Export Supply and Demand for US Cattle Hides

1
Export Supply and Demand for US Cattle Hides

• Presented by Clare Shannon, Caitlin Walsh Mike
  Bain

2
Cattle Hides

• Cattle hides are a by product of the production
  of beef.
• We are looking at the excess supply demand
  functions, not the simple demand supply
  functions.
• Because cattle hides are such a small part of the
  cow, one can expect that a change in price would
  have little or no impact on the of cows
  slaughtered. Therefore, one can assume that the
  supply of hides is perfectly inelastic

3
Excess Demand

• At any price, the demand function represents the
  amount of foreign quantity demanded over the
  foreign quantity supplied
• Excess demand is inversely related to price, and
  determinants of excess demand fn. will be those
  of both the foreign demand supply fn.
• Factors that influence excess demands for hides
• 1. Foreign Population
• 2. Foreign income
• 3. of substitutes for hides
• 4. tastes
• 5. of cattle slaughtered abroad

4
Excess Supply

• Supply of hides to export market at a given price
  represents the excess quantity of hides produced
  in U.S. over the demand by Americans, where
  excess supply is positively related to price
• Factors that influence excess supply for hides
• 1. U.S. Population
• 2. level of U.S. income
• 3. of substitutes for hides
• 4. U.S. tastes
• 5. of cattle being slaughters in U.S.

5

• This model is a simultaneous equation system that
  determines equilibrium price and quantity of
  hides exported (export market will only be in
  equilibrium when domestic foreign markets are
  in equilibrium).
• Demand equation modeled as function of
• Price (P)
• Production of cattle hides abroad (Sf)
• Time trend (T)
• random error (E1)
• Supply equation modeled as function of
• Price (P)
• U.S. hide production (Sd)
• U.S. purchasing power (Dd)
• Time trend (T)
• Random error (E2)
• the analysis is exploratory, and the results are
  only suggestive of the relationships that might
  be discovered with more complete data - Article

6
Question 1

• a) The export demand equation as a linear
  function is
• Ed ?? ?iP ?2Sf ??T Ei
• b)
• Endogenous variables EEd, P
• Exogenous variables Sf, T, Ei

7
Explanation of Under, Over, or Just Identified

• - Identification is a precondition for the
  application of Two-Staged Least Squares (2SLS)
  for equations in a simultaneous systems
• - A structural equation is identified only when
  enough of the systems predetermined variables
  are omitted from the equation in question to
  allow that equation to be distinguished from all
  the others in the system.
• - A necessary (but not sufficient) requirement
  for identification is the order condition
• The order condition requires that the number
  of predetermined variables in the system be
  greater than or equal to the number of slope
  coefficients in the equation of interest.

8

• An equation is
• Under identified when predetermined variables in
  the system are less than the number of slope
  coefficients in the equation
• Over identified when predetermined variables in
  the system are great than the number of slope
  coefficients in the equation
• Just identified when predetermined variables in
  the system are equal to the number of slope
  coefficients in the equation
• Therefore,
• c)
• The demand equation is over identified because
  the number of predetermined variables (exogenous
  plus lagged endogenous) in the system Sf, T, Sd,
  Dd are greater than the number of slope
  coefficients in the demand equation ?1, ?2, ?3.

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Question 2

• a) The export supply equation as a linear
  function is
• E ?? ?iP ?2Sd ??Dd ?4T E2
• b) Endogenous variables EEs, P
• Exogenous variables Sd, Dd, T, E2
• c) The supply equation is just identified because
  the number of predetermined variables (exogenous
  plus lagged endogenous) in the system Sf, T, Sd,
  Dd is equal to the number of slope coefficients
  in the supply equation ?1, ?2, ?3, ?4.

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Question 3

• a) From EdEs, we get the reduced form equation
  for equilibrium price
• P ?? - ?? ?2Sd ??Dd - ?2Sf T(?4 - ??)
  E2 Ei
• ?i - ?i
• b) From subbing in our equilibrium price into the
  demand equation we get the reduced form equation
  for equilibrium quantity
• Q - ???i ?i?0 - ?2?i Sf T(?i?4 - ???i) -
  ?i Ei ?i?2Sd ?i??Dd ?iE2
• ?i - ?i

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Farris Theory

• Demand Equation Ed ?? ?iP ?2Sf ??T Ei
• Price (P) and foreign supplies (Sf) will be
  negatively related to exports (E)
• Time (T) will be positively related to exports
  (E)
• Supply Equation Es ?? ?iP ?2Sd ??Dd
  ?4T E2
• Price (P), U.S. hide production (Sd), and time
  (T) will be positively related to exports (E)
• US purchasing power (Dd) will be negatively
  related to exports

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• c) Taking the derivatives of our reduced form
  equation for equilibrium price we would expect
  the exogenous variables to be
• ?P ?2 ()
• ?Sd (?1 - ?1)² ()
• ?P ?3 (-) -
• ?Dd (?1 - ?1)² ()
• ?P -?2 ()
• ?Sf (?1 - ?1) ()
• ?P ?4 - ?3 () (-)
• ?T (?1 - ?1)² ()
• Taking the derivatives of our reduced form
  equation for equilibrium quantity we would expect
  the exogenous variables signs to be
• ?Q - ?2?1 - (-)()
• ?Sf (?1 - ?1)² ()
• ?Q ?1?3 (-)(-)
  
• ?Dd (?1 - ?1)² ()
• ?Q ?1?2 (-)()
  -
• ?Sd (?1 - ?1)² ()
• ?Q ?1?4 - ?3?1 (-)() ()() -
• ?T (?1 - ?1)² ()

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Question 4
14

• b) Taking the derivatives of our reduced form
  equation for equilibrium price estimation from
  part a
• P 385.62 9.7728Sd 0.94147Dd 10.067Sf
  2.1191T 0.6604
• ?P/?Sd -9.7728
• ?P/?Dd 0.94147
• ?P/?Sf 10.067
• ?P/?T -2.1191
• Therefore all the signs on the coefficients are
  consistent with Farris Theory except for the T
  variables which represents Time Trend which
  Farris used as a proxy variable.
• A proxy variable is used when an explanatory
  variable is unobservable and contains measurement
  errors and thus a bias estimate results.

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Q -64.641 0.013211P 1.0884Sd
0.039237Sf 0.048803Dd 1.1063T d) ?Q/?P
0.013211 ?Q/?Sd 1.0884 ?Q/?Sf
-0.039237 ?Q/?Dd - 0.048803 ?Q/?T 1.1063 By
taking the derivatives once again, we see that
signs are all consistent with Farris Theory.

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Question 5

• When an equation is just identified, it implies
  that its coefficients can be derived uniquely
  from the reduced form coefficients this
  procedure is known as Indirect Least Squares
  (ILS).

Steps in finding ILS 1. Estimate reduced form
equations 2. Is the equation just identified? If
yes 3. Take the OLS estimated coefficients of
the reduced form equation and generate
new variables 4. Plug these new variables back
into the original equation and run an OLS
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Indirect Least Squares
18

• b) Yes, the signs of the estimated structural
  coefficients are consistent with Farris theory.
• Proof
• Es ?? ?iP ?2Sd ??Dd ?4T E2
• () () (-)
  ()
• Our Results
• ?? -65.215
• ?1 1.1506
• ?2 1.0195
• ?? -1.0507
• ?4 0.99406

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Question 6

• Two-Staged Least Squares (2SLS) is a method used
  to create instrumental variables to replace the
  dependent variables where they appear as
  explanatory variables in simultaneous equations.
  2SLS does this by running a regression on the
  reduced form of the right hand side endogenous
  variables in need of replacement and then using
  the fitted values for those reduced-form
  regressions as the instrumental variables. More
  specifically the two-step procedure consists of
• Stage one Run OLS on the reduced-form equations
  for each of the endogenous variables that appear
  as explanatory variables in both equations.
• Stage two Substitute the reduced form fitted
  values for the values that appear on the right
  side of the structural equations, and then
  estimate these revised structural equations with
  OLS. (In our case, the command 2sls does this for
  us).
• Therefore
• Source
• A.H. Studenmund, Using Econometrics A Practical
  Guide (fourth edition), Addison Wesley, 2000.

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Question 6
a) 2SLS E P Sd Dd T (Dd Sd Sf T ) / dn rstat
R-SQUARE 0.9675 R-SQUARE ADJUSTED
0.9531 VARIANCE OF THE ESTIMATE-SIGMA2
0.47677 STANDARD ERROR OF THE ESTIMATE-SIGMA
0.69049 SUM OF SQUARED ERRORS-SSE 6.6748
MEAN OF DEPENDENT VARIABLE 9.0286 VARIABLE
ESTIMATED STANDARD T-RATIO PARTIAL
STANDARDIZED ELASTICITY NAME COEFFICIENT
ERROR -------- P-VALUE CORR. COEFFICIENT AT
MEANS P 0.17109E-01 0.1638E-01 1.045
0.296 0.329 0.0845 0.1745 SD
1.1265 0.2247 5.014 0.000 0.858
1.2023 3.6967 DD -0.52472E-01
0.2034E-01 -2.580 0.010-0.652 -1.3231
-3.2604 T 1.1145 0.3280 3.398
0.001 0.750 1.1724 7.7153 CONSTANT
-66.144 15.08 -4.386 0.000-0.825
0.0000 -7.3260 b) F (R2/ 1- R2)
((N-K-1)/K) ( 0.9675/1-0.9675)
((14-4-1)/4) 29.7669232.25 F
66.9755 F.10 3.92 Therefore Fgt F.10
which implies we reject HO in favour of Ha and
conclude that at a 10 level of significance
there is a regression.

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• The signs of the estimated coefficients from the
  2SLS estimationion from part a are all consistent
  with Farris Theory.
• 2SLS Farris Theory
• P P
• Sd Sd
• Dd - Dd -
• T T

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Question 7
a) 2SLS E P Sf T (Dd Sd Sf T) / dn rstat
R-SQUARE 0.8282 R-SQUARE ADJUSTED
0.7767 VARIANCE OF THE ESTIMATE-SIGMA2
2.5225 STANDARD ERROR OF THE ESTIMATE-SIGMA
1.5882 SUM OF SQUARED ERRORS-SSE 35.315 MEAN
OF DEPENDENT VARIABLE 9.0286 VARIABLE
ESTIMATED STANDARD T-RATIO PARTIAL
STANDARDIZED ELASTICITY NAME COEFFICIENT
ERROR -------- P-VALUE CORR. COEFFICIENT AT
MEANS P -0.83331E-01 0.4002E-01 -2.082
0.037-0.550 -0.4117 -0.8498 SF
-0.72057 0.4951 -1.455 0.146-0.418
-0.9453 -3.1690 T 1.6705 0.5831
2.865 0.004 0.671 1.7571
11.5638 CONSTANT -59.091 15.68 -3.769
0.000-0.766 0.0000 -6.5449 b) F
(R2/ 1- R2) ((N-K-1)/K) (0.8282/1-
0.8282) ((14-3-1)/3) 4.8203.33
F 16.066 F .10 5.23 Therefore Fgt F.10
which implies we reject HO in favor of Ha and
conclude that at a 10 level of significance
there is a regression.
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• c) The signs of the estimated coefficients from
  the 2SLS estimationion from part a are all
  consistent with Farris Theory.
• 2SLS
  Farris Theory
• P -
  P -
• Sf -
  Sf -
• T
  T

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Question 8

• a) using ?1 (P/E) to find point price elasticity
  of demand,
• where
• ?1 coefficient of the price in the export
  demand equation
• P the mean value of price, from running
  basic stat command
• E the mean value of exports, from running
  basic stat command
• NAME N MEAN ST. DEV VARIANCE
  MINIMUM MAXIMUM
• P 14 92.071 19.650
  386.11 69.700 139.70
• E 14 9.0286 3.9769
  15.816 3.1000 15.100
• 2SLS of Demand equation
• VARIABLE ESTIMATED STANDARD T-RATIO
  PARTIAL STANDARDIZED ELASTICITY
• NAME COEFFICIENT ERROR --------
  P-VALUE CORR. COEFFICIENT AT MEANS
• P -0.83331E-01 0.4002E-01 -2.082
  0.037-0.550 -0.4117 -0.8498

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• Therefore,
• ?1 (P/E) - 0.08331(92.071/9.0286)
• - 0.8498
• Elastic Egt1
• Inelastic Elt 1
• Unit Elastic E 1
• b) Therefore, the export demand for cattle hides
  is inelastic (meaning it is not effected by
  price).

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Question 9

• Log-Log Models
• - when the dependent variable as well as all
  explanatory variables are transformed into
  logarithms
• The log-log transformation on the entire equation
  will transform a non-linear equation into a
  linear equation so that regressions can be done

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• a) genr Eloglog(E)
• genr Ploglog(p)
• genr Sfloglog(Sf)
• genr Ddloglog(Dd)
• genr Sdloglog(Sd)
• 2SLS Elog Plog Sflog T (Sflog Sdlog Ddlog T) / DN
  RSTAT
• VARIABLE ESTIMATED STANDARD T-RATIO
  PARTIAL STANDARDIZED ELASTICITY
• NAME COEFFICIENT ERROR -------- P-VALUE
  CORR. COEFFICIENT AT MEANS
• PLOG -1.8256 0.7503 -2.433
  0.015-0.610 -0.7530 -3.9173
• SFLOG -5.2444 3.737 -1.404
  0.160-0.406 -1.4113 -9.1797
• T 0.24423 0.1097 2.226
  0.026 0.576 2.1045 7.2731
• CONSTANT 14.322 9.872 1.451
  0.147 0.417 0.0000 6.8239
• Ed 14.322 -1.8256PLOG 5.2444SFLOG
  0.24423T

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• C) F (R2/ 1- R2) ((N-K-1)/K)
• ( 0.6501/ 1- 0.6501) ((14-3-1)/3)
• 1.8579 3.33
• F6.19
• F 10 3.92
• Therefore Fgt F.10 which implies we reject HO in
  favor of HA and conclude that at a 10 level of
  significance there is a regression.

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• d) 2sls Elog Plog Sdlog Ddlog T (Sdlog Sflog
  Ddlog T) / DN RSTAT
• VARIABLE ESTIMATED STANDARD T-RATIO
  PARTIAL STANDARDIZED ELASTICITY
• NAME COEFFICIENT ERROR -------- P-VALUE
  CORR. COEFFICIENT AT MEANS
• PLOG -0.44876E-01 0.2814 -0.1595
  0.873-0.053 -0.0185 -0.0963
• SDLOG 4.9780 1.132 4.399
  0.000 0.826 1.4656 8.0153
• DDLOG -8.2522 2.486 -3.319
  0.001-0.742 -2.9935 -24.8314
• T 0.29686 0.7541E-01 3.936
  0.000 0.795 2.5581 8.8406
• CONSTANT 19.039 6.828 2.789
  0.005 0.681 0.0000 9.0718
• Es 19.039- 0.044876PLOG 4.9780SDLOG
  8.2522DDLOG 0.29686T
• e) Farris Theory Log-Log Model
• P P -
  
• Sd Sd
  
• Dd - Dd -
  

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• f) F (R2/ 1- R2) ((N-K-1)/K)
• ( 0.9602/ 1- 0.9602) ((14-4-1)/4)
• 24.12 2.25
• F 54.28
• F.10 4.54
• Therefore Fgt F.10 which implies we reject HO in
  favor of HA and conclude that at a 10 level of
  significance there is a regression.

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Question 10

• ?1 -1.8256 test this number against the
  t-critical value with D.F.10 which is (1.812)
• b) When compared to the range (1.812), we see
  that the estimated coefficient of Plog is
  insignificant at the 90 level.
• c) We cannot tell whether or not the price
  elasticity of export demand for cattle hides is
  elastic or inelastic, because one cannot be sure
  that it will fall within the specified range.
• d) Point Price elasticity from question 8a
  -0.8497, therefore, it is within our range of
  (1.812)

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3SLS

• Single equation estimation methods lead to
  estimates that are consistent but, in general,
  not asymptotically efficient.
• The lack of asymptotic efficiency is due to the
  disregard of the correlation of the errors across
  equations.
• If we do not take into account the correlation
  b/w the errors of different equations, we are not
  using all the available information about each
  equation and therefore, do not attain asymptotic
  efficiency.
• This can be overcome by running 3SLS which takes
  the correlation between errors into
  consideration, therefore, the estimates of the
  coefficients are consistent and asymptotically
  efficient

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Question 11

• To obtain the linear versions of the export
  demand and supply functions using 3SLS, we must
  run the systems simultaneously.
• system 2 Dd Sd Sf T / dn
• ols E P Sf T
• ols E P Sd Dd T
• a)
• VARIABLE ESTIMATED STANDARD T-RATIO
  PARTIAL STANDARDIZED ELASTICITY
• NAME COEFFICIENT ERROR --------
  P-VALUE CORR. COEFFICIENT AT MEANS
• P -0.83331E-01 0.4002E-01 -2.082
  0.037-0.550 -0.4117 -0.8498
• SF -0.72057 0.4951 -1.455
  0.146-0.418 -0.9453 -3.1690
• T 1.6705 0.5831 2.865
  0.004 0.671 1.7571 11.5638
• CONSTANT -59.091 15.68 -3.769
  0.000-0.766 0.0000 -6.5449
• Therefore, the estimated linear version of demand
  using 3SLS is
• Ed -59.091 0.083331P 0.72057Sf 1.6705T

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• b)
• 2SLS
• VARIABLE ESTIMATED
• NAME COEFFICIENT
• P -0.83331E-01
• SF -0.72057
• T 1.6705
• CONSTANT -59.091

• 3SLS
• VARIABLE ESTIMATED
• NAME COEFFICIENT
• P -0.83331E-01
• SF -0.72057
• T 1.6705
• CONSTANT -59.091

The estimated coefficients obtained in 2SLS and
3SLS are consistent with each other. This is
due to the fact that The omission of exactly
identified equations will not affect the
three-stage least squares estimates of the
coefficients of the remaining equations.
(Kmenta, Jan, Elements of Econometrics, 1986)
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Question 12

• a) To obtain the linear versions of the export
  demand and supply functions using 3SLS, we must
  run the systems simultaneously.
• system 2 Dd Sd Sf T / dn
• ols E P Sf T
• ols E P Sd Dd T
• VARIABLE ESTIMATED STANDARD T-RATIO
  PARTIAL STANDARDIZED ELASTICITY
• NAME COEFFICIENT ERROR -------- P-VALUE
  CORR. COEFFICIENT AT MEANS
• P 0.12200E-01 0.1623E-01 0.7516
  0.452 0.243 0.0603 0.1244
• SD 1.0539 0.2223 4.740
  0.000 0.845 1.1248 3.4584
• DD -0.55010E-01 0.2031E-01 -2.709
  0.007-0.670 -1.3871 -3.4181
• T 1.2349 0.3236 3.816
  0.000 0.786 1.2990 8.5486
• CONSTANT -69.640 15.00 -4.643
  0.000-0.840 0.0000 -7.7132
• Therefore, the estimated linear version of supply
  using 3SLS is
• Es -69.640 0.0122P 1.0539Sd 0.05501Dd
  1.2349T

36

• 2SLS
• VARIABLE ESTIMATED
• NAME COEFFICIENT
• P 0.17109E-01
• SD 1.1265
• DD -0.52472E-01
• T 1.1145
• CONSTANT -66.144

• ILS
• VARIABLE ESTIMATED
• NAME COEFFICIENT
• PI 1.1506
• SDI 1.0195
• DDI -1.0507
• TI 0.99406
• CONSTANT -65.215

3SLS VARIABLE ESTIMATED NAME COEFFICIENT
P 0.12200E-01 SD 1.0539
DD -0.55010E-01 T 1.2349
CONSTANT -69.640
b) In obtaining the estimated coefficients
of the Export Supply function for Two-Staged
Least Squares, Indirect Least Squares and
comparing these results to the Three-Stage Least
Squares, we see that each variable shares the
same sign. We also see that the variables are
very similar among these different forms of least
squares. From research on the 2SLS and ILS, we
have learned that the estimated coefficients in
both tests are suppose to be equal. The
discrepancies of the coefficients could be due to
different estimating techniques.



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The End!