more HH

notebooks/FarmHousehold.ipynb

@@ -23,6 +23,9 @@
     "\n",
     "When households are embedded in well functioning competitive markets however we tend to expect the household's decisions to become separable: acting as a profit-maximizing firm it first optimally chooses labor and other input allocations to extract maximum profit income from the farm and then makes optimal choices over consumption and leisure subject to its income budget which includes those maximized profits and income from selling its labor endowment.  In the simple example above of two otherwise identical households the separable farm household model would predict that both households run farms of similar size and use wage labor markets to equalize land-labor ratios and hence marginal products of labor across farms.  The larger household would be a net seller of labor on the market compared to the smaller household. \n",
     "\n",
+    "Without the separation property the common approach of many studies to separately estimate consumer demand from output supply functions is no longer valid.\n",
+    "\n",
+    "\n",
     "Another way to state the separation hypothesis is that if they have access to markets the marginal production decisions of farms (and firms more generally) should not depend on their owners' ownership of tradable factors (except in so far as it might raise their overal income) or their preferences in consumption. When markets are complete then production decisions will be separable, the price mechanism will equalize the marginal products of factors across uses, and the initial distribution of tradable factors should not matter for allocative efficiency (the first and second welfare theorems).  Much of modern micro-development since at least the mid 1960s however is concerned with how transactions costs, asymmetric information, conflict and costly enforcement can lead to market frictions and imperfections that make production decisions non-separable, which then means that the initial distribution of property rights (over land and other tradable factors) may in fact well matter for determining the patterns of production organization and its efficiency in general equilibrium. A good example of such analysis is Eswaran and Kotwal (1986) paper on \"Access to Capital and Agrarian production organization,\" which explores how the combination of transaction costs in labor hiring and in access to capital can lead to a theory of endogenous class structure or occupational choice which can change dramatically depending on the initial distribution of property rights. "
    ]
   },
@@ -424,6 +427,13 @@
     "$$p \\cdot F_L (\\bar T_i,L) = w$$"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The separation property is immediately apparent from this first order condition, as this equation alone is enough to determine the farm's optimum labor demand which depends only on the production technology and the market wage, and not at all on household preferences.  While the quantity of labor demanded here does depend on the households' ownership of land, with a functioning labor market the number of workers per unit land will be the same across all farms and hence also independent of household land endowment."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -624,7 +634,13 @@
    "source": [
     "## Testing for Separation in Household models\n",
     "\n",
-    "There are basically two"
+    "There are a few related approaches to testing for separation. \n",
+    "\n",
+    "  1. One approach attempts to test the implication of the separation hypothesis that labor demand should be independent of household preference shifters $A$ (i.e. demographic characteristics of the household. Basically this approach regresses labor demand on prices, fixed non-traded inputs, and a measure of $A$.  The null hypothesis is that the model is separable and the coefficient on A is zero. Therefore an insignificant estimated coefficient is interpreted as a failure to reject the null hypothesis of separation.  There are econometric issues such as simultaneity bias to worry about of couse. This is the approach of papers such as Lopez(1984), Benjamin (1992) and many others.\n",
+    "  \n",
+    "  2. Another approach builds from the observation that under separation the shadow price of labor or the marginal product of labor on the farm -- call it $w^*$ -- should equal the market wage $w$.  Since the shadow wage is not directly observed it must be calculated off an estimated production function.  If estimates of $w*$ have been estimated across farms the separation test boils down to a test of whether $\\beta_0 = 0$ and $\\beta_1 =1$ in the regression $w^* = \\beta_0 +\\beta_1 w$.  Issues of endogeneity and other econometic concerns must be addressed.  This is the approach of Jacoby (1993), Skoufias (1994) and others.\n",
+    "  \n",
+    "  3. Kien Le (2010) proposes a semi-parametric method that combines elements of both of the above approaches but uses less data. his apprach boils down to regressing the log of the measured value of output per worker on each farm against the market wage and a few controls. "
    ]
   },
   {
@@ -636,6 +652,15 @@
     " - market equilibrium determination of equilibrium real wage (given distribution of farms/endowments)\n",
     " - selective separability"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {