Purpose: The purpose of this paper is to examine how households’ engagement in concurrent business (CB), which is measured by the contribution of off-farm income to household income, affects the farm size–technical efficiency (TE) relationship in Northern China.Design/methodology/approach: This paper applies a stochastic frontier analysis method to analyze data on 1,006 rural households collected from four major wheat-producing provinces in Northern China, adopting a translog specification for the underlying production function.Findings: The analysis yields three findings. First, the farm size–TE relationship is inverted U-shaped for all CB engagement levels higher than 5 percent, and the most technically efficient farm size increases with the level of household CB engagement. Second, how TE varies with the level of CB engagement depends on farm size: an inverted-U relationship for relatively small farms (20μ). Finally, the overall TE score, 0.88, suggests that wheat output can be increased by 12 percent in Northern China if technical inefficiency were eliminated.Originality/value: Unlike most previous studies that examine the impacts of farm size and households’ off-farm business involvement separately, this paper examines how these two factors interact with each other.

In the era of Internet of people and things, big data are merging. Conventional computation algorithms including correlation measures become inefficient to deal with big data problems. Motivated by this observation, we present three fuzzy correlation measurement algorithms, that is, the centroid based measure, the integral based measure, and the a-cut based measure using fuzzy techniques. Data of Shanghai stock price index (SSI) and exchange rates of main foreign currencies over China Yuan from 22 January 2013 to 17 May 2018 are used to check the effectiveness of our algorithms, and, more importantly, to observe the causality relationship between Shanghai stock price index and these main exchange rates. We observed some findings, as below. (1) The usage of the highest, lowest or closing values in daily exchange rates and stock prices has impact on the significant Granger causes of exchange rates over SSI, but does not produce any opposite cause from SSI to exchange rates; (2) No matter which of our fuzzy measurement algorithms is used, HKDCNY and USDCNY are positively related with SSI, and EURCNY negatively correlated with SSI is always recognized as a Granger cause to Shanghai stock price index with the significance level being 1%; (3) Both the optimism level and the uncertainty level are observed having impact on the correlation coefficients, but the later brings more significant changes to results of Granger causality tests.