# **6.2 Difference-in-Difference Estimates: The Regression Model**

Difference-in-Difference estimates and their standard error, according to Greene (2002), most often derive from using Ordinary Least Squares (OLS) in repeated cross sections (or a panel) data on individuals in treatment and control groups (no treatment) for a period before and after a specific intervention. As Meyer (1995) argues, the great appeal of DD estimation comes from its simplicity as well its potential to circumvent many of the endogeneity problems that typically arise when making comparisons between individuals.

The standard DD estimates the following regression:

# _Yist=As+Bt+cXist+βIst+εist_

where _As_ and _Bt_ are fixed effects for states and years respectively, _Xist_ are relevant individual controls and εist is a error term. The estimated impact of the intervention is the OLS estimate _β_ . Standard errors used to form confidence interval for _β_ are usually OLS standard errors sometimes corrected to account for correlation of shocks within each year. Considering the data characteristics mentioned earlier, this study will assume that the estimated coefficient of intervention is variable (given _Xist_ ) but does not help to determine program participation (land titles were given randomly and households were mostly unaware about receiving the title).

Hence, this specification is a common generalization of the most basic DD, and it will be the foundation for this particular study’s econometric technique. The basic assumption is that changes in the outcome variable over time would have been exactly the same in both the treatment and the control group in the absence of the intervention.

# **6.3 Difference-in-Difference Estimates: Land Title Specification**

In this paper, formally, the dependent variable is hours weekly hours of work of child labor force _Yist_ (the outcome of interest for household _i_ in group _s_ by time _t_ ). The dependent variable would be posted as the difference among weekly hours of child labor in 2008 and 2007.

Also, _δ_ indicates whether the household lives in a neighborhood that has been reached by the program -- being the dummy for whether the land title has affected the group _s_ at time _t_ ; with fixed effects and _Xi_ is a vector of characteristic controls.

Hence, the coefficient _δ_ is the estimated program effect, which provides a measure of conditional average difference in time worked by children in households in the program area versus the non-program area.

In addition, _Xi_ includes the following controls: sex (dummy), marital status (dummy, example: single) and ethnicity (dummy, example: African Brazilian).

Another set of variables included, to extend to include fixed effects, and convergent with Becker & Lewis’s (1973) suggestion, level of income -- measured in terms of minimum wage (please refer to question number P-38 at Appendix A for details). Furthermore, weekly hours of adult work is an essential variable to understand child labor according to Rosenzweig (1981).

Patrinos & Psacharapoulos (1994) for Paraguay, Grootaert (1998) for Ghana, and Heady (2003) for Pakistan conclude that the more people there are in the family, the higher are the chances of having child labor. Given such a framework, the number of household members is also included. The same applies for the years of education of the family head. For income, 14