. Overall, we find that gender gaps close most strongly following a shock to the government wage bill.19 However, this spending component amplifies the particularly adverse effects experienced by certain male subgroups during recessions. 4.1 The effect on gender gaps differs across fiscal components Figure 1shows the responses of gender gaps in wages (first row) and employment rates(secondrow)toshocksthatraisethegovernmentwagebill,governmentpurchases from the private sector and government investment by 1% on impact, respectively. The effects of an increase in government purchases and investment expenditure on gender gaps are small in magnitude and mostly not statistically significant. In contrast, a positive government wage bill shock significantly reduces both wage and employment gaps between genders. 19 We also find clear-cut evidence of a Granger-causality from government expenditure to gender gaps, but little evidence of causality in the opposite direction. Results are available upon request. 123 316 SERIEs (2022) 13:309–334 Fig. 1 IRFs of gender gaps to shocks in different spending components. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively Exploring the effects of a wage bill shock on full-time men and women separately reveals that the reduction in wage gaps is driven by a significant increase in female wages and a fall in male wages (Fig. 4). In addition, the employment gap closes since employment falls among men but remains unchanged among women. Expansions in government purchases and investment spending lead to a rise in male wages in the short run, leaving female wages unchanged, and a reduction in employment rates for both genders in the medium run. To start with, note that, overall, these government spending shocks tend to have positive effects on wages (for women in the case of a wage bill shock, for men in the case of goods purchases and investment spending shocks) but negative effects on employment. As Finn (1998) showed, an increase in the number of public employees is predicted to crowd out private employment. Increases in public wages or employment also put upward pressure on private sector wages, inducing a negative labor demand effect. In addition,if the fiscalexpansionisfinanced withincreased labor incometaxes, workers may reduce their labor supply or ask for higher pre-tax real wages. These results are also in line with empirical findings reported in Alesina et al. (2002) and Ramey (2013). Alesina et al. (2002) show that increases in public spending raise labor costs and lead to declining profits. Ramey (2013) provides evidence that increases in government purchases of private goods and in the government wage bill have negative effects on private activity and employment. 123 SERIEs (2022) 13:309–334 323 Fig. 4 IRFs of wages and employment rates to different spending shocks. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively Fig. 5 IRFs of wages and employment rates for young, less-educated and blue-collar workers to shocks to the government wage bill. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively 123 324 SERIEs (2022) 13:309–334 Fig. 6 IRFs of wages and employment rates for young, less-educated and blue-collar workers to shocks to government purchases of goods and services. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively Fig. 7 IRFs for wages and employment rates for young, less-educated and blue-collar workers to shocks to government investment spending. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively 123 SERIEs (2022) 13:309–334 325 Fig. 8 IRFs of wages and employment rates for publicand private-sector workers to shocks to the government wage bill. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively Fig. 9 IRFs of wages and employment rates to different spending shocks using a Cholesky identification. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively 123 326 SERIEs (2022) 13:309–334 Fig. 10 IRFs of wages and employment rates for part-time workers to different spending shocks. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively Fig. 11 IRFs of wages and employment rates for unmarried workers to different spending shocks. These graphs plot the responses of gender gaps together with the responses of male and female variables. Notes Dashed lines and shaded areas indicate the 90% and the 68% confidence bands respectively 123 SERIEs (2022) 13:309–334 327 C Stylized facts See Figs. 12,13,14,15,16,17,18, and 19. Fig. 12 Historical evolution of government spending components. Notes “Other” includes consumption of general government fixed capital. Source Bureau of Economic Analysis Fig. 13 Unemployment rates for population subgroups, 1979–2019. Source Own calculations based on CEPR-CPS MORG 123 328 SERIEs (2022) 13:309–334 Fig. 14 Public sector wage premium compared to for-profit private sector (median full-time earnings) in 2015 Fig. 15 Female-to-male full-time median earnings ratio by sector 123 SERIEs (2022) 13:309–334 329 Fig. 16 Distribution of men and women across private sector occupations (averages for the period 2003– 2019). Source CEPR-CPS, own calculations Fig. 17 Distribution of men and women across public sector occupations (averages for the period 2003– 2019). Source CEPR-CPS, own calculations 123 330 SERIEs (2022) 13:309–334 Fig. 18 Distribution of fulland part-time women across private sector occupations (averages for the period 2003–2019). Source CEPR-CPS, own calculations Fig. 19 Distribution of fulland part-time men across private sector occupations (averages for the period 2003–2019). Source CEPR-CPS, own calculations 123 SERIEs (2022) 13:309–334 331 D VAR estimation method and algorithm for computing impulse response functions The procedure to identify the shocks follows the approach described in Arias et al. (2018) to make independent draws from the posterior distribution of structural parameters conditional on the sign and zero restrictions. The VAR model can be written in the following general form: y tA0= p  k=1 y t−kAk+c+ t,(1) where ytis the vector of nendogenous variables, tan×1 vector of exogenous structural shocks. The reduced form representation of this model is: y t=x tD+u t,(2) where D=BA −1 0,u t= tA−1 0and E(utu t)==(A0A 0)−1, and B= [A 1...A pc]. The matrices Dand are the reduced-form parameters, A0and B the structural parameters. Let hbe any continuously differentiable mapping from the set of symmetric positive definite n×nmatrices into the set of n×nmatrices such that h(X)h(X)=X. In particular, h(X)could be the Cholesky decomposition of X.Wehave(A0,B)= (h()−1,Dh()−1). We denote f(h()−1,Dh()−1)a function, with dimensions nr×n,whichstackstheimpulseresponses fortherhorizons wheresignrestrictionsare imposed, such that it satisfies f(h()−1Q,Dh()−1Q)=f(h()−1,Dh()−1)Q for any orthogonal matrix Q∈O(n). Zero restrictions can be defined using matrices Zjof dimension zj×nr, with zjbeing the number of zero restrictions imposed on f(h()−1,Dh()−1). The parameters (D,) satisfy the zero restrictions if Zjf(h()−1Q,Dh()−1Q)ej=0, for 1 ≤j≤n, where ejis the jth column of the identity matrix In. The main steps of the algorithm are the following: 1. Draw (D,)from the posterior distribution of the reduced-form parameters. 2. Draw X=[x1,...,xn]from an independent standard normal distribution. 3. Let Q=N1N 1x1 N 1x1... NnN nxn N nxn,where the columns of matrix Njform an orthonormal basis for the null space of the (j−1+zj)×nmatrix Mj: Mj=N1N 1x1 N 1x1... Nj−1N j−1xj−1   N j−1xj−1   Zjf(D,) for 1 ≤j≤ns, where nsis the number of structural shocks considered. 4. Keep the draw if it satisfies all the sign restrictions. 5. Repeat steps 2–4 for Mdraws of orthogonal matrices Q. 6. Repeatsteps1–5forNdrawsfrom theposterior distribution oftheVAR parameters. 7. For all accepted draws, compute and save the corresponding impulse response. 8. Lastly, calculate the median, the 5th, the 16th, the 84th and the 95th percentiles of all the impulse responses. 123 332 SERIEs (2022) 13:309–334 E Data definitions and sources See Table 3. Table 3 Data definitions and sources Variable Source Definition Government expenditures and receipts Government investment Bureau of Economic Analysis Gross government investment (Item 3, Table 3.9.5) Government wage bill Bureau of Economic Analysis Compensation of general government employees (Item 4, Table 3.10.5) Government purchases of private-sector goods and services Bureau of Economic Analysis Intermediate goods and services purchased (Item 6, Table 3.10.5) Net tax revenue Bureau of Economic Analysis Current tax receipts (Item 2, Table 3.1.) plus Contributions for government social insurance (Item 7) plus Current transfer receipts (Item 13) minus Current transfer payments (Item 19) minus Subsidies (Item 27) Other macroeconomic variables Total output Bureau of Economic Analysis Gross Domestic Product (Item 1, Table 1.1.5) Interest rate FRED Federal Funds Rate (Item FEDFUNDS) GDP deflator Bureau of Economic Analysis Prices Indexes for Gross Domestic Product (Item 1, Table 1.1.4) Inflation rate Quarterly growth rate of GDP deflator Population U.S. Bureau of Labor Statistics Civilian noninstitutional population (item LNU00000000) Labor market variables Hourly wage CEPR extracts of CPS MORG; Authors’ calculations Average real hourly wage of male (female) workers Employment rate CEPR extracts of CPS MORG; Male (female) employment rate is constructed as the ratio of men Authors’ calculations (women) employed to total male (female) working-age population Table3.1:GovernmentCurrentReceiptsandExpenditures;Table3.9.5:Government ConsumptionExpendituresand Gross Investment;Table3.10.5: Government ConsumptionExpenditures and GeneralGovernment Gross Output 123