Table 2 shows the variance of the earning distribution in the overall economy, broken down by two components: a) Variability within sectors; b) Variability between sectors. Despite the substantial differences in relative earnings, 97.5 percent of variance in log wages is explained by within-sector variance.<sup>63</sup> Table 3 shows the descriptive statistics for the unemployed population. The estimated unemployment rate for the year 2003 is quite high: 18.5 percent (s.e. of .00274). Mean unemployment duration is quite high (51.5 weeks),<sup>64</sup> and higher than the mean non-employment duration for the employed population (6.9 months).

# **4.2 Labor Market Dynamics**

Standard static analysis of labor markets that analyze stocks of workers in different states does not tell us anything about where those workers arrived from, how long they will stay, or where they will go next. I construct a set of statistics to analyze labor market dynamics and derive some stylized facts about movement across sectors in the Colombian labor markets, using the retrospective questions from the cross-section database.

## **4.2.1 Annual Discrete Transition Matrix**

Individuals in the sample fall into four labor market states: unemployed ( _U_ ), employed in the formal sector ( _F_ ) _,_ employed in the informal sector ( _I_ ), and other ( _O_ ).<sup>65</sup> I estimate an annual discrete transition matrix by estimating gross worker flows across states.<sup>66</sup> Let _mij_ be the number of individuals in the 2003 sample who were in state _i_ in 2002 and state _j_ in 2003. I observe some, but not all the transitions between states from 2012 to 2013.<sup>67</sup> When considering transitions into unemployment, I observe all transitions _mUU , mFU , mIU_ and _mOU ._ When considering transitions into the formal sector, I observe _mFF , mIF_ and _mUF_ + _mOF_ . When considering transitions into the informal sector, I observe _mFI , mII_ and _mUI_ + _mOI_ . I also observed the following transitions into the ‘other’ state: _mOO_ and _mUO_ .

To recover _mUI_ , _mOI_ , _mUF_ and _mOF_ the following assumptions are made:

> 63It would be interesting if workers were assigned randomly to sectors, to see whether selection reduces or increases inequality, or what the aggregate wage variability would be if sectoral labor force quality were held constant (see Heckman & Sedlacek, 1985).

> 64This estimate can be upward biased because: 1) Unemployment duration is only observed for the currently unemployed; 2) It is more likely to have workers with higher lengths of unemployment in a sample of unemployed workers at a particular point in time (a ‘stock’ sample).

> 65Other includes the inactive population.

> 66Another approach may be to think about an underlying continuous-time Markov process that generates the discrete time mobility process, and therefore, estimate the transition probabilities accordingly. See Maloney and Bosch, 2007.

> 67In the survey, I have the following questions for the employed: 1) How long (months) have you been employed continuously in the current job?; 2) How long (months) were you without employment between your current job and the previous job? With these questions I can identify job-to-job transitions, and non-employment (unemployment or inactive) to job transitions.

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