A large policy debate revolves about the causes and consequences of child labour. Extensive child labour at early ages is often considered as harmful and there is substantial theoretical and empirical interest in determining the causes for child labour. Therefore, we would like to analyze the relationship between wealth (e.g. the number of cattle or other assets) and child labour, using household data collected in several villages in rural Africa. Suppose we have data on Y and X iv where Y, is the number of hours worked by child i in village v and X, is family wealth.
A large policy debate revolves about the causes and consequences of child labour. Extensive child labour at early ages is often considered as harmful and there is substantial theoretical and empirical interest in determining the causes for child labour. Therefore, we would like to analyze the relationship between wealth (e.g. the number of cattle or other assets) and child labour, using household data collected in several villages in rural Africa. Suppose we have data on Y and X iv where Y, is the number of hours worked by child i in village v and X, is family wealth.
a) Explain how this is related to the concept of Panel Data.
b) Explain how you could estimate the relationship between wealth and child labour using pooled OLS, Random Effect (RE), Fixed Effect (FE) estimators. Write down the estimation equations and the conditions needed to guarantee consistency. Compare the FE and the OLS estimators: Is either of these two estimators based on weaker assumptions than the other?
c) Describe one example how conventional exogeneity (often called "contempora- neous" exogeneity) could be violated. Could you also find an example how strict exogeneity but not conventional exogeneity could be violated?
d) Are there any variables that you would like to include as control variables? Why? Why would you not want to include the variable "Number of hours child attended school"?
e) An alternative estimator would be OLS with village-dummy variables. Can you explain under which conditions on the sampling process (i.e. data collection process) the estimates of these village-dummies would be consistent?
Now suppose that you were able to re-interview the same households two years later again, such that you have data on Y and X where the subscript t refers to time.
f) How could this additional data help you to deal with any remaining concerns about endogeneity?
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