Theoretical and empirical foundation of the NARDL model

The theoretical framework of the nonlinear autoregressive distributed lag (NARDL) model is based on the introduction of the asymmetric cointegrating regression model and derives the associated asymptotic theory [19]. NARDL is an econometric model used for analyzing the dynamic relationships between variables in time series data, particularly in the context of nonlinearity [19]. The NARDL model extends the traditional autoregressive distributed lag (ARDL) model by incorporating nonlinearities in the relationships between variables [20, 21]. It allows for asymmetric and nonlinear effects, capturing both short-term and long-term dynamics. This makes it suitable for investigating complex relationships that may exhibit nonlinear patterns, such as threshold effects, asymmetries, or asymmetric adjustment speeds. It draws on the idea that economic variables are interconnected and influenced by their past values, as well as the values of other relevant variables. The key components of the NARDL framework include the lagged values of variables, error correction terms, and various nonlinear functions to capture the nonlinearity in the relationships [19]. The model allows for the estimation and testing of the short-term and long-term effects, as well as the direction and magnitude of these effects, considering potential asymmetries. Researchers and economists utilize the theoretical framework of NARDL to analyze and understand the dynamics between variables in a time series setting. Several studies have employed the NARDL model to analyze the impact of various shocks on economic variables, providing a solid theoretical foundation for its application in this research.

For instance, Aruga [22] used the NARDL model to investigate the effects of the COVID-19 pandemic on the Tokyo wholesale tuna market, and the findings showed that an increase in the hours of stay-at-home during the first SOE had an adverse impact on all three tuna prices in the long run. Jannat et al. [23] applied the NARDL model to examine the impact of international markets on imported and exported non-cereal crops in Bangladesh. They found evidence of asymmetric effects: the world potato and rapeseed prices led to an increase in Bangladesh potato and rapeseed prices when they were increasing. Furthermore, Van Treeck [24] has employed the NARDL model in his analysis of asymmetric wealth effects on United States (US) consumption and found that liquidity constraints and loss-aversion can be reconciled inter-temporally, with the former dominating in the short-run and the latter in the long-run. Delatte and López-Villavicencio [25] applied the NARDL technique in their analysis of long-run asymmetries in the pass-through from exchange rates to consumer prices in developed economies. These studies emphasized the importance of capturing such nonlinearities and asymmetries to gain a comprehensive understanding of the relationship between variables. Overall, the theoretical and empirical framework of NARDL provides a systematic approach for modeling and analyzing nonlinear relationships in time series data, enabling researchers to explore complex dynamics that go beyond the linear assumptions of traditional econometric models.

Furthermore, there are previous studies investigating the impacts of human mobility changes related to COVID-19 on markets other than seafood such as those examining the effects on Japanese fuel prices [26], levels of CO₂ emissions [27], agricultural commodity markets in developing economies [28], and food prices in Europe [29], seafood safety and human health [30], and policy response to COVID-19 in the ASEAN region [31]. For a study examining the impact of the pandemic on Japanese fisheries, Sugimoto et al. [32] surveyed stakeholders of Japanese fisheries including scientists involved in the seafood business and fisheries sector to reveal negative changes in 2020 sales compared to a year earlier caused by the pandemic. However, this study did not use the actual market price of seafood to find out how the pandemic caused impacts on the Japanese seafood market. A report from Global Fishing Watch is also supporting this demand-oriented shock in the Japanese seafood market, showing that fishing hours did not decline during the COVID-19 pandemic in Japan, rather they increased [33]. Thus, the price decline in Japan during the pandemic is similar to the case of fishermen’s impoverishment due to a bumper harvest caused by the decline in demand. Errhalt [33] discussed how Japanese fisheries had to sell fish when domestic demand decreased during the pandemic.

Research gap

Considering the unique nature of the COVID-19 pandemic and its potential impact on seafood prices in Japan, it is reasonable to expect that the shocks experienced in this context may exhibit non-linear and asymmetric effects. The disruption in supply chains (sales volume), changes in the number of COVID-19 cases, and people staying at home during the different state of emergency periods have likely influenced seafood prices differently depending on the product category (cheap vs. luxury). To the best of our knowledge, no previous study has specifically employed the NARDL model to investigate the impacts of COVID-19 on seafood prices in Japan, particularly focusing on the comparison between cheap and luxury products. By adopting the NARDL model, this research aims to fill this gap and contribute to the existing literature by providing a nuanced understanding of the dynamics between COVID-19 shocks and seafood prices, capturing both short-term and long-term effects as well as any potential asymmetries.

To bridge this gap, the present study tests how the cheap and luxury seafood prices at different SOE periods during 2020–2021 in Japan have been influenced by the SOE measures taken to restrict human mobility. Hence, this is one of the pioneer studies to identify how daily prices of luxury and cheap seafood are affected by changes in human mobility during the COVID-19 pandemic. The research aims to answer two primary questions:

1. How does COVID-19 affect seafood consumption patterns at different SOE periods?
2. What are the symmetric and asymmetric effects of the COVID-19 pandemic on the seafood market?

Following this, the first contribution of the study is that the study results provide imperative information for the stakeholders of the seafood market to prepare and deal with shocks that could occur when a similar restriction controlling human mobility is imposed in the future to deal with a crisis like the COVID-19 pandemic. The second contribution is that by comparing the effects (short-run and long-run) of the pandemic on cheap and luxury seafood, the study can provide some evidence on which type of seafood might be more vulnerable to a measure restricting human mobility during the pandemic- whereas early literature on pandemics largely ignored this area.

The four states of emergency and the luxury and cheap seafood markets

The study focuses on the effect of the COVID-19 pandemic on fresh seafood traded at the Toyosu Wholesale Fish Market since this market is one of the world’s largest wholesale seafood markets, replacing the former Tsukiji Fish Market. Another reason for investigating the Tokyo seafood market is that Tokyo is known as the fourth most expensive metropolis in the world and has the highest cumulative number of COVID-19 cases among all Japanese cities [34].

As seen in Fig 1, the first wave of COVID-19 cases in Tokyo, Japan began in March 2020. Since then, the SOE has been announced four times by the Tokyo Metropolitan Government to reduce the number of COVID-19 cases.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Daily COVID-19 cases detected in Tokyo and the SOE periods.

Source: Tokyo Metropolitan Government [45].

https://doi.org/10.1371/journal.pone.0291395.g001

Thus, we picked daily prices per kilogram and daily total trade volumes (kg) of horse mackerel (aji), sardine (iwashi), and mackerel (saba) to represent the prices for cheap popular seafood. In Japan, the three seafood have been traditionally and commonly consumed by households and are known as taishu gyo, which means major popular cheap fish for the masses. As a comparison to the cheap seafood, we also chose daily prices of the three-luxury seafood, Japanese tiger shrimp (kuruma ebi), channel rockfish (kinki or kichiji), and sea urchin (uni). These seafood products are traded in the same category as the cheap seafood examined in this study at the Toyosu wholesale market, fresh seafood, and had a higher average price within the fresh seafood category and are well known as luxury seafood. There are two types of trades in the Toyosu market; negotiation and auction. However, only the tiger shrimp and sea urchins were traded under the auction system so the prices of all other products (horse mackerel, sardine, mackerel, and rockfish) are based on the negotiated trade. In addition, for all products, the daily medium price is used when this price is available, and the average of the high and low prices is applied when the medium price was missing (Table 1).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Description of variables.

https://doi.org/10.1371/journal.pone.0291395.t001

Moreover, we chose the sales prices of different seafood products as the dependent variable and the residential index, sales volume, and COVID-19 parameters as independent variables for our model for several reasons. To make informed decisions, businesses and policymakers must understand the factors influencing seafood prices at different SOE periods. It is possible to gain insight into how these factors affect price determination not only in the short run, but also in the long run, by analyzing the relationship between sales prices and people staying at home (residential index), sales volume, and the number of COVID-19 cases. Moreover, in economic models, sales volume is often used to represent demand [35]. The impact of demand fluctuations on seafood prices can be assessed by incorporating sales volume as an independent variable. On the other hand, the residential index can represent consumer behavior changes, which can offer insights into shifts in demand and supply dynamics during the pandemic. Additionally, COVID-19 influences people’s movements and may capture changes in market conditions, such as disruptions in the supply chain or shifts in consumer preferences due to the pandemic. Studying the relationship between prices, the residential index, sales volume, and COVID-19 variables can provide insights into pricing strategies’ effectiveness. With the residential index, COVID-19, and sales volume as independent variables in a NARDL model, we can provide comprehensive insight into market dynamics, pricing strategies, and the impact of external events such as COVID-19 on seafood prices.

The periods when Tokyo was under the SOE are summarized in Table 2. Since the Tokyo government enacted a semi-SOE where the restaurants’ business hours were limited to 9:00 pm for some of the SOEs like the third SOE (12–24 April 2021 and 21 June–11 July 2021), we anticipate that the impact of SOE on human mobility will be sustained for a given period before and after the SOE. To capture these pre- and post-effects, we designated our SOE periods as those four weeks before and after the SOE and our SOE periods include these pre and post four weeks besides the actual days when the SOE was enforced.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Tokyo’s state of emergency periods during 2020–2021.

https://doi.org/10.1371/journal.pone.0291395.t002

Although the SOE measure conducted in Tokyo was not a harsh lockdown regulation with severe penalties, the business hours of restaurants and bars were regulated from 5 am to 8 pm, large public events were prohibited, and the Tokyo metropolitan government requested companies to have their employees work from home. To capture the changes in human mobility during the SOE periods, we obtained an index measuring the daily changes in the hours of stay in the residential area for Tokyo. The “residential” index obtained from the Google Global Mobility Report is the one used for this purpose, representing the changes in the Tokyo residents’ number of hours spent in the residential area relative to the baseline day defined as the median value between 3 January and 6 February 2020 [36].

Since the SOE restriction affected the restaurants the most, we expect that the effect of reduction in human mobility related to SOE is different between cheap popular seafood mostly consumed at homes and luxury seafood particularly prepared in restaurants [7].

Econometric model

Since the study wanted to identify both the short-run and long-run impacts of the human mobility changes on seafood prices, we applied the auto-regressive distributed lag (ARDL) model proposed by Pesaran et al. [20]. One of the primary motivations for using the ARDL model is that it can provide valid results even with the sample size is relatively small and can prevent omitted variables and auto-correlation problems [20]. Within the ARDL framework, we used the NARDL model developed by Shin et al. [19] to capture the asymmetric adjustment patterns regarding the positive and negative shocks of human mobility on prices.

Based on the prior model developed for investigating the effects of human mobility on the fuel markets [26], the impact of variations in human mobility during the COVID-19 pandemic on cheap and luxury seafood market prices was examined using the following model: (1) where price_t is either one of the daily seafood prices investigated in this study. Similarly, home_t is the stay-at-home index reflecting the changes in human mobility during the SOE periods and volume_t is the total daily volume of trades at the Toyosu market for each of the six seafood products, and COVID is the daily COVID-19 cases in Tokyo. b₁, b₂ and b₃ are the coefficient of the variables.

Before employing the econometric approaches, we conducted both conventional stationarity tests and those with the effect of a structural break in the time series data. For this purpose, we employed the Augmented Dickey-Fuller (ADF), the Zivot & Andrews (ZA) [37], and the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests. Table 3 illustrates the results of these unit root tests. The outcome ensures that none of the underlying series is stationary at the second difference, and all variables are at least stationary at their levels or first differences.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Unit root tests.

https://doi.org/10.1371/journal.pone.0291395.t003

After confirming the unit root result, the NARDL estimation was performed. Initially, the existence of long-run relationships among the price, volume, and home variables was tested through the NARDL bound test for cointegration [38]. The statistically appropriate lag lengths for the NARDL were determined based on the Akaike Information Criterion (AIC).

The NARDL model is based on the following ARDL unrestricted error correction model: (2) where p is the lag of the dependent variable, and q and r are that of the independent variables.

Finally, based on Eq (2), the NARDL model was applied to estimate the relationship presented in Eq (1). For applying the NARDL, the volume and home variables were decomposed into positive and negative cumulative sums. However, the reason to set the lags of the positive and negative partial sums is the same because the variables that we considered are split into negative and positive parts. Therefore, it should be the same number of lags [19].

The positive and negative shocks of changes in the trade volume and hours spent at home are defined below: (3) where S represents the endogenous variables of our interest (home or volume), and and denote the partial sums of positive and negative changes of these variables.

Based on the decomposition in Eq (3), the volume and home in Eq (2) are replaced by the positive and negative partial sums of these variables. Using these variables, the NARDL unrestricted error correction model was estimated under the following equation: (4)

The Breusch–Godfrey test for autocorrelation [39, 40] and the Breusch & Pagan [41] test for heteroskedasticity were used to determine whether the models had serial correlations and heteroskedasticity issues. None of our models featured some serial correlation issue under the 5% significance threshold, as shown by the Breusch–Godfrey (BG) test findings in Table 4. Based on the 1% significance threshold, the Breusch-Pagan-Godfrey (BPG) test indicated that most of our models are homoscedastic, except shrimp at the SOE-1 and the Mackerel (under SOE-2 & SOE-3) model, which had heteroscedasticity. To address the issues of serial correlation and heteroscedasticity, we estimated the ARDL model coefficients using the Newey–West heteroscedasticity and autocorrelation corrected (HAC) standard errors. The cumulative sum (CUSUM) and cumulative sum square (CUSUM square) tests were also used to assess the stability of the NARDL models. Most of the models except for the sardine in the SOE-2 satisfied the stability test (see S1 Fig). EViews 12 was used to run the NARDL model.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. Serial correlation and heteroskedasticity tests.

https://doi.org/10.1371/journal.pone.0291395.t004