Intertemporal production and intertemporal substitution in output supply and input demand

ABSTRACT

This article presents an intertemporal model of production with multiple inputs to investigate substitution opportunities facing firms over time. The firm’s intertemporal profit maximization problem is characterized with the familiar cost function, and various intertemporal substitution elasticities are delineated for output supply and input demand. The absence of intertemporal substitution in production can imply production smoothing, and allowance for intertemporal substitution in labour demand reinforces the prediction of the real business cycle model. For aggregate US manufacturing, we find substantial substitution in output supply and labour demand over time due to intertemporal changes in output price and wage rates.

KEYWORDS:

• Intertemporal equilibrium conditions
• the cost function
• intertemporal substitution
• production smoothing
• real business cycles

JEL CLASSIFICATION:

• D24
• D92
• E23

Acknowledgement

We thank the referee for helpful comments and suggestions to improve the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ We combined two KLEMS data sets for 1949–2001 and 1987–2007.

² We have also examined whether output and input quantities as well as output and input prices are stationary or nonstationary. We have employed the DF-GLS unit root testing procedure of Elliott, Rothenberg and Stock (1996). The results suggest that almost all variables are nonstationary or difference-stationary with a trend. This can be taken to imply that most changes in prices are temporary rather than permanent. To save space, we do not report these results, but they are available upon request.

³ It is assumed that adjustment costs are separable from the firm’s production costs. In this case, the firm’s input decision is separated from the investment decision.

⁴ It is tempting to conduct a cointegration analysis for our model. However, cointegration is designed to detect a long-run relationship among variables, but intertemporal substitution is concerned with short-run movements among variables. Thus, a cointegration analysis is not appropriate for our model.

⁵ We have estimated the SUR model. These results are available upon request. However, we do not rely on these results for our analysis.

⁶ We have examined various model specifications as well as different sets of instruments. Initially, we have included the lagged dependent variable as an independent variable in each equation, to consider a possible dynamic structure of the system. However, the coefficient of the lagged dependent variable is insignificant in all equations. Moreover, there is no significant evidence of autocorrelations in the residuals in all equations when the lagged dependent variables are excluded. We have also included the linear trend but found that its coefficient is mostly insignificant. We have treated all regressors (except for Δln TFP and constant) as endogenous, and used one or two past values of the endogenous regressors as instruments. For example, the instrument for Δln P is given as Δln P(−1) and/or Δln P(−2). In addition, we have also considered adding the past value of the level variable (e.g. ln P(−1) and/or ln P(−2)) as instrument. We have chosen the results using one past values of the first difference and level variables (e.g. Δln P(−1) and ln P(−1)) as instruments. A linear trend and quadratic trend functions were also added as instruments.

Additional information

Funding

Kim’s research was supported by a Faculty Summer Research Fellowship from Gordon Ford College of Business, Western Kentucky University.