An attempt to identify grey employment Estimation of wage under-reporting

and tests of the predictions

Péter Elek - János Köllő – Balázs Reizer - Péter A. Szabó

SEBA – IE CASS – IEHASEconomics of Crisis, Education and LabourChinese - Hungarian International Conference30th June -1st July 2011, Budapest

Eötvös Loránd University, Institute of Economics, Central European University, Reformed Presbyterian Church of Central and Eastern Europe

We try to identify cases, when total remuneration consists of a reported MW and an unreported ‘envelope wage’. We do so in 3 steps:

(i) Estimate a double hurdle (DH) model of the wage distribution, which takes into account:

(i) the crowding of low-productivity workers at the MW (truncation)(ii) reporting of MW instead of the full wage (tax evasion)

(ii) Relying on the DH results:

(i) we estimate the probability that a MW earner is paid an ‘envelope wage’(ii) simulate the ‘genuine’ wages of MW earners(iii) classify MW earners and their firms as ‘cheaters’ and ‘non-cheaters’

(iii) Test if our DH estimates have predictive power

We look at strong exogeneuous shocks (Hungary 2001-2, 2007) to which cheaters and non-cheaters were expected to respond differently

Test 1: Doubling of the MW (2001-2002)

The expectation is that under-reporting contained the growth of labor costs so the MW shock had weaker effect on cheating firms

Test 2: Introduction of a minimum contribution base = 2MW (2007)

Main rule: firms had to pay 2MW contribution even for wages lower than 2MW

Firms were allowed to pay w<2MW but they faced a high risk of audit. Firms continuing to pay MW faced particularly high risk.

Cheating firms had incentive to raise the reported wages of their ‘disguised’ MW earners (up to paying them an official wage of 2MW)

Furthermore, we expect that cheating firms were adversely affected by the reform so their output and employment fell

Motivation (1): Scarce results on „fake” MWs

Ample anecdotal evidence of „fake” MWs but scarce results on their magnitude and distribution across sectors, occupations, firm size, etc.

Inspection of aggregate, country-level dataShare of MW earners versus the Kaitz-indexSize of the spike at the MW is correlated with estimated size of the informal

economy (Tonin 2006)

Survey-based evidenceTurkey (Erdogdu 2008), Baltic states (Masso & Krillo 2009, Meriküll & Staehr

2008, Kris et al. 2007), EU (Eurobarometer 2007)

Indirect evidence from gap between reported income and consumptionBenedek at al. (2006): consumption fell in high-income households with MW

earners during the large hikes in Hungary

Tonin (2007): food consumption fell in household affected by the hikes compared to unaffected households of similar income

Motivation (2): policy relevance

• Mostly in CEEs, MW policies are strongly influenced by the belief that ‘nearly all’ MW earners are paid envelope wages

• Governments are tempted to whiten the grey economy by raising the MW and/or increasing the tax burden on low wages (Bulgaria 2003, Croatia 2003, Hungary 2001-2002, 2007)

Motivation (3): Hungary’s unusual MW policies

• Hungary’s unusual MW policies provide a unique opportunity to study wage under-reporting. Furthermore, the data background is better than in most countries

MW in Hungary – Doubling the MW in 2001-2002.1

.3.5

.7

1990 1995 2000 2005 2010

MW/AW MW/MEDW

05

10

15

20

1990 1995 2000 2005 2010

>5 employees >10 employees >20 employees

MW/average wage, MW/median wage Fraction paid near the MW (5%)

Decision to raise the MW from Ft 25,500 to Ft 40,000 (2001) and Ft 50,000 (2002). Over 70% inrease in real terms, given anticipated inflation. Primarily motivated by ‘making work pay’

Followed by a huge increase in the share of MW earners. The data clearly suggest that it was partly explained by the spread of envelope wages

After the large hikes: many MW earners in high-wage occupations

By 2003, the share of MW earners reached high levels among

• Small firm managers (27.4%)• Managers of larger firms (11.9%)• Lawyers, business and tax advisors etc. (14.9%)• Professionals in construction (17.9%)

In businesses engaged in cash transactions with customers

• Blue collars in house building (20.6%) versus civil engineering (4.3%)• Personal services (22%) versus other branches of services (<7%)

0.2

.4.6

Den

sity

11 12 13 14 15log gross monthly earnings

Kernel density estimate Normal density

Engineers and science

01

23

Den

sity

10.5 11 11.5 12 12.5log gross monthly earnings

Kernel density estimate Normal density

Unskilled laborers and casual workers

0.1

.2.3

.4D

ensi

ty

10 12 14 16log gross monthly earnings

Kernel density estimate Normal density

Top managers

After the large hikes: wage distributions

WS 2003

MW in Hungary: minimum contribution base, 2007.1

.3.5

.7

1990 1995 2000 2005 2010

MW/AW MW/MEDW

05

10

15

20

1990 1995 2000 2005 2010

>5 employees >10 employees >20 employees

MW/average wage, MW/median wage Fraction paid near the MW (5%)

Introduction of a minimum contribution base (2MW). MW viewed as a signal of wage under-reporting

MW earners suddenly disappeared in all categories of firms. We believe it was partly explained by cheaters’ reaction to the increased risk of audit

Data• All data come from the Wage Survey: linked employer-employee data

covering over 150,000 workers in more than 15,000 firms, annually.

• The WS covers all large firms (>20 employees) and a random sample of smaller firms (5-20)

• SMEs (5-50) report data on all workers. Larger firms report data on a sample of workers

• The surveys are cross-section but firms can be linked across years directly and workers can be linked indirectly

***

• DH model: cross-sections 2003, 2006

• Test 1: panel of small firms observed in 2000 and 2003

• Test 2: panels of workers and firms observed in 2006 and 2007

The double hurdle (DH) model

• A worker’s genuine wage is observed if – her productivity is above the MW (jumps the first hurdle) – and her wage is fully reported (jumps the second hurdle)

• The genuine log wage:

• The reported log wage (where m=log(MW)):

• where (u,v) is normally distributed with variance matrix:

uXy

otherwise

0vZ and muX if

m

yy*

1

2

S

The DH model – More insight

• Tobit is a special case if the second hurdle is not effective

• DH model first proposed by Cragg (1971) and widely used then in environmental economics, models of consumer choice, banking etc.

• But only by Shelkova (2007) to analyse wage distributions

Assumptions behind the DH model

• Unlike equilibrium models (e.g. Tonin 2006), we assume that many workers with productivity below the MW stayed in their jobs during/just after the episodes under investigation. Both hurdles were effective

When the plan of raising the MW to Ft 50,000 was announced, 32.7% of the employees earned less than that

When the double contribution base was announced, 58% earned less than 2MW

• Generally, taxes can be evaded by reporting any wage below the genuine wage. Reporting the MW is the cost-minimising choice only if it does not increase the risk of audit. We assume that was true in Hungary prior to 2007*

*) Elek and Szabó (2009) model a case of under-reporting, when the observed wage is not necessarily equal to the MW

Preliminary transformation of wages

• Log wages are not truncated normal because of the crowding of wages just above the MW

• Preliminary transformation is neededMartinez-Espineira (2006) Moffatt (2005) use Box-Cox. Yen and Jones (1997) use inverse hyperbolic sine

• We apply:

rmxrrmxrxxg if /exp

10.

51

11

1.5

12

g(y)

10.5 11 11.5 12y

Transformed log wages are normal

• r is estimated by two methods: – maximum likelihood on

a cross section– from a quasi panel

• Transformed log wages are approximately truncated normal

0.5

11

.52

De

nsi

ty

10 12 14 16

log wages

Panel A

0.5

11

.52

De

nsi

ty

10 12 14 16

transformed log wages

Panel B

rmxrrmxrxxg if /exp

The DH model – Estimation

• Likelihood function is given as:

• Maximum likelihood estimate is consistent and asymptotically normal if the distributional assumptions are correct

my

iiiii

myii

mxymxyzzmxL

**

*

2

*

1,,

1

1

/,1

Calculation of under-reporting probabilities and simulation of genuine wages

• Under-reporting probabilities for MW-earners:

• The „genuine” wage of each MW earner can be simulated:– Simulate (u,v) bivariate normal variables with

covariance matrix S until Xβ+u<m or Zγ+v<0 holds – Then the genuine log wage: y=max(Xβ+u, m)

ZmX

ZmXmXmyvZmuXP

,1

,/ | 0 ,

1,,

1,,*

Classification of workers and firms

• Workers: different criteria applied: cheater if MW is reported and:(1) P>0.5, (2) w>MW (3) w>1.5 MW.

Further thresholds were tested (1.1MW, 2MW) without the qualitative conclusions being affected

• Firms: cheater if at least one employee is caught cheating/victim of cheating

Results - DH

DH estimates (for 2003)

• 5-8% of all employees and 35-55% of the MW earners estimated to receive envelope wages

• Mean simulated (‘genuine’) earnings of ‘cheating’ MW earners exceeded 220% of the MW

• But we still have a huge spike at the MW (true MW earners)

• Similar results for 2006

02

000

400

06

000

800

0F

req

uenc

y

0 100000 200000 300000 400000 500000Simulated wage of MW earners 2003

Cheating and non-cheating MW earnersby occupation

0 10 20 30

UnskilledConstruction

TradeCleaners

DriversPorters_guardsArchitects_etal

IndustryAgriculture

Office_clerksServices

AdministratorsAssemblers

ManagersTechnicians

ProfessionalsTeachers_doctors

Cheater if P>0.5

MW earners classified on the basis of the DH estimates

non-cheater cheater

Cheating and non-cheating MW earnersby firm size

0 10 20 30 40

Size_5_10

Size_11_20

Size_21_50

Size_51_300

Size_301_plus

Cheater if P>0.5

MW earners classified on the basis of the DH estimates

non-cheater cheater

Cheating and non-cheating MW earnersby industry

0 10 20 30

Construction

Hotels_restaurants

Trade

Real_estate

Manufacturing

Agriculture

Services

Mining

Transport

Financial

Electricity_at_al

Cheater if P>0.5

MW earners classified on the basis of the DH estimates

non-cheater cheater

Cheating and non-cheating MW earnersby ownership

0 5 10 15 20

Domestic

Mixed

Foreign

Cheater if P>0.5

MW earners classified on the basis of the DH estimates

non-cheater cheater

Tests of the predictions

Test 1 – Empirical specificationThe MW substantially increased the

costs of employing low-wage workers

For firms starting or continuing under-reporting, the implied cost increase was smaller (for identical workers)

The difference between cheaters and non-cheaters in terms of total cost increase varied with exposure

Therefore we test if 1= 2 for• wage growth• residual wage growth• employment growth share of unskilled workersbetween 2000 and 2003

Exposure to the MW hike

Implied growthin the costof employing low-wage workers

1

2

non-cheater

cheater

ln(.) = 1(exposurecheater)+ 2(exposurenon-cheater)+Z + u

Test 1 - MeasurementWe have 4x3x2x2=48 equations/dependent var

Alternative measures of exposure (4x)• Fraction affected = earning less than Ft 40,000 in May 2000• Fraction affected = earning less than Ft 50,000 in May 2000• MW shock = average wage increase implied by the first MW hike under full compliance,

constant employment and no spillover (Machin-Manning-Rahman 2003)• MW shock = average wage increase implied by the first and second MW hikes under full

compliance, constant employment and no spillover (Machin-Manning-Rahman 2003)

Alternative measures of fraudulent behavior (3x)• Cheater if for at least one worker w>MW or w>1.5MW or P>0.5

Controls - base-period values (yes, no)• Firm size• Average wage• Capital/labor ratio• Profit/worker• Dummy for value subtractors• Skill shares, average age, share of men• Local unemployment rate• Industry dummies

Alternative samples (2x)• All firms versus only low-wage firms

Test 1 - sample

• 263 small firms (5-20 workers) observed in 2000 and 2003 in the WS

• We choose small firms because they report data on all of their employees exposure and skill composition are precisely measured

• Disadvantage: small firms are randomly sampled, year by year, so the panel is rather small

• Selection to the estimation sample from the base-period population of small firms is examined with probit. The results hint at random selection

Test 1 – Results (example)

Effects of exposure to the MW hike on wages and employment in 2000-2003 (Excerpts from Tables 6-9)

Dependent:

1 (cheaters)

2 (non-cheaters)

F-test H0: 1=2

Log change of the average wage

0.9665*** 1.5171*** 9.86***

Log change of the average residual wage

0.7571*** 1.1218*** 4.60***

Log change of employment

-0.4276* -1.1279*** 4.75**

Pct points change in unskilled share

-0.2472*** -0.6401*** 9.32***

Proxy of exposure: MW shock (average wage increase if firms increase the wages of affected workers to Ft 40,000 and nothing else happens) Proxy of cheating: P>0.5 for at least one MW employee in 2003 Sample: only low-wage firms (at least one worker earning less than Ft 40,000 in May 2000) Controls: yes

Residual wage: firm-level mean residuals from benchmark Mincer equations estimated using WS 2000 and WS 2003

Test 1 – Results from different specifications

Test1: Results from different specifications

(48 specifications = 100%)

Dependent: change of the Average

wage Residual

wage Employ-

ment Unskilled

share (+) (+) (-) (-) Non-cheaters: |1|>0 – effect of MW hike significant 100 100 77 100 Cheaters: |2|>0 – effect of MW hike significant 100 100 10 40 |1| > |2| - effect of MW hike on non-cheaters is stronger 100 100 100 100 H0: 1=2 rejected 100 73 69 100

Test 2 – Models and samples

• Wage change regressions using the data of MW earners (as of 2006) also observed in 2007

w* | (w0*=MW0) = f(X, cheater dummy)

• Probits. Same worker panel

Pr(w1*=2MW1 | w0*=MW)=(X, cheater dummy)

• Firm-level regressions for wages, employment and sales. Sample: firm panel 2006-2007

lnL=h(Z, cheater dummy)

Test 2 – Resultsindividual regressions

Table 10: The effect of estimated cheating behavior on wage growth between May 2006 and May 2007

(OLS, 7042 observations) Proxy used

P>0.5 w>MW w>1.5 MW Controls Coefficient St. error Coefficient St. error Coefficient St. error

No 19825*** 1552 8703*** 1072 10706*** 1268 Education 15699*** 1275 5742*** 980.1 7263*** 1141 All 12095*** 1339 3472*** 1014 5089*** 1173 *** p<0.01, ** p<0.05, * p<0.1. Controls (all variables relate to 2006): Dummies for education (college graduate, secondary school and vocational school), work experience in years, dummies for gender, municipality and firm size categories

Table 11: The effect of estimated cheating behavior on the probability that a worker paid the MW in May 2006 was paid 2MW in May 2007

(Probit marginal effects, 7042 observations) Proxy used P>0.5 w>MW w>1.5 MW Controlls Coefficient St. error Coefficient St. error Coefficient St. error

No 0.133*** 0.0175 0.0479*** 0.00903 0.0583*** 0.0107 Education 0.0845*** 0.0141 0.0256*** 0.00753 0.0296*** 0.00868 All 0.0431** 0.0192 0.0111 0.00739 0.0144 0.00901 *** p<0.01, ** p<0.05, * p<0.1

Controls (all variables relate to 2006): Dummies for education (college graduate, secondary school and vocational school), work experience in years, dummies for gender, municipality and firm size categories

Test 2 – Resultsfirm-level regressions

Proxies of ‘cheating’ beavior Controls P>0.5 w>MW w>1.5 MW

Change of average wage (log) No 0.134*** 0.00860 0.0775*** 0.00636 0.0875*** 0.00668 Yes 0.0778*** 0.00992 0.0365*** 0.00740 0.0432*** 0.00750 Change of employment (log) No -0.0329*** 0.00907 -0.0274*** 0.00645 -0.0314*** 0.00688 Yes -0.0262*** 0.00960 -0.0196*** 0.00681 -0.0244*** 0.00725 Change of sales revenues (log) No -0.0640*** 0.0152 -0.0242** 0.0113 -0.0284** 0.0128 Yes -0.0499*** 0.0167 -0.0151 0.0120 -0.0170 0.0136 *** p<0.01, ** p<0.05, * p<0.1. Sample: Firms observed in the Wage Survey in 2006 and 2007. Number of observations 4150 except for sales revenues (4173). Controls include skill shares, average wage, average age and dummies for sectors, regions, type of municipality and state ownership

Effect of cheating behavior on changes of wages, employment and sales

Conclusions

• The DH model seems to locate ‘fake’ MWs with some precision

• The model might be used for statistical profiling but, more importantly,it points to the limits of tax enforcement

• True MW earners exist. Substantially raising the MW (+taxes) in order to ‘whiten the grey economy’ may adversely affect non-cheating firms and workers

• Research: merging cheaters and non-cheaters leads to strongly biased estimates of MW effects