Exploring County Truck Freight Transportation data

By : Henry Myers

 Part 1 is focused on explaining the spatial econometrics and statistics used

 Part 2 explains the economic production function

 Part 3 reviews the data and the data sources  Part 4 results and estimation methods  Part 5 making sense out of the current

results and describes future work

 Spatial Statistics focuses on finding clusters or dispersions that cannot otherwise be considered random

 Econometrics focuses on the model and the theory that generates the model

 The coefficients of the independent variables “parameters” are estimated using regression analysis

 Local Moran’s I   Spatial lag model assumes spatial dependence in

the parameters   Spatial error model assumes spatial dependence

in the errors   Spatial regime model assumes that the location

has some explanatory power of system being studied

 Anselin’s spatial chow-test indicates the spatial regime model   The spatial chow model test the evaluates the

residuals of the constrained (spatial) model against the unconstrained model.

  The null hypothesis of the spatial chow test is that the there is no difference between the two models

 A function the relates the output of an economy, firm, or industry back to factor inputs.   Factor inputs are Capital, Labor, Natural Resources.

 They assume a technological relationship   This relationship gives raise to the concept of

substitution in industry behavior   Industries act like an agent with budget constraint, the

Marginal rate of (technical) Substitution

 The Constant elasticity of Substitution is centered around the elasticity of substitution   CES Production Functions was first introduced in the

work of Arrow, Chenery, Minhas, and Solow

 If the substitution of elasticity equals 0 use a linear production function

 If the substitution of elasticity equals 1 use a Cobb Douglas

 If the substitution of elasticity approaches negative infinity use a Leontief(fixed proportions)

 No general accepted method for estimating CES with inputs above 2   All methods of estimation end up with equal

partial substitutions <Uzawa, 1975>

  Leontief assumes a technical knowledge of the system   The ratio at which factors of production are used

  Linear production function   Easy to read, but fails in demonstrating returns to scale

  Assume the Cobb-Douglas case, elasticity of substitution equals zero

  Trans-log Cobb-Douglas check for homogenous of degree one.

  Sum of the independent variable coefficients equal one and that cross elasticity equal zero

  If homogenous of degree one, it can be said that doubling of factor input leads to a doubling of output

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Marginal Production

Total Production

Marginal and Total Production

  U.S Department of Transportation Highway statistic series   MV9: As reported to USDOT by the state, number of

Tractor-Trucks registered to that state that year   MV11: As reported to USDOT by the state, number of

Semi-Trailers registered to that state that year   BEA: estimated truck freight transportation value   NCHRP: Provides the method for converting between

“receipts” and tonnage transported per year   BLS: Wage and Labor quantity for the state and MSA   Implan: 2007 County level Total proprietor income,

total employment in that sector   Individual states for county level trailer and truck

registrations

Local Moran’s I Result for Trans-Log

Moran’s I of 0.1484 with a z-score of 2.03

 From just the OLS residuals, Identified spatial dependence

 Moran’s I confirms a Spatial Dependence primarily in the Center for Freight and Infrastructure Research and Education (CFIRE) region

 Test of both the Spatial Error and Spatial Lag model

 Without a clear theory on why spatial regime would exist in the CFIRE region, the regime area is unknown   CFIRE encompasses Illinois, Indiana, Iowa, Kansas,

Kentucky, Michigan, Minnesota, Missouri, Ohio, and Wisconsin

  Start with a single random location and give it the value of 1

  Include a dummy variable in the regression for the random area

 Using Anselin’s spatial chow test   Test the residuals from the constrained spatial regime

model against the standard model

  If we reject the spatial chow test null hypothesis and the Akaike information criterion (AIC) is lower, expand the random area by 1 neighbor

  Iterate the process until chow test statistic is maximized, the AIC is minimized, and the regime is greater than equal to 2

 The Random Regime area starting with Illinois includes Wisconsin, Iowa, Missouri, Indiana, Ohio, Michigan, Kentucky, Tennessee, Arkansas, Mississippi

 In comparison to CFIRE   Kansas and Minnesota are excluded

  What’s going on Minnesota and Kansas?   Tennessee, Arkansas, Mississippi are included

 Pros and Cons of the Random Regime   We identify and area that is causing an omitted

variable bias   This does not tell us why that area is a regime.

Table  1  

Model   Coefficients   Tests   AIC  

Const   Labor   Truck   Trailer   Regime   JB   BP  

Standard   10.525   0.737   0.227   0.15   N/A   0.887   0.866   6.183  

Regime   10.502   0.788   0.187   0.152   0.173   0.851   0.158   2.452  

Moran’s I of 0.0112 with a z-score of 0.4

 Visual inspection of the National OLS residuals, Identify a strong influence of CFIRE region on the System

 Moran’s I confirms a Spatial Dependence primarily in the CFIRE region

 The Random Regime Area encompasses 80% of the CFIRE region

 The study should be conducted until the Random Regime Area omitted variable is found

 The area in the Random regime has increasing returns to scale

Table  2  

Method   Weight   Coeficients   R^2   LR   AIC  

rho   Const   Labor   Truck   Trailer  

Lag   Q-­‐1   0.32   10.11   0.68   0.21   0.15   0.96   0.26   -­‐1.44  

  Marginal Rates of Technical Substitution   Given the Marginal Productivity at the county level we can

assume a substitution exist based on cost of the input and it’s marginal production

  MSA wage data can be broke down to the county level   IRS depreciation data for trucks and trailers

  Testing Marginal Production by Commodity purchases   Implan provides business to business annual transactions   Separate the counties by flow percentage   Each type of flow could require a new type of Truck/

Trailer and have a different marginal production