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Unemployment Duration and Re-employment Wages: A Control Function - - PowerPoint PPT Presentation

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Unemployment Duration and Re-employment Wages: A Control Function Approach Marta C. Lopes 1 1 NovaSBE, Universidade Nova de Lisboa 23 rd London Stata User Group Meeting September 7, 2017 Marta C. Lopes (NovaSBE) A Control Function Approach

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SLIDE 1

Unemployment Duration and Re-employment Wages: A Control Function Approach

Marta C. Lopes1

1NovaSBE, Universidade Nova de Lisboa

23rd London Stata User Group Meeting September 7, 2017

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 1 / 13

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SLIDE 2

What is the Control Function approach?

Table of Contents

1

What is the Control Function approach?

2

Application on Unemployment Duration and Re-employment Wages Institutional Setting First Stage - Survival Analysis Second Stage - Wage Equation Control for Selection

3

Take-home

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 1 / 13

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SLIDE 3

What is the Control Function approach?

What is the Control Function approach?

“The control function approach to estimation is inherently an instrumental variables method.” (in Wooldridge, 2015)

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 2 / 13

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SLIDE 4

What is the Control Function approach?

What is the Control Function approach?

“The control function approach to estimation is inherently an instrumental variables method.” (in Wooldridge, 2015)

1

Identify the endogenous variable in the “structural equation” y1 = γ1y2 + δX + u1 (1)

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 2 / 13

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SLIDE 5

What is the Control Function approach?

What is the Control Function approach?

“The control function approach to estimation is inherently an instrumental variables method.” (in Wooldridge, 2015)

1

Identify the endogenous variable in the “structural equation” y1 = γ1y2 + δX + u1 (1)

2

Find appropriate instrumental variables (z), such that E(z′u1) = 0

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 2 / 13

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SLIDE 6

What is the Control Function approach?

What is the Control Function approach?

“The control function approach to estimation is inherently an instrumental variables method.” (in Wooldridge, 2015)

1

Identify the endogenous variable in the “structural equation” y1 = γ1y2 + δX + u1 (1)

2

Find appropriate instrumental variables (z), such that E(z′u1) = 0

3

Obtain, in a reduced form, the generalized residuals (v2) – 1st stage y2 = πX + βz + v2 (2)

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 2 / 13

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SLIDE 7

What is the Control Function approach?

What is the Control Function approach?

“The control function approach to estimation is inherently an instrumental variables method.” (in Wooldridge, 2015)

1

Identify the endogenous variable in the “structural equation” y1 = γ1y2 + δX + u1 (1)

2

Find appropriate instrumental variables (z), such that E(z′u1) = 0

3

Obtain, in a reduced form, the generalized residuals (v2) – 1st stage y2 = πX + βz + v2 (2)

4

Add the generalized residuals to the 2nd stage y1 = γ1y2 + δX + ρv2 + e1 (3)

Remember: y2 − v2 = ˆ y2

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 2 / 13

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SLIDE 8

What is the Control Function approach?

Control Function: Advantages

OLS Control for endogenous variables

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 3 / 13

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SLIDE 9

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS Control for endogenous variables

  • Marta C. Lopes (NovaSBE)

A Control Function Approach September 7, 2017 3 / 13

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SLIDE 10

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS Control for endogenous variables

  • Linear First Stage
  • Marta C. Lopes (NovaSBE)

A Control Function Approach September 7, 2017 3 / 13

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SLIDE 11

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS CF Control for endogenous variables

  • Linear First Stage
  • Non-linear First Stage
  • Marta C. Lopes (NovaSBE)

A Control Function Approach September 7, 2017 3 / 13

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SLIDE 12

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS CF Control for endogenous variables

  • Linear First Stage
  • Non-linear First Stage
  • OLS

Heckit Control for selection bias

  • Marta C. Lopes (NovaSBE)

A Control Function Approach September 7, 2017 3 / 13

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SLIDE 13

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS CF Control for endogenous variables

  • Linear First Stage
  • Non-linear First Stage
  • OLS

Heckit Control for selection bias

  • Non-linear First Stage
  • Binary Endogenous Variable
  • Marta C. Lopes (NovaSBE)

A Control Function Approach September 7, 2017 3 / 13

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SLIDE 14

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS CF Control for endogenous variables

  • Linear First Stage
  • Non-linear First Stage
  • OLS

Heckit CF Control for selection bias

  • Non-linear First Stage
  • Binary Endogenous Variable
  • Non-binary Discrete Endogenous Variable
  • Marta C. Lopes (NovaSBE)

A Control Function Approach September 7, 2017 3 / 13

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SLIDE 15

What is the Control Function approach?

Control Function: Advantages

OLS 2SLS CF Control for endogenous variables

  • Linear First Stage
  • Non-linear First Stage
  • OLS

Heckit CF Control for selection bias

  • Non-linear First Stage
  • Binary Endogenous Variable
  • Non-binary Discrete Endogenous Variable
  • In the context of the our application, we can also obtain:

Hausman Test Inverse Mills Ratio

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 3 / 13

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SLIDE 16

Application on Unemployment Duration and Re-employment Wages

Table of Contents

1

What is the Control Function approach?

2

Application on Unemployment Duration and Re-employment Wages Institutional Setting First Stage - Survival Analysis Second Stage - Wage Equation Control for Selection

3

Take-home

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 3 / 13

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SLIDE 17

Application on Unemployment Duration and Re-employment Wages

Unemployment Duration and Re-employment Wages

There is not a single theory which justifies the earnings losses of displaced workers (Carrington and Fallick, 2015).

job-specific human capital (Becker, 1962) matching (Jovanovic, 1979) wage-productivity gap (Lazear, 1981) signalling (Gibbons and Katz, 1989) unionism (Hildreth and Oswald, 1997) intra-household reallocation (Lundberg, 1985) health (Kessler, House and Turner, 1987)

Estimation issue: simultaneity present in the relationship between joblessness duration and re-employment wage log(PostWi) = α0 + α1 log(UDi) + X ′β + ui

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 4 / 13

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SLIDE 18

Application on Unemployment Duration and Re-employment Wages Institutional Setting

Unemployment Benefits Rules in Portugal

Unemployment insurance (UI) involuntarily unemployed working for a minimum period potential duration = f (age, job history) daily benefit based on remunerations of past 2 years

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 5 / 13

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SLIDE 19

Application on Unemployment Duration and Re-employment Wages Institutional Setting

Figure: Percentage of individuals by age group and potential duration of unemployment benefit, before and after the 2007 reform

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 6 / 13

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SLIDE 20

Application on Unemployment Duration and Re-employment Wages First Stage - Survival Analysis

First Stage - Identification Strategies

Identify the exogenous variation in the joblessness duration: Potential Duration of Unemployment Benefits

Vast literature indicates strong correlation between potential duration of UB and joblessness duration. The rules are not directly related to the wage but include two of the determinants (age, experience).

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 7 / 13

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SLIDE 21

Application on Unemployment Duration and Re-employment Wages First Stage - Survival Analysis

First Stage - Identification Strategies

Identify the exogenous variation in the joblessness duration: Potential Duration of Unemployment Benefits

Vast literature indicates strong correlation between potential duration of UB and joblessness duration. The rules are not directly related to the wage but include two of the determinants (age, experience).

Age Discontinuity in the Potential Duration of Unemployment Benefits

Individuals with 29 or 30 years old have, on average, similar labour supply characteristics but are entitled to different potential durations. There is room for enough difference on experience.

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 7 / 13

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SLIDE 22

Application on Unemployment Duration and Re-employment Wages First Stage - Survival Analysis

First Stage - Identification Strategies

Identify the exogenous variation in the joblessness duration: Potential Duration of Unemployment Benefits

Vast literature indicates strong correlation between potential duration of UB and joblessness duration. The rules are not directly related to the wage but include two of the determinants (age, experience).

Age Discontinuity in the Potential Duration of Unemployment Benefits

Individuals with 29 or 30 years old have, on average, similar labour supply characteristics but are entitled to different potential durations. There is room for enough difference on experience.

Change in the Potential Duration of Unemployment Benefits

As the benefits require involuntary unemployment there is no room for strategic behaviour. The policy change did not affect all the individuals in the same way. Correlation with age is -0.03 and correlation with experience is 0.18.

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 7 / 13

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SLIDE 23

Application on Unemployment Duration and Re-employment Wages First Stage - Survival Analysis

First Stage - Results

Table Accelerated Failure Time Unemployment Duration Equation

Variable (1) Difference in Potential Rules .089 (.0002) Age (groups) [30,40[ .284 (.004) [40,45[ .592 (.004) ≥45 1.449 (.004) Log likelihood

  • 18 481

N 18 543

Notes: standard errors in parenthesis below the estimates. The equations also include gender dummy, tenure quadratic polynomial, reasons

  • f

unemployment dummies, unemploy- ment rate and six region dummies.

Use all the unemployed individuals (both re-employed and not re-employed) to identify the exogenous

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 8 / 13

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SLIDE 24

Application on Unemployment Duration and Re-employment Wages Second Stage - Wage Equation

Second Stage - Results

Variable OLS CF Ln(Duration)

  • .076
  • .049

(.005) [.012] 1st stage residuals

  • .068

[.028] Ln(Previous Wage) .566 .568 (.011) [.016] Age (groups) [30,40[ .016 .012 (.012) [.012] [40,45[

  • .008
  • .020

(.018) [.019] ≥45 .007

  • .021

(.017) [.021] Constant 3.084 3.109 (.091) [.111] Adj R2 .264 .265 N 8 423

Notes: bootstrapped standard errors in squared parenthesis below the esti-

  • mates. The equations also include the

controls of the first stage.

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 9 / 13

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SLIDE 25

Application on Unemployment Duration and Re-employment Wages Second Stage - Wage Equation

Problem: Simultaneity unemployment duration ↑

← →

reservation wage ↓

← →

re-employment wage ↓

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 10 / 13

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SLIDE 26

Application on Unemployment Duration and Re-employment Wages Second Stage - Wage Equation

Problem: Simultaneity unemployment duration ↑

← →

reservation wage ↓

← →

re-employment wage ↓ Solution: Include the generalized residuals from the first stage Statistic: Hausman test

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 10 / 13

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SLIDE 27

Application on Unemployment Duration and Re-employment Wages Second Stage - Wage Equation

Problem: Simultaneity unemployment duration ↑

← →

reservation wage ↓

← →

re-employment wage ↓ Solution: Include the generalized residuals from the first stage Statistic: Hausman test Problem: Selection Individuals who got a job = individuals who did not get a job

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 10 / 13

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SLIDE 28

Application on Unemployment Duration and Re-employment Wages Second Stage - Wage Equation

Problem: Simultaneity unemployment duration ↑

← →

reservation wage ↓

← →

re-employment wage ↓ Solution: Include the generalized residuals from the first stage Statistic: Hausman test Problem: Selection Individuals who got a job = individuals who did not get a job Solution: Include the hazard rate from the first stage Statistic: Inverse Mills ratio

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 10 / 13

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SLIDE 29

Application on Unemployment Duration and Re-employment Wages Control for Selection

Second Stage - with selection control

Variable OLS CF CF+S Ln(Duration)

  • .076
  • .049
  • .052

(.005) [.012] [.012] 1st stage residuals

  • .068
  • .072

[.028] [.029] 1st stage hazard

  • .310

[.292] Ln(Previous Wage) .566 .568 .569 (.011) [.016] [.016] Age (groups) [30,40[ .016 .012 .008 (.012) [.012] [.013] [40,45[

  • .008
  • .020
  • .028

(.018) [.019] [.022] ≥45 .007

  • .021
  • .037

(.017) [.021] [.028] Constant 3.084 3.109 3.157 (.091) [.111] [.117] Adj R2 .264 .265 .265 N 8 423

Notes: bootstrapped standard errors in squared paren- thesis below the estimates. The equations also include the controls of the first stage.

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 11 / 13

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SLIDE 30

Application on Unemployment Duration and Re-employment Wages Control for Selection

Selection direction

The hazard rate is the ratio between the density and the cumulative density functions. That is, it can be interpreted as an Inverse Mills Ratio. From the estimated coefficient we can then calculate the correlation between the two residuals.

ˆ σ2 = 1

N

  • i
  • ˆ

v2

i + ˆ

αˆ λi

  • (4)

ˆ

v2

i - squared individual residuals from second stage

ˆ α - estimated coefficient of the hazard rate in the second stage ˆ λi - estimated individual hazard rate from the first stage ˆ ρ = ˆ α ˆ σ

(5) Provides the correlation between the two residuals, which in this case is 0.21 but not statistically significant.

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 12 / 13

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SLIDE 31

Take-home

Table of Contents

1

What is the Control Function approach?

2

Application on Unemployment Duration and Re-employment Wages Institutional Setting First Stage - Survival Analysis Second Stage - Wage Equation Control for Selection

3

Take-home

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 12 / 13

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SLIDE 32

Take-home

Take-home

Control Function Approach is nothing more than an IV method

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13

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SLIDE 33

Take-home

Take-home

Control Function Approach is nothing more than an IV method It allows for both linear and non-linear first stage

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13

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SLIDE 34

Take-home

Take-home

Control Function Approach is nothing more than an IV method It allows for both linear and non-linear first stage Namely for the estimation of survival analysis models which can include more individuals than those used for the second stage

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13

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SLIDE 35

Take-home

Take-home

Control Function Approach is nothing more than an IV method It allows for both linear and non-linear first stage Namely for the estimation of survival analysis models which can include more individuals than those used for the second stage Provides a test for endogeneity

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13

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SLIDE 36

Take-home

Take-home

Control Function Approach is nothing more than an IV method It allows for both linear and non-linear first stage Namely for the estimation of survival analysis models which can include more individuals than those used for the second stage Provides a test for endogeneity Provides a test for selectivity

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13

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SLIDE 37

Take-home

Take-home

Control Function Approach is nothing more than an IV method It allows for both linear and non-linear first stage Namely for the estimation of survival analysis models which can include more individuals than those used for the second stage Provides a test for endogeneity Provides a test for selectivity Note: Stata command to be constructed soon

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13

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SLIDE 38

Take-home

Thank you! m.lopes.15@ucl.ac.uk

Marta C. Lopes (NovaSBE) A Control Function Approach September 7, 2017 13 / 13