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When the variable of model is large, the Lasso method and the Adaptive Lasso method can effectively select variables. This paper prediction the rural residents’ consumption expenditure in China, based on respectively using the Lasso method and the Adaptive Lasso method. The results showed that both can effectively and accurately choose the appropriate variable, but the Adaptive Lasso method is better than the Lasso method in prediction accuracy and prediction error. It shows that in variable selection and parameter estimation, Adaptive Lasso method is better than the Lasso method.

Consumption, investment and export have always been referred to as the “troika” of economic growth. In China, investment and export are the main power of economic growth for a long time. But compared with the investment and the export, the level of residents’ consumption in our country is very low, especially the rural residents’ consumption which depressed for a long time. So, the government also stressed several times that we need to focus on expanding domestic demand, especially consumer demand. Therefore, discovering the main factors influencing the rural residents’ consumption in China has a very important practical significance.

There are many empirical studies of literature about consumer spending in China. For example, by using panel data of 31 Chinese provinces from 2000 to 2011 through regression analysis, Zhao [

In this paper, we are using R statistical software’s Lars packages and Msgps packages, modeling and projections for rural residents’ consumption expenditure about China by using the Lasso method and the Adaptive Lasso respectively.

Supposing this paper has model data

Which

Usually write model (1) as the following form:

Which

Lasso method to estimate is defined as:

here s ≥ 0 is the penalty parameter. The optimal solution of (3) is called the Lasso solution; the entire Lasso solution can be obtained by changing the s values, at this time, this paper uses k-fold CV and Mallows C_{p} criteria to choose the best model. k-fold CV is a common method of evaluation model, it roughly put all of the observation data divided into k equal parts, and then take turns to use one of the k − 1 parts for the training set, used to fitting data, the remaining part is a test set, totally calculating k times, get the k index of the mean square error of fitting test set, do an average, then repeat all of the steps of the above, then select the model of the minimum average mean square error. C_{p} criteria is also a standard which used to assess a regression model, if select a p independent variables from the k independent variables to involved in regression, then C_{p} criteria is defined as:

Therefore, this paper can choose a model with minimum C_{p}.

Lasso method selects variables, at the same time, it is good in estimates the unknown parameters, can solve the multicollinearity problems that exist in the model better, especially the high-dimensional data processing.

Adaptive Lasso method to estimate is defined as:

In Type (5),

meters, _{p} criteria, AIC criteria, GCV criteria and BIC criteria can be used to choose the best model [

Due to Lasso method use the same weight of all coefficient, and the Adaptive Lasso methods based on different variables given different weights, with a smaller weight punish the variable which regression coefficient is larger, with a larger weight punish the variable which regression coefficient is smaller, improved the Lasso method in variable selection, which cannot meet the model selection of consistency and parameter estimation lack of convergence speed to

In this paper, on the basis of the theory of economics and the research of Yu and Zhang [

In this article, the dependency ratio data was from Statistical Yearbook of China Population. The interest rate data was from the website of the people’s bank of China, interest rates will be subject to the one-year rate stipulated by the central bank, if there are multiple interest rate in a year, then use weighted average, the weight of the interest rate used in accounted for the proportion of 12 months. Other variable data are from 1981-2015 periods, China Statistical Yearbook.

From

variable | meaning | variable | meaning |
---|---|---|---|

x_{1} | Residents’ disposable income | x_{9} | Young dependency ratio |

x_{2} | GDP growth rate | x_{10} | Education situation |

x_{3} | Inflation | x_{11} | Spending on social security |

x_{4} | The first industrial output value | x_{12} | Employment figure |

x_{5} | The tertiary industry output value | x_{13} | Income distribution gap |

x_{6} | The annual fixed asset investment | x_{14} | Spending habits |

x_{7} | The interest rate | x_{15} | Highway mileage |

x_{8} | population | x_{16} | Post and telecommunications business |

than the value of C_{p} criteria, so this paper selects the most optimal Lasso solution according to Mallows C_{p} criteria. This article gets minimum C_{p} value when step is 20, then the model is optimal, in the end, this paper chooses 11 variables such as

LASSO model:

On this basis, this paper predicts China rural residents’ consumer spending from 2008 to 2014, forecasting results are shown in

From

Through the use of Adaptive Lasso method (see _{p} criteria, AIC criteria, GCV criteria and BIC criteria is 9.767, 10.11, 11.14, 8.263, the BIC value is minimum which can fitting the model best, so this paper chooses BIC criteria to modify the model and finally selects 13 variables such as

year | Y (billion) | Predicted value (billion) | relative error |
---|---|---|---|

2008 | 2767.726 | 2531.852 | 0.08522 |

2009 | 2900.533 | 2702.854 | 0.06815 |

2010 | 3197.46 | 2993.954 | 0.06365 |

2011 | 3896.959 | 3667.178 | 0.05896 |

2012 | 4231.038 | 4023.456 | 0.04906 |

2013 | 4712.732 | 4601.321 | 0.02364 |

2014 | 5185.961 | 5089.899 | 0.01852 |

consumption expenditure; But the GDP growth rate, young dependency ratio, education, employment figure, income distribution gap, consumption habits and post and telecommunications business are have a negative effect on the rural residents’ consumption expenditure; Other factors are not significant in affect the rural residents’ consumption expenditure, are not elected to the model.

Adaptive LASSO model:

On this basis, this paper predicts China rural residents’ consumer spending from 2008 to 2014, forecasting results are shown in

From

year | Y (billion) | Predicted value (billion) | relative error |
---|---|---|---|

2008 | 2767.726 | 2590.408 | 0.064066 |

2009 | 2900.533 | 2776.138 | 0.042887 |

2010 | 3197.46 | 3068.92 | 0.040201 |

2011 | 3896.959 | 3716.852 | 0.046217 |

2012 | 4231.038 | 4099.892 | 0.030996 |

2013 | 4712.732 | 4701.812 | 0.002317 |

2014 | 5185.961 | 5178.577 | 0.001424 |

Based on the Lasso method and the Adaptive Lasso method to construct predictive model of rural residents’ consumption expenditure in China respectively, inflation is the most important factors influencing the rural residents’ consumption expenditure; and residents’ disposable income, inflation, the annual fixed asset investment and highway mileage factors are all have positive effects on the two models; and the GDP growth rate, population, employment figure, income distribution gap, consumption habits and post and telecommunications business all have a reverse effect on the two models. To this end, this article puts forward the following suggestions:

1) Control the level of inflation in China. Inflation has a great influence on rural residents’ life. On the one hand, inflation makes the price of agricultural and sideline products increase, and increase the income of farmers. On the other hand, inflation makes the rural consumer goods and services prices increase and the farmers’ real income down. Thus, the inflation can be controlled by using these ways, such as the tightening of monetary policy, fiscal policy and income policy, positive supply policy, currency reform and other measures to restrain inflation.

2) Raising the income level of rural residents. Raise the income level of rural residents, so that they will have more consumption. The government can implement active employment policy, provide more employment platform, give more job training for rural surplus labor about mount guard, expand the source of raising income, and provide modest fiscal policy of subsidies for agricultural production to increase the income of rural residents.

Tao, X.T. and Zhang, H.M. (2016) Prediction of Rural Residents’ Consumption Expenditure Based on Lasso and Adaptive Lasso Methods. Open Journal of Statistics, 6, 1166-1173. http://dx.doi.org/10.4236/ojs.2016.66094