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					   The importance of accounting for unobserved
heterogeneity, state-dependence and differences in
         residual variances across groups
My focus for today:
                                          Land Market
                                           Decisions




                                                        Time-series
                          Panel Data
                                                           Data




          Participation    Extent of                    Prices and
                                            Rents
           decision       Participation                   Rents




 Binary     Ordinal       Multinomial
 models     Models         Models
Theoretical Model – Skoufias (1995)
   In the literature, participation in land rental markets is
    considered to be a response to imperfections in markets
    for other inputs (e.g. Bullocks and family labour for
    developing countries)

   Based on their non-land endowments each farm will have
    a desired cultivated area (DCA) which achieves the
    optimal input mix

   The amount of land a farm will wish to transact (Y*) will
    be the difference between DCA and their land
    endowment.

   We do not observe Y* but rather whether the farms
    participates (and the actual area transacted) – Thus it
    seems natural to use a latent variable approach….
Literature on Binary Participation
Decisions:




   Relevant feature of these papers:
     Fairly recent (mostly World Bank working papers)
     Literature is focused on developing countries
     Often static pooled/cross-section models are employed
      ○ Hence unable to take account of unobserved heterogeneity/state-dependence
     Differences in farms activities are not explicitly considered
What we do….
1.   This paper looks at farmers’ land market participation decisions in a
     developed country (Ireland).

2.   We use panel data techniques to take account of unobserved
     heterogeneity.

3.   Farm participation in a given year is strongly linked to past
     participation so we take account of this state dependence by using
     a dynamic model.

4.   Dealing with state-dependence leads to the initial conditions
     problem (explained later). We compare the approach of Heckman to
     that of Wooldridge.

5.   In Ireland farms are engaged in different systems so we also make
     an attempt to consider any differences across systems.


     (Next week, I’ll be looking at a related paper on the impact of ‘decoupling’!)
The Farm Systems:
   Dairying
   Dairying and Other
    Activities
   Cattle Rearing
   Cattle Rearing and
    Other Activities
   Sheep
   Tillage
Data
   Panel of National Farm Survey: 2000-2008
     9 years data
     10,513 observations for 2,129 farms
     Approx. ¼ of farms and 45% of observations are for farms
      present in all years.
   Land Market Participation:
                                  Number of obs.   Percentage
    Renting only                   5,085            48.37
    Leasing only                    463              4.40
    Renting and Leasing             311              2.96
    Neither Renting nor Leasing    4,654            44.27


    All                           10,513           100
Proportion of farms renting/leasing/both/neither
Proportion of farms renting/leasing/both/neither
by System
  Further ‘evidence’ of state dependence
      Compare this years decision (row) to last years decision
       (column):
                                  Renting Leasing Renting Neither         All
                                  only (%) only (%) and     Renting
                                                    Leasing nor
                                                    (%)     Leasing
                                                            (%)
Renting only (%)                     93.43     0.07    1.67        4.82   100
Leasing only (%)                      2.19    79.45    2.47       15.89   100
Renting and Leasing(%)               22.73     3.31   72.73        1.24   100
Neither Renting nor Leasing (%)       5.39     1.53    0.11       92.97   100

      Note: this apparent ‘state dependence’ could be spurious!
Econometric Framework
   We adopt a latent variable framework, where observed
    participation is determined by an unobserved variable,
    Y*. This variable is related to farms characteristics (X),
    including the past participation decision and the levels of
    other inputs.
   The model:


   Unfortunately, σ2, the variance of εit, is not identified, so we
    divide across by σ to normalize the variance to unity. Since Yit
    is affected only by the sign of Yit*, it is unaffected by this
    normalization!
     For convenience I continue to use β where really I mean β/σ
Unobserved Heterogeneity
   Incorporating a term for unobserved
    heterogeneity, μi implies:

   Firstly whether we believe μi is correlated
    with our explanatory variables determines
    how we should proceed:
     Yes => use Fixed Effects estimation
     No => use Random Effects estimation
     Maybe => Mundlak formulation (add individual
     time means of X’s as control variables and then
     use RE) – This is the approach we take
Some considerations with μi
   Secondly, since unobserved heterogeneity will influence a farms
    initial decision whether to participate, there will be correlation
    between a lagged dependent variable (Yit-1) and the unobserved
    heterogeneity – this is known as the initial conditions problem.

   Solutions to this problem have been suggested by
      ○ Heckman (1981a, 1981b)
      ○ Orme (1997,2001)
      ○ Wooldridge (2005)


   Holden, Deininger and Ghebru adopt the Wooldridge approach using
    a balanced panel.

   Akay (2009) suggests Wooldridge can be used on unbalanced panel
     For my data Wooldridge for balanced and unbalanced are similar for the full panel,
      but are quite different if I break the sample into pre- and post- decoupling
Solutions to
initial conditions problem
   Heckman’s approach:
     Use a reduced form model to approximate the
     decision in the first period.

     Where Z contains the exogenous elements of X,
     and possibly instruments also.
   Wooldridge’s approach:
     Assume that unobserved heterogeneity can be
     specified as:

     Can then use standard random effects estimator
     with regressors
    Coefficients
                    Pooled                   Panel RE               Panel              Dynamic             Wooldridge
                    [Ignoring unobserved     [ignoring state-       Mundlak            [Ignoring initial   [ignoring
                    heterogeneity and        dependence and         [ignoring state-   conditions          differences across
                    state-dependence]        assuming cov(X,u)=0]   dependence ]       problem]            systems]

Lagged renting                -                         -                  -                   3.15***               2.18***
Initially Renting             -                         -                 -                    -                     1.98***
Age                               0.02**                  0.11***         0.14***                 0.01                  0.03
Age2                         -0.0003***                 -0.001***       -0.001***             -0.0001               -0.0003
Job                                 0.05                    -0.04            -0.05                0.02                  0.01
Female                          -0.22***                  -1.03**         -1.00**                -0.20                 -0.34
Area owned                    -0.005***                  -0.03***        -0.04***             -0.01***              -0.02***
Unpaid labour                    0.13***                  0.53***             0.13               -0.04                 -0.02
Paid labour                         0.06                     0.11         -0.51**               -0.32*               -0.49**
Fertiliser                        0.05**                  0.47***           0.23**                0.05                  0.10
Machinery                        0.21***                  0.49***           0.16**                0.03                  0.05
Ability                          0.22***                  1.26***           0.53**                0.07                  0.19
No. of Livestock                 0.01***                  0.04***         0.03***              0.02***               0.02***
Soil2                            0.13***                     0.37            0.54*                0.11                  0.16
Soil3                            0.22***                    0.64*         0.99***                 0.03                 -0.03
Soil4                            0.23***                     0.62         0.95***               0.18**                0.32**
Soil5                            0.26***                     0.28           0.81**              0.21**                  0.23
Decoupling
Dummy                             -0.08***                  -0.07           -0.06                -0.01                -0.001
Constant                          -2.53***              -10.40***       -13.02***             -2.77***              -4.24***
    Average Partial Effects
                    Pooled                 Panel RE                   Panel              Dynamic             Wooldridge
                    [Ignoring unobserved   [ignoring state-           Mundlak            [Ignoring initial   [ignoring
                    heterogeneity and      dependence and             [ignoring state-   conditions          differences across
                    state-dependence]      assuming cov(X,u)=0]       dependence ]       problem]            systems]

Lagged renting                                                                                   0.86***               0.44***
Initially Renting                                                                                                     0.37***
Age                              0.002**                 0.02***             0.02***              0.001                 0.002
Age2                         -0.0001***              -0.0002***          -0.0001***           -0.00001              -0.00002
Job                                 0.02                   -0.01               -0.01              0.002                 0.001
Female                          -0.08***                 -0.14**             -0.11**               -0.02                -0.03
Area owned                      -0.02***              -0.004***           -0.005***           -0.001***              -0.02***
Unpaid labour                    0.04***                 0.07***                0.01             -0.004                -0.001
Paid labour                         0.02                    0.01             -0.06**              -0.03*              -0.04**
Fertiliser                        0.02**                 0.06***              0.03**              0.005                  0.01
Machinery                        0.07***                 0.07***              0.02**              0.003                 0.004
Ability                          0.07***                 0.17***              0.06**                0.01                 0.01
Number of
Livestock                      0.003***                  0.01***           0.004***            0.002***              0.002***
Soil2                           0.04***                     0.05              0.06*                0.01                  0.01
Soil3                           0.07***                    0.09*            0.11***               0.004                -0.002
Soil4                           0.08***                     0.08            0.10***              0.02**                0.02**
Soil5                           0.09***                     0.04             0.09**              0.02**                  0.02
Decoupling
Dummy                           -0.03***                      -0.01             -0.01             -0.001            -0.00004
Comparing groups
   We face a difficulty when making comparisons across groups
    e.g. across system [or between pre- and post- decoupling]

   Could use interaction terms but:
     Ai and Norton (2003) show that for interaction terms coefficients, their
       signs and their significance levels may all be incorrect when using non-
       linear models.


   Instead we estimate the model separately for each system
    but:
     Allison (1999), Hoetker (2004, 2007): since coefficients are confounded
       with the variance of the unobserved term, direct comparisons are valid
       across models only if the variances are the same!
‘Solution’
   Solutions:
     Look at differences in significance and sign
      ○ May not be any differences….
     Look at ratio’s of coefficients
      ○ Need large samples to test differences
      ○ Difficult to interpret ratios of coefficient and may be fairly meaningless

     Williams (2009) suggests estimating heterogeneous
      choice models e.g. heteroskedastic probit but
      ○ Need to think whether this is consistent with Wooldridges
        approach [Heckmans almost certainly won’t converge]
      ○ Keele and Park (2006) suggest that if the variance equation is
        mis-specified then estimates may be even more biased!!
      ○ Need to use ‘gllamm’ in Stata – very very slow!
     Use Tobit instead – I’ll be doing this anyway 
      ○ Variance of error term is identified in these models!
                    Dairying       Dairying and         Cattle-       Cattle and           Mainly             Tillage
                                   Other Activities     Rearing       Other                Sheep
                                                                      Activities

Lagged renting           2.46**              2.45***        2.67***           2.71***               2.65***             1.59***
Initially Renting       1.30***              0.81***        1.10***           1.07***                 1.67              1.64***
Age                        0.02                 0.04         -0.01             0.11**                0.17**               0.01
Age2                    -0.0003               0.0003        0.0002            -0.001*               -0.002*             -0.0001
Job                     -0.41**               0.64**          0.19                 -0.29              -0.27               -0.13
Female                    -0.50                -0.41         -0.21                 -0.15             0.004                1.09*
Area owned                -0.01              -0.03***      -0.06***          -0.04***                 -0.01               -0.01
Unpaid labour             -0.02               1.13**          0.06                 -0.42            -0.006                -0.75
Paid labour               -0.56                 0.58         -0.64                 -1.18              0.45               -0.84*
Fertiliser               -0.36*                 0.16          0.29                 0.20               0.06                0.22
Machinery                  0.07                -0.09          0.06                 0.07               -0.14               0.20
Ability                 -0.84**              -1.06***        0.53*                 0.23               -0.87               0.19
No. Livestock           0.04***                0.01*         0.03**            0.02**                 0.02               -0.001
Soil2                     0.40*                -0.05         -0.38                 -0.14              -0.34             0.58***
Soil3                     -0.04                 0.16          0.01                 -0.03              -0.72               -0.47
Soil4                      0.28                 0.06          0.24                 0.13               0.16                -0.82
Soil5                     0.57*                 0.57          0.19                 -0.05              -0.20                N/A
Decoupling
Dummy                      0.13                -0.14         -0.03                 0.16               0.09                -0.32
Constant                -6.32***             -6.42***        -0.95            -4.80**               -7.16**             -6.31**
                    Dairying       Dairying and         Cattle-       Cattle and           Mainly              Tillage
                                   Other Activities     Rearing       Other                Sheep
                                                                      Activities

Lagged renting          2.14***              2.29***        2.62***           2.46***               3.03***              1.37***
Initially Renting       1.51***              0.79***        1.10***           1.09***                0.64**              1.47***
Age                      -0.001                 0.03         -0.02             0.12**                0.14**                0.04
Age2                    -0.0001               0.0004        0.0002           -0.001**           -0.001**                 -0.001
Job                     -0.49***               0.42*          0.19             -0.36*                 -0.21               -0.22
Female                    -0.75                -0.18         -0.15                 -0.50             -0.043                1.11
Area owned              -0.01**               -0.02**      -0.06***          -0.04***                 -0.01              -0.02**
Unpaid labour              0.11                 0.73         -0.03                 -0.40               0.15               -0.54
Paid labour             -0.65**                -0.21         -0.40                 -0.42               0.20               -0.43
Fertiliser                -0.15                 0.30          0.23                 0.26               -0.06                0.11
Machinery                  0.07                 0.08          0.10                 0.07               -0.12              0.79***
Ability                 -0.86**               -0.72**         0.41                 0.05               -0.40               -0.41
No. Livestock           0.04***                 0.01         0.03**           0.002**                 0.004               0.005
Soil2                   0.467**                 0.08         -0.47*                -0.20              -0.03              0.60***
Soil3                      0.04                 0.19          -0.11                -0.09             -0.56*                0.02
Soil4                      0.29                 0.12          0.14                 -0.08               0.11               -0.47
Soil5                     0.48*                0.60*          0.08                 -0.12              -0.14                 N/A
Decoupling
Dummy                     0.20*                -0.12         -0.01                 0.26*              -0.02               -0.30
Constant                -5.43***              -4.61**        -1.35           -4.74***               -6.89***         -7.87***
                    Dairying       Dairying and        Cattle-       Cattle and      Mainly Sheep     Tillage
                                   Other Activities    Rearing       Other           Didn’t
                                   Didn’t converge                   Activities      converge
Lagged renting           1.85***               1.24*       3.49***         1.74***            31.47             1.35***
Initially Renting        1.88***                5.51         0.80          2.56***          3921.00             1.01***
Age                        0.10                -0.23         0.39            -0.11           240.36              0.001
Age2                     -0.001                0.002       -0.004            0.001            -3.91             0.0002
Job                        0.20                 1.81         0.06             0.53          -816.29               0.12
Female                     0.50               -20.83        -6.96          1.17***         -1490.34              -5.68
Area owned               -0.001                -0.04        0.005          0.0001            -33.77              0.014
Unpaid labour              0.16                 1.61         2.10             0.67          -437.01               0.02
Paid labour                0.29                 4.51        -0.75            -2.77           390.99              -0.01
Fertiliser               -0.86**               -0.34         0.28            -0.34            20.53               0.29
Machinery                 -0.04                -2.55        -0.46             0.05          -201.56         -1.02***
Ability                    0.33                -3.28         1.97             0.99          2318.21               0.47
No. Livestock             -0.01                -0.02        -0.01            -0.01            -0.15              -0.01
Soil2                     -0.09                -0.42        -8.48             0.62            29.46              -0.18
Soil3                     -0.44                -0.31        -0.26             0.38           362.58              -0.64
Soil4                      0.05               -18.89        -0.40            0.75*           848.62              -5.87
Soil5                      0.51               -21.10        -0.71            -6.23         -1098.42                N/A
Decoupling
Dummy                     -0.21                 0.45        -0.49           -0.57*           172.98               0.32
Constant               -12.06***              -18.84        -9.87            -2.78          3573.05              -3.47
Conclusions
   It is important to take account of unobserved heterogeneity
    and the possibility of correlation between the random effect
    and the explanatory variables.
   State dependence is crucial if we are to understand the
    factors influencing participation decisions.
   However failure to take account of the initial conditions leads
    us to overstate this state-dependence.
   It is important to consider each farm system separately as
    there appear to be differences in the influence of the factors
    influencing participation decisions
   The models suggest that land market participation is not
    being used as a means to overcome input market
    imperfections.

				
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posted:10/2/2012
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