Structural Change via Threshold Effects: 

Estimating U.S. Meat Demand Using Smooth 

Transition Functions and the Effects of 

Demographic Composition of the Labor Force 

Across Time 

Nestor M. Rodriguez*, James Eales**

December 1, 2015
Nestor M. Rodriguez*, James Eales**

Disclaimer: The views expressed are those of the authors

and should not be attributed to ERS or USDA.

* Research Agricultural Economist, ERS-USDA

** Professor, Purdue University
Introduction Nestor M. Rodriguez*, James Eales**

General Overview 

• Structural change has been a focus in the food demand

literature. Studies have analyzed structural change using a

variety of different approaches and methodologies.

• This paper uses time and demographic changes in U.S. labor

markets as motivation to examine structural change under a

new context.

• Over the past five decades, there have been large changes in

the composition of the U.S. labor force. Specifically, more

females have entered the labor force.
Introduction Nestor M. Rodriguez*, James Eales**

General Overview 

• Previous literature has noted how females entering the labor

force has affected the demand for different food products.

• This study re-examines the effects of time and female labor

participation on U.S. consumer meat demand.

• Additionally, it will analyze and compare the effects of the

general unemployment rate with more specific measures of

unemployment that account for female unemployment relative

to the total unemployed population.
Introduction Nestor M. Rodriguez*, James Eales**

General Overview 

• The goals of this study are:

– To measure structural change in meat demand over time

and when it occurred over the last fifty years

– To measure structural change in U.S. meat demand and

compare the effects when taking into account time, general

unemployment, female labor participation, and female

unemployment relative to the total unemployed population

over the last fifty years.
Introduction Nestor M. Rodriguez*, James Eales**

U.S. Meat Consumption: 1960-2013 

Figure: American meals have traditionally revolved around meat

consumption. Looking at the figure above, it suggests that underlying

preferences in meat demand have changed over this time period.
Data

Data

Nestor M. Rodriguez*, James Eales**

• Quarterly data on consumption and retail prices for beef, pork,

chicken were collected from various USDA sources for the

1960 to 2013 period. To account for seasonality, quarterly

dummy variables are used.

• Data on the unemployment rate, unemployed female

population and total unemployed population were collected

from the Federal Reserve Bank of St. Louis. Specifically, the

FRED system compiles indicators in a host of areas.

• The data was collected in quarterly format.
Methodology

Methodology

Nestor M. Rodriguez*, James Eales**

• When modeling meat demand, a framework that has been

employed is what is known as an Inverse Demand System.

• In such a system, normalized prices adjust to exogenous

changes in quantities. Short-run supplies are assumed to be

perfectly inelastic because of production lags and a reasonably

short shelf-life.

• The Inverse Almost Ideal Demand System (IAIDS) will be used

here.

• It was introduced by Eales and Unnevehr and also developed

independently by Moschini and Vissa.
Methodology

Methodology

Nestor M. Rodriguez*, James Eales**

• The Inverse AIDS model is:

wi = αi + Σjγij ln(qj) + βi(ln(Q)) (1)

where wi

is the budget share for good i for i = 1 and qjis the

quantity for good j. The quantity index, lnQ, is defined by:

1

lnQ = α0 + Σiαi

ln(qi) + ΣiΣjγij ln(qi)ln(qj) (2)

2

• An approximation to the quantity index, the Stone Quantity

Index is used:

lnQ = Σiwi

ln(qi) (3)
Methodology

Methodology

Nestor M. Rodriguez*, James Eales**

• Interpretation of ordinary demand relies largely on evaluation

of elastiticies. For inverse demands, interpretation is based on

comparable measures called flexibilities. They measure the

percentage change in normalized prices due to changes in

quantities.

• Flexibilities can be calculated from the above estimated

coefficients.
Methodology Nestor M. Rodriguez*, James Eales**

Methodology 

• In order to model structural change, the following model is

developed:

wit = f (Xt

, θ1)(1 − G(t; γ, c)) (4)

+f (Xt

, θ2)G(t; γ, c) + eit
Methodology Nestor M. Rodriguez*, James Eales**

Methodology 

• Where θi

is the set of parameters explaining meat demand for

two different regimes that are determined by a transition

variable, t

∗

.

• Transitions occur from regime one to regime two according to

the transition function G, which is a function of t

∗

. γ and c

are parameters that describe characteristics of the transition

function.

• The model above is an offshoot of the time-varying regression

models considered in a univariate context by Terasvirta. These

are known as Smooth Transition Regression (STR) models.
Methodology Nestor M. Rodriguez*, James Eales**

Methodology 

• A common specification of the transition function is the first

order logistic function:

� �−1 −γ(t−c)

G(t; γ, c) = 1 + e

σt , γ > 0 (5)

• Where γ is the speed of adjustment parameter that determines

the speed with which the model shifts from one regime to

another.

• The centrality parameter, c, determines at what point in the

sample the structural change is fifty percent complete.
Methodology Nestor M. Rodriguez*, James Eales**

• Methodology:Time Varying - Smooth Transition Regression

(TV-STR) Model

wit = [f (Xt

, θ1)(1 − G(t; γ1, c1)) (6)

+f (Xt

, θ2)G(t; γ1, c1)](1 − G(t; γ2, c2))

+[f (Xt

, θ3)(1 − G(t; γ1, c1)) 

+f (Xt

, θ4)G(t; γ1, c1)](G(t; γ2, c2)) + eit 
Results Nestor M. Rodriguez*, James Eales**

Results 

Table: Basic IAIDS Model

Uncompensated Flexibilities 

Beef Chicken Pork

Beef -0.704 -0.091 -0.085

Chicken -0.395 -0.502 -0.293

Pork -0.273 -0.206 -0.609

Scale -0.879 -1.190 -1.088

Table: LLK : 1609.57. In the basic Inverse AIDS model, all own-price

flexibilities are negative. All scale flexibilities are negative and in the

vicinity of negative one.
Results Nestor M. Rodriguez*, James Eales**

STR IAIDS LSTAR (TIME) (One)

Beef Chicken Pork

Beef -0.761 0.0587 0.0053

Chicken -0.348 -0.860 -0.4395

Pork -0.196 -0.2229 -0.672

Scale -0.697 -1.645 -1.092

LLK : 1643.71 γ = 6.24

STR IAIDS LSTAR (TIME) (Two)

Beef Chicken Pork

Beef -0.777 -0.155 -0.185

Chicken -0.136 -0.360 -0.132

Pork -0.329 -0.190 -0.533

Scale -1.118 -0.630 -1.053

c = 0.425(1983)

Figure: LSTAR Transition Function Over Time
Results Nestor M. Rodriguez*, James Eales**

STR IAIDS LSTAR (UNE) (One)

Beef Chicken Pork

Beef -0.555 0.028 -0.030

Chicken -0.799 -0.952 -0.465

Pork -0.254 -0.092 -0.581

Scale -0.556 -2.217 -0.928

LLK : 1641.813 γ = 1033.201

STR IAIDS LSTAR (UNE) (Two)

Beef Chicken Pork

Beef -0.768 -0.143 -0.117

Chicken -0.197 -0.325 -0.189

Pork -0.300 -0.239 -0.622

Scale -1.030 -0.712 -1.162

c = −0.101

Figure: Trans Function-UNE Figure: Trans Function
Results Nestor M. Rodriguez*, James Eales**

STR IAIDS LSTAR (FLR) (One)

Beef Chicken Pork

Beef -0.760 -0.201 -0.199

Chicken -0.164 -0.226 -0.111

Pork -0.342 -0.203 -0.522

Scale -1.161 -0.503 -1.067

LLK : 1649.82 γ = 1.61

STR IAIDS LSTAR (FLR) (Two)

Beef Chicken Pork

Beef -0.861 0.290 0.165

Chicken -0.589 -1.616 -0.724

Pork 0.185 -0.091 -0.762

Scale -0.405 -2.931 -0.668

c = 0.019

Figure: Trans Function-FLR Figure: Trans Function
Results Nestor M. Rodriguez*, James Eales**

STR IAIDS LSTAR (FEMTOT) (One)

Beef Chicken Pork

Beef -0.809 -0.112 -0.107

Chicken -0.126 -0.456 -0.144

Pork -0.278 -0.200 -0.679

Scale -1.028 -0.725 -1.158

LLK : 1624.014 γ = 2.199

STR IAIDS LSTAR (FEMTOT) (Two)

Beef Chicken Pork

Beef -0.574 -0.105 -0.107

Chicken -0.681 -0.531 -0.362

Pork -0.309 -0.156 -0.511

Scale -0.786 -1.575 -0.975

c = 0.016

Figure: Trans Function-FEMTOT Figure: Trans Function
Results Nestor M. Rodriguez*, James Eales**

STR IAIDS TVSTR (FEMTOT) (I)

Beef Chicken Pork

Beef -0.774 0.098 -0.014

Chicken -0.083 -1.069 -0.173

Pork -0.377 -0.139 -0.837

Scale -0.691 -1.326 -1.353

LLK : 1675.306 γ1 = 34.079

STR IAIDS LSTAR (FEMTOT) (II)

Beef Chicken Pork

Beef -0.735 0.031 -0.014

Chicken -0.428 -0.828 -0.427

Pork -0.188 -0.193 -0.642

Scale -0.717 -1.685 -1.024

c1 = −0.0017

Figure: Trans Function-FEMTOT Figure: Trans Function
Results Nestor M. Rodriguez*, James Eales**

STR IAIDS TVSTR (FEMTOT) (III)

Beef Chicken Pork

Beef -1.109 -0.049 -0.093

Chicken 0.223 -0.499 -0.312

Pork 0.042 -0.289 -0.574

Scale -1.252 -0.589 -0.821

LLK : 1675.306 γ2 = 14.308

STR IAIDS LSTAR (FEMTOT) (IV)

Beef Chicken Pork

Beef -0.678 -0.174 -0.294

Chicken -0.159 -0.351 -0.097

Pork -0.506 -0.158 -0.347

Scale -1.147 -0.608 -1.012

c2 = 0.447(1984ish)

Figure: Trans Function-FEMTOT Figure: Trans Function-Time
Conclusion Nestor M. Rodriguez*, James Eales**

Conclusion 

• Structural change in U.S. meat demand was examined using

an Inverse AIDS model in combination with smooth transition

regressions.

• Results indicate that structural change did occur over the last

fifty years.

– In terms of time, there was a smooth transition from one

regime to another around 1983.

– In terms of unemployment, there was an abrupt change that

occurred many times over the time period.
Conclusion Nestor M. Rodriguez*, James Eales**

Conclusion 

• In terms of female labor participation, there were several

regime changes. These occurred from the mid-60s until the

mid-80s.

• In terms of measuring the female unemployed population as a

proportion of the general unemployed population, there were

many regime changes that occurred over the time period and

results seem to coincide with overall changes in meat

consumption.

• In terms of measuring the effects of the female unemployed

population as a proportion of unemployed population over

time, there were two distinct regimes due to time, with many

regime changes in each regime.
Conclusion

Conclusion

Nestor M. Rodriguez*, James Eales**

• This methodology not only pinpoints when there was structural

change but also suggest what consumers might be reacting to.

• This provides researchers with another tool to add to their

toolkit in modeling structural change.

• These results can be informative to industry, policy makers,

and researchers who examine and analyze this particular

market.
Conclusion Nestor M. Rodriguez*, James Eales**

Thank you!