Archive for the ‘Working Papers’ Category

Critique of Reinhart & Rogoff Garners International Attention

Wednesday, April 17th, 2013
Thomas Herndon

Thomas Herndon

On April 15, UMass Amherst Economics Department Graduate Student Thomas Herndon and Professors Michael Ash and Robert Pollin published a working paper titled, Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff. In the paper the authors examine Reinhart and Rogoff’s research on the relationship between public debt and GDP growth for advanced economies in the post-World War II period. Reinhart and Rogoff argue that the rate of economic growth for these countries has consistently declined precipitously once the level of government debt exceeds 90 percent of the country’s GDP. In recent years, Reinhart and Rogoff’s results have been highly influential as support for austerity policies in both Europe and the United States.

Herndon, Ash and Pollin find that a series of data errors and unsupportable statistical techniques led to an inaccurate representation of the actual relationship between public debt levels and GDP growth. They find that when properly calculated, average GDP growth for advanced economies at public debt-to-GDP ratios over 90 percent is not dramatically different than when debt-to-GDP ratios are lower.

Almost immediately the Herndon, Ash, Pollin findings went viral with lots of social media buzz on Twitter and Facebook. The story has garnered extensive national and international coverage. Below is a list of media coverage to date.

New York Times, 5/22/13
A Keynesian Victory, but Austerity Stands Firm

Socialist Worker, 5/22/13
The end of austerity?

New York Times, 5/21/13
Sharing Abuse Fairly

The New American, 5/21/13
If This Is the End of “Austerity,” When Did Austerity Begin?

All Africa, 5/20/13
Nigeria: Why Country Needs Expansionary Macroeconomic Policies

Business World, 5/18/13
Ultra Mega Data and Their Pitfalls

Daily Star, 5/18/13
Economists aren’t humble, so don’t believe everything they say

The Reporter, 5/18/13
What use are economists?

New York Times, 5/17/13
Europe’s Economics Chief Tries to Peel Off ‘Mr. Austerity’ Label 

The Christian Science Monitor, 5/17/13
EU austerity hawks shrug off criticism of flawed academic paper

Orlando Sentinel, 5/17/13
‘I know it when I see it’

Jamaica Gleaner, 5/17/13
Fake Deficit Hawks As Ideological Austerity-Pushers

Oman Tribune, 5/1/13
Errors mar influential economic study on austerity

Huffington Post, 4/30/13
2 More Grad Students Claim To Find Another Flaw In Reinhart-Rogoff Research

Boston.com, 4/30/13
UMass economists take on Harvard

The Wall Street Journal, 4/30/13
The Reinhart and Rogoff Distraction

WBUR, 4/30/13
The Economics Earthquake

The New Yorker, 4/29/13
The Rogoff and Reinhart Controversy: A Summing Up

New York Magazine, 4/29/13
How the Media Broke Up With Austerity

Huffington Post, 4/29/13
Marathon Bombings Suspect to ‘Reinhart-Rogoff-gate’: Two Very Different UMASS Students Made News Last Week

Quartz, 4/29/13
The grad student who exposed Reinhart and Rogoff: They still can’t get their facts straight

New York Times, 4/29/13
Debt and Growth – A Response to Reinhart and Rogoff

Republican, 4/29/13
UMass Thomas Herndon shines light on austerity and ‘Growth in a Time of Debt’

The Washington Post, 4/28/13
The economist whodunit

Republican, 4/28/13
Editorial: UMass posts win over Harvard in most esoteric arena

Hindu Business Line, 4/28/13
Research blues in social sciences

The Spectator, 4/27/13
Reinhart and Rogoff’s faulty spreadsheet doesn’t destroy the case for austerity

Aljazeera, 4/27/13
Austerity debunked

The Sydney Morning Herald, 4/27/13
Austerity slips out of fashion amid growing recession risk

Financial Post, 4/25/13
Despite Rogoff/Reinhart data scandal, high debt still a problem

The Globe and Mail, 4/25/13
A simple data error, and Europe’s austerity pain

The Chronicle of Higher Education, 4/24/13
‘They Said at First They Hand’t Made a Spreadsheet Error, When They Had’

The Cap Times, 4/24/13
John Nichols: Paul Ryan’s austerity agenda is based on serious mistake

The Washington Post, 4/24/13
The Reinhart/Rogoff Brawl

MSN, 4/24/13
Colbert turns austerity movement into punch line

MSNBC, 4/24/13
How an Excel spreadsheet error hurt the economy
Debunked: The Harvard study that Republicans used to push austerity

National Review, 4/24/13
A Flawed Landmark

The Irish Times, 4/24/13
Economics: Austerity loses an article of faith

Raw Story, 4/24/13
Colbert takes on UMass ‘Poindexter’ who debunked pro-austerity study

Chicago Tribune, 4/23/13
Half-baked theories continue to direct global history

The Wall Street Journal, 4/23/13
The Doctoral Student Who ‘Happed’ Reinhart and Rogoff

The Washington Post, 4/23/13
Austerity doctrine exposed as flimfam

The Colbert Report, 4/23/13
Austerity’s Spreadsheet Error

The Mermaid’s Tale, 4/23/13
A lesson on lessening, from economics

The Hindu, 4/23/13
Beware the nostrums of economists

The Real News Network, 4/23/13
28-year old PhD student debunks the most influential austerity study

NPR, 4/22/13
European Austerity Yields Meager Results In 2012

Spectrum IEEE, 4/22/13
IT Hiccups of the Week: Excel Spreadsheet Error Heard Around the World

Brisbane Times, 4/22/13
Austerity on trial as debate reignites

Business Insider, 4/22/13
Herndon Responds to Reinhart and Rogoff

New York Times, 4/22/13
Replicating Research: Austerity and Beyond
Very Sensitive People

BBC, 4/21/13
More Or Less, Austerity: A Spreadsheet Error?

CNN International, 4/21/13
Graduate student: Didn’t take long to find errors in prominent pro-austerity study

AlterNet, 4/21/13
Unbelievable! Bowles and Simpson Release New Deficit-Reduction Plan Based on Discredited Austerity Research

The Independent [Ireland], 4/21/13
In theory and in practice, austerity fails

The Independent [UK], 4/21/13
Osborne should choose his guides more carefully

Financial Times, 4/21/13
Perils of placing faith in a thin theory

Sydney Morning Herald, 4/20/13
The consequences of dodgy data

Quartz, 4/20/13
An economist’s mea culpa: I relied on Reinhart and Rogoff

Salon, 4/20/13
When wonks burn politicians

The Economist, 4/20/13
The 90% Question

Bloomberg, 4/19/13
Finance Chiefs Endorse Cuts as Reinhart-Rogoff Challenged

BBC, 4/19/13
Reinhart, Rogoff… and Herndon: The student who caught out the profs

New York Magazine, 4/18/13
Grad Student Who Shook Global Austerity Movement

EuroNews, 4/18/13
European austerity programmes based on Excel error?

TruthOut, 4/18/13
Media Relied Upon Discredited Reinhart-Rogoff Research To Stoke Debt Fears

The Fiscal Times, 4/18/13
Drama over Rogoff-Reinhart Paper Changes Nothing… and Everything

Forbes, 4/18/13
That Reinhart and Rogoff Committed a Spreadsheet Error Completely Misses the Point

IBN, 4/18/13
How Thomas Herndon, a student, took on Harvard economists and won

The Courier Mail, 4/18/13
EDITORIAL: Debt can be a powerful tool

The Business Times, 4/18/13
Key study on austerity may be flawed

Seeking Alpha, 4/18/13
Chart of The Day, Reverse-Causality Edition

The Guardian, 4/18/13
Making a comedy of errors: a serious story you may have missed

The Telegraph, 4/18/13
Debunking austerity claims makes no difference to Europe’s monks and zealots

The Economist, 4/18/13
The ivory fortress

BBC, 4/18/13
Austerity justification study ‘inaccurate’

NPR, 4/18/13
Despite Flaws, Harvard Economists Stand By Research

The Nation, 4/18/13
Paul Ryan’s Austerity Agenda Relies on Bad Math, Coding Errors and a ‘Significant Mistake’

Reuters, 4/18/13
Chart of the day, reverse-causality edition
Sharp-eyed student takes on famed economists over basic errors- and wins

Businessweek, 4/18/13
FAQ: Reinhart, Rogoff, and the Excel Error That Changed History

New York Magazine, 4/18/13
Meet the 28-Year-Old Grad Student Who Just Shook the Global Austerity Movement

NDTV, 4/18/13
How a student took on two big Harvard economists. And won.

Slate MoneyBox blog, 4/18/13
Arin Dube Demolishes Reinhart/Rogoff Causal Argument

Harvard Business Review, 4/17/13
Reinhart, Rogoff, and How the Macroeconomic Sausage Is Made

Forbes, 4/17/13
Reinhart and Rogoff; and The Dangers of Tipping Points, Real and Otherwise
Does Public Debt Inhibit Growth? Or Do Recessions Increase Debt?

Huffington Post, 4/17/13
Reinhart And Rogoff Pushed Partisan Austerity Argument, Now Claim Academic Neutrality

The League of Ordinary Gentlemen, 4/17/13
Reinhart and Rogoff Don’t Matter

Media Matters, 4/17/13
Major Errors Undermine Key Argument For Austerity Frequently Cited By Media

War of Ideas blog, 4/17/13
Reinhart Rogoff redux

Albany Business Review, 4/17/13
Study used to justify budget cuts may contain errors

Boston Business Journal, 4/17/13
Three UMass Profs. expose flaw in Harvard research that underpinned austerity

The Independent, 4/17/13
Harvard economists admit errors in austerity blueprint paper

Investor’s Business Daily, 4/17/13
Debt Study Flawed; Debt Crisis Still Remains

Quartz, 4/17/13
Reinhart and Rogoff’s defense is misleading and here’s why

Mother Jones, 4/17/13
Should We Be Afraid of Debt Levels Above 30%

MarketWatch, 4/17/13
Reinhart and Rogoff’s second, longer response to critique

Yahoo!Finance, 4/17/13
Did a Spreadsheet Error Cost You Your Job?
Did Harvard Economists Make an Excel Error that Led to Economic Austerity?

The Daily Beast, 4/17/13
Rogoff and Reinhart Respond
Did Reinhart and Rogoff Flub a Major Statistic?
What’s the Cost of an Excel Error?

Reuters, 4/17/13
Counterparties: R-squared regression analysis

The Guardian, 4/17/13
Rogoff and Reinhart defend their numbers

The Mirror, 4/17/13
George Osborne’s favourite “godfathers of austerity” economists admit to making error in their research

Maclean’s, 4/17/13
Why justifying austerity just got harder

CBC News, 4/17/13
Key pro-austerity study based on incorrect math

The Maddow Blog, 4/17/13
Republican response required to Reinhart/Rogoff

MSNBC, 4/17/13
Ryan’s favorite pro-austerity study filled with ‘serious errors’

The New Yorker, 4/17/13
The Crumbling Case for Austerity Economics

CNNMoney, 4/17/13
Debt’s impact on growth: Latest study doesn’t settle debate
Damn Excel! How the ‘most important software application is of all time’ is ruining the world

Time, 4/17/13
Why the Argument for Austerity Took a Big Hit Yesterday

The Wall Street Journal, 4/17/13
Reinhart, Rogoff Admit Excel Mistake, Reubt Other Critiques

The Washington Post, 4/17/13
Austerity? Oops.

Salon, 4/17/13
Whoops! Turns out debt doesn’t ruin economies

Financial Times, 4/17/13
Austerity after Reinhart and Rogoff

Rortybomb, 4/17/13
Guest Post: Reinhart/Rogoff and Growth in a Time Before Debt

Slate MoneyBox blog, 4/17/13
Further Thoughts on Reinhart and Rogoff

CNBC, 4/17/13
Why the Fuss Over Reinhart and Rogoff is Overblown
Reinhart-Rogoff Error Sparks Austerity Debate

Boston Herald, 4/17/13
Harvard deficit paper disputed

The New York Times, 4/17/13
With Debt Study’s Errors Confirmed, Debate on Conclusion Goes On
Does High Debt Cause Slow Growth?
Blame the Pundits, Too
Research on Government Debt is Challenged

Financial Times, 4/17/13
Harvard duo defend case for austerity

The Telegraph, 4/17/13
This time is different – thanks to data manipulation
Don’t worry, Prof Rogoff – to err is what makes us human
Row erupts over study into public debt as economists turn on Rogoff and Reinhart

Key research on austerity by Ken Rogoff and Carmen Reinhart ‘contains serious errors’

Bloomberg, 4/17/13
7 Data Disasters More Embarassing Than Reinhart and Rogoff’s
Reinhart and Rogoff Never Made a Good Case for Austerity
Reinhart-Rogoff on Debt and Growth: Fake but Accurate?
Reinhart-Rogoff Acknowledge Mistake in 2010 Paper Cited by Ryan
Reinhart-Rogoff Paper Cited by Ryan Faulted by UMass Economists

Finfacts Ireland, 4/17/13
Top US economists accused of dodgy calculations on debt impact

Quartz, 4/16/13
How influential was the Rogoff-Reinhart study warning that high debt kills growth?
Fixing this Excel error transforms high-debt countries from recession to growth

Mother Jones, 4/16/13
Quote of the Day: Excel Error Destroys the World

The Daily Beast, 4/16/13
Austerity Guru Voodoo

The Dish, 4/16/13
The Austerity Typo?

Reuters, 4/16/13
UPDATE 2-Influential economic study on austerity may be flawed

Esquire The Politics Blog, 4/16/13
Math is Hard

Think Progress, 4/16/13
What The Austerity Paper’s Intellectual Collapse Tells Us About Modern Journalism
11 Republicans Who Cited a Faulty Study To Push For Drastic Spending Cuts
New Research Undermines The GOP’s Austerity Agenda

The Maddow Blog, 4/16/13
‘The Excel Error Heard Round the World’

The Atlantic, 4/16/13
The Great Debt Delusion: How Math Keeps Proving Austerity Wrong

CNN, 4/16/13
Economists’ case for austerity attacked

Bloomberg Businessweek, 4/16/13
The Twitterverse Goes Nuts Over Economists’ Clash

Los Angeles Times, 4/16/13
Economists rebut, sort of, critique on high-debt, low-growth study
How an Excel error fueled panic over the federal debt

TruthOut, 4/16/13
How Much Unemployment Did Reinhart and Rogoff’s Arithmetic Mistake Cause?

The Wall Street Journal, 4/16/13
Seminal Economic Paper on Debt Draws Criticism
Is 90% Really a Sovereign-Debt Red Line? A New Paper Says No
Reinhart-Rogoff Response to Critique

Salon, 4/16/13
GOP’s go-to economics study debunked

UPI.com, 4/16/13
UMass study refutes Harvard study on federal debt ratio

Slate MoneyBox blog, 4/16/13
Is The Reinhart-Rogoff Result Based on a Simple Spreadsheet Error?
Reinhart and Rogoff Respond

The Guardian, 4/16/13
How much unemployment did Reinhart and Rogoff’s arithmetic mistake cause?

The Hill, 4/16/13
Researchers claim ‘serious errors’ in GDP study cited by deficit hawks

Business Insider, 4/16/13
Shocking Paper Claims that Microsoft Excel Coding Error is Behind The Reinhart-Rogoff Study on Debt
Breaking: Reinhart/Rogoff Shot Full of Holes

Huffington Post, 4/16/13
Influential Reinhart-Rogoff Pro-Austerity Research Riddled With Errors: Study

The Washington Post, 4/16/13
Austerity’s foundations continue to crumble
Is the evidence for austerity based on an Excel spreadsheet error?

The New York Times, 4/16/13
Reinhart-Rogoff, Continued
Response From Reinhart and Rogoff
A Study That Set the Tone for Austerity Is Challenged
Holy Coding Error, Batman

Financial Times Alphaville, 4/16/13
Raining on Reinhart and Rogoff

Financial Times Money Supply, 4/16/13
Reinhart-Rogoff Initial Response

Marketwatch Markets Stream blog, 4/16/13
The spreadsheet error in Reinhart and Rogoff’s famous paper on debt sustainability

Wall Street Pit blog, 4/16/13
Austerity Research Fail

AdvisorOne, 4/16/13
Oops! Reinhart-Rogoff Research Tripped Up by Typo

The American Prospect, 4/16/13
Reinhart and Rogoff’s Theory of Government Debt is Dead

US News & World Report, 4/16/13
How an Excel Error Helped Lead the World Into Austerity
How a Slip of the Finger Changed the Economic Policy Debate

Foreign Policy, 4/16/13
Were Reinhart and Rogoff wrong about the debt-growth connection?

On the Economy, 4/16/13
Not to Pile On, But…Correcting Reinhart and Rogoff

Lawyers, Guns & Money, 4/16/13
But Austerity Is Science!

Daily Kos, 4/16/13
Researchers finally replicated Reinhart-Rogoff, and there are serious problems

The Globe and Mail, 4/16/13
Bad math? Reinhart-Rogoff study on perils of debt called into question

Working Paper: Do Women Top Managers Help Women Advance? A Panel Study Using EEO-1 Records

Wednesday, July 13th, 2011

The following working paper by Fidan Ana Kurtulus and Donald Tomaskovic-Devey is available on our website:

Do Women Top Managers Help Women Advance? A Panel Study Using EEO-1 Records

Abstract:

The goal of this study is to examine whether women in the highest levels of management ranks of firms help reduce barriers to advancement in the workplace faced by women. Using a panel of over 20,000 private-sector firms across all industries and states during 1990-2003 from the U.S. Equal Employment Opportunity Commission, we explore the influence of women in top management on subsequent female representation in lower-level managerial positions in U.S. firms. Our key findings show that an increase in the share of female top managers is associated with subsequent increases in the share of women in mid-level management positions within firms, and this result is robust to controlling for firm size, workforce composition, federal contractor status, firm fixed effects, year fixed effects and industry-specific trends. The influence of women in top management positions is stronger among federal contractors, in firms with larger female labor forces, and for white women. We also find that the positive influence of women in top leadership positions on managerial gender diversity diminishes over time, suggesting that women at the top play a positive but transitory role in women’s career advancement.

Working Paper: Worker Attitudes Towards Employee Ownership, Profit Sharing and Variable Pay

Wednesday, July 13th, 2011

The following working paper by Fidan Ana Kurtulus, Douglas Kruse and Joseph Blasi is available on our website:

Worker Attitudes Towards Employee Ownership, Profit Sharing and Variable Pay

Abstract:

Using the NBER Shared Capitalism Database comprised of over 40,000 employee surveys from 14 firms, we investigate worker attitudes towards employee ownership, profit sharing, and variable pay. Specifically, our study uses detailed survey questions on preferences over profit sharing, forms of employee ownership like company stock and stock option ownership, as well as preferences over variable pay in general, to explore how preferences for these different types of output-contingent pay vary with worker risk aversion, residual control, and views of co-workers and management. Our key results show that, on average, workers want at least a part of their compensation to be performance-related, with stronger preferences for output-contingent pay schemes among workers who have lower levels of risk aversion, greater residual control over the work process, and greater trust of co-workers and management

Working Paper: What Types of Organizations Benefit From Teams, and How Do They Benefit?

Tuesday, July 12th, 2011

The following working paper by Jed Devaro and Fidan Ana Kurtulus is now available on our website:

What Types of Organizations Benefit From Teams, and How Do They Benefit?

Abstract

Using data from a large cross-section of British establishments, we ask how different firm characteristics are associated with the predicted benefits to organizational performance from using team production.  To compute the predicted benefits from using team production, we estimate structural models for financial performance, labor productivity, and product quality, treating the firm’s choices of whether or not to use teams and whether or not to grant teams autonomy as endogenous. One of the main results is that many firm characteristics are associated with larger predicted benefits from teams to labor productivity and product quality but smaller predicted benefits to financial performance. For example, this is true for union recognition as measured by the number of recognized unions in an establishment. Similarly, when a particular firm characteristic is associated with lower benefits from teams to labor productivity or product quality, the same characteristic is frequently associated with higher predicted benefits to financial performance. This is true for the degree of financial participation and employee ownership and also for establishment size and a number of industries. These results highlight the advantages of analyzing broader measures of organizational performance that are more inclusive of the wide spectrum of benefits and costs associated with teams than the labor productivity measures frequently studied in the teams literature.

Working Paper: The Great Austerity War: What Caused the Deficit Crisis and Who Should Pay to Fix It?

Tuesday, July 12th, 2011

The following working paper by James Crotty is now available on our website:

The Great Austerity War: What Caused the Deficit Crisis and Who Should Pay to Fix It?

Abstract

Rapidly rising deficits at both the federal and state and local government levels, along with longterm financing problems in the Social Security and Medicare programs, have triggered a onesided austerity-focused class war in the US. Similar class conflicts have broken out around the globe. A coalition of the richest and most economically powerful segments of society and conservative politicians who represent their interests has demanded that deficits be eliminated by public-sector austerity – severe cuts at all levels of government in spending that either supports the poor and the middle class or funds crucial public investment. These demands constitute a deliberate attempt to destroy the New Deal project, begun in the 1930s, whose goal was to subject capitalism to democratic control. The right-wing coalition seeks to replace that project with a modernized version of the ‘free-market’ capitalism of the 1920s. In this paper I argue that our deficit crisis is the result of a shift from the New-Deal-based economic model of the early post-war period to today’s neoliberal, free-market model, a shift initiated under Ronald Reagan and continued under the presidents who succeeded him. The new model has generated slow growth, rising inequality and rising deficits. Rising deficits in turn created demands for austerity. After tracing the long-term evolution of our current deficit crisis, I show that this crisis can be resolved by raising taxes on upper-income households and large corporations, cutting war spending, and adopting a Canadian or European style health care system. There is no need to accept austerity. Calls for austerity should be seen as what they are – an attack by the rich and powerful against the basic interests of the American people.

Working Paper: Is Environmental Justice Good for White Folks?

Friday, July 30th, 2010

The following working paper by Michael Ash, James K. Boyce, Grace Chang, and Helen Scharber is now available on our website:

Is Environmental Justice Good for White Folks?

Abstract

This paper examines spatial variations in exposure to toxic air pollution from industrial facilities in urban areas of the United States, using geographic microdata from the U.S. Environmental Protection Agency’s RiskScreening Environmental Indicators project. We find that average exposure in an urban area is positively correlated with the extent of racial and ethnic disparity in the distribution of the exposure burden. This correlation could arise from causal linkages in either or both directions: the ability to displace pollution onto minorities may lower the effective cost of pollution for industrial firms; and higher average pollution burdens may induce whites to invest more political capital in efforts to influence firms’ siting decisions. Furthermore, we find that in urban areas with higher minority pollutionexposure discrepancies, average exposures tend to be higher for all population subgroups, including whites. In other words, improvements in environmental justice in the United States could benefit not only minorities but also whites.

Working Paper: Is there a tendency for the rate of profit to fall?

Wednesday, July 7th, 2010

The following working paper by Deepankar Basu and Panayiotis T. Manolakosis now available on our website:

Is  there a tendency for the rate of profit to fall?  Econometric evidence for the U.S. economy, 1948-2007

Abstract

The law of the tendential fall in the rate of pro t has been at the center of theoretical and empirical debates within Marxian political economy ever since the publication of Volume III of Capital. An important limitation of this literature is the absence of a comprehensive econometric analysis of the behaviour of the rate of pro t. In this paper, we attempt to ll this lacuna in two ways. First, we investigate the time series properties of the pro t rate series. The evidence suggests that the rate of pro t behaves like a random walk and exhibits “long waves” interestingly correlated with major epochs of U.S. economic history. In the second part, we test Marx’s law of the tendential fall in the rate of pro t with a novel econometric model that explicitly accounts for the counter-tendencies. We find evidence of a long-run downward trend in the general pro t rate for the US economy for the period 1948-2007.

Working paper: Cyclical patterns of employment, utilization, and profitability

Tuesday, May 11th, 2010

The following working paper by Ben Zipperer and Peter Skott is now available on our website:

Cyclical patterns of employment, utilization, and profitability

Abstract

The interaction between income distribution, accumulation, employment and the utilization of capital is central to macroeconomic models in the ‘heterodox’ tradition. This paper examines the stylized pattern of these variables using US data for the period after 1948. We look at the trends and cycles in individual time series and examine the bivariate cycical patterns among the variables.

Working paper: Employment and Distribution Effects

Tuesday, May 11th, 2010

The following working paper by Fabian Slonimczyk and Peter Skott is available on our website:

Employment and Distribution Effects

Abstract
This paper analyzes the effects of the minimum wage on wage inequality, relative employment and over-education. Using an efficiencywage model we show that over-education can be generated endogenously and that an increase in the minimum wage can raise both total and low-skill employment, and produce a fall in inequality. Evidence from the US suggests that these theoretical results are empirically relevant. The over-education rate has been increasing and our regression analysis suggests that the decrease in the minimum wage may have led to a deterioration of the employment and relative wage of low-skill workers.