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Intertemporal substitution in import demand and the role of habit formation: an application of Euler equation approach for Pakistan



The study examines the importance of intertemporal substitution in import demand considering the role of habit formation. A two-goods version of the permanent income model is used in which time-non-separability in consumers’s preferences is assumed. The model is estimated using annual data for Pakistan at disaggregated level covering the period from 1977 to 2017.


The objective of the study is to estimate elasticities of substitution along with parameters of habit formation for consumption goods at a disaggregated level.


The study employs co-integration for the estimation of parameters of elasticities of substitution and generalized method of moments (GMM) for the estimation of the parameters of habit formation from Euler equations.


The estimates of intertempral elasticity of substitution suggest that the nature of commodity group (necessity/luxury) plays an important role when consumers are making intertemporal choices. Moreover, the study finds that intratemporal elasticity of substitution is larger than intertempral elasticity of substitution in almost all cases in Pakistan, suggesting that imported and domestic goods are best described as substitutes in Edgeworth-Pareto sense. In addition, the inclusion of habit formation delivers results with plausible signs and the habit formation process seems significant for certain commodity groups including tea, beverages, tobacco products and drugs.


The study concludes that there is a possibility of crowding out effect on domestic consumption and the depreciation of local currency may improve Pakistan’s balance of trade.

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Fig. 1


  1. 1.

    The time-separable utility functions assume that current utility is a function of current consumption while time non-separable utility functions assume that current utility is function of current as well as past consumption.

  2. 2.

    The study collects 2735 estimates of IES from 169 published articles in their analysis of intertemporal substitution for 104 countries.

  3. 3.

    In 2016, out of 192 countries in the IMF, Pakistan was one of the only 9 countries, whose monetary policy framework did not fit into any type of exchange rate arrangements, studied by the IMF.

  4. 4.

    Two goods are Edgeworth substitutes (complements) in utility if an increase in the consumption of first good diminishes (increases) the marginal utility of the second good (Amano et al. 1998; Dawood and Francois 2018).

  5. 5.

    The studies estimating IES usually consider non-durable consumption goods as a proxy for aggregate consumption and exclude durables goods because of the volatility of spending on durables goods (Havranek 2015). Moreover, durable goods are more easily substituted across periods, therefore, inclusion of durables goods may lead to high estimates of IES (Thimme 2017).

  6. 6.

    Conversely, an approach that allows for non-separability between domestic and imported consumption goods (composite good) may not be an appropriate specification to adopt when modeling the behavior of domestic and imported consumption goods at the same time. If consumption of imported good is more volatile than the consumption of domestic goods, then, the estimates of IES of the whole consumption bundle (composite good) may be biased downward (Thimme 2017).

  7. 7.

    The standard classification for groups and sub-groups also includes raw materials and durable goods. However, the study has constructed new groups (i.e. drugs, paints and lighting fixtures etc.) which include only those imported items which are considered as non-durable consumer goods. The study has constructed these commodity groups (sub-groups) from more disaggregated data following Head and Ries (2001). Details of commodity groups are given in Table 5 in the appendix.

  8. 8.

    All these data sources, ASP, PSYB, CMIP, FTSP, MSB and MBS are publications of Pakistan Bureau of Statistics, Government of Pakistan.

  9. 9.

    In the construction of unit value indices, the study has used average quantity of each imported commodity for the sample period as the base year quantity.

  10. 10.

    Bhutto government devalued rupee against US dollar in May, 1972 from Rs 4.76 to Rs 9.90. It was in 1973, when Pakistan enjoyed trade surplus for the last time.

  11. 11.

    The figures reported in this sub-section are based on the data taken from Pakistan Economic Surveys.

  12. 12.

    Although, Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root test is available, however, it is argued that researchers should be cautious about the properties of the KPSS test while focusing consumption data because there is higher probability that KPSS test will reject null-hypothesis for consumption data, despite the fact that it can be defined as a mean reverting time-series process (Jönsson 2011).

  13. 13.

    The estimates of β2 and β3 are theoretically restricted to non-negative values, negative estimates are theoretically inadmissible as they violate standard preference properties. Therefore, negative estimates are usually not included in the discussion (Havranek et al. 2015).

  14. 14.

    It is a well-established empirical regularity and explained by Thimme (2017) that consumption in developing countries is related to subsistence considerations. Similarly, Ogaki et al. (1996) discussed that first subsistence level of consumption will be achieved in developing countries, and then the portion of the left-over budget will be used for other items. This argument allow us to consider that if consumers are purchasing commodities like floor covering or lighting fixtures, then it is based on the portion of their budget left after subsistence has been satisfied. Therefore, it can be argued that these commodities are consumed by relatively high income consumers.

  15. 15.

    However, the study has included only those estimates of IES in the second step of analysis; which are theoretically acceptable following Nishiyama (2005).

  16. 16.

    Hall (1988) estimating IES for consumption goods argues that estimates of IES are unlikely to be much above 0.1 for the UK.


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Correspondence to Farzana Naheed Khan.

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Table 5 Selected Sample of Non-durable Commodity Groups and Subgroups
Table 6 ADF and PP Unit Root Tests Results
Fig. 2

Real Imports, Exports and Balance of Trade for Selected Consumption Groups

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Khan, F.N., Ahmad, E. Intertemporal substitution in import demand and the role of habit formation: an application of Euler equation approach for Pakistan. Port Econ J (2020).

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  • Import demand
  • Elasticity of substitution
  • Time non-separable preferences
  • Euler equation
  • Habit formation
  • Depreciation

JEL classification

  • C22
  • E21
  • F14