Abstract
Based on the high-frequency price data, this article estimates the extent of price stickiness, identifies the pricing model, and applies the micro-results to analyze the dynamic characteristics of inflation. The results show that the price moves downward steadily during the COVID-19 epidemic. Secondly, the commodity price displays low stickiness, and the pricing model shows the time-dependent pricing (TDP) model in general. Finally, the inflation inertia is negative, indicating the macro-control is effective on COVID-19 epidemic and has the feature of contradiction to the economic cycle. And inflation inertia mainly comes from food commodities, which means that the anchoring object of the policy should be food commodities during the COVID-19 pandemic.
1. Introduction
In recent years, epidemics have affected human health and social stability. The COVID-19 epidemic that outbroke at the end of 2019 posed a great challenge to economic and social development. It has broken the original balance between supply and demand and directly affected macroeconomic stability. Therefore, it is increasingly important to ensure effective macro-control measures when we face the impact of the outbreak.
Price stickiness refers to the fact that price does not react to market in time, making price sticky [1]. Price stickiness is usually observed in daily life. However, it is not individual commercial price stickiness but aggregate price patterns and inflation that affect the macroeconomic operation [2], which lead to discussions on the pricing model and the relationship between price stickiness and inflation. Previous studies have shown that price stickiness is closely related to price adjustment [3–5]. At present, price adjustment mainly falls into two models: One is the time-dependent pricing (TDP) model, that is merchants adjust the price in a fixed time which price changes are exogenous. The other is the state-dependent pricing (SDP) model, that is the adjustment of commodity prices by merchants depends on the market. The price changes are endogenous.
There have been abundant researches on price stickiness. In the early stage, due to the difficulty in obtaining price data, they mainly focused on specific categories of commodities. Based on this, scholars concluded that commodity prices had high price stickiness [6, 7]. Moreover, menu cost [8, 9], sticky information [10], and consumer sentiment [11] were the main causes of price stickiness. With the development of e-commerce, the sample range was expanded. Bils and Klenow found that price changes were frequent, and the price lasted less than 4.3 months when they investigated 350 sorts of goods price from the Bureau of Labor Statistics [12]. Similarly, Klenow and Kryvtsov detected that the price lasted 3.8 months, and the pricing model adopted the time-dependent pricing (TDP) model on the basis of the data from BLS from 1988 to 2003. The web crawler technology further enriched the commodity category and frequency [13]. Cavallo held that the pricing model was the combination of SDP and TDP by capturing daily online commodity data of five countries [14]. Jiang et al. supported this view. They also found that the price lasted 2 months or less, and the price adjustment model was the combination of SDP and TDP by the data from China’s high-frequency goods price [15].
Some research on price stickiness found that it was related to inflation inertia. Lunnemann and Matha studied the price data of 15 EU countries and found that the price stickiness of service price and regulated service was positively correlated with the inertia of service price inflation [16]. Mato reached the same conclusion based on Brazilian commodity prices [17]. In contrast, Cecchetti and Debelle found that the higher the price stickiness, the lower the inflation inertia [6].
It can be seen that price stickiness is closely related to the pricing model, and there are differences in price setting behavior, resulting in changing the inflation inertia. Moreover, there is no unified conclusion about the relationship between price stickiness and inflation inertia. At the same time, empirical research on price stickiness under the outbreak is still very scarce. Therefore, this article uses online high-frequency price data to study the price stickiness during COVID-19, observes the pricing model and inflation inertia, and provides more reliable empirical evidence for macroeconomic models.
The purpose of this article is to investigate the price stickiness during COVID-19. Compared with the previous literature, the contributions are mainly as follows: Firstly, we use web crawling technology to get the daily commodity prices on COVID-19. The micro-results are used to analyze inflation inertia for the first time, which effectively connects the micro-basis with the macro-application. Secondly, we attempt to measure the price stickiness when the epidemic outbroke. At the same time, the variance decomposition method is used to judge the pricing mode. This article finds that price performs low stickiness, and the pricing model is state-dependent pricing on COVID-19. Finally, we construct an AR model to analyze the inflation inertia and find that inflation inertia is negative, which means the effectiveness of macro-management during the outbreak. And inflation inertia mainly comes from food commodities, which means that the anchoring object of the policy should be food commodities on COVID-19.
The rest of the article is organized as follows: Section 2 introduces data acquisition and data processing; Section 3 shows the measurement results of price stickiness; Section 4 analyzes inflation inertia based on the results of price stickiness; and Section 5 obtains conclusions.
2. Data
2.1. Data Collection
This article collects the commodity price from Taobao platform with the web crawling technology [18, 19]. The data acquisition process is as follows: The first step is to access the Taobao platform with Python to obtain information such as product names, classification, links, and others and store the commodity information in the MySQL database. The second step is to retrieve the product links from the database and matched them on a price comparison website to acquire the historical prices of commodities. The final step is to process the price data with Python and measure the price stickiness to further analyze the inflation.
Compared with offline data, online data are used to study price changes with certain advantages. Firstly, online data increase the frequency of price analysis, and daily data could reflect the price changes more flexibly. Secondly, more enterprises select online sales as an alternative to offline sales when they consider the segmented domestic market. Thirdly, online and offline data are the same about 72% of the time, and online data have a good representation.
2.2. Data Source
The data collected in this article covers 48,073 sorts of commodity information on Taobao from December 2019 to August 2020, with a total of 7,712,415 observations. We match the commodities with eight categories that are divided by State Statistics Bureau (NBS) to facilitate the subsequent analysis. We divided the goods category into food; clothing; residence; household equipment; transport, post, and telecommunication; culture, education, and recreation; medicine and health care; and other goods and services. The data description of commodity is shown in Table 1.
2.3. Data Preprocessing
This article refers to the existing literature and preprocesses the original data in combination with the characteristics of online price as follows:
2.3.1. Missing Value Processing
This article uses daily price data to analyze price stickiness. Some random factors (i.e., software problems, message interrupt, etc.) might result in the missing of price information on a certain day or period, which is required to add the missing information. Therefore, we use the price of missing values in the previous period to replace the missing price until the new price appears [19, 20].
2.3.2. Outlier Processing
The abnormal fluctuations in price will affect the measurement of price stickiness and interferes with the price changes. This article defines the values that the price increased by over 500% or the price decreased by over 90% as outlier value, according to the former research [21]. We choose to eliminate the outlier value to ensure the reliability of results, considering a small number of abnormal values in the dataset.
2.3.3. Period Processing
The sample period referred to the time span from the first appearance of the price to its last time [22]. This article gets rid of the sample periods of less than 7 days to warranty the measurement feasibility.
This article ultimately selects 47,219 commodities and 7,709,816 observations by processing the missing value, abnormal value, and sample period.
3. Measurement of Price Stickiness
3.1. Price Index
The price index is an index that reflects price changes. This article measures the price index by indexing the commodity price obtained by Taobao. We use the Jevons geometric index formula to calculate the commodity price index.
Firstly, we calculate the relative price of each commodity i in period t, where is the price of commodity i at day t, and is the price of commodity i at day t-1.
Secondly, the relative prices of all commodities are geometrically averaged in period t,
Finally, using equation (2), the first day of the sample period is set to 100 to obtain the commodity price index,
Figure 1 shows the trend of commodity price index, in which the green dotted line indicates the outbreak time of COVID-19 in China: January 20, 2020. We can see that the price moves downward steadily during the COVID-19 epidemic.
In order to further study the changes of commodity prices on COVID-19, we analyze eight categories of commodities that are divided by NBS. The results are shown in Figure 2.
3.2. Descriptive Statistics
This section makes the descriptive statistics of price changes. The statistical results are reported in Table 2. We find that 81.24% of the commodities generally change price during the sample period, price adjustments of a commodity are 15.70 times, and commodity price shows low price stickiness. In the meantime, commodities of price increased account for 34.65%, while the decreased goods are 65.35%. It can be drawn that the majority of commodity price is changed and the price moves downward during COVID-19. Then we further classify the commodities into eight categories, and the results are similar to the above.
3.3. Frequency and Period
This section evaluates the price stickiness by calculating the frequency and period of price changes. On the one hand, the price frequency refers to the number of price changes during the sample period. We figure up the price frequency based on the methods of Gopinath and Rigobon (GR methods) [23]. The detailed methods are as follows:
We calculate the price frequency of commodity i in category d:where is the price change times of commodity i in category d. denotes the numbers of observations. Using (4), we divide the commodities into eight categories that are provided by NBS and calculate the price frequency of each category by using the median method, :
In order to get the overall price frequency, we calculate the change frequency of eight categories of commodities by the weighted average method where the weight of eight categories of goods is based on the method of He [24]. The overall price frequency is:where is the relative weight of goods i. In order to ensure the robustness of the results, we adopt the BK method to measure the price adjustment frequency. The BK method was used by Bils and Klenow. They calculated the arithmetic mean of each category of goods based on a single good price frequency and got the overall price frequency by the weighted average method. On the other hand, price period refers to the duration of the price until it changes. We obtain the price period according to the method of Jin et al. (4), which is
It can be seen that there is a negative relationship between price frequency and period, that is to say, the higher the price frequency, the shorter the price period, indicating that the price stickiness is higher. The specific results of price frequency and period are shown in Table 3.
The price stickiness is low during the COVID-19 epidemic as shown in Table 3. According to the GR method and BK method, the overall price frequency is 7.85% and 9.65%, respectively, and the overall price period is 12.23 days and 9.86 days. The extent of price stickiness is far lower than the result of existing studies. Jiang et al. (2020) discovered that the price frequency is 2.24% (GR method) and 3.39% (BK method). As shown in Table 3, the results show that the price period is shorter and price adjustment is more frequent during COVID-19.
We find that there are differences in the price frequency and period among eight main categories. The extent of price stickiness is ranked from low to high: clothing; other goods and services; household equipment; transport, post, and telecommunication; culture, education, and recreation; medicine and health care; food; and residence. It can be drawn that clothing goods have the lowest price stickiness, whose price frequency is 13.50% and the price period is 6.90 days. The results explain that the commodities that change the price make up 13.50% and price adjustment cycle is 6.90 days. Residence goods have the highest price stickiness. Its price frequency is 4.17% and the price period is 23.48 days, which prove that commodities of clothing are best sold during the COVID-19 epidemic. The results are similar to the findings of Jin (2013).
3.4. Price Size
The preceding section discovers that the price stickiness is low during the COVID-19 epidemic by estimating the price stickiness in terms of price frequency and period. In order to further observe the price stickiness, this section measures the size of price changes. The detailed processes are as follows:
We calculate the price size of commodity i at t in category d, :where is the price of commodity i at day t in category d. denotes the price of commodity i at day t-1 in category d. Using (7), we divide the commodities into eight categories that are provided by NBS and calculate the price size of each category by using the GR method and the BK method, and are
In order to get the overall size of price change, we calculate the size of eight categories of commodities by the weighted average method. The overall price frequencies based on eq (9) and (10) are
Based on the results of Table 4, during the COVID-19 epidemic, the scale of price change was small, and the difference between the scale of price increase and price decrease was not obvious. The size of price changes is 13.62% and 13.18% by calculating separately with the GR and BK methods, which is less than the results of previous studies. Jin found that the price adjustment range was 24.90%. Jiang et al. found that the median of commodity price adjustment is 19.49% and the arithmetic average is 20.07%. Meanwhile, we find that the difference between the price size increased and that decreased is 0.04%, indicating that the price change is symmetrical during COVID-19. Combined with the results in Table 1, we find that the times of price reduction are greater than that of price raise. Therefore, we obtain that the price moves downward steadily during the COVID-19 epidemic. One cause is that the pricing behavior of merchants will consider consumer sentiment in accordance with fair pricing theory. The abnormal fluctuation of prices causes the consumers’ negative emotion, which would influence the partnership between merchants and consumers [25, 26]. Therefore, merchants do not arbitrarily change price during the epidemic, when they will consider the consumer feelings that merchants should deliver the altruism to consumers.
We find that there are differences in the price size among eight categories of goods which are divided by NBS. The size of price change is ranked from low to high: residence; other goods and service; household equipment; transport, post, and telecommunication; medicine and health care; culture, education, and recreation; food; and clothing. The commodity of clothing has the maximum difference in the price increase and decrease, which is 1.06%. Residence goods have the minimum difference, which is 0.06%. The size of price changes among eight main categories of commodities has no significant difference, explaining that the price changes are relatively symmetrical. Thus, this article discovers that the prices of eight categories of commodities move downward stably.
3.5. Pricing Model
Based on the price frequency and size, this article finds that the price moves downward steadily during the COVID-19 epidemic. We inspect the pricing model with the variance decomposition method (short for KK method) proposed by Klenow and Kryvtsov in order to further analyze the source of price fluctuations. KK method decomposes the variance of price changes into time-dependent pricing (TDP) terms and state-dependent pricing (SDP) term and compares the variance contribution rate between the two, so as to obtain the pricing model. The details are as follows:
Let represents an indicator of a price change for commodity i in day t:where denotes the log of price of commodity i in day t. We use the following equation for aggregate inflation, :=
As shown, eq (13) represents that the aggregate inflation can be expressed as extensive margin and intensive margin. is the fraction of the commodities’ changing price changes in day t, that is the numbers of merchants adjusting price when inflation occurs. signifies the weighted-average magnitude of adjusting price in day t, that is the magnitude of price changes by merchants when inflation occurs. According to the model of Klenow and Krystov, the external environment could influence the pricing behaviors of merchants when inflation () is relevant to fraction (). Instead, pricing behavior cannot be influenced when inflation () is irrelevant to fraction . Therefore, we reach that the pricing model is the time-dependent pricing (TDP) model if inflation () is uncorrelated with fraction (). When inflation rate () is relevant to magnitude () and fraction (), the pricing model is the state-dependent pricing (SDP) model. The results are shown in Table 5.
We find that coefficients of is negative and small in Table 5, indicating that there exists low inflation phenomenon on COVID-19. Meanwhile, the overall inflation decomposition result of all commodities price displays that and have a higher relevance degree where the correlation coefficient is 0.601, and the regression coefficient of is significant at 1% level. The correlation coefficient of and is 0.095, and the regression coefficient of is not significant. The results show that the pricing model fits the time-dependent pricing (TDP) model during the COVID-19 epidemic, which explain that most merchants can flexibly change price based on the market environment. In addition, we get that the pricing models of eight categories of commodities are heterogeneous. The correlation coefficient of clothing goods is 0.286. At the same time, the regression coefficient of is significant. It indicates that the pricing model of clothing goods is state-dependent pricing (SDP) model where and are highly related to and regression results are significant. However, the pricing model of other category goods is time-dependent pricing(TDP) model where regression between and is not significant at the 1% level. It shows that the price changes of these commodities are limited during the COVID-19 epidemic.
Then, the variance decomposition of the inflation () is made to clarify the contributions of time-dependent pricing (TDP) term and state-dependent pricing (SDP) term. The first-order Taylor expression is carried out on (13):where denotes extensive margin, and represents intensive margin. When the TDP model is dominant, and are equal to 0 that the inflation variance is decided by the TDP term. However, when the SDP model is dominant, is not equal to 0, that is the SDP term has an influence on the inflation variance. The results of the inflation variance decomposition are shown in Table 6.
The variance decomposition results are reported in Table 6. We discover that proportion of TDP term is far more than that of SDP terms, which verify the results in Table 5. However. TDP terms of clothing goods exceed 100%. The reason might be that the mean of raises the TDP term and the variance of lowers the SDP term when we consider the high frequency of price changes during the COVID-19 epidemic.
As we know, commodity prices move downward steadily; meanwhile, the low inflation phenomenon exists during the COVID-19 epidemic. The overall pricing model is time-dependent pricing model, and the pricing models of categorized commodities are heterogeneous. The results led to problems that whether macro-policies should respond to price changes during COVID-19. If so, what commodities should policy anchor? An analysis of the dynamic characteristics of inflation is required to answer these questions. Zhang (2008) supposed that the key to understand the dynamic characteristics of inflation was to identify the inertial characteristics, namely inflation inertia [27]. The next section analyzes the dynamic process of inflation by measuring the inflation inertia.
4. Inflation Inertia
4.1. AR Model
Inflation inertia refers to the duration which inflation deviated from the equilibrium state due to being disturbed by random factors [28]. As a general rule, the greater inflation inertia is, the more obvious hysteresis effect of policies is. Therefore, it is of great significance to policy regulation by accurately measuring the inflation inertia. By referring to the existing literature on the measurement of inflation inertia [27, 29], we evaluate the inflation inertia by making use of the sum coefficients in the AR model. The AR model is as follows:where is the inflation rate, and represents the sum of coefficients in the AR model, which measures the inflation inertia. Considering the collinearity caused by the lag of explanatory variable, OLS will result in deviations of estimated results [30]. Therefore, this article takes the median unbias estimation that was proposed by Roy and Fuller [31] in order to ensure the robustness of the results.
4.2. Empirical Results
The estimated results are reported in Table 7. It can be seen that the overall inflation inertia is less than 0. The main reason is that the economy is at the low inflation state during the COVID-19 epidemic. We use the Jevons geometric index formula to process price index according to the method of Guo [32]. The overall commodity price index is 96.83, which contribute that the inflation inertia is reversal. The results are similar to the research of Chen [33]. It illustrates that macroeconomic policies are featured by going against the economic cycle, and macro-management is effective [34]. Food commodities has a higher inflation inertia than non-food commodities. It can be sure that the inflation inertia mainly comes from food commodities during the COVID-19 epidemic. The reasons may include that food commodities have the largest weight that reach nearly 1/3 among the eight categories of commodities, and the proportion of food expenditure is relatively high that achieves 30.16%. The fluctuation of food price caused by the COVID-19 epidemic will directly affect the dynamic characteristics of inflation.
Further, the impact of COVID-19 may cause the structural mutation of model estimation. When the outbreak happened at the initial stage, people would be in a greater demand for some commodities that improves the price of these commodities. With the outbreak is to be gradually brought under control, the demand for commodities will weaken. The commodity price will go through a significant adjustment, bringing out the structural mutation of the AR model during COVID-19. On this account, we conduct a structural breakpoint test by referring the method of Zivot and Andrews [35]. As shown in Table 8, commodities of clothing and culture, education, and recreation did not have obvious structural mutations, while the other commodities have significant structural breakpoints. In order to get more accurate estimation results, we divided the time series into two stages based on the structural breakpoint and held that commodities of food still have great inflation where coefficients are −0.208 and −0.684%, respectively. Meanwhile, this article discovers that there is a great difference among commodities of food, residence, household equipment, and medicine and health care.
The above results show that the demand for commodities of food, residence, supplies and services, and medical services greatly increase during the early period of the COVID-19 epidemic and the price of that is increased. However, with the gradual control of COVID-19, the demand for such commodities is reduced, and the accumulation of commodity supply makes the inflation inertia larger.
5. Conclusions
Based on the online high-frequency price data, this article measures the price stickiness of commodities during the COVID-19 epidemic and analyzes pricing models and inflation inertia, which provide the micro-basis for macro-policy. The main conclusions are as follows:
Firstly, the commodity price moves downward steadily during the COVID-19 epidemic. On the whole, most commodities of price shows a downward trend during the sample period. In the meantime, the commodities of price has a minor change size, and the difference between the size increased and that decreased is not obvious. The price of eight categories of goods is similar to the aggregate price performance. The reason lies in that merchant will formulate pricing strategy based on consumer sentiment. The abnormal fluctuations of prices cause the consumers’ negative emotion, which would influence the partnership between merchants and consumers. Therefore, price moves downward steadily under the consumer sentiment.
Secondly, the commodity price displays the low stickiness, and the pricing model shows time-dependent pricing (TDP) model in general. We find that most commodities show a time-dependent pattern through eight commodity classification and only clothing commodity belongs to state-dependent pricing (SDP) model. The results show that the price adjustment of most commodities is limited during the COVID-19 period.
Thirdly, we construct AR model to estimate inflation inertia and clarify the dynamic characteristics of inflation. The results show that the inflation inertia is negative, which means that the macro-control is effective during the COVID-19 epidemic and has the characteristics of going against the economic cycle. It indirectly indicates that COVID-19 is a short-term market shock, and inflation inertia mainly comes from commodities of food, which means that government should regulate the inflation by aiming at food goods during the COVID-19 epidemic.
This article affirms the price stickiness of commodities during the COVID-19 epidemic and thus has practical significance. However, there are still some limitations that need to be further studied. Firstly, we just consider the price stickiness during the COVID-19 epidemic, ignoring the control of other emergencies and limiting the scope of application of our conclusions. Secondly, the data have not been fully mined, and the processing method of high-frequency data still needs to be further improved. Thirdly, the sample data need to be expanded. For example, Amazon and JD can be added as research objects, but it is difficult to obtain and match cross platform commodity information. This is a key issue that needs to be solved in subsequent studies.
Data Availability
The dataset that support the findings of this study can be accessed upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.