pith. sign in

arxiv: 2605.17100 · v1 · pith:5T5BBGYUnew · submitted 2026-05-16 · 💰 econ.GN · q-fin.EC

Distributional Decomposition of Consumption Inequality Change During COVID-19

Utkarsh Anand , Xin Liu This is my paper

Pith reviewed 2026-05-20 14:47 UTC · model grok-4.3

classification 💰 econ.GN q-fin.EC
keywords consumption inequalitydistributional decompositionCOVID-19distribution regressionhousehold consumptionasset holdingsconditional distributioninequality change
0
0 comments X

The pith

Changes in the conditional distribution of consumption explain most of the decline in consumption inequality among male-headed households from 2018 to 2022.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper decomposes observed shifts in U.S. consumption inequality during the COVID-19 period by applying distribution regression to Consumer Expenditure Survey data. It builds counterfactual distributions that hold the consumption structure or individual variables fixed between 2018 and 2022. The analysis finds that alterations in the conditional distribution of consumption account for the bulk of the measured decline in inequality for male-headed households. Increases in asset holdings raised inequality across multiple measures, while changes in other household characteristics lowered it. The work restricts attention to reliably measured consumption components to limit the impact of data errors.

Core claim

Using distribution regression on Consumption Expenditure Interview Survey data, the authors construct counterfactual distributions to isolate the contributions of different factors to changes in consumption inequality between 2018 and 2022. They find that changes in the conditional distribution of consumption explain most of the observed decline in consumption inequality among male-headed households. The rise in asset holdings significantly increased consumption inequality, while changes in a set of household characteristics reduced it.

What carries the argument

Distribution regression, which models the full conditional distribution of consumption given household variables and builds counterfactual inequality measures by holding that distribution or selected variables fixed across years.

If this is right

  • Most of the decline in consumption inequality traces to shifts in how consumption responds to household traits rather than to shifts in the traits themselves.
  • Rising asset holdings during the period worked to increase inequality in every inequality measure examined.
  • Changes in household characteristics operated in the opposite direction and helped narrow the distribution.
  • The patterns remain visible when the analysis is limited to well-measured consumption items.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar decompositions applied to other economic shocks could show whether conditional consumption responses routinely dominate inequality movements.
  • Policies that alter consumption patterns during crises may affect inequality through the conditional distribution even if they leave average levels unchanged.
  • Standard inequality statistics that ignore conditional distributions may miss important sources of change during rapid economic shifts.

Load-bearing premise

The distribution regression approach and chosen counterfactual scenarios correctly isolate the contribution of each variable without bias from unobserved household heterogeneity or from the survey's sampling and measurement limitations.

What would settle it

Re-running the decomposition on alternative consumption aggregates, with added controls for unobserved factors, or using a different counterfactual construction and finding that conditional distribution changes no longer explain most of the inequality decline would undermine the central result.

Figures

Figures reproduced from arXiv: 2605.17100 by Utkarsh Anand, Xin Liu.

Figure 1
Figure 1. Figure 1: Density curves for log real consumption (left panel) and log real assets (right panel) [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Observed quantile functions (top-left), observed differences between the quantile [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Observed distribution functions (top-left), observed differences between the distri [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Additional decompositions of QE and DE with 95% uniform confidence bands. [PITH_FULL_IMAGE:figures/full_fig_p037_4.png] view at source ↗
read the original abstract

We decompose the U.S. consumption inequality distributional changes during the COVID-19 phase. Analyzing the Consumption Expenditure Interview Survey data, we decompose observed changes in consumption inequality into components attributable to several individual variables. Using a distribution regression method, we construct counterfactual distributions under the scenario in which the consumption structure or any specific variable would have remained the same between the two years before and after the onset of the COVID-19 pandemic. We find that changes in the conditional distribution of consumption explain most of the observed decline in consumption inequality among male-headed households between 2018 and 2022. The rise in asset holdings has significantly increased the consumption inequality in all measures. Moreover, the changes in a set of household characteristics have significantly reduced the consumption inequality. Our analyses focus on the well-measured consumption components that are robust to the measurement errors in consumption data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper decomposes changes in U.S. consumption inequality between 2018 and 2022 using Consumption Expenditure Interview Survey data. It applies distribution regression to construct counterfactual distributions that isolate the contribution of shifts in the conditional distribution of consumption F(y|x) from shifts in the distribution of covariates x. The central finding is that changes in the conditional distribution explain most of the observed decline in consumption inequality among male-headed households, while the rise in asset holdings increased inequality and changes in other household characteristics reduced it. The analysis restricts attention to well-measured consumption components.

Significance. If the counterfactual construction is valid, the results indicate that pandemic-related changes in consumption behavior conditional on observables drove the inequality reduction more than compositional shifts in household characteristics. This contributes to understanding crisis impacts on consumption distributions. The restriction to well-measured components is a clear strength that addresses a common concern in consumption data. The repeated cross-section design, however, leaves the decomposition vulnerable to bias from time-varying unobserved heterogeneity.

major comments (2)
  1. [Distribution regression method and counterfactual construction] The decomposition relies on the distribution regression counterfactuals correctly isolating the contribution of changes in F(y|x) versus the marginal distribution of x. In the repeated cross-section CE Interview Survey spanning 2018–2022, any differential selection into male-headed households, changes in reporting, or omitted time-varying factors correlated with both x and consumption (e.g., pandemic liquidity or labor shocks) would bias the attribution toward the conditional-distribution component. This assumption is load-bearing for the headline claim that conditional changes explain most of the decline.
  2. [Results and decomposition tables] No standard errors, confidence intervals, or robustness checks to variable selection, functional form, or sample restrictions are referenced in the reported results. Without these, it is impossible to assess whether the quantitative dominance of the conditional-distribution component is statistically distinguishable from zero or sensitive to modeling choices.
minor comments (2)
  1. [Abstract] The abstract would be strengthened by reporting the sample sizes for the 2018 and 2022 male-headed household subsamples and the exact consumption categories retained as 'well-measured.'
  2. [Methodology] Notation for the counterfactual distributions should be defined explicitly (e.g., the precise form of the reweighted or re-estimated F) to make the decomposition components transparent.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions will be made.

read point-by-point responses

  1. Referee: [Distribution regression method and counterfactual construction] The decomposition relies on the distribution regression counterfactuals correctly isolating the contribution of changes in F(y|x) versus the marginal distribution of x. In the repeated cross-section CE Interview Survey spanning 2018–2022, any differential selection into male-headed households, changes in reporting, or omitted time-varying factors correlated with both x and consumption (e.g., pandemic liquidity or labor shocks) would bias the attribution toward the conditional-distribution component. This assumption is load-bearing for the headline claim that conditional changes explain most of the decline.

    Authors: We acknowledge that repeated cross-sectional data cannot fully eliminate concerns about time-varying unobserved heterogeneity, differential selection, or reporting changes that may correlate with both covariates and consumption outcomes. Our analysis restricts attention to male-headed households and well-measured consumption components to reduce certain measurement-related biases, and we include a rich set of observables such as asset holdings. We agree this is a substantive limitation of the design. In the revision we will add an explicit discussion of the identifying assumptions underlying the distribution regression counterfactuals, note the potential for bias from omitted pandemic-specific shocks, and report additional subsample robustness checks (e.g., by age or region) where data permit. revision: partial

  2. Referee: [Results and decomposition tables] No standard errors, confidence intervals, or robustness checks to variable selection, functional form, or sample restrictions are referenced in the reported results. Without these, it is impossible to assess whether the quantitative dominance of the conditional-distribution component is statistically distinguishable from zero or sensitive to modeling choices.

    Authors: We agree that standard errors and systematic robustness checks are necessary to evaluate the precision and sensitivity of the decomposition results. In the revised manuscript we will report bootstrap standard errors for all decomposition components and add tables showing results under alternative covariate sets, different distribution regression specifications (e.g., varying link functions or polynomial orders), and modified sample restrictions such as age cutoffs or exclusion of extreme asset values. These additions will allow readers to assess statistical distinguishability and robustness directly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; decomposition is definitional but externally grounded

full rationale

The paper applies distribution regression to the CE Interview Survey to construct counterfactual consumption distributions holding either the conditional distribution F(y|x) or the covariate distribution fixed across 2018–2022. The reported finding that changes in the conditional distribution explain most of the inequality decline is the direct numerical outcome of subtracting these two counterfactuals from the observed change; it does not reduce to a fitted parameter by construction in the manner of a self-definitional loop or a prediction that merely renames the fit. The method relies on external repeated-cross-section data and standard ignorability assumptions rather than self-citation chains or uniqueness theorems imported from the authors' prior work. A score of 2 reflects only the normal methodological self-reference common to decomposition papers, not load-bearing circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the Consumption Expenditure Interview Survey provides reliable measures for the selected consumption components and that the distribution regression model correctly identifies marginal contributions without omitted-variable bias.

axioms (2)
  • domain assumption The Consumption Expenditure Interview Survey data accurately reflects consumption patterns for the well-measured components selected by the authors.
    The abstract explicitly states that analyses focus on well-measured components robust to measurement errors.
  • domain assumption Counterfactual distributions constructed by holding the conditional consumption structure fixed correctly isolate the contribution of each variable.
    This is the core modeling choice invoked when the paper constructs counterfactuals under unchanged consumption structure or specific variables.

pith-pipeline@v0.9.0 · 5668 in / 1368 out tokens · 45249 ms · 2026-05-20T14:47:02.150584+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages

  1. [1]

    2002 , url=

    Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings , author=. 2002 , url=

    work page 2002

  2. [2]

    2008 , publisher=

    On the failure of the bootstrap for matching estimators , author=. 2008 , publisher=

    work page 2008

  3. [3]

    American Economic Review , volume=

    Reference points and effort provision , author=. American Economic Review , volume=. 2011 , publisher=

    work page 2011

  4. [4]

    Rank estimation of a generalized fixed-effects regression model

    Jason Abrevaya. Rank estimation of a generalized fixed-effects regression model. Journal of Econometrics. 2000. doi:https://doi.org/10.1016/S0304-4076(99)00027-5

    work page doi:10.1016/s0304-4076(99)00027-5 2000

  5. [5]

    Empirical Economics , volume=

    The effects of demographics and maternal behavior on the distribution of birth outcomes , author=. Empirical Economics , volume=. 2001 , publisher=

    work page 2001

  6. [6]

    , title=

    Abrevaya, Jason and Dahl, Christian M. , title=. Journal of Business & Economic Statistics , volume=. 2008 , url=

    work page 2008

  7. [7]

    Journal of Health Economics , volume=

    Inequality measurement for ordered response health data , author=. Journal of Health Economics , volume=. 2008 , url=

    work page 2008

  8. [8]

    2012 , note=

    The Validity of Consumption Data: Are the Consumer Expenditure Interview and Diary Surveys Informative? , author=. 2012 , note=

    work page 2012

  9. [9]

    American Economic Review , volume=

    Has consumption inequality mirrored income inequality? , author=. American Economic Review , volume=

    work page

  10. [10]

    Chunrong Ai and Xiaohong Chen , TITLE=

    work page

  11. [11]

    1974 , publisher=

    A new look at the statistical model identification , author=. 1974 , publisher=

    work page 1974

  12. [12]

    Estimating

    Alan, Sule and Attanasio, Orazio and Browning, Martin , journal=. Estimating. 2009 , doi=

    work page 2009

  13. [13]

    and Grootendorst, Paul and Veall, Michael R

    Alan, Sule and Crossley, Thomas F. and Grootendorst, Paul and Veall, Michael R. , journal=. Distributional effects of `general population' prescription drug programs in. 2005 , publisher=

    work page 2005

  14. [14]

    The American Statistician , volume=

    The Power to See: A New Graphical Test of Normality , author=. The American Statistician , volume=. 2013 , url=

    work page 2013

  15. [15]

    2006 , edition=

    Infinite Dimensional Analysis: A Hitchhiker's Guide , author=. 2006 , edition=

    work page 2006

  16. [16]

    Journal of Economic Education , volume=

    A Note on the Economic Meaning of Correlations between Teaching and Research Outputs , author=. Journal of Economic Education , volume=. 1980 , publisher=

    work page 1980

  17. [17]

    Journal of Health Economics , volume=

    Measuring health inequality using qualitative data , author=. Journal of Health Economics , volume=. 2004 , publisher=

    work page 2004

  18. [18]

    American Economic Review , volume=

    Employer learning, statistical discrimination and occupational attainment , author=. American Economic Review , volume=. 2005 , publisher=

    work page 2005

  19. [19]

    2005 , publisher=

    Cross section and panel data estimators for nonseparable models with endogenous regressors , author=. 2005 , publisher=

    work page 2005

  20. [20]

    Quarterly Journal of Economics , volume=

    Employer Learning and Statistical Discrimination , author=. Quarterly Journal of Economics , volume=

    work page

  21. [21]

    1982 , pages=

    Two Stage Least Absolute Deviations Estimators , author=. 1982 , pages=. doi:10.2307/1912608 , url=

    work page doi:10.2307/1912608 1982

  22. [22]

    On the distribution of the two-sample

    Anderson, TW , journal=. On the distribution of the two-sample. 1962 , publisher=

    work page 1962

  23. [23]

    Annals of Mathematical Statistics , volume=

    Asymptotic theory of certain ``goodness of fit'' criteria based on stochastic processes , author=. Annals of Mathematical Statistics , volume=. 1952 , url=

    work page 1952

  24. [24]

    Journal of the American Statistical Association , volume=

    A test of goodness of fit , author=. Journal of the American Statistical Association , volume=. 1954 , publisher=

    work page 1954

  25. [25]

    1982 , publisher=

    Formulation and estimation of dynamic models using panel data , author=. 1982 , publisher=

    work page 1982

  26. [26]

    1987 , publisher=

    Consistency in nonlinear econometric models: A generic uniform law of large numbers , author=. 1987 , publisher=

    work page 1987

  27. [27]

    Econometric Theory , volume=

    Laws of large numbers for dependent non-identically distributed random variables , author=. Econometric Theory , volume=. 1988 , url=. doi:10.1017/S0266466600013396 , publisher=

    work page doi:10.1017/s0266466600013396 1988

  28. [28]

    Journal of Multivariate Analysis , volume=

    An empirical process central limit theorem for dependent non-identically distributed random variables , author=. Journal of Multivariate Analysis , volume=. 1991 , publisher=

    work page 1991

  29. [29]

    Econometric Theory , volume=

    Generic uniform convergence , author=. Econometric Theory , volume=. 1992 , url=

    work page 1992

  30. [30]

    Handbook of Econometrics , volume=

    Empirical process methods in econometrics , author =. Handbook of Econometrics , volume=. 1994 , publisher=

    work page 1994

  31. [31]

    1994 , url=

    Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity , author=. 1994 , url=

    work page 1994

  32. [32]

    1998 , publisher=

    Hypothesis testing with a restricted parameter space , author=. 1998 , publisher=

    work page 1998

  33. [33]

    2012 , number=

    Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power , author=. 2012 , number=

    work page 2012

  34. [34]

    2012 , url=

    Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure , author=. 2012 , url=

    work page 2012

  35. [35]

    On the Number of Bootstrap Repetitions for Bootstrap Standard Errors, Confidence Intervals, and Tests , author=

    work page

  36. [36]

    2000 , publisher=

    A Three-step Method for Choosing the Number of Bootstrap Repetitions , author=. 2000 , publisher=

    work page 2000

  37. [37]

    2001 , publisher=

    Evaluation of a three-step method for choosing the number of bootstrap repetitions , author=. 2001 , publisher=

    work page 2001

  38. [38]

    On the Number of Bootstrap Repetitions for

    Andrews, Donald Wilfrid Kao and Buchinsky, Moshe , journal=. On the Number of Bootstrap Repetitions for. 2002 , publisher=

    work page 2002

  39. [39]

    Review of Economics and Statistics , volume=

    A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter , author=. Review of Economics and Statistics , volume=. 2014 , publisher=. doi:10.1162/rest_a_00369 , url=

    work page doi:10.1162/rest_a_00369 2014

  40. [40]

    International Statistical Review , volume=

    An introduction to functional central limit theorems for dependent stochastic processes , author=. International Statistical Review , volume=. 1994 , publisher=

    work page 1994

  41. [41]

    2010 , doi=

    Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection , author=. 2010 , doi=

    work page 2010

  42. [42]

    2016 , doi=

    Conditional Inference With a Functional Nuisance Parameter , author=. 2016 , doi=

    work page 2016

  43. [43]

    American Economic Review , volume=

    On the evolution of firm size distributions , author=. American Economic Review , volume=. 2008 , publisher=

    work page 2008

  44. [44]

    Quantile Regression under Misspecification, with an Application to the

    Angrist, Joshua and Chernozhukov, Victor and Fern\'. Quantile Regression under Misspecification, with an Application to the. 2006 , doi=

    work page 2006

  45. [45]

    2017 , url=

    Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework , author=. 2017 , url=

    work page 2017

  46. [46]

    Some tests of specification for panel data:

    Arellano, Manuel and Bond, Stephen , journal=. Some tests of specification for panel data:. 1991 , publisher=

    work page 1991

  47. [47]

    Identifying Distributional Characteristics in Random Coefficients Panel Data Models

    Arellano, Manuel and Bonhomme, St. Identifying Distributional Characteristics in Random Coefficients Panel Data Models. Review of Economic Studies , volume =. 2012 , month =. doi:10.1093/restud/rdr045 , url =

    work page doi:10.1093/restud/rdr045 2012

  48. [48]

    Econometrics Journal , year=

    Nonlinear Panel Data Estimation via Quantile Regressions , author=. Econometrics Journal , year=

    work page

  49. [49]

    Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework , journal =

    Arellano, Manuel and Blundell, Richard and Bonhomme, St. Earnings and Consumption Dynamics: A Nonlinear Panel Data Framework , journal =. doi:https://doi.org/10.3982/ECTA13795 , url =

    work page doi:10.3982/ecta13795

  50. [50]

    Recovering Latent Variables by Matching , journal =

    Arellano, Manuel and Bonhomme, St. Recovering Latent Variables by Matching , journal =. 2021 , publisher =

    work page 2021

  51. [51]

    2015 , note=

    Inference on Optimal Treatment Assignments , author=. 2015 , note=

    work page 2015

  52. [52]

    Exports versus

    Arnold, Jens M and Hussinger, Katrin , journal=. Exports versus. 2010 , publisher=

    work page 2010

  53. [53]

    Pakistan Economic and Social Review , pages=

    Growth and consumption inequality in Pakistan , author=. Pakistan Economic and Social Review , pages=. 2011 , publisher=

    work page 2011

  54. [54]

    2006 , doi=

    Identification and Inference in Nonlinear Difference-in-Differences Models , author=. 2006 , doi=

    work page 2006

  55. [55]

    1987 , url=

    On the Measurement of Poverty , author=. 1987 , url=

    work page 1987

  56. [56]

    What really happened to consumption inequality in the

    Attanasio, Orazio and Battistin, Erich and Ichimura, Hidehiko , booktitle=. What really happened to consumption inequality in the. 2007 , publisher=

    work page 2007

  57. [57]

    Consumption inequality over the last half century: some evidence using the new

    Attanasio, Orazio and Pistaferri, Luigi , journal=. Consumption inequality over the last half century: some evidence using the new

    work page

  58. [58]

    The evolution of income, consumption, and leisure inequality in the

    Attanasio, Orazio and Hurst, Erik and Pistaferri, Luigi , booktitle=. The evolution of income, consumption, and leisure inequality in the. 2014 , publisher=

    work page 2014

  59. [59]

    and Pistaferri, Luigi , Title =

    Attanasio, Orazio P. and Pistaferri, Luigi , Title =. Journal of Economic Perspectives , Volume =. 2016 , Pages =

    work page 2016

  60. [60]

    and Manning, Alan and Smith, Christopher L

    Autor, David H. and Manning, Alan and Smith, Christopher L. , Title =. American Economic Journal: Applied Economics , Volume =. 2016 , Pages =

    work page 2016

  61. [61]

    Biometrika , volume=

    A note on the estimation of a distribution function and quantiles by a kernel method , author=. Biometrika , volume=. 1981 , url=

    work page 1981

  62. [62]

    2020 , institution=

    Initial impacts of the pandemic on consumer behavior: Evidence from linked income, spending, and savings data , author=. 2020 , institution=

    work page 2020

  63. [63]

    Health Economics , volume=

    Does reporting heterogeneity bias the measurement of health disparities? , author=. Health Economics , volume=. 2008 , doi=

    work page 2008

  64. [64]

    Annals of Mathematical Statistics , volume=37, number=3, year=1966, month=

    A Note on Quantiles in Large Samples , author=. Annals of Mathematical Statistics , volume=37, number=3, year=1966, month=

    work page 1966

  65. [65]

    doi:, url=

    Matthew Baker and Travis Smith and David Powell , title=. doi:, url=

    work page

  66. [66]

    Social connections and incentives in the workplace: Evidence from personnel data , author=

    work page

  67. [67]

    , journal=

    Banks, David L. , journal=. Histospline smoothing the. 1988 , doi=

    work page 1988

  68. [68]

    Quadratic

    Banks, James and Blundell, Richard and Lewbel, Arthur , journal=. Quadratic. 1997 , publisher=

    work page 1997

  69. [69]

    Barakat, H. M. Barakat , title=. Statistics & Probability Letters , volume=

    work page

  70. [70]

    and Duzhak, Evgeniya A

    Barnett, William A. and Duzhak, Evgeniya A. , title=. Economic Theory , volume=. 2010 , url=

    work page 2010

  71. [71]

    and Eryilmaz, Unal , title=

    Barnett, William A. and Eryilmaz, Unal , title=. Macroeconomic Dynamics , volume=. 2016 , url=

    work page 2016

  72. [72]

    2003 , url=

    Consistent tests for stochastic dominance , author=. 2003 , url=

    work page 2003

  73. [73]

    SIAM Journal on Numerical Analysis , volume=

    An improved algorithm for discrete l_1 linear approximation , author=. SIAM Journal on Numerical Analysis , volume=. 1973 , publisher=

    work page 1973

  74. [74]

    Bayarri, M. J. and Berger, J. O. and Forte, A. and Garc. Criteria for. Annals of Statistics , volume=. 2012 , url=

    work page 2012

  75. [75]

    Nebraska Journal of Economics and Business , volume=

    The influence of location on faculty salaries at major universities , author=. Nebraska Journal of Economics and Business , volume=. 1982 , publisher=

    work page 1982

  76. [76]

    Beatty, Timothy K. M. , journal=. Semiparametric quantile. 2009 , publisher=

    work page 2009

  77. [77]

    and Sullivan, James X

    Bee, Adam and Meyer, Bruce D. and Sullivan, James X. , title =. Improving the Measurement of Consumer Expenditures , publisher =. 2015 , url =

    work page 2015

  78. [78]

    Review of Economic Studies , volume=

    Inference on Treatment Effects after Selection among High-Dimensional Controls , author=. Review of Economic Studies , volume=. 2014 , url=

    work page 2014

  79. [79]

    Journal of Business & Economic Statistics , volume=

    Semiparametric approaches to welfare evaluations in binary response models , author=. Journal of Business & Economic Statistics , volume=. 2004 , publisher=

    work page 2004

  80. [80]

    Nature Human Behaviour , volume=

    Redefine statistical significance , author=. Nature Human Behaviour , volume=. 2018 , url=

    work page 2018

Showing first 80 references.