Estimation of Demand for Beef Imports in Indonesia: An Autoregressive Distributed Lag (ARDL) Approach

Abstract

Import policies for food products, including beef, need to support national food security while protecting the domestic food industry. This study aims to develop a model for beef import demand of Indonesia. The study employed annual secondary data from various sources from 1990 to 2019. Autoregressive distributed lag (ARDL) and the error correction models (ECM) were adapted for predicting the long-run and short-run beef import demand, by considering income growth, domestic production, relative price, and exchange rate. The bounds test showed that gross domestic product (GDP) growth per capita, domestic beef production, and the exchange rate had no significant effect on the beef import demand in the long run; nonetheless, the relative beef price between local and international market had a considerable impact (5.353%). In the short run, GDP growth per capita and domestic beef production significantly affected beef import demand (0.036% and −0.9%, respectively). Error correction term (ECT) corrected the disequilibrium of the import demand model in current year towards the following year (17.60%). This finding is confirmed by the fully modified ordinary least squares (FMOLS), dynamic ordinary least squares (DOLS), and canonical co-integrating regression (CCR) methods. Ultimately, this study can serve as an instrument for formulating policy related to beef imports in Indonesia.

1. Introduction

Due to population and economic growth, demand for beef is estimated to increase in developing countries [1,2]. Data have shown that Indonesia has experienced a beef shortage in the last three decades (see

Table 1. Import, production, and consumption of beef in Indonesia during the period of 1990–2019.

Year	Beef Import (1000 tons)	Beef Production (1000 tons)	Beef Consumption (1000 tons)	Beef Consumption Per Capita (kg)
1990	4.83	301.15	305.86	1.18
1991	5.34	308.13	313.43	1.19
1992	12.74	333.91	346.46	1.29
1993	13.64	388.59	402.14	1.48
1994	24.62	367.08	391.60	1.41
1995	61.40	308.82	369.61	1.31
1996	102.28	315.49	417.09	1.46
1997	124.88	307.59	432.22	1.49
1998	33.30	367.70	400.70	1.36
1999	74.00	310.50	384.26	1.29
2000	99.02	323.55	422.52	1.40
2001	61.23	343.59	404.57	1.32
2002	49.84	339.16	387.98	1.25
2003	66.81	359.30	421.63	1.34
2004	89.34	416.41	504.46	1.58
2005	99.52	326.39	425.01	1.31
2006	106.16	368.04	473.80	1.44
2007	161.73	275.36	433.70	1.30
2008	206.56	304.26	490.39	1.45
2009	264.13	269.01	532.39	1.56
2010	276.59	313.66	589.60	1.70
2011	176.46	428.41	604.01	1.72
2012	137.00	455.07	590.80	1.66
2013	141.51	464.60	605.62	1.68
2014	220.37	412.05	631.17	1.73
2015	192.35	419.67	611.63	1.66
2016	285.48	419.35	704.35	1.89
2017	284.19	431.18	712.77	1.89
2018	346.61	431.15	775.11	2.03
2019	405.19	429.76	831.35	2.16
Average	137.57	361.30	497.21	1.52

Source: [3].

). Before 1990, Indonesia was able to meet the demand for beef by relying on domestic production. However, since 1990, domestic beef production has started to fall behind the domestic consumption given the increasing trend of domestic consumption, especially after 2015.The upward trend in consumption was driven by an increase in beef consumption per capita with an average increase of 2.45% per year [3]. In 2019, with beef consumption of 831.35 thousand tons or a growth rate of 3.85% per annum, Indonesia imported 405.19 thousand tons of beef to fill the shortage [3]. Given these statistics, dependence on imports is a serious problem and threatens food security in Indonesia. Therefore, efforts to balance domestic demand and supply must be addressed.

According to statistics [4,5], Figure 1 shows that, during the time period of 1990–2019, domestic beef price in Indonesia has been higher than the international market price. This price difference has been increasing over time with a surge in 2010 and then remained large thereafter. In 1999, the domestic price for the consumer was USD 2.86 per kg, or 55.03% higher than the international market price of USD 1.84; in 2019, the domestic beef price for consumer was USD 8.35 per kg, or 75.37% higher than the international market price of USD 4.76 per kg, with the average difference of 74.58% for the entire period. The relatively higher domestic price compared to the international price might be attributed to the high volume of beef imports for Indonesia. In trade theory, the relative price between the domestic price and international price plays a critical role in dictating the direction and volume of trade.

Research has focused on beef import policy in the past decade. One argument is that domestic beef production, a main source of income for farmers [6], should be safeguarded because domestic beef producers can be adversely affected by importation [7]. In Indonesia, around 90% of the cattle were reared by approximately 6.5 million smallholder ranchers living in rural areas [8]. On the other hand, the increasing beef demand drove up the domestic price for beef. The significant difference in beef prices between the domestic market and the international market has been seized by importers to make a fortune by importing massively, which in turn adversely affected smallholder farmers. In order to keep beef prices affordable for the general public as well as protect smallholder farmers, the Minister of Agriculture of Indonesia issued decree number 50/2011 concerning the recommendations for the approval of carcasses, meat, offal, and/or processed meat for beef imported to Indonesia. Through this regulation, the government can control import by setting quotas and regulating import licensing. However, there are obstacles to enforce the regulation, namely politically and technically. The political obstacle, e.g., is the constant pressure from beef-producing countries to lift the quota restrictions. The technical obstacle mainly concerns accuracy in terms of calculating import quotas. The import quota is calculated based on the estimated production on the government balance sheet of and the current demand. For setting the quotas, a critical success factor would depend on the accuracy and measurability of the calculations. An import demand model might be inasmuch as needed to assist policymaking so that food security can be maintained while protecting the wellbeing of smallholder farmers.

A wealth of previous studies have investigated the factors associated with beef cattle import. In addition to the population growth, the increase in demand is also caused by the increased consumption per capita due to the rise in income [9]. Empirical evidence found that China’s beef consumption has grown significantly from 5.0 million tons in 2000 to 7.7 million tons in 2019 due to the country’s strong income growth [10]. Along the line, Hupková et al. [11] reported that declining purchasing power in Slovakia during the 1993–2003 period caused a decline in beef consumption. Similarly, in China, Cheng et al. [12] claimed that real gross domestic product (GDP) has a positive effect on meat import quantity.

Commodity prices may also have a powerful influence on imports. Rudatin [13] using the error correction model (ECM) approach, studied beef imports in Indonesia, revealing that the price of imported beef negatively affects the import demand. On the other hand, the local beef price positively associated with beef import demand. Uzunoz and Akcay [14] used a double logarithmic-linear function to analyze the factors affecting import demand for wheat between 1984 and 2006 in Turkey. They found that import demand significantly reduced domestic production; in addition, the import demand was positively affected by real domestic prices, the GDP per capita, and the exchange rate. Andersson [15], using a vector autoregression (VAR) and a vector error correction model (VECM), reported that domestic production and imported price individually have a negative impact on beef import quantity whereas gross national income gives positive effect on import in both models. Matlasedi [16] attempts to estimate the aggregate import demand in South Africa by exploring relative price and exchange rate. The results showed that import demand in South Africa was influenced negatively by exchange rates and positively by relative prices as well as GDP.

There are several methods to estimate import demand, e.g., ordinary least square (OLS), Eagle Granger, Johansen Test, ECM, and autoregressive distributed lag (ARDL). However, most time-series data are not stationary, using traditional OLS methods will generate false results and be misleading [17]. A cointegration test method developed by Engle and Granger [18] and Johansen and Juselius [19] can determine the relationship between non-stationary variables. The ECM can be obtained if the variables are I(1) and a cointegration relationship exists. However, this test cannot be used when the variables have a mixed order of integration or are non-stationary. This limitation can be overcome by adapting the ARDL model.

The ARDL modeling has become a popular and widely used method to deal with time-series data in various fields [16,20,21,22,23,24,25]. ARDL is an ordinary least square (OLS) model that can analyze non-stationary and mixed order integration for time-series data. A simple linear transformation can generate a dynamic ECM from ARDL. Similarly, the ECM combines short-run dynamics with long-run equilibrium without sacrificing the long-run information, avoiding issues such as spurious relationships caused by non-stationary time-series data. The ARDL approach has many advantages over other methods, i.e., it does not require the stationarity level of data, it can be used for small sample size, it allows a different suitable lag length to be used for each time series, and it can accommodate long-run and short-run models [17,21]. In addition, the ARDL estimation provides unbiased assessment results in the long run [26].

Several studies have estimated beef cattle import demand, e.g., Ratnasari and Sastri [27] used OLS and robust regression method, Ashari and Wibowo [28] used panel data regression, and Rudatin [13] used the Johansen test and ECM. Nonetheless, to the best of the authors’ knowledge, the ARDL approach has not been explored to determine the factors influencing beef import. Therefore, this study aims to fill this gap in the extant literature by developing a model for beef import demand of Indonesia. Based on the literature review, this study therefore adapts the ARDL approach by considering GDP per capita growth, domestic beef production, the relative beef price between the domestic market and international market, and the exchange rate.

The findings of this study could contribute to a more comprehensive understanding of Indonesia’s beef import demand by exploring its determinants. Once the determinants and their impacts of import demand are unveiled, policymakers can accordingly formulate beef import policies towards promoting the triple goals, i.e., meeting the domestic demand, lowering the domestic beef price, and protecting smallholder farmers. In other words, beef demand can be satisfied for domestic consumers, while domestic beef price is at a reasonable level such that smallholder cattle farmers can earn a fair return and the general public can afford to consume beef.

2. Materials and Methods

2.1. Data Collection

This study uses a secondary time-series annual data obtained from various sources for the time period of 1990–2019, including beef import quantity, the growth of GDP per capita, the domestic beef production, the domestic beef price, the international beef price, and the exchange rate of Indonesian Rupiah (IDR) against the US dollar currency.

Table 2. The descriptive statistics of the variables for the time period of 1990–2019.

Variable	Beef Imports (000 Ton)	GDP per Capita Growth (%)	Domestic Beef Production (000 Ton)	Domestic Beef Price (USD)	International Beef Price (USD)	Exchange Rate (IDR to USD)
Mean	137.570	3.491	361.298	5.239	2.949	8236.029
Median	104.219	4.046	351.441	4.405	2.610	9150.158
Maximum	405.191	6.562	464.599	8.664	4.949	14,236.940
Minimum	4.826	−14.351	269.012	1.559	1.726	1842.813
Std. Dev.	107.714	3.613	56.952	2.288	1.020	4079.235
Skewness	0.757	−4.212	0.229	0.362	0.592	−0.442
Kurtosis	2.715	21.327	1.749	1.624	1.920	2.016
Observations	30	30	30	30	30	30

Source: [3,4,5,29,30]. Note: GDP = gross domestic product; USD = United States Dollar; IDR = Indonesia Rupiah.

summarizes the descriptive statistics of the variables used in this study. During the study period, on average, Indonesia imported 137.570 thousand tons of beef with domestic beef production of 361.298 thousand tons on the annual basis. GDP per capita in Indonesia experienced an average growth rate of 3.491%. Furthermore, the mean domestic price of beef for the consumer is USD 5239 per kg, higher than the international market price of beef by USD 2949 per kg.

2.2. Model Specification

This study assumes that beef imports in Indonesia is determined by per capita income growth, domestic beef production, the relative beef price of domestic market to international market, and exchange rate. That is, this study investigates a multivariate framework as expressed in Equation (1).

LnImp = f(GDPGrowth, LnProd, LnRelPric, LnExRate)

(1)

where Ln denotes the natural logarithm of variables, Imp denotes beef import quantity, GDPGrowth represents the growth rate of GDP per capita, Prod represents the domestic beef production, RelPric stands for the relative price of beef (local beef price divided by international beef price), and ExRate is the exchange rate of IDR against USD. A log-linear import demand function based on Equation (1) can be written as Equation (2).

$$LnIm{p}_t={\theta }_0+{\theta }_{1}GDPGrowt{h}_t+{\theta }_{2}LnPro{d}_t+{\theta }_{3}LnRelPri{c}_t+{\theta }_{4}ExcRat{e}_t+{\epsilon }_t$$

(2)

2.3. Data Analysis

In the time-series analysis study, the first step is to perform a unit root test to determine the order of integration variables. The stationarity test needs to be performed so that the ARDL model would not crash in an incorporated stochastic pattern of second difference I(2) [17]. A unit root analysis was adopted to validate the time-series data using the basic version of the Augmented Dickey–Fuller (ADF) unit root test proposed by Dickey and Fuller [31] as well as the Philips–Perron (PP) test developed by Phillips and Perron [32].

The study inspects the cointegration relationship among the variables using the ARDL bounds test developed by Pesaran et al. [33]. The bounds testing method for ARDL was chosen instead of, for example, the Engle and Granger [18] and Johansen and Juselius [19] approaches, because it can be performed in a different order of stationarity. The ARDL approach can also simultaneously estimate the long-run and short-run parameters of the model. The ARDL bounds test can be expressed as Equation (3).

$$\begin{gathered} ∆LnIm{p}_t={\theta }_0+{{\displaystyle \sum }}_{i=1}^p{\theta }_1∆LnIm{p}_{t-1}+{{\displaystyle \sum }}_{i=1}^q{\theta }_2∆GDPGrowt{h}_{t-1}+{{\displaystyle \sum }}_{i=1}^r{\theta }_3∆LnPro{d}_{t-1}+ \\ {{\displaystyle \sum }}_{i=1}^s{\theta }_4∆LnRelPri{c}_{t-1}+{{\displaystyle \sum }}_{i=1}^t{\theta }_5∆LnExrat{e}_{t-1}+{\theta }_{6}LnIm{p}_{t-1}+{\theta }_{7}GDPGrowt{h}_{t-1}+{\theta }_{8}LnPro{d}_{t-1}+ \\ {\theta }_{9}LnRelPri{c}_{t-1}+{\theta }_{10}LnExrat{e}_{t-1}+{\epsilon }_t \end{gathered}$$

(3)

where θ₀ stands for the constant, θ₁–θ₅ are the short-run coefficients, θ₆–θ₁₀ are the long-run coefficients, ε_t is the error term, and (p, q, r, s, t) represent the number of lags for each one of the variables included in the model

The hypothesis for the cointegrated test is represented in

Table 3. Hypothesis for the bound test.

Model	Null Hypothesis (H0)	Alt. Hypothesis (H1)
Equation (3)	${\theta }_6={\theta }_7={\theta }_8={\theta }_9$$={\theta }_{10}$	${\theta }_6\ne {\theta }_7\ne {\theta }_8\ne {\theta }_9\ne {\theta }_{10}$

. Narayan [34] proposes two critical values in the cointegration test. The H₀ is rejected when the measured F-statistic exceeds the upper bound critical value, indicating that the variables in the model are cointegrated. If the F-statistic is less than the lower bound critical value, the H₀ cannot be rejected, which indicates that the variables are not cointegrated. The findings are inconclusive if the measured F-statistic (Wald-test) falls between the lower and upper bounds.

In this study, ECM was developed to measure the speed of variables towards equilibrium in the long run. ECM is the lagged OLS residuals obtained from running the long run model. Consequently, Equation (4) can express the ARDL version of the ECM for the import demand model.

$$\begin{gathered} ∆LnIm{p}_t={\theta }_0+{{\displaystyle \sum }}_{i=1}^p{\theta }_1∆LnIm{p}_{t-1}+{{\displaystyle \sum }}_{i=1}^q{\theta }_2∆GDPGrowt{h}_{t-1}+{{\displaystyle \sum }}_{i=1}^r{\theta }_3∆LnPro{d}_{t-1}+ \\ {{\displaystyle \sum }}_{i=1}^s{\theta }_4∆LnRelPri{c}_{t-1}+{{\displaystyle \sum }}_{i=1}^t{\theta }_5∆LnExrat{e}_{t-1}+\lambda EC{T}_{t-1}+{\epsilon }_t \end{gathered}$$

(4)

where λ explains the speed of change, and

$$EC{T}_{t-1}={\theta }_{6}LnIm{p}_{t-1}+{\theta }_{7}GDPGrowt{h}_{t-1}+{\theta }_{8}LnPro{d}_{t-1}+{\theta }_{9}LnRelPri{c}_{t-1}+{\theta }_{10}LnExrat{e}_{t-1}+{\epsilon }_t$$

(5)

Since the regression models attempt to eliminate errors, residual diagnostics is the most critical component of diagnostic testing in economic modeling [35]. Serial correlation, the natural distribution of residuals, and heteroscedasticity problems were tested using residuals diagnostic tests. The linearity was tested using Ramsey’s RESET test. The stability was analyzed using cumulative sum (CUSUM) and cumulative sum square (CUSUMQ) tests proposed by Borensztein et al. [36], Alimi [22], and Dogan [21].

In addition to the ARDL approach, this study also employs the fully modified least squares (FMOLS), dynamic least squares (DOLS), and canonical cointegrating regression (CCR) methods. These methods were utilized to test the consistency and robustness of the ARDL model’s long-term elasticities [37]. Furthermore, the FMOLS, DOLS, and CCR approaches eliminate the endogeneity bias and serial correlation issues [38,39].

3. Results

3.1. The Unit Root Test

The unit root test is subjected to both order levels and the first differences in all variables. The results of two-unit root tests (ADF and PP) are displayed in

Table 4. Unit root test results.

Unit Root Test Method	Variable	Level		First Differences
		Intercept	Intercept and Trend	Intercept	Intercept & Trend
ADF	LnImp	−2.324	−2.889	−4.264 **	−5.455 **
	GDPGrowth	−3.870 **	−3.824 *	−3.11 *	−2.300
	LnProd	−2.349	−2.935	−6.641 **	−6.513 **
	LnRelPric	−4.143 **	−4.747 **	−5.176 **	−3.055
	LnExrate	−1.590	−1.789	−5.567 **	−2.861
PP	LnImp	−2.763	−3.082	−5.309 **	−5.501 **
	GDPGrowth	−3.807 **	−3.703 *	−15.572 **	−16.125 **
	LnProd	−2.285	−2.997	−9.264 **	−9.212 **
	LnRelPric	−4.108 **	−4.793 **	−11.319 **	−13.468 **
	LnExrate	−1.590	−1.761	−5.569 **	−5.615 **

*, ** denote the 5% and 1% levels, respectively. Note: ADF = Augmented Dickey–Fuller; PP = Philips–Perron.

. Both ADF and PP unit root tests yield similar results. The stationarity test clearly shows that none of the variables is I(2). All variables are stationary at their level or their first differences. Due to the level of stationarity that occurs in a mixture of order levels I(0) and I(1), the ARDL method is therefore suitable for the analysis.

3.2. ARDL Model Estimation

The Akaike information criteria (AIC) can assist the selection of the best model [40]. The final model used in this paper was an ARDL (1,1,1,0,0), i.e., the dependent variable (Imp) has one lag; the independent variables, GDP growth per capita and beef production, (Prod) have one lag; and the relative prices (RelPric) and exchange rate (Exrate) have zero lag.

Table 5. The estimated results of the ARDL (1,1,1,0,0) model.

Regressor	Coefficient	Standard Error	t-Statistic	p-Value
LnImpt-1	0.824 **	0.094	8.747	0.000
GDPGrowth	0.036	0.018	2.061	0.052
GDPGrowtht-1	−0.032 *	0.014	−2.244	0.036
LnProd	−0.900 *	0.394	−2.284	0.033
LnProdt-1	0.973 *	0.397	2.449	0.023
LnRelPric	0.940 **	0.321	2.926	0.008
LnExrate	−0.047	0.149	−0.318	0.754
C	0.402	1.903	0.211	0.835
R2 = 0.965	Adj R2 = 0.954	DW = 1.859	F stat = 83.877 **

*, ** denote the 5% and 1% levels, respectively.

shows the estimated results of the ARDL model. This ARDL model is significant (F statistics = 83.877) and had no autocorrelation problems (DW = 1859). The ARDL model also has high explanatory power given R² = 0.965, indicating that the 96.5% variations in beef imports in Indonesia can be explained by the chosen independent variables.

3.3. ARDL Cointegration Test

The bounds test was used to verify the cointegration that indicates a long-term relationship in the model.

Table 6. Bounds test results.

Lag Length	F-Statistic	k	Critical Value						Outcome
			1%		5%		10%
			Upper Bound	Lower Bound	Upper Bound	Lower Bound	Upper Bound	Lower Bound
ARDL (1,1,1,0,0)	5.623	4	6.670	4.768	4.774	3.354	3.994	2.752	Cointegrated

Note: ARDL = autoregressive distributed lag.

presents the results of the bounds test. Since there are four regressors in the model, i.e., K = 4, at the 95% confidence interval (CI), the F-statistic of Wald test = 5.623, higher than upper bound critical value of 4.774 [35]; therefore, the null hypothesis is rejected to favor the alternative hypothesis. It can be concluded that the variables in the import demand model are cointegrated or have a long-run relationship.

3.4. The Long-Run and Short-Run ARDL Import Demand ECM

Given that cointegration between variables in the ARDL model exists, the next step is to estimate the long-run and short-run models, and the results are shown in

Table 7. The results of long-run and short-run ARDL import demand model.

Variable	Coefficient	Std. Error	t-Statistic	Prob.
Long-run
GDPGrowth	0.023	0.111	0.204	0.841
LnProd	0.417	1.973	0.211	0.835
LnRelPric	5.353 *	2.363	2.265	0.034
LnExcRate	−0.270	0.976	−0.277	0.785
Short-run
C	0.402 **	0.056	7.195	0.000
ΔGDPGrowth	0.036 **	0.010	3.562	0.002
ΔLnProd	−0.900 *	0.323	−2.783	0.011
ECTt-1	−0.176 **	0.030	−5.786	0.000
R2	0.804
Adjusted R2	0.781
F-statistic	34.215 **

*, ** denote the 5% and 1% levels, respectively.

. The long-run and the short-run coefficients are consistent regarding the signs and magnitude.

The results show that relative price exerts a positive impact on beef imports in Indonesia at a 5% significance level while per capita income growth, domestic beef production, and exchange rate are not statistically significant. The results suggest that a 1% increase in relative beef prices will increase beef imports by 5.353%, which is not only in line with previous studies by Uzunoz and Akcay [14], Rudatin [13], Cheng et al. [12], Andersson [15], and Matlasedi [16], but also echoes the trade theory. In this study, the relative price is defined as the ratio of the domestic beef price to the beef price in the global market. Therefore, the higher the relative price is, the more import demand is because it is relatively cheaper to buy beef from overseas. Two factors might be attributed to the high relative prices for beef in Indonesia, one is the shortage caused by low domestic production, as a consequence, the market price for beef is pushed up; the other is inefficiency in the supply chain channel coupled with the existence of cartel trade [41]. Setiaji et al. [42] also pointed out that market inefficiency in the beef supply chain is due to an oligopoly caused by cartel involvement in Indonesia.

Regarding the short-run model, as expected, it is found that income growth and domestic production have a positive and negative impact on beef import, respectively. A 1% increase in GDP growth per capita will lead to a slight increase of 0.036% in beef imports, which is consistent with previous literature, e.g., Uzunoz and Akcay [14], Permani [9], Cheng et al. [12], Matlasedi [16], and Zhu et al. [10]. On the other hand, a 1% increase in domestic production will instead decrease beef imports by 0.9%. This finding is in agreement with the previous studies by Andersson [15], and Uzunoz and Akcay [14] reporting that domestic production contributes to a decline in imports. Finally, the error correct term is found to be negative and significant (−0.176), indicating that the speed of adjustments towards long-run equilibrium is 17.56% annually.

In sum, the shortage of domestic beef production might be the primary driver of high domestic beef price and thereupon stimulates more beef imports. Forasmuch, enhancing domestic beef production must be the top priority to curtail beef imports. As suggested by Komalawati et al. [43], beef imports should only be a short-term solution to the shortage of beef supply in Indonesia. Beef production can be increased in several ways, e.g., recruiting more farmers, increasing cattle population, and improving cattle productivity. According to Said [44], beef cattle productivity in Indonesia is still low because of a low reproductive rate, low conception rate (56%), high calf mortality (5–10%), lengthy calving interval (18–21 months), and poor cattle health. Adapting technological innovation to improve productivity could be an effective way to reduce the dependence on imports. Furthermore, Agus and Widi [8] stated that efforts should be made to limit productive female cattle being slaughtered, improve breeding and reproduction technologies and feeding technology, develop beef cattle raising-related technology, empower cattle farmers, facilitate technology transfer, intensify the fattening system, and promote cattle–crop integration. However, given the fact that the cattle industry contributes a significant amount of greenhouse gases, the alternative sources of protein, e.g., plant-based protein, insect, and in vitro meat, shall be considered and promoted by the government.

3.5. Results of the Diagnostic Tests

Table 8. ARDL diagnostic test.

LM Test Statistic	Result	Critical Value (5%)	Probability
Normality using Jarque-Bera (χ2)	0.188	3.841	0.910
Serial correlation LM using Breusch–Godfrey (χ2)	0.036	3.841	0.819
Heteroscedasticity using Breusch–Pagan–Godfrey (χ2)	0.899	14.067	0.462
Linearity test (Ramsey’s Reset test)	0.241	2.086	0.812

shows the results of the diagnostic test. The ARDL model passed the linear regression assumptions, i.e., residual normality, serial correlation, heteroscedasticity, and linearity. The test statistic of the Jarque–Bera test is 0.188 (<χ2 critical value, 3.841); therefore, the null hypothesis cannot be rejected, suggesting that the residuals in the model are normally distributed. Meanwhile, the result of the Breusch–Godfrey test is 0.036 (<χ2 critical value, 3.841), indicating that the model has no autocorrelation problem. The model also does not seem to be heteroscedastic based on the Breusch–Pagan–Godfrey test (χ2 = 0.899 < χ2 critical value, 14.067). As shown in the linearity test, the dependent and independent variables are also linear (t = 0.241 < t critical value, 2.086).

The structure stability in the model was tested using the cumulative sum (CUSUM) and cumulative sum of squares (CUSUMSQ), as shown in Figure 2. The ARDL model was stable when the plots of CUSUM and CUSUMSQ were within the critical limits at the 5% significance level.

3.6. Results of Alternative Assessment Techniques

The FMOLS, DOLS, and CCR results were almost similar to those of the ARDL long-run model, which demonstrates the robustness of the ARDL model. According to these three methods, a 1% increase in the relative price of beef raises beef imports by 3.532%, 4.272%, and 3.369% at the 1% significance level (

Table 9. Results of alternative approaches (dependent variable: lnImp).

Variables	LnImp (Dependent Variable)
	FMOLS Model		DOLS Model		CCR Model
	Coefficient	t-Statistic	Coefficient	t-Statistic	Coefficient	t-Statistic
GDPGrowth	−0.074	−2.012	0.086	0.488	−0.135 *	−2.081
LnProd	0.295	0.439	−0.665	−0.728	0.813	1.169
LnRelPric	3.532 **	5.970	4.272 **	3.163	3.369 **	4.651
LnExcRate	0.988 **	5.761	0.823	1.924	0.815 **	4.737
C	−7.688 *	−2.114	−1.631	−0.398	−8.603 *	−2.394
R2	0.792		0.960		0.681
Jarque-Bera	1.785 (0.410)		0.230 (0.891)		6.631 (0.036)

*, ** denote the 5% and 1% levels, respectively.

). Thus, the FMOLS, DOLS, and CCR models supported the ARDL long-run model.

4. Conclusions and Implications

This study aims to establish an import demand model for beef in Indonesia by taking into consideration of the GDP growth per capita, beef production, the relative price of beef between the local market and the international market, and the exchange rate using an ARDL approach for the time period of 1990–2019. The cointegration test was performed for the investigation and the error correction model was estimated to examine the short-run relationship among the variables. Finally, the analyses of the FMOLS, DOLS, and CCR were conducted to confirm the robustness of the ARDL model’s long-term effects.

The findings of the bounds test revealed that beef imports and its determinants have a long-run equilibrium relationship. The results of the long-run and short-run models are consistent with economic theory and previous studies. This study identified a relationship between the beef production against imports in the short run. Beef imports can be reduced by 0.9% if domestic beef production increases by one percent. Moreover, the results also show that, in the long run, the import demand will be increased by 5.353% when the relative price of beef increases by one percent. However, the exchange rate does not affect the import demand in both the short-run and long-run models. Disequilibrium on the import demand model in the current year will be corrected in the following year by an adjustment speed of 17.6%. In addition, the results of FMOLS, DOLS, and CCR analyses are also consistent with the long-run model.

High level of beef imports in Indonesia has caused a series of problems in the past decades, i.e., creating a source of the trade deficit, increasing carbon footprint through importation, crippling local cattle industry, impoverishing smallholder cattle farmers, causing harm on domestic food safety net, etc. Although the caused problems are presently extensively, the results of this study unveil that the high relative beef price and low domestic production are the main factors contributing to the high level of beef imports. These findings can provide useful information for assisting the government’s efforts to lower the volume of beef imports. That is, the Indonesian government can exercise the policy instruments that aim to increase domestic production, which in turn can expect to lower the domestic beef price or the relative beef price of the local market to the global market. To be more specific, domestic production can be increased by adopting new technology innovation for insemination and feeding, which can further improve the calving interval and cattle productivity. On the other hand, market price information should be made available and transparent at all levels in the supply chain so that the market mechanism can fully function. In addition, domestic prices must also be monitored by encouraging and supervising all stakeholders in the supply chain to engage in economic activities that bring fair returns.

There are several limitations in this study. First, the annual data are used for analyses. Accordingly, the results are pertaining to the average annual beef import demand, which cannot reflect the seasonal or monthly variation within a year. Second, due to data availability, a 30-year annual time-series data set is used in this study, there are some important variables that have not been included in the model, e.g., prices or quantity of substitute meats such as poultry and seafood. This is because the addition of variables will have an impact on reducing the degree of freedom which will ultimately affect the validity and reliability of the model. Therefore, this study can be further modified by using quarterly or monthly data to accommodate several other important variables.