Ag Econ 635 Topics in Consumer Demand Analysis State Adjustment Model Dr. Oral Capps, Jr. Texas A&M University Spring 2008

Dynamics of Consumer Expenditures: Application of Complete Demand Systems

Introduction Non-technical description of dynamic demand systems Dynamic models provide information on adjustment, habit, and inventory features Objectives: Justification of dynamic demand systems Description of methods to incorporate dynamic structures into demand systems Description of state adjustment model and dynamic linear expenditure model Empirical examples

Justification Static Demand Systems: By assumption consumer adjustment instantaneously to new equilibria due to changes in income or price, while all other factors remain constant. Dynamic Demand Systems: Permit processes of gradual adjustment to changes not only in the economic environment but also to changes in tastes and preferences; account for adjustments that occur through time due to habit persistences or stock adjustments.

Incorporation of Dynamic Structures into Demand Systems (1) Ad Hoc Procedures addition of trend variables to the demand equations introduction of trend variables into the parameters of models state adjustment model (2) Dynamic Utility Functions certain parameters of the utility function depend on past consumption Quadratic Model Dynamic Linear Expenditure Model Translog Demand Model Almost Ideal Demand System (3) Control Theory Format Maximization of a discounted utility function subject to wealth and stock constraints Phlips (1974) Lluch (1974) Klijn (1977) } examples } examples

Popular Dynamic Models ( 1) State Adjustment Model: Houthakker and Taylor (1970) A directly specified demand system SIT = physical stock or psychological stock αI= stock coefficient ( < 0 for physical stocks, > 0 for psychological stocks) θI = autonomous consumption levels KI, VI = short-run derivatives of consumption with respect to income and price = rate of change in stock of commodity I δI = depreciation rate δI - αI = reaction or adjustment coefficient

(2) Dynamic Linear Expenditure System Demand functions arise from maximization of utility function βI, γI underlying structural parameters To derive long-run conditions in both models, assume = 0 which implies that the stock adjustment has reached an equilibrium state; consequently, impacts of changes in income and/or prices can be analyzed into short-term and long-term effects.

Empirical Examples Green, Hassan, and Johnson (1978) Analysis of consumer expenditures, four groups: (1) durables (2) semi-durables (3) non-durables (4) services Structure of consumer behavior in Canada 1947-72 State adjustment model Dynamic linear expenditure model

The Role of Inventories and Habits on Elasticities Habit formation relative to inventory behavior decreases as the time interval decreases With short time periods such as a month, inventory behavior tends to dominate demand relationships If inventory adjustment dominates in the short-run, the elasticity of demand generally increases as the time interval is shortened. Pasour & Schrimper – the relative importance of inventory behavior with respect to the length of the adjustment period is an empirical question, & its importance can vary form commodity to commodity. The State Adjustment Model (Houthakker and Taylor) Key Point: past behavior is embodied in a state variable, encompassing both stocks held by consumers and habits formed by past consumption The model has two equations: (1) A short-run demand function (2) A stock depreciation equation Example: Consumer demand for beef, pork, chicken (from Wohlgenant & Hahn, AJAE 1982.)

(1) (2) Stocks depreciate at a declining geometric rate over time Si  the state of the ith commodity Pi  the real (deflated) price of the ith commodity y  per capita real consumer income qi  per capita consumption of the ith meat commodity If the inventory effect dominates Bi < 0; the larger the physical stock, the smaller the consumer demand at t. If habits dominate, the larger the (psychological) stock of habits and the greater the demand at t. (Bi > 0) The state variable in equation (1) is unobservable, but can be estimated with equation (2). The two respective equations are formulated in continuous time, so it is necessary for empirical implementation to approximate them by discrete time.

Replace (following Winder; Houthakker and Taylor; Phlips) and replace

After many tedious steps of algebra,

More compactly

The structural parameter i is over-identified. A unique estimate of i is obtained if the following restrictions hold:

Long-Run derivatives obtained by setting Reaction or adjustment coefficient If habit persistence dominates, the long-run elasticities will be larger than the short-run elasticities. If inventory behavior is dominant, the short-run elasticities will be larger.

Nerlove’s Partial Adjustment Model Test H0: i = 2 (partial adjustment model is same as state adjustment model.)