The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data
The standard approach for fitting a Cobb-Douglas production function to micro data with zero values is to replace those values with "sufficiently small" numbers to facilitate the logarithmic transformation. In general, the estimates obtai...
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| Format: | Policy Research Working Paper |
| Language: | English en_US |
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World Bank, Washington, DC
2014
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| Online Access: | http://documents.worldbank.org/curated/en/2000/12/748706/treatment-non-essential-inputs-cobb-douglas-technology-application-mexican-rural-household-level-data http://hdl.handle.net/10986/19733 |
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okr-10986-197332021-04-23T14:03:44Z The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data Soloaga, Isidro AGRICULTURAL PRODUCTION AGRICULTURE ASSETS AUTONOMY BANKING CRISES CONSUMERS DEMOGRAPHICS DEVELOPMENT ECONOMICS DIVISION OF LABOR ECONOMETRICS ECONOMIC THEORY ECONOMIC WELFARE EMPIRICAL EVIDENCE EMPLOYMENT EXCHANGE RATE EXPENDITURES FARMERS FERTILIZERS FUNCTIONAL FORMS HEALTH INSURANCE INSURANCE INTERNATIONAL TRADE LABOR FORCE LABOR SUPPLY LAND LOCATION MARGINAL PRODUCTIVITY MAXIMUM LIKELIHOOD ESTIMATION MAXIMUM LIKELIHOOD METHOD MICROECONOMIC ANALYSIS POLICY RESEARCH POLITICAL ECONOMY PRODUCERS PRODUCTION FUNCTION PRODUCTION FUNCTIONS PRODUCTION INPUTS PRODUCTIVE ASSETS PRODUCTIVITY GROWTH RETURNS TO SCALE SAVINGS TAXATION VALUE OF OUTPUT The standard approach for fitting a Cobb-Douglas production function to micro data with zero values is to replace those values with "sufficiently small" numbers to facilitate the logarithmic transformation. In general, the estimates obtained are extremely sensitive to the transformation chosen, generating doubts about the use of a specification that assumes that all inputs are essential (as the Cobb-Douglas does) when that is not the case. The author presents an alternative method that allows one to estimate the degree of essentiality of the production inputs while retaining the Cobb-Douglas specification. By using the properties of translatable homothetic functions, he estimates by how much the origin of the input set should be translated to allow the Cobb-Douglas functional form to capture the fact that the data have a positive output even when some of the inputs are not used. To highlight the empirical importance of the approach, he applies it to Mexican farm-level production data that he gathered. Many households did not use family or hired labor in farm production, or had different capital composition (that is, zero value for non-land farm assets). The estimations provide a clear measurement of the degree of essentiality of potentially non-essential inputs. They also indicate the size of the error introduced by the common "trick" of adding a "small" value to zero input values. 2014-08-26T21:39:09Z 2014-08-26T21:39:09Z 2000-12 http://documents.worldbank.org/curated/en/2000/12/748706/treatment-non-essential-inputs-cobb-douglas-technology-application-mexican-rural-household-level-data http://hdl.handle.net/10986/19733 English en_US Policy Research Working Paper;No. 2499 CC BY 3.0 IGO http://creativecommons.org/licenses/by/3.0/igo/ World Bank, Washington, DC Publications & Research :: Policy Research Working Paper Publications & Research Latin America & Caribbean Mexico |
| repository_type |
Digital Repository |
| institution_category |
Foreign Institution |
| institution |
Digital Repositories |
| building |
World Bank Open Knowledge Repository |
| collection |
World Bank |
| language |
English en_US |
| topic |
AGRICULTURAL PRODUCTION AGRICULTURE ASSETS AUTONOMY BANKING CRISES CONSUMERS DEMOGRAPHICS DEVELOPMENT ECONOMICS DIVISION OF LABOR ECONOMETRICS ECONOMIC THEORY ECONOMIC WELFARE EMPIRICAL EVIDENCE EMPLOYMENT EXCHANGE RATE EXPENDITURES FARMERS FERTILIZERS FUNCTIONAL FORMS HEALTH INSURANCE INSURANCE INTERNATIONAL TRADE LABOR FORCE LABOR SUPPLY LAND LOCATION MARGINAL PRODUCTIVITY MAXIMUM LIKELIHOOD ESTIMATION MAXIMUM LIKELIHOOD METHOD MICROECONOMIC ANALYSIS POLICY RESEARCH POLITICAL ECONOMY PRODUCERS PRODUCTION FUNCTION PRODUCTION FUNCTIONS PRODUCTION INPUTS PRODUCTIVE ASSETS PRODUCTIVITY GROWTH RETURNS TO SCALE SAVINGS TAXATION VALUE OF OUTPUT |
| spellingShingle |
AGRICULTURAL PRODUCTION AGRICULTURE ASSETS AUTONOMY BANKING CRISES CONSUMERS DEMOGRAPHICS DEVELOPMENT ECONOMICS DIVISION OF LABOR ECONOMETRICS ECONOMIC THEORY ECONOMIC WELFARE EMPIRICAL EVIDENCE EMPLOYMENT EXCHANGE RATE EXPENDITURES FARMERS FERTILIZERS FUNCTIONAL FORMS HEALTH INSURANCE INSURANCE INTERNATIONAL TRADE LABOR FORCE LABOR SUPPLY LAND LOCATION MARGINAL PRODUCTIVITY MAXIMUM LIKELIHOOD ESTIMATION MAXIMUM LIKELIHOOD METHOD MICROECONOMIC ANALYSIS POLICY RESEARCH POLITICAL ECONOMY PRODUCERS PRODUCTION FUNCTION PRODUCTION FUNCTIONS PRODUCTION INPUTS PRODUCTIVE ASSETS PRODUCTIVITY GROWTH RETURNS TO SCALE SAVINGS TAXATION VALUE OF OUTPUT Soloaga, Isidro The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data |
| geographic_facet |
Latin America & Caribbean Mexico |
| relation |
Policy Research Working Paper;No. 2499 |
| description |
The standard approach for fitting a
Cobb-Douglas production function to micro data with zero
values is to replace those values with "sufficiently
small" numbers to facilitate the logarithmic
transformation. In general, the estimates obtained are
extremely sensitive to the transformation chosen, generating
doubts about the use of a specification that assumes that
all inputs are essential (as the Cobb-Douglas does) when
that is not the case. The author presents an alternative
method that allows one to estimate the degree of
essentiality of the production inputs while retaining the
Cobb-Douglas specification. By using the properties of
translatable homothetic functions, he estimates by how much
the origin of the input set should be translated to allow
the Cobb-Douglas functional form to capture the fact that
the data have a positive output even when some of the inputs
are not used. To highlight the empirical importance of the
approach, he applies it to Mexican farm-level production
data that he gathered. Many households did not use family or
hired labor in farm production, or had different capital
composition (that is, zero value for non-land farm assets).
The estimations provide a clear measurement of the degree of
essentiality of potentially non-essential inputs. They also
indicate the size of the error introduced by the common
"trick" of adding a "small" value to
zero input values. |
| format |
Publications & Research :: Policy Research Working Paper |
| author |
Soloaga, Isidro |
| author_facet |
Soloaga, Isidro |
| author_sort |
Soloaga, Isidro |
| title |
The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data |
| title_short |
The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data |
| title_full |
The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data |
| title_fullStr |
The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data |
| title_full_unstemmed |
The Treatment of Non-Essential Inputs in a Cobb-Douglas Technology : An Application to Mexican Rural Household-Level Data |
| title_sort |
treatment of non-essential inputs in a cobb-douglas technology : an application to mexican rural household-level data |
| publisher |
World Bank, Washington, DC |
| publishDate |
2014 |
| url |
http://documents.worldbank.org/curated/en/2000/12/748706/treatment-non-essential-inputs-cobb-douglas-technology-application-mexican-rural-household-level-data http://hdl.handle.net/10986/19733 |
| _version_ |
1764440498999656448 |