The dynamic effects of price delays on soybean production in Türkiye

Os efeitos dinâmicos dos atrasos nos preços sobre a produção de soja na Turquia

ABSTRACT:

This study examined the relationship between soybean production and soybean prices in Türkiye during 2000-2023 using distributed lag models such as Koyck and Almon. Soybean production was considered as the dependent variable, while the price series, composed of current and lagged soybean prices, was used as the explanatory variable. According to the results of the Koyck model, soybean production has been influenced by price changes up to seven years in the past. It takes approximately 7.5 years for changes in soybean prices to significantly impact production levels. The explanatory power of lagged price changes in soybean production changes was found to be 81%. Additionally, the model results also indicated that an increase of 1 TL increase in soybean prices leads to an approximate increase of approximately 54 tons in production, while an increase of 1 TL in the price from the previous period increases production by 48 tons. The results suggested that soybean production responds to price signals with a long adjustment period. By quantifying the dynamic response of soybean production to price signals, this study provided policy-relevant insights into the effectiveness of agricultural pricing mechanisms in reducing Türkiye’s structural dependence on soybean imports. However, the analysis conducted using the Almon model revealed that the model was not statistically significant. According to the model, only 37% of the variation in soybean production can be explained by changes in lagged prices. Examining the model coefficients showed that prices in previous periods positively influence current production levels. Soybeans, which rank among the most imported oilseed crops in Türkiye and hold strategic importance, particularly for the feed industry. However, domestic soybean production remains well below the level required to meet current demand. Despite recent increases in support for soybean production, the limited competitiveness of soybeans against alternative crops in the regions where they are grown restricts the desired expansion of production.

Key words:
soybean; Koyck model; Almon model; distributed lag models

RESUMO:

Este estudo examinou a relação entre a produção e os preços da soja na Turquia durante o período de 2000 a 2023, utilizando modelos de defasagem distribuída, como os de Koyck e Almon. A produção de soja foi considerada a variável dependente, enquanto a série de preços, composta pelos preços atuais e defasados da soja, foi utilizada como variável explicativa. De acordo com os resultados do modelo de Koyck, a produção de soja foi influenciada por variações de preços de até sete anos no passado. São necessários aproximadamente 7,5 anos para que as variações nos preços da soja impactem significativamente os níveis de produção. O poder explicativo das variações de preços defasadas nas variações da produção de soja foi de 81%. Além disso, os resultados do modelo também indicaram que um aumento de 1 TL no preço da soja leva a um aumento aproximado de 54 toneladas na produção, enquanto um aumento de 1 TL no preço em relação ao período anterior aumenta a produção em 48 toneladas. Os resultados sugerem que a produção de soja responde aos sinais de preço com um longo período de ajuste. Ao quantificar a resposta dinâmica da produção de soja aos sinais de preço, este estudo forneceu informações relevantes para políticas públicas sobre a eficácia dos mecanismos de precificação agrícola na redução da dependência estrutural da Turquia em relação às importações de soja. No entanto, a análise realizada utilizando o modelo de Almon revelou que o modelo não foi estatisticamente significativo. De acordo com o modelo, apenas 37% da variação na produção de soja pode ser explicada por mudanças nos preços defasados. O exame dos coeficientes do modelo mostrou que os preços em períodos anteriores influenciam positivamente os níveis de produção atuais. A soja, que está entre as oleaginosas mais importadas pela Turquia, possui importância estratégica, particularmente para a indústria de ração animal. No entanto, a produção doméstica de soja permanece bem abaixo do nível necessário para atender à demanda atual. Apesar dos recentes aumentos no apoio à produção de soja, a limitada competitividade da soja em relação a culturas alternativas nas regiões onde é cultivada restringe a expansão desejada da produção.

Palavras-chave:
soja; modelo de Koyck; modelo de Almon; modelos de defasagem distribuída

INTRODUCTION

Soybeans are considered a vital food source due to their high protein content. They are often utilized as meal or cake after oil extraction, which is a process that results in a by product that is highly nourishing. While soybean oil is the most widely produced and consumed vegetable oil on a global scale, soybean meal is the most utilized raw material in the feed industry (NAZLICAN, 2006). Despite having favorable climatic conditions for soybean cultivation, the level of production in Türkiye has not reached the desired level. This is mainly due to the crops being predominantly cultivated as a second crop and farmers opting for alternative crops with lower production costs. (USDA, 2025).

Although, soybean production in Türkiye has not followed a constantly stable trend, production quantities have exhibited periodic fluctuations largely influenced by weather conditions, market dynamics, and agricultural support policies. According to data from the Turkish Statistical Institute (TURKSTAT), soybean production increased by 47% (180,000 tons) in 2013 compared to the last year. However, production followed a volatile pattern in following years, rising again to 182,000 tons in 2021. This upward trend; however, could not be continued; by 2023, production had declined by approximately 11.3%, falling to 137,500 tons (TURKSTAT, 2024). Türkiye is a net importer in soybean trade, and soybeans rank first among imported oilseed crops.

A foundational subject in economic research pertains to the impact of price fluctuations on the production of goods and services. From an economic perspective, an increase in market prices is theoretically expected to result in a rise in production. This relationship has been thoroughly examined both conceptually and empirically, particularly in the context of agricultural commodities, across different spatial (e.g., crop types, geographic regions) and temporal (e.g., time series, trends, panel data analyses) dimensions. In this view, various theories (e.g., Cobweb Theorem) and economic models have been developed to enhance comprehension of production behavior. These models have been used to generate forecasts, conduct policy analyses, and draw inferences regarding production strategies. The primary objective of a rational producer is to maximize income derived from one or more products, and to achieve this under the most favorable pricing conditions. Consequently, when the other factors remain constant (ceteris paribus), producers are expected to increase output during periods of high prices, whereas production tends to decrease when prices are low (DE SILVA et al., 2014).

In this context; however, the variable of time carries greater significance, and the prevalence of the delay between the determination of production and prices plays a key role in decision-making (GUJARATI, 2004). In the field of economics, scholars have recently begun to examine production-price relationships in the economy, economists have increasingly tended to examine such relationships for agricultural products by considering the fact that the production process requires a certain amount of time to respond to changes in prices. Accordingly, it has been emphasized that the lagged response of prices in influencing production decisions must be considered (DE SILVA et al., 2014). Distributed lag models are among the most used methods in time series analysis for the examination of dynamic relationships. These models are particularly favored for analyzing the impact of prices on agricultural production decisions and have been successfully applied in various studies to estimate the relationship between production quantity and prices. A substantial corpus of literature exists within the international academic domain that investigates the relationship between agricultural product prices using distributed lag models.

There are many studies in literature on it. The Koyck and Almon distributed lag models have been successfully applied in numerous studies to examine the relationship between agricultural production and prices. YURDAKUL (1998) conducted an analysis of the relationship between cotton production and prices using both the Koyck and Almon models with data from the period 1985-1997. Similarly, DIKMEN (2006) studied tobacco and ERDAL et al. (2009) analyzed the relationship between potato production and prices under free market conditions in Türkiye, also using the Koyck model. GÜNDÜZ et al. (2009) determined the effect of lagged prices on the production of edible legumes (chickpeas and lentils) in Türkiye and concluded that lagged prices had no significant effect on their production while DOĞAN & GÜRLER (2013) examined the influence of prices on onion production. In the context of international literature, DE SILVA et al. (2014) examined the relationship between black tea production and prices in Sri Lanka, while HASAN & KHALEQUZZAMAN (2015) investigated the correlations between garlic production and prices in Bangladesh. Both studies used the Koyck model. GÜRER (2020) employed the Koyck and Almon models to evaluate the lagged effects of livestock subsidies on the value of livestock production. ÖZSAYIN (2017) investigated the relationship between milk production and prices, while AVCIOĞLU & AKSOY (2021) analyzed the correlation between pistachio production and income in Türkiye. TURGUT et al. (2023) studied the relationship between sunflower production and prices, and ÇUKUR & ÇUKUR (2023) examined the price-production relationship for almonds using the Koyck model. Similarly, ÇUKUR et al. (2023) employed this model to investigate the effect of prices on walnut production. Despite the growing international application of these models, there is a lack of studies in Türkiye has been observed that specifically examine product price relationships using both the Koyck and Almon models.

This is examined the relationship between soybean production quantities and prices in Türkiye during the period 2000-2023. This study emploeds the Koyck and Almon approaches to analyze and compare using distributed lag models

MATERIALS AND METHODS

Conceptual framework

This study determined the relationship between soybean production and soybean prices by using Dynamic Distributed Lag Models. Specifically, the Koyck and Almon approaches have been applied. In the analysis, soybean production quantity is considered the dependent variable, while soybean price is considered as the independent variable. The study encompasses the period from 2000 to 2023. Soybean prices are expressed as farmgate prices (TL/kg), and the Consumer Price Index (CPI) was used to adjust the price series for inflation. The time series data on soybean production and prices were obtained from the Turkish Statistical Institute (TURKSTAT, 2024).

In the context of regression analysis concerning time series data, the term “Distributed Lag Model” is used when the model included not only the current values but also the lagged (past) values of the explanatory variables. When a model incorporates lagged values of the dependent variable as regressors, it is classified as an autoregressive model, distinguishing it from models that only include lagged independent variables. Autoregressive and Distributed Lag Models are widely used in econometric analysis (GUJARATI, 2004).

Y = α + βX_t + βX_{t - 1} + βX_{t - 2} + u_t (1)

The model previously presented is an example of a distributed lag model, the following equation is an example of an autoregressive model.

Y_t = α + βX_t + γY_{t - 1} + ut (2)

The distributed lag model is a type of dynamic model used to analyze the lagged effects of an independent variable (X) on a dependent variable (Y) over time. This model enabled the visualization of the temporal diffusion of a causal relationship by revealing how a one-unit change in X influences Y across different time periods. Distributed lag models are generally classified into two main categories: finite lag models and infinite lag models (SITORUS, 2023). The inclusion of lagged variables in econometric models is often justified by behavioral, technical, and institutional factors-for instance, gradual shifts in consumer preferences, technological adjustment delays, and contract-based rigidities in input procurement. Given that these factors cause economic variables to exert their effects over time, it is essential to account for lagged effects in modeling. One commonly used variant of infinite distributed lag models is the geometric lag model, often known as the Koyck specification. This approach assumed that the influence of lagged values of the independent variable declines exponentially as the lag length increases, capturing a gradually diminishing impact over time. (GUJARATI, 2004).

Estimation of the coefficients in the distributed lag model

Y_t= α + β₀X_t+β₁X_{t - 1}+ ... +β_pX_{t - k}+ u_t (3)

β_k= β_o 𝜆^k where, k = 1, 2, 3,….

When the Koyck model is applied, it yields the following infinite distributed lag model:

𝑌𝑡 = 𝛼 + 𝛽₀𝑋_𝑡 + 𝛽₀𝜆𝑋_{𝑡 - 1} + 𝛽₀𝜆²𝑋_{𝑡 - 2} + 𝛽₀𝜆³𝑋_{𝑡 - 3} + ... + 𝛽₀𝜆^𝑘𝑋_{𝑡 - 𝑘} + u_𝑡 (4)

By lagging the Koyck model by one period and multiplying it by λ, the following equation is obtained:

𝜆𝑌_𝑡-1 = 𝛼𝜆 + 𝛽₀𝜆𝑋_{𝑡 - 1} + 𝛽₀𝜆²𝑋_{𝑡 - 2} + 𝛽₀𝜆3𝑋_{𝑡 - 3} + 𝛽₀𝜆⁴𝑋_{𝑡 - 4} + ... + 𝛽₀𝜆^{𝑘 + 1}𝑋_{𝑡 - 𝑘 - 1} + 𝜆u_{𝑡 - 1} (5)

When equation 3 is derived from equation 2, the following holds:

𝑌_𝑡 -𝜆𝑌_{𝑡 - 1} = 𝛼 - 𝛼𝜆 + 𝛽₀𝑋_𝑡 + 𝛽₀𝜆^𝑘𝑋_{𝑡 - 𝑘} + u_𝑡 - 𝜆u_{𝑡 - 1} (6)

When k → ∞, 𝜆𝑘⁺¹ → 0, thus

𝛽₀𝜆^{𝑘 + 1}𝑋^{𝑡 - 𝑘 - 1} → 0

𝑌_𝑡 - 𝜆𝑌_{𝑡 - 1} = 𝛼 - 𝛼𝜆 + 𝛽₀𝑋_𝑡 + 𝛽₀𝜆^𝑘𝑋_{𝑡 - 𝑘} + u_𝑡 - 𝜆u_{𝑡 - 1} (7)

𝑌_𝑡 = 𝛼(1 - 𝜆) + 𝜆𝑌_{𝑡 - 1} +𝛽₀𝑋_𝑡 + u_𝑡 - 𝜆u_{𝑡 - 1} (8)

𝑌_𝑡 = 𝛼∗ + 𝜆𝑌_{𝑡 - 1} + 𝛽₀𝑋_𝑡 + 𝑉_𝑡 (9)

Here, α* = α(1 - λ) and Vt = ut - λut - ₁

By estimating the values of α∗, 𝛽₀, and λ, we can then estimate the values of α and the other β’s as follows:

$\widehat{a}=\frac{\widehat{𝛼}}{k-1}$ (GUJARATI & PORTER, 2009).

The Almon approach in distributed lag models

The Almon model is a highly effective method for modeling lagged effects in time series analyses. This phenomenon is particularly prevalent in the domains of policy evaluations, economic forecasting, and financial modeling. The employment of variations and refined estimators of the model offers advantages in addressing issues such as multicollinearity. Consequently, the Almon model and its derivatives hold a significant place in econometric analysis. Although, the Koyck distributed lag model is commonly used in practice, it relies on the assumption that the β coefficients decline geometrically as the lag length increases. In the Almon scheme, the dependent variable Y is regressed not on the original X variables but on the constructed variables Z. Consequently, the obtained estimates of α and a_i will possess all the desired statistical properties, provided that the stochastic disturbance u term satisfies the classical linear regression model assumptions. From this perspective, the Almon technique has a distinct advantage over the Koyck method. The Koyck model is confronted with significant estimation challenges stemming from the inclusion of the stochastic explanatory variableY_t-1 and the potential correlation between the disturbance term and this lagged dependent variable. After estimating the coefficients, a from equation 5, the original β coefficients can be estimated from equation 3 as follows:

${\widehat{B}}_0={\widehat{a}}_0$

${\widehat{B}}_1={\widehat{a}}_0+{\widehat{a}}_1+{\widehat{a}}_2$

${\widehat{B}}_k={\widehat{a}}_0+k{\widehat{a}}_1+k^2{\widehat{a}}_2$

One of the primary practical issues to address before applying the Almon lag model is the prior determination of the maximum value of the lag length, denoted as k. Information criteria are designed to measure the amount of information about the dependent variable contained in each set of regressors. They serve as goodness-of-fit measures similar in nature to the R² statistic. The two most widely used criteria are the Akaike Information Criterion (AIC) and the Schwarz/Bayesian Information Criterion (SBIC). These criteria are generally computed in logarithmic form using the following formulas.

$AIC=-2\ast ln\left(L\right)+2\ast k$

$BIC=-2\ast ln\left(L\right)+2\ast ln\left(N\right)\ast k$

The main component of both information criteria is the sum of squared residuals, which we aimed to minimize as much as possible. Therefore, the criteria are minimized, and the model with the smallest AIC or SBIC value is selected (PARKER, 2025).

These criteria may also be used to determine the suitable degree of the polynomial. Initially, the model should be estimated using a relatively large lag length (q), and then the lag length should be gradually reduced to examine whether there is a significant deterioration in the model’s goodness-of-fit. This approach provided a flexible and empirical method for understanding the lag structure of the model. After determining the lag length, the degree of the polynomial m must also be selected. In general, it is necessary to ensure that the polynomial degree is no less than one greater than the number of inflection points in the curve relating βi to i. Once the polynomial degree (m) and the lag length (k) have been specified, the Z variables are computed accordingly. The Z variables are calculated as follows for an equation with a polynomial degree of 2 and a lag length of 5.

Z_0t = $\sum _{i=0}^5{X}_{t-i}$ = (Xt + X_t-1 + X_t-2 + X_t-3 + X_t-4 + X_t-5)

Z_1t = $\sum _{i=0}^5{İX}_{t-i}$ = (X_t-1 + 2X_t-2 + 3X_t-3 +4 X_t-4 + 5X_t-5)

Z_2t = $\sum _{i=0}^5{i}^2{X}_{t-1}$ = (X_t-1 + 4X_t-2 + 9X_t-3 +16 X_t-4 + 25X_t-5) (10)

In this context, the Z variables are linear combinations of the X variables, a factor that serves to increase the likelihood of observing multicollinearity in the Z variables.

It is important to note that it is also subject to certain limitations in practical applications in Almon approach. The primary concern pertains to the reliance on the researcher’s subjective judgment in determining both the degree of the polynomial and the maximum lag length. This reliance may result in exaggerated standards errors of the estimated coefficients, consequently rendering them statistically insignificant based on conventional t-tests. However, given the possibility that linear combinations of these coefficients may retain statistical significance, the issue of multicollinearity may not be substantial as initially perceived. Indeed, even under such circumstances, meaningful inferences regarding the model can still be drawn, and estimates of the total effect may yield reliable results (GUJARATI & PORTER, 2009).

Soybean production in Türkiye

A substantial proportion (92%) of the areas dedicated soybean cultivation areas in Türkiye are situated within in the Mediterranean Region. According to official data from TURKSTAT for 2023, Çukurova region is the primary center for soybean production in Türkiye, accounting for more than 90% of total national output (USDA, 2025). The soybean production in Türkiye reveals significant fluctuation overtime. In 2023, the production of soybeans exhibited a decline of 11.3% compared to the previous year, while the prices of soybeans experienced a decrease of 9.5%. In 2023, the total soybean production in Türkiye amounted to 137,500 tons. Given the inability of domestic production to meet domestic demand for soybeans, Türkiye has been compelled to import substantial quantities of the commodity. The steady increase in demand from the domestic market, particularly for animal feed, including poultry and aquaculture, is expected to result in a further increase in soybean imports in the coming years. Nevertheless, the government persists in its efforts to augment support for soybean production, with the objective of fostering domestic cultivation. Nevertheless, the lower profitability of soybeans in comparison to alternative crops in the areas where soybeans are cultivated is a primary factor impeding the augmentation of soybean production.

DISCUSSION

In this section of the study, the relationship between soybean production volume and producer prices was analyzed using a dynamic econometric framework based on the Koyck approach. The coefficient correlation between the two variables was found to be 0.51.

In this study, the assessment of the normality of the analyzed data was conducted in accordance with the guidelines proposed by KLINE (2011) and TABACHNICK & FIDELL (2013). The skewness value (2.074) divided by its standard error (2.151) yielded a value of 0.96, while the kurtosis value divided by its standard error (2.151) resulted in a value of 1.87. Since both values are below the critical threshold of 1.96, soybean prices were normally distributed.

The following variables were examined in the study: Qt represents soybean production (in tons) in period t, and Pt denotes the producer price of soybeans (in TL/kg). To estimate the dynamic model, the optimal lag length for soybean prices was first determined. To identify the lag length, commonly used information criteria in literature-namely the Akaike Information Criterion (AIC) and the Schwarz Bayesian Criterion (SBC). The value obtained from this analysis is presented below. The lag structure that minimizes the AIC and SBC values was selected, in accordance with the approach outlined by GUJARATI (2004). In the initial stage, a very large value of the lag length (k) was examined, after which the suitability of the model was tested by progressively shortening the lag length (DAVIDSON & MACKINNON, 1993). The Akaike and Schwarz information criteria calculated for different lag lengths are reported in table 1.

Table 1
Lag length.

Lag lengths	-----------------------AIC*---------------------	------------------------SIC**---------------------
k = 0	28.97729	29.07532
k = 1	26.83698	27.13105
k = 2	27.25189	27.74201
k = 3	27.47172	28.15790
k = 4	26.80684	27.68906
k = 5	26.38140	27.45967
k = 6	23.80974	25.08407
k = 7	20.85011*	22.32049*

• ^*According to the Akaike and Schwarz information criteria, the lowest Schwarz value is obtained at a lag length of k = 7.
• ^*AIC = Akaike Information Criterion, ^**SIC = Schwarz Information Criterion.

As shown in table 2, the model is statistically significant at the 1% level. The variables used for soybean production explain approximately 81% of the variation in output. The Durbin-Watson statistics indicate that all values are close to 2, suggesting the absence of serial correlation. However, the inclusion of a lagged dependent variable violates one of the underlying assumptions of the Durbin-Watson d test. Therefore, an alternative method is required to test for serial correlation in the presence of a lagged dependent variable. One such alternative is the Durbin h test (BHATT, 2025). The calculated Durbin h value is 0.27, and since it lies within the critical range of -1.96 < h < 1.96 under the standard normal distribution, the null hypothesis of no autocorrelation cannot be rejected.

Table 2
Results of Koyck model.

	Constant (α)	Pt (β)	Qt-1 (λ)
coefficient	15743.93	53.925	0.883
t value	0.878	0.019	7.777
P-value	0.39	0.99	0.000

• R² = 0.81 F= 4.387 P = 0.000 DW = 1.909.

According to the Akaike and Schwarz criteria, the lowest Schwarz value was obtained at a lag length of k = 7. The relationship between soybean production and price was estimated using the classical ordinary least squares (OLS) method.

$Meanlag=\frac{\mathrm{\lambda }}{(1-\mathrm{\lambda })}=\frac{0.883}{(1-0.883)}=7.5$

$Medianlag=-\frac{\log 2}{\log \mathrm{\lambda }}=\frac{0.30103}{-0.5414}=5.61$

As demonstrated in table 2, Koyck model is found to be statistically significant at the 1% level. The variables used for soybeans account for 81% of the variation in production. The results from the Durbin-Watson statistics indicate that all values are close to 2, suggesting the absence of serial correlation. The model demonstrated that all coefficients on lagged production variables exert a positive effect on current production. According to the estimated coefficients, a 1 TL increase in soybean prices is associated with an approximate 54 tons increase in soybean output. Preliminary findings indicated that the time required for changes in soybean prices to have a significant impact on production is 7.5 years, based on the mean lag length. In other words, 88% of the total change in soybean production occurs within 7.5 years, and the effect of price changes on production drops to zero after this period.

The coefficient calculations according to the Koyck specification are presented below.

$Q_t=𝛼+{𝛽}_0{P}_1+𝜆Q_{t-1}+u_{t}ve{b}_k={𝜆}^k{𝛽}_0$

${𝛽}_k={𝜆}^k{𝛽}_0$

${𝛽}_0={𝜆}^0{𝛽}_0$ = (0.883)⁰53.925 = 53

${𝛽}_1={(𝜆}^1{𝛽}_0)={(0.833)}^1(53.925)=48$

${𝛽}_2={(𝜆}^2{𝛽}_0)={(0.833)}^2(53.925)=42$

${𝛽}_3={(𝜆}^3{𝛽}_0)={(0.833)}^3(53.925)=37$

${𝛽}_4={(𝜆}^4{𝛽}_0)={(0.833)}^4(53.925)=33$

${𝛽}_5={(𝜆}^5{𝛽}_0)={(0.833)}^5(53.925)=29$

${𝛽}_6={(𝜆}^6{𝛽}_0)={(0.833)}^6(53.925)=26$

${𝛼}_0=\frac{𝛼}{1-𝜆}=\frac{15743.93}{0.1172}=134336$

The regression results for soybean production and the lagged soybean price are presented below:

$Q_t=𝛼+{\mathrm{\beta }}_0{P}_t+\left(𝜆{\mathrm{\beta }}_0\right)P_{t-1}+\left({𝜆}^2{\mathrm{\beta }}_0\right)P_{t-2}+\left({𝜆}^3{\mathrm{\beta }}_0\right){𝛽}_3{P}_{t-3}+\left({𝜆}^4{\mathrm{\beta }}_0\right){𝛽}_4{P}_{t-4}+\left({𝜆}^5{𝛽}_0\right){𝛽}_5{P}_{t-5}+\left({𝜆}^6{\mathrm{\beta }}_0\right){𝛽}_6{P}_{t-6}+\left({𝜆}^7{\mathrm{\beta }}_0\right){𝛽}_7{P}_{t-7}$

$Q_t=134336+53P_t+48P_{t-1}+42P_{t-2}+37P_{t-3}+33P_{t-4}+29P_{t-5}+26P_{t-6}+23P_{t-7}$

It can be stated that the lagged effects of soybean prices on soybean production diminish over time, as indicated by the λ coefficient in the regression equation, which lies between 0 and 1-a characteristic of a Koyck type model. According to the regression equation, in the absence of any change in prices, the baseline level of soybean production is 134336 tons. A 1 TL increase in the price from the previous period has been shown to result in an increase of 48 tons in soybean production. The finding indicated that the lagged price values of soybeans exert a positive impact on soybean production, though this effect undergoes a gradual decrease over time. While individual lag coefficients may not be statistically significant, the overall dynamic structure of the model and the estimated lag pattern still provide useful information regarding the temporal adjustment process between prices and production.

An Almon model was constructed by taking lag periods into account, and the corresponding “Z” values were obtained. For these Z values, the polynomial degree was set at m = 2, and the lag length at k = 7. The coefficients derived from the model were found to be statistically insignificant (Table 3).

β₀ = 3597.76

β₁ = 3770.64

β₂ = 4207.45

β₃ = 4908.18

Β₅ = 872.83

β₅ = 7101.41

β₆ = 8593.91

β₇ = 10350.3

Table 3
Results of Almon model.

	Coefficient	Standard error	t statistics	P-value
c	-195955.4	174445.2	-1.123.306	0.2816
Z0	3597.759	4386.381	0.820211	0.4269
Z1	40.91967	4816.001	0.008497	0.9933
Z2	131.9621	720.4180	0.183174	0.8575

• R² = 0.31 F = 1.940 P = 0.173 DW = 0.477 Log likelihood: -204.2766.

Based on obtained value, Almon model can be expressed as follows.

$Q_t=-195955.4+3597.76P_t+3770.64P_{t-1}+4207.45P_{t-2}+4908.18P_{t-3}+872.83P_{t-4}+7101.41P_{t-5}+8593.91P_{t-6}+10350.3P_{t-7}$

The Almon model, which was developed to determine the relationship between soybean production and prices, was found to be statistically insignificant. The coefficient of determination (R²) of the estimated Almon model, which aimed to explain the relationship between soybean production and lagged prices, was calculated as 0.37. This finding suggested that only 37% of the observed variation in soybean production can be attributed to changes in lagged prices.

An examination of the model coefficients indicated that all previous price levels have a positive influence on production. Specifically, a 1 TL increase in the previous year’s price is associated with an increase of 3,770 tons in production. This finding aligns with the theory of supply, which posits that supply varies in response to price changes.

CONCLUSION

The objective was to determine the role of price in the production of soybeans, a crucial feed resource and industrial commodity in Türkiye. This study investigated how lagged price values influence production. It excluded other variables that may affect production. The study analysed data from the 2000 to 2023 period. It uses the Koyck and Almon distributed lag models to analyses the data. To this end, the Koyck and Almon models were used. The correlation coefficient between soybean production and producer prices was found to be 0.51. The Koyck model analysis determined the optimal lag length for soybean price at 7 years, based on the Akaike Information Criterion (AIC) and the Schwarz Information Criterion (SIC). These findings suggested that soybean production, as measured by annual data, is influenced by price movements over the previous seven years. The Koyck model results also demonstrate that the adjustment period for price changes to fully manifest in production is approximately 7.5 years. The examination of lagged coefficients for production in the model revealed a positive relationship, suggesting that past price increases have a favorable effect on current production. According to the model estimates, a 1 TL increase in soybean price results in an approximate 54 tons increase in soybean production. An examination of the delayed effects of price on soybean production reveals in the absence of a price change, the baseline soybean production level is 134336 tons. A 1 TL increase in the price from the previous period has been shown to be associated with an approximate 48 tons increase in soybean production. These findings demonstrate that the lagged values of soybean prices exert a positive effect on soybean production.

This study found that the Koyck model was found to be statistically significant at the 1% level, and the variables used for soybeans explained 81% of the variance in production. However, the analysis conducted using the Almon model did not yield a significant result. According to this model, only 37% of the variation in soybean production can be explained by changes in lagged prices. An examination of the model coefficients reveals that prices in previous periods have consistently contributed to increasing production.

In 2024, the Turkish Ministry of Agriculture and Forestry introduced the Agricultural Production Plan to prevent supply surpluses or shortages and to ensure supply security for strategic crops. This new production model prioritizes the conservation of water resources by promoting the cultivation of less water-intensive crops in areas facing water scarcity. However, the effects of this plan are not expected to be felt in the immediate future. It is anticipated that this production planning may have a positive impact on soybean production in the coming years.

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• CR-2025-0297.R2
• DATA AVAILABILITY STATEMENT
  Raw data is available directly with the corresponding author.
• DECLARATION OF USE OF ARTIFICIAL INTELLIGENCE
  The author did not use artificial intelligence to develop this paper.

Edited by

• ASSOCIATE EDITOR:
  Leandro Souza da Silva (0000-0002-1636-6643)

• SCIENTIFIC EDITOR:
  Silviu Beciu (0000-0002-1722-8664)

Data availability

Raw data is available directly with the corresponding author.

Publication Dates

• Publication in this collection
  14 Sept 2026
• Date of issue
  2026

History

• Received
  04 June 2025
• Accepted
  13 May 2026
• Reviewed
  05 July 2026