Differences in Differences (DiD) specifications

Given that the survey allows us to observe the labour market before and after the policy

intervention, and based on the assumption that all three zones exhibit the same trends in

the pretreatment period, it is possible to implement DiD estimates. This section describes

the econometric specifications used to evaluate the minimum wage effect on real earnings.

Regarding the econometric specifications, the control group represents the counter-

factual of the treated observations, but in terms of the econometric estimation of the

treatment effect, it also corresponds to the reference group used to measure the rela-

tive difference generated by the intervention. In other words, for invalid control groups,

the choice of the reference group can alter significantly the magnitude of the estimated

impact. Then, using the fact that there are two untreated zones, and with the aim at

verifying the robustness of the model, we use two different specifications for all the sub-

sequent estimations. In the first of these specifications only individuals in Zone C are

included in the control group. In this case, observations from Zone A are not dropped

from the analysis; instead, a dummy variable for this zone is included as a regressor. For

the second specification, the control group is created using all the untreated individuals

in the sample, so we combine control zones A and C.

is the preferred control group because of its size. In the sample, 80% of the observations

correspond to Zone C.

So, in the first specification, equation (2.1a), we have the traditional DiD equation,

in which are included binary variables for identifying the treated zone (ZoneB) and

the post-treatment period (P eriod2), as well as the interaction of these two dummy

variables, which corresponds to the DiD variable (ZoneB ∗ P eriod2). For the second

specification, (2.1b), we include as independent variables the dummy variable ZoneA and

— for completeness— its interaction with the post-treatment period dummy, P eriod2.

Thus, the DiD specifications are the following:

ln(wi) = β0+ δ1ZoneBi∗ P eriod2i+ δ2P eriod2i+ δ3T rendB + δ5T rendA&C

+ δ4EmpRate + β1ZoneBi+ k

X

k=2

βkXki+ ei (2.1a)

ln(wi) = β0+ δ1ZoneBi∗ P eriod2i+ δ2P eriod2i+ δ3T rendB + δ4T rendA + δ5T rendC

+ δ6EmpRate + δ7ZoneAi∗ P eriod2i+ β1ZoneBi + β2ZoneAi+ k

X

k=3

βkXki+ ei

(2.1b)

where the dependent variable ln(wi) corresponds to the natural log of real hourly wages.

δ1 is the parameter of interest in both equations. In equation (2.1a), it corresponds to the

estimated impact of the minimum wage increase on Zone B with respect to individuals

in both, zones A and C. On the other hand, in (2.1b) δ1 is the estimated effect of the

intervention with respect only to individuals in Zone C. If the control groups are valid, δ1

from equations (2.1a) and (2.1b) should not be different.

It is important to highlight that the coefficient δ2 in equation (2.1b) is not a treatment

effect, the purpose is not trying to measure the impact on the untreated Zone A. It is

included only for completeness in the model in order to avoid losing all the observations

For the set of independent variables, P eriod2i is an indicator variable that takes the

value of 1 if the observation corresponds to the post-treatment period,4 _{and 0 otherwise.}

ZoneBi and and ZoneAi are dummy variables that identify the observations that belong

to Zone B or A, respectively.5

T rendB is a simple linear quarterly trend for Zone B to control, to some extent, for

the macroeconomic time trend in the treated zone that, by the nature of the survey, is

not possible to include variables at the macroeconomic level in the model. Depending

on the control group used, equation (2.1a) includes a common linear trend for zones A

and C (T rendA&C), while equation (2.1b) controls separately for each zone’ linear trend

including T rendA and T rendC by separately.

To control for the labour market conditions at the regional level, we include quar-

terly employment rates by state (EmpRate), defined as the proportion of individuals

with working activities with respect to the active labour market population. Regarding

potential endogeneity problems by the inclusion of this variable, Appendix 2.D presents

some analytical arguments, as well as the Durbin-Hu-Hausman test to demonstrate the

exogeneity of this covariate in the wage equation.

Xk corresponds to the set of socio-demographic variables at the individual level. It is

composed of variables for age, squared age, a binary variable for gender, an educational

variable (schooling level), and an indicator of rural residence. Interactions of schooling

level with rural residence and gender are also included. Finally, ei corresponds to the

error term.

In addition to the full sample specification, each model is also estimated restricting

the sample to the following age thresholds: individuals between 12 and 29 years old,

4_{The intervention was announced on Monday, 26 November 2012 and it was in force on Tuesday,} November 27. ENOE allows to identify the week when the interview took place for urban municipalities and the month of interview for rural observations. Thus, P eriod2i = 1 for those urban observations interviewed at least on the ninth week of the fourth quarter of 2012, and for rural observations interviewed after December 2012; P eriod2i= 0 otherwise. See Appendix 2.A for a more detailed explanation on the variables construction.

5_{Although ENOE contains a variable for identifying the minimum wage zones, we use directly the} official classification from CONASAMI. See Appendix 2.A for the codes of the municipalities included in each zone.

between 30 and 49 years old, and finally, individuals aged equal or older than 50. We also

investigate the difference of the impact by gender. To check the robustness of the model,

we also estimate the effect excluding self-employed workers.

Furthermore, in order to evaluate how the estimated effect is changing over time, a

second set of specifications are estimated in Subsection 2.5.2, where the post-treatment

period variable, P eriod2i, is decomposed into four quarterly dummy variables: 2013 Q1,

2013 Q2, 2013 Q3 and, 2013 Q4. These four time-dummy variables are included in the

models with their respective DiD regressors to explore the dynamics of the effect.

ln(wi) = β0+ 4 X j=1 δjZoneBi∗ 2013 Qji+ 4 X j=1 δj+42013 Qji

+ δ9T rendB + δ10T rendA&C + β1ZoneBi+ k X k=2 βkXki+ ei (2.2a) ln(wi) = β0+ 4 X j=1 δjZoneBi∗ 2013 Qji+ 4 X j=1 δj+4ZoneAi∗ 2013 Qji+ 4 X j=1 δj+82013 Qji

+ δ13T rendB + δ14T rendA + δ15T rendC + β1ZoneBi+ β2ZoneAi+ k

X

k=3

βkXki+ ei

(2.2b)

Restricting the sample to waged individuals implies the systematic exclusion of the

unemployed and inactive labour market population. Then, we implement sample correc-

tion procedures in all the regressions presented in the chapter. A general description of

this procedure is developed in the following subsection. Appendix 2.F presents the pooled

OLS estimates for the main specifications without sample selection bias correction.