TITLE: Rural-Urban Migration and Crop Productivity
This proposal is a perfect example of nonesense regression equation. The basic equation under study is:
Yield = a + b Migration + c Remittances + d Household Characteristics+ Other relevant variables.
The question being asked is: Does Migration from Bagh affect Crop Productivity in Bagh?
In general, nonesense regression happens when there is NO DIRECT EFFECT of independent variable on DEPENDENT variable. This point is never made very clearly in econometrics textbooks, which is why students often make mistakes of this type. TO understand why this is a problem, think about this example carefully:
QUESTION: WHAT IS YIELD?
Answer: It is the ratio of output to inputs.
OUTPUT is crops, milk, animal meat -- these can be converted to a value by multiplying by prices.
INPUT is Land, Labor, Fertilizer, Water - rainfall or other, seeds, Tractors etc.
Conclusion 1: Yield is COMPLETELY determined by the factors named above.
Note: Migration is NOT a determinant of the yield -- if it varies by a lot BUT NONE of the factors named above change, there will be NO CHANGE IN YIELD. Since this point seems to be unclear to some students, I will repeat it in different words:
Migration increases or decreases BUT inputs to farming remain same, then outputs will also remain the same, and hence yield will remain the same. This means that migration can change without having ANY effect on yield. This means that migration is NOT a direct determinant of the yield.
This is what we mean when we say that there is NO DIRECT EFFECT of migration on yield.
MIGRATION CAN ONLY EFFECT YIELD IF IT AFFECTS one of the variables in the OUTPUTS or INPUTS -- there is NO OTHER WAY for migration to effect yields.
How could migration affect outputs? Well, for example, if there are more people and they use more meat then the demand for meat will be higher and a farm might produce more meat from the same stock of animals -- that would increase yield. If the demand was lower than same stock of animal might be maintained while producing less meat.
How could migration affect inputs? A direct channel is if some laborers are reduced from the working pool so input of labor decreases. Other indirect channels are possible.
NOW: If we want to model HOW MIGRATION AFFECTS YIELDS, WE HAVE TO MODEL THE CHANNEL BY WHICH THIS EFFECT TAKES PLACE.
Either Migration leads to reduced demand for outputs, which would lead to lower price of outputs, which would lead to farms producing a different level production.
OR Migration affects inputs. Then we would write an equation: LABOR SUPPLY = TOTAL LABOR - MIGRATION.
PRODUCTIVITY = OUPUT divided by INPUTS = LABOR SUPPLY
Now we have a TWO EQUATION system The first equation tells us how MIGRATION affects the DETERMINANTS of Yield, the second tells us how the determinants affect productivity. THIS can tell us how migration affects yield. A direct regression of MIGRATION on YIELDS is wrong because MIGRATION is NOT a direct determinant of yield and it can only affect yield through changing one or more of the direct determinants. Which determinants are affected MUST be a part of a model for finding this out. If migration affects DEMAND then a rather complicated simultaneoous equation model taking into account supply and demand factors must be constructed. Such a model will allow us to figure out the impact of migration on yields, but also give us much more information on the correct model for agricultural production function and the supply and demand for agricultural products.
A similar story can be told about REMITTANCES and about HOUSEHOLD CHARACTERISTICS. Neither of these is a direct determinant of the yield. Let us think about both a little bit more.
Remittances increase money in the hands of people of Bagh. This can have two effects. Demand Side effects will mean that more income will lead to increased demand for agricultural products. Farmers will respond to this increase demand by increasing production. Now depending on economies of scale in production, increased production could increase or decrease yields. If there are constant returns to scale then production can increase without any effect on yield -- double inputs leads to double outputs increasing supply but yield remains exactly the same.
One CANNOT put remittances into a supply equation for agricultural production -- yields are a supply side phenomenon. One can put it into a demand for agricultural production equation and then see how production levels change with changes in demand. This will require simultaneous equations modelling, and cannot be done via single equation methods.
Household characteristics (HC) is a different type of variable. Again HC does not directly affect yields. Rather, we may think that HC will affect the WAY in which production takes place. For example, more educated households might use more advanced techniques -- more fertilizer and tractors, for example. So now we will build an equation asking if Tractors used + level of Fertilizer use depends on HC. Then How does Tractors/Fertilized affect yield. Again we have a two stage method by which HC will affect yields, both stages have to specified and estimated separately. We cannot directly put HC into an equation for yield.