CREST-ENSAE Mini-course Microeconometrics of Modeling Labor Markets Using Linked Employer-Employee Data John M. Abowd portions of today’s lecture are the work of Kevin McKinney (U.S. Census Bureau) and Ian Schmutte (University of Georgia) June 6, 2013

Topics May 30: Basics of analyzing complex linked data June 3: Basics of graph theory with applications to labor markets June 6: Matching and sorting models June 10: Endogenous mobility models Online course materials 6 June 2013© John M. Abowd and others, 20132

Lecture 3 More results on graph sampling More results on using modularity to find communities Matching and sorting models 6 June 2013© John M. Abowd and others, 20133

MORE APPLICATIONS OF SAMPLING GRAPHS (WORK OF MCKINNEY) 6 June 2013© John M. Abowd and others, 20134

Generating Connected Samples Let B be the upper right-hand corner of the adjacency matrix of the realized mobility network, as defined in lecture 2 B has I rows (one for each worker) B has J columns (one for each employer) Elements of B are the counts of the number of periods that worker i was employed by employer j 6 June 2013© John M. Abowd and others, 20135

Projection onto the Employer Nodes The projection of the bipartite graph of the realized mobility network onto employer nodes is accomplished by computing a new adjacency matrix P F = B T B Let S F be the column sums of B (employer degree distribution Then the adjacency matrix of the employer projection is AF = 1(P F - diag(S F )>0), where 1() is the element-wise indicator function 6 June 2013© John M. Abowd and others, 20136

Generating Connected Samples Accomplished by taking a sample of nodes from the employer projection where each node has a constant steady state selection probability of 1/(I – J) rather than the usual random walk procedure where each node would have selection probability of degree(node j )/(2|P F |) where |P F | is the number of edges in the employer projection 6 June 2013© John M. Abowd and others, 20137

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MORE APPLICATIONS OF MODULARITY MODELING (WORK OF SCHMUTTE) 6 June 2013© John M. Abowd and others,

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6 June 2013© John M. Abowd and others,

Modularity Determined Communities in Brazilian Linked EE Data RAIS graphs display the projection of the RMN in RAIS data ( ) onto plants. After the projection, take a 5 percent random sample of plants along with their associated edges. The graph shows the structure after eliminating small degree nodes (degree <= 10). This shows about 25 percent of edges. Colors in the graph correspond to the maximum modularity partition of nodes into 15 communities at modularity of 0.65, which is very strong 6 June 2013© John M. Abowd and others,

PSID Communities (Industry x Occupation Pseudo-employers) 6 June 2013© John M. Abowd and others,

Raw Graph of Brazilian Data 6 June 2013© John M. Abowd and others,

Maximum Modularity Communities in Brazilian EE Data 6 June 2013© John M. Abowd and others,

Other Applications of Coloring Different definitions of communities (minimum cuts, maximum likelihood clustering) Showing conditional independence – Conditional independence can be used to massively increase the parallelization of a particular computation – This permits much faster estimation 6 June 2013© John M. Abowd and others,

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6 June 2013© John M. Abowd and others,

SORTING AND MATCHING MODELS 6 June 2013© John M. Abowd and others,

How to Fit Matching Models Setting up equilibrium matching models Example using the Shimer (2005) model – Lecture based on Abowd, Kramarz, Perez-Duarte, and Schmutte (2012)Abowd, Kramarz, Perez-Duarte, and Schmutte (2012) Some critiques of these approaches 6 June 2013© John M. Abowd and others,

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6 June 2013© John M. Abowd and others,

The Critique of Eeckhout and Kircher See Eeckhout and Kircher (2011)Eeckhout and Kircher (2011) Without frictions, their proposition 1 states that for any production function that can induce positive sorting there exists a production function that can induce negative sorting with the same equilibrium wage function 6 June 2013© John M. Abowd and others,

The Critique of Eeckhout and Kircher See Eeckhout and Kircher (2011)Eeckhout and Kircher (2011) With search frictions, for every supermodular production function (production complements) that induces positive sorting, there exists a submodular production function (production substitutes) that induces the same wage distribution once the firm types are relabeled (reversing their order) 6 June 2013© John M. Abowd and others,

What to Do? First, these points were made in the Abowd and Kramarz handbook paper (1999) regarding interpretations of the AKM decomposition as structural1999 Eeckhout and Kircher are much more general Must use additional outcomes – Actual vacancy data – Actual production data 6 June 2013© John M. Abowd and others,

Summary Sampling matters for estimation of decomposition regardless of interpretation Maximum modularity methods produce interesting measures of the mobility communities in linked EE data Structural models of matching and sorting are feasible but the interpretation of the results may not be general 6 June 2013© John M. Abowd and others,