require panel data and that is why the ELMPS for Egypt and the ENOE for Mexico are appropriate data sets for the analysis. All transition matrices describe transitions among five different labor market states: public sector employment, private formal sector employment, private informal sector employment, unemployment, and out of labor force. The computation of transition matrices for each individual country follows standard procedures. By construction, the sample is restricted to individuals interviewed in both rounds. The transition matrices are disaggregated by sex. Panel weights are used.

A frequency gap exists between the six-yearly ELMPS and quarterly ENOE. Even with the panel structure of the ENOE, one can at most compute annual transitions. Six-yearly transitions from Egypt and annual transitions from Mexico are clearly not comparable, as individuals not only have far more time to transition but also age to different extents. In the absence of data that allow for directly comparable transition, harmonization is in order.

In principle, we can either infer continuous-time transition intensity matrices for both labor markets or simulate in discrete time six-yearly transition matrices in Mexico based on annual ones. However, the former approach is riddled with issues that make it less reliable and can only be imperfectly addressed by existing techniques.<sup>10</sup> We therefore opt for simulation. In the simulations, we assume labor market transitions in each period to be discrete-time Markov processes. That is, the transition probability for each worker from one state to another depends on and only on her initial state. Hence, Markov processes are “memoryless,” as each individual’s history is irrelevant. This is unlikely to be entirely accurate, as the probability of one’s transition would depend on whether, or to where, one has recently transitioned but delivers a feasible solution to the problem of comparability.

Further, we assume the transition probability matrix in each period to always be the empirical annual transition matrix observed from 2005 Q1 to 2006 Q1. This assumption is unlikely to be entirely accurate as well. Individuals age and change transition behavior over time. The underlying macroeconomy will have changed as well, leading to cyclical changes in employment and favoring some sectors over others. The assumption is that a six-year horizon is not long enough to generate significant departures from the underlying steady state equilibrium. See Appendix A.2 for a more complete discussion of the limitations of our simulation method.

To simulate the transitions, we firstly model the individual labor market transition process. Starting from each initial state, we draw a possible transition outcome in accordance with the transition probability matrix, representing one transition. Then the same procedure is repeated with the new initial state changed to the result of the previous draw. This process is done six times in total, modeling transitions after six years.

We then apply the Monte Carlo method to calculate the six-yearly transition probability matrix i �. For each possible initial state , the aforementioned procedure is repeated 100,000 �pp ii

> 10 These issues of estimation are of two types: aliasing problems and embeddability problems. The former refers to the fact that the estimated transition intensity matrix is not necessarily unique. The latter refers to the fact that there could be no solution whose estimated parameters satisfy the requirements of probability distributions. See Bosch and Maloney (2007) or Fougère and Kamionka (2005) for a more complete discussion.

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