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The study uses the cointegration and common cycle analysis to test whether there are short-run and long-run co-movement relationships between incomes and varies consumption expenditure variables. The analysis aims to detect the long-run co-movements between income and five types of consumption variables, which provides supporting evidence for the common brief that income drives consumption in the long-run. In addition, the analysis also attempts to detect if there are short-run co-movements between income and consumption.

The paper attempts to establish a variant of consumption function and use it to examine the presence of short-term fluctuations in consumption for Hong Kong. From its foundation, the study of the decision adjustments in consumption expenditure was supposed to improve our understanding on the structure of the consumption pattern in the long run and how economy reacts to income-boosting policies in the short run. Empirical researches have had much greater success when focusing on establishing the long run income-consumption relationship and rather less success when exploring the relationship in the short run. The culture of short-termism is rooted in business and political decisions and processes, many companies and policymakers are biased toward short-term fixes, which in turn influences their practices. In this regard, since not all stakeholders are interested in long run results over an extended period of time, the short run dynamic in the consumption function warrant careful studies. The current study fills this void.

Most of the prior researches have focused on the long run consumption function with an emphasis on the applicability of explaining the variations in durable goods consumption patterns [

Theoretical arguments and common wisdom have it that income drives consumption in long run implying income and consumption are drifting upward or downward together at roughly the same rate. Variants have been proposed to explain the variations in consumption behaviors. The permanent income and life-cycle consumption theories argue that people will determine whether the changes in income is temporary and thereby how they prefer to spread their consumption over time [

In contrast to Hall’s hypothesis, Flavin [

Some categories of expenditure may subject to short-term fluctuations in the changes in income. Using the UK data, Cook [

The consumption and income series used in this study are multiplicative seasonally adjusted observations from 1973(1) to 2015(2) on consumers’ expenditure on durable products, on non-durable products, on food, on service and abroad. The data of disposable income prior to 1998 was not collected by the Census, gross domestic product is used as a proxy for income. The data series are scaled by population. The natural logarithms of these series will be denoted as du (durable), nd (non-durable), f (food), s (service), a (abroad) and y (income). It throws no surprise that these series are typical economic I(1) series, as indicated by results of ADF tests applied to them (see

Level | 1st Difference | |||||
---|---|---|---|---|---|---|

Variable | lag included | ADF test statistics | p−value | lag included | ADF test statistics | p−value |

y | 7 | −1.173 | 0.991 | 6 | −6.726 | 0.000 |

d | s4 | −1.813 | 0.692 | 3 | −4.650 | 0.000 |

nd | 5 | −2.413 | 0.371 | 4 | −3.618 | 0.007 |

f | 4 | −1.815 | 0.692 | 3 | −7.724 | 0.000 |

s | 4 | −1.565 | 0.801 | 3 | −4.475 | 0.000 |

o | 4 | −0.225 | 0.992 | 3 | −4.575 | 0.000 |

A pair of series is said to have common features if the two conditions are met: (a) the differences of both series have a cycle, that is, both are serially correlated; (b) the non-zero linear combination of the pair does not have a cycle. Given a pair of series, x_{t} and y_{t}, the following equations are fitted to detect if the individual series having a cycle:

Δ x t = α 1 + α 2 Δ x t − 1 + α 3 Δ y t − 1 + η 1 t (1)

Δ y t = β 1 + β 2 Δ x t − 1 + β 3 Δ y t − 1 + η 2 t (2)

The series is said to have a cycle if the null of the relevant Lagrange multiplier tests (LM) is rejected. Given that both series exhibit a cycle, the commonality of these cycles is checked by fitting the following equations:

Δ x 1 t = μ 1 + μ 2 Δ x t − 1 + μ 3 Δ y t − 1 + ε 1 t (3)

Δ x 2 t = λ 1 + λ 2 Δ x t − 1 + λ 3 Δ y t − 1 + ε 2 t (4)

where x_{1t} and x_{2t} are the residuals obtained from the following fitted equation, respectively, estimated by the two-stage least squares method with Δx_{t-1} and Δy_{t-1} and a cointegrating combination of x_{t} and y_{t} as instruments:

Δ x t = γ 1 + γ 2 Δ y t − 1 + x 1 t (5)

Δ y t = δ 1 + δ 2 Δ x t − 1 + x 2 t (6)

From the above analysis, it throws no surprise to find a long run relationship

Variable | lag included | Test statistics | p-value | Conclusion |
---|---|---|---|---|

y, d | 4 | −1.972 | 0.047 | Variables are cointegrated at the 5% significance level |

y, nd | 5 | −1.594 | 0.104 | Variables are NOT cointegrated at the 10% significance level |

y, f | 4 | −2.137 | 0.032 | Variables are cointegrated at the 5% significance level |

y, s | 4 | −5.430 | 0.000 | Variables are cointegrated at the 1% significance level |

y, o | 4 | −3.275 | 0.001 | Variables are cointegrated at the 1% significance level |

Equation (1) | Equation (2) | ||||
---|---|---|---|---|---|

Variable | LM | p-value | LM | p-value | Conclusion |

y, d | 0.137 | 0.711 | 5.378 | 0.020 | Not both series display a cycle at the 10% significance level |

y, nd | 21.535 | 0.000 | 28.658 | 0.000 | Both series each have a cycle at the 1% significance level |

y, f | 2.254 | 0.133 | 21.476 | 0.000 | Not both series display a cycle at the 10% significance level |

y, s | 8.807 | 0.003 | 8.736 | 0.003 | Both series each have a cycle at the 1% significance level |

y, o | 5.758 | 0.016 | 20.821 | 0.000 | Both series each have a cycle at the 1% significance level |

Equation (5) | Equation (6) | ||||
---|---|---|---|---|---|

Variable | LM | p-value | LM | p-value | Conclusion |

y, nd | 0.092 | 0.762 | 20.937 | 0.000 | Series do not have a common cycle at the 10% significance level |

y, s | 7.935 | 0.005 | 3.348 | 0.067 | |

y, o | 5.774 | 0.016 | 20.831 | 0.000 |

between income and consumption variables, since it fits into the theoretical argument of the income-consumption relationship. However, collectively, the analysis found no short-run relationship exhibit between income and consumption. In other words, the changes in income do not cause short-term fluctuation in consumption. Therefore, in short-term there is no signal for the market to anticipate slumps or booms if incomes were to drop or to rise. Since short-run co-movements between income and consumption may be attributed to consumers’ behaviour in which they willing to spend more immediately when their incomes have been raised, the finding of no short-run co-movement could imply that Hong Kong consumers tend not to make short-term decision, regardless of the categories of goods or services being considered. These results mirror the findings of Hofstede’s research; Hong Kong scored 61 in terms of long-term orientation when compared to 51 and 26 for UK and US, respectively [

Au, A.K.M. and Yeung, M.C.H. (2018) Short-Run and Long-Run Co-Movements in the Income- Consumption Relationship. Theoretical Economics Letters, 8, 814-819. https://doi.org/10.4236/tel.2018.85057